Partially double-stranded splint adaptors and methods of use

Abstract

The present disclosure provides compositions comprising nucleic acid partially double- stranded splint adaptors, and methods for preparing nucleic acid libraries using the partially double-stranded splint adaptors. The partially double-stranded splint adaptors can be ligated to double stranded nucleic acid fragments to form library-splint complexes having double stranded nicks, where the nicks can be ligated to form covalently closed circular molecules, which can then be subjected to downstream amplification and sequencing workflows.

Description

PARTIALLY DOUBLE-STRANDED SPLINT ADAPTORSAND METHODS OF USECROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to, and benefit of, U.S. Provisional Application No. 63 / 566,062, filed on March 15, 2024, the contents of which are incorporated by reference in their entirety.INCORPORATION BY REFERENCE OF SEQUENCE LISTING

[0002] The contents of the electronic sequence listing (ELEM_031_001WO_SeqList_ST26.xml; Size: 29,358 bytes; and Date of Creation: March 13, 2025) are herein incorporated by reference in their entireties.TECHNICAL FIELD

[0003] The present disclosure provides compositions comprising nucleic acid partially double-stranded splint adaptors, and methods for preparing nucleic acid libraries using the partially double-stranded splint adaptors. The partially double-stranded splint adaptors can be ligated to double stranded nucleic acid fragments to form library-splint complexes having double stranded nicks, where the nicks can be ligated to form covalently closed circular molecules, which can then be subjected to downstream amplification and sequencing workflows.BACKGROUND

[0004] The present disclosure relates to methods of preparing and sequencing libraries of covalently closed circular molecules. Improvements in next generation sequencing technology have greatly increased sequencing speed and data output, resulting in the high sample throughput of current sequencing platforms. Efficient preparation of closed circular library molecules having target sequences is important for downstream amplification and sequencing workflows. Another aspect of increasing sequencing throughput is the addition of unique index sequences to DNA fragments during library preparation, which allows large number of libraries to be pooled and sequenced simultaneously during each sequencing run.

[0005] Accordingly, there is a need for new methods for producing and sequencing circular library molecules containing target sequences and unique index sequences, which arecompatible for downstream next generation sequencing technologies. Provided herein are compositions, methods and kits addressing this need.SUMMARY

[0006] In some aspects, provided herein is a method for forming a plurality of concatemer molecules immobilized to a support, comprising: providing a plurality of linear double stranded nucleic acid fragments (100), wherein a3’ end of both strands of an individual linear double-stranded nucleic acid fragment (100) comprises a terminal adenine base (“A”); providing a plurality of partial double stranded splint adaptors (200), wherein individual partial double stranded splint adaptors (200) in the plurality comprise a first, second and third oligonucleotide hybridized together to form a nucleic acid molecule having single stranded and double stranded portions, wherein individual partial double stranded splint adaptors (200) comprise a first double stranded region formed by hybridization of the first and third oligonucleotides, wherein the first double stranded region can be ligated to a first end of a linear double stranded nucleic acid fragment (100), wherein individual partial double stranded splint adaptors (200) comprise a second double stranded region formed by hybridization of the first and second oligonucleotides, wherein the second double stranded region can be ligated to a second end of the same double stranded nucleic acid fragment (100); wherein the first oligonucleotide comprises a universal primer binding site for a surface capture primer (210)and wherein a 3’ end of the first oligonucleotide comprises a terminal thymine base (“T”); wherein a 3’ end of the second oligonucleotide comprises a terminal thymine base (“T”); contacting the plurality of partial double stranded splint adaptors (200) with a plurality of linear double-stranded nucleic acid fragments (100), wherein the contacting is conducted under a condition suitable for hybridizing the terminal adenine base at the 3’ end of both strands of the linear double-stranded nucleic acid fragments (100) with the terminal thymine base at the 3’ end of the first oligonucleotide and the terminal thymine base at the 3’ end of the second oligonucleotide, thereby circularizing the double stranded nucleic acid fragments and forming a plurality of library-splint complexes (300), individual library-splint complexes (300) having a first nick or gap and a second nick or gap which are enzymatically ligatable; contacting the plurality of library-splint complexes (300) with a plurality of DNA ligase enzymes under a condition suitable to enzymatically ligate the first and second nicks or gaps, thereby generating a plurality of covalently closed circular library molecules (400) which are partially double stranded;contacting the covalently closed circular library molecules (400) with an alkaline condition to generate a plurality of single stranded covalently close circular library molecules (500); distributing the plurality of single stranded covalently closed circular library molecules (500) onto a support having a plurality of surface capture primers immobilized on the support, wherein the distributing is conducted under a condition suitable for hybridizing individual single stranded covalently closed circular library molecules (500) to individual immobilized surface capture primers, thereby immobilizing the plurality of single stranded covalently closed circular library molecules (500) to the support; contacting the plurality of single stranded covalently closed circular library molecules (500) with a plurality of stranddisplacing polymerases, a plurality of nucleotides and a plurality of compaction oligonucleotides, under a condition suitable to conduct a rolling circle amplification reaction on the support using the plurality of surface capture primers as amplification primers and the plurality of single stranded covalently closed circular library molecules (500) as template molecules, thereby generating the plurality of concatemer molecules immobilized to the support; and sequencing the plurality of concatemer molecules.

[0007] In some embodiments, the first double stranded region is at a first end of the partial double-stranded splint adaptor.

[0008] In some embodiments, the second double stranded region is at a second end of the partial double-stranded splint adaptor that is opposite the first end.

[0009] In some embodiments, a first end of the partial double-stranded splint adaptor comprises a 5’ overhang followed by the first double-stranded region.

[0010] In some embodiments, the first end of the partial double-stranded splint adaptor comprises a 3’ overhang followed by the first double-stranded region.

[0011] In some embodiments, the first end of the partial double-stranded splint adaptor comprises a blunt end followed by the first double-stranded region.

[0012] In some embodiments, a second end of the partial double-stranded splint adaptor comprises a 5’ overhang followed by the second double-stranded region, wherein the second end is opposite the first end.

[0013] In some embodiments, a second end of the partial double-stranded splint adaptor comprises a 3’ overhang followed by the second double-stranded region, wherein the second end is opposite the first end.

[0014] In some embodiments, a second end of the partial double-stranded splint adaptor comprises a blunt end followed by the second double-stranded region, wherein the second end is opposite the first end.

[0015] In some embodiments, a 5’ end of the first and / or third oligonucleotide is phosphorylated.

[0016] In some embodiments, the first oligonucleotide comprises a sample index sequence (230).

[0017] In some embodiments, the support comprises a plurality of surface pinning primers immobilized thereon, and wherein the first oligonucleotide comprises a universal primer binding site for a surface pinning primer (220).

[0018] In some embodiments, the first oligonucleotide comprises a short random sequence.

[0019] In some embodiments, the short random sequence is 3-6 nucleotides in length, optionally wherein the short random sequence is 3 nucleotides in length (NNN).

[0020] In some embodiments, the third oligonucleotide comprises a portion that can hybridize to the short random sequence of the first oligonucleotide.

[0021] In some embodiments, the portion of the third oligonucleotide that can hybridize to the short random sequence comprises an 18-carbon spacer, multiple C3 spacer phosphoramidites, a trimethylene glycol spacer, or a polyethylene glycol spacer.

[0022] In some embodiments, the 18-carbon spacer comprises a hexa-ethyleneglycol spacer.

[0023] In some embodiments, a portion of the second oligonucleotide hybridizes to a portion of the first oligonucleotide.

[0024] In some embodiments, the portion of the second oligonucleotide that hybridizes to the portion of the first oligonucleotide hybridizes to at least a portion of the universal primer binding site for the surface capture primer (210).

[0025] In some embodiments, a portion of the third oligonucleotide hybridizes to a portion of the first oligonucleotide.

[0026] In some embodiments, the first oligonucleotide comprises a universal primer binding site for a surface pinning primer (220), and wherein the portion of the third oligonucleotide that hybridizes to the portion of the first oligonucleotide hybridizes to a portion of the universal primer binding site for the surface pinning primer (220).

[0027] In some embodiments, the third oligonucleotide comprises a sequence (231) that hybridizes to a sample index sequence (230) of the first oligonucleotide.

[0028] In some embodiments, the first oligonucleotide comprises, from 5’ to 3’: the universal primer binding site for the surface capture primer (210), a universal primer bindingsite for a surface pinning primer (220), a short random sequence, a sample index sequence (230), and a 3’ terminal thymine.

[0029] In some embodiments, the second oligonucleotide comprises, from 5’ to 3’ : a sequence that hybridizes to at least a portion of a universal primer binding site for the surface capture primer (210), and a 3’ terminal thymine.

[0030] In some embodiments, the third oligonucleotide comprises, from 5’ to 3’: a sequence (231) that hybridizes to a sample index sequence (230) of the first oligonucleotide, a spacer, optionally wherein the spacer comprises an 18-carbon spacer, multiple C3 spacer phosphoramidites, a trimethylene glycol spacer, or a polyethylene glycol spacer, and a sequence (221) that hybridizes to a portion of a universal primer binding site for a surface pinning primer (220) of the first oligonucleotide.

[0031] In some embodiments, individual linear double stranded nucleic acid fragments (100) comprise an insert sequence and the terminal adenine base at the 3’ ends of both strands.

[0032] In some embodiments, individual linear double stranded nucleic acid fragments (100) in the plurality comprise the same insert sequence, or comprise different insert sequences.

[0033] In some embodiments, the terminal thymine bases of the first and second oligonucleotides hybridize to the terminal adenine bases at the 3’ ends of the linear double stranded nucleic acid fragments (100).

[0034] In some embodiments, enzymatically ligating at step (d) comprises ligating the first and second ends of the partial double stranded splint adaptors (200) to both ends of individual linear double stranded nucleic acid fragments (100).

[0035] In some embodiments, individual partial double stranded splint adaptors (200) comprise 5’ overhangs at both ends, and enzymatically ligating at step (d) comprises sticky - end ligation.

[0036] In some embodiments, individual partial double stranded splint adaptors (200) comprise double stranded regions at both ends, and enzymatically ligating at step (d) comprises blunt-end ligation.

[0037] In some embodiments, partial double-stranded splint adaptors do not include additional universal binding sites for a forward sequencing primer and a reverse sequencing primer.

[0038] In some embodiments, individual sample index sequences in the plurality of partial double stranded splint adaptors (200) comprise the same sequence, or comprise different sequences.

[0039] In some embodiments, individual covalently closed circular molecules comprise: a first insert region (110) on a first strand which is hybridized to a second insert region on a second strand (111); a universal primer binding site for a capture primer (210) which is hybridized to at least a portion of the second oligonucleotide (211); a universal primer binding site for a pinning primer (220) which is hybridized to a sequence (221) of the third oligonucleotide; a short random sequence; and a sample index sequence (230) which is hybridized to a sequence (231) of the third oligonucleotide.

[0040] In some embodiments, individual concatemer molecules comprise two or more copies of: a universal primer binding site for a capture primer (210), a first insert region (110), a sample index sequence (230), a short random sequence, and a universal primer binding site for a surface pinning primer (220), wherein (a)-(e) can be arranged in any order.

[0041] In some embodiments, the covalently closed circular library molecules are denatured at step (e), thereby generating single stranded covalently closed circular library molecules.

[0042] In some embodiments, the plurality of surface capture primers is located at random and non-predetermined positions on the support, or wherein the plurality of surface capture primers is located at predetermined positions on the support.

[0043] In some embodiments, a plurality of surface pinning primers is located at random and non-predetermined positions on the support, or wherein the plurality of surface pinning primers is located at predetermined positions on the support.

[0044] In some embodiments, the rolling circle amplification reaction comprises a plurality of compaction oligonucleotides.

[0045] In some embodiments, 5’ and 3’ regions of individual compaction oligonucleotides hybridize to a concatemer molecule to pull together distal portions of the concatemer molecule, thereby causing the concatemer molecule to form a compact DNA nanoball.

[0046] In some embodiments, the support is configured on a flow cell, or an interior of a capillary lumen.

[0047] In some embodiments, the support comprises at least one hydrophilic polymer coating layer, and the plurality of surface capture primers are immobilized to the at least onehydrophilic polymer coating layer, and wherein the at least one hydrophilic polymer coating layer has a water contact angle of no more than 45 degrees.

[0048] In some embodiments, the at least one hydrophilic polymer coating layer comprises polyethylene glycol (PEG), poly(vinyl alcohol) (PVA), poly(vinyl pyridine), poly(vinyl pyrrolidone) (PVP), poly(acrylic acid) (PAA), polyacrylamide, poly(N- isopropyl acrylamide) (PNIPAM), poly(methyl methacrylate) (PMA), poly(2-hydroxylethyl methacrylate) (PHEMA), poly(oligo(ethylene glycol) methyl ether methacrylate) (POEGMA), polyglutamic acid (PGA), poly-lysine, poly-glucoside, streptavidin, or dextran.

[0049] In some embodiments, the at least one hydrophilic polymer coating layer comprises polymer molecules having a molecular weight of at least 1000 Daltons.

[0050] In some embodiments, the at least one hydrophilic polymer coating layer comprises branched polymer molecules having 4-8 branches.

[0051] In some embodiments, the support comprises: a) a first coating layer comprising a first monolayer of hydrophilic polymer molecules tethered to the support; b) a second coating layer comprising a second monolayer of hydrophilic polymer molecules tethered to the first monolayer; and c) a third coating layer comprising a third monolayer of hydrophilic polymer molecules tethered to the second monolayer, and wherein the hydrophilic polymer molecules of the first layer, second layer or third layer comprise branched polymer layers.

[0052] In some embodiments, one or more of the at least one hydrophilic polymer coating layers comprise the plurality of surface capture primers at a surface density of least 1000 / pm2.

[0053] In some embodiments, the sequencing at step (h) comprises contacting the plurality of concatemer molecules with (i) a first plurality of sequencing primers, (ii) a plurality of sequencing polymerases, and (iii) a plurality of nucleotide reagents, under conditions suitable for hybridizing sequencing primers to individual concatemer molecules to generate a plurality of nucleic acid duplexes on the individual concatemer molecules, and wherein the conditions are suitable for binding nucleic acid duplexes with sequencing polymerases and nucleotide reagents.

[0054] In some embodiments, the first plurality of sequencing primers is soluble.

[0055] In some embodiments, the first plurality of sequencing primers hybridizes to the universal primer binding site for the surface capture primer (210) or to a universal primer binding site for a surface pinning primer (220).

[0056] In some embodiments, individual nucleotide reagents in the plurality of nucleotide reagents comprise an aromatic base, a five-carbon sugar and 1-10 phosphate groups.

[0057] In some embodiments, the plurality of nucleotide reagents comprises one or more types of nucleotide reagent selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

[0058] In some embodiments, the plurality of nucleotide reagents comprises a combination of two or more types of nucleotide reagent selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

[0059] In some embodiments, at least one nucleotide reagent in the plurality of nucleotide reagents lacks a detectable reporter moiety.

[0060] In some embodiments, at least one nucleotide reagent in the plurality of nucleotide reagents is labeled with a detectable reporter moiety.

[0061] In some embodiments, individual nucleotide reagents in the plurality of nucleotide reagents comprise at least one chain terminating nucleotide comprising (i) an aromatic base, (ii) a sugar having a 3’ chain terminating moiety that inhibits polymerase-catalyzed nucleotide incorporation, and (iii) 1-10 phosphate groups.

[0062] In some embodiments, the at least one chain terminating nucleotide comprises a removable chain terminating moiety at the 3' sugar group, and wherein the removable chain terminating moiety comprises an alkyl group, alkenyl group, alkynyl group, allyl group, aryl group, benzyl group, azide group, azido group, O-azidomethyl group, amine group, amide group, keto group, isocyanate group, phosphate group, thio group, disulfide group, carbonate group, urea group, or silyl group.

[0063] In some embodiments, the at the at least one chain terminating nucleotide comprises a removable chain terminating moiety at the 3' sugar group, and wherein the removable chain terminating moiety comprises a 3’-O-amino group, a 3’-O-aminomethyl group, a 3 ’-O-m ethylamino group, or derivatives thereof.

[0064] In some embodiments, the at least one chain terminating moiety is cleavable or removable with a chemical compound to generate an extendible 3' OH moiety on the sugar group.

[0065] In some embodiments, the plurality of nucleotide reagents comprises at least one multivalent molecule, wherein the at least one multivalent molecule comprises: (1) a core; and (2) a plurality of nucleotide arms, individual nucleotide arms comprising (i) a core attachment moiety, (ii) a spacer comprising a PEG moiety, (iii) a linker, and (iv) a nucleotide moiety.

[0066] In some embodiments, sequencing the plurality of concatemer molecules at step (h) comprises: contacting the plurality of concatemer molecules with (i) a first plurality ofsequencing polymerases and (ii) a plurality of first sequencing primers, and wherein the contacting is conducted under conditions suitable to form a plurality of complexed polymerases comprising a sequencing polymerase bound to a nucleic acid duplex, wherein the nucleic acid duplex comprises a portion of an individual concatemer molecule hybridized to an individual first sequencing primer; contacting the plurality of complexed sequencing polymerases with a plurality of nucleotides under conditions suitable for binding at least one nucleotide to a complexed polymerase, wherein the nucleotides in the plurality are labeled with a detectable reporter moiety, optionally wherein the detectable reporter moiety comprises a fluorophore; incorporating at least one nucleotide into a 3’ end of the first sequencing primers, thereby generating a plurality of first sequencing read products by extending the first nucleic acid sequencing primers; and detecting the at least one nucleotide and identifying the nucleobase of the at least one nucleotide.

[0067] In some embodiments, the first sequencing primers are soluble.

[0068] In some embodiments, individual first sequencing primers hybridize to the universal primer binding site for the surface capture primer (210) or to a universal primer binding site for a surface pinning primer (220).

[0069] In some embodiments, the method comprises repeating steps (a)-(d) at least once.

[0070] In some embodiments, the sequencing at step (h) comprises: contacting a first plurality of polymerases with (i) the plurality of concatemer molecules and (ii) a plurality of sequencing primers, wherein the contacting is conducted under a condition suitable to bind the first plurality of polymerases with the plurality of concatemer molecules and the plurality of sequencing primers, thereby forming a plurality of first complexed polymerases comprising a polymerase bound to a nucleic acid duplex, wherein the nucleic acid duplex comprises a concatemer molecule hybridized to a sequencing primer; contacting the plurality of first complexed polymerases with a plurality of multivalent molecules to form a plurality of multivalent-complexed polymerases under a condition suitable for binding complementary nucleotide moieties of the multivalent molecules to at least two of the plurality of first complexed polymerases thereby forming a plurality of multivalent-complexed polymerases, wherein at least one of the multivalent molecules in the plurality of multivalent molecules is labeled with a detectable reporter moiety, and wherein individual multivalent molecules in the plurality comprises: (1) a core; and (2) a plurality of nucleotide arms, individual nucleotide arms comprising (i) a core attachment moiety, (ii) a spacer comprising a PEG moiety, (iii) a linker, and (iv) a nucleotide moiety; detecting the plurality of multivalent- complexed polymerases; and identifying the base of the complementary nucleotide moietiesthat are bound to the plurality of first complexed polymerases, thereby determining sequences of the plurality of concatemer molecules.

[0071] In some embodiments, the sequencing primers hybridize to the universal primer binding site for the surface capture primer (210) or to a universal primer binding site for a surface pinning primer (220).

[0072] In some embodiments, the method comprises dissociating the plurality of multivalent-complexed polymerases and removing the plurality of first sequencing polymerases and their bound multivalent molecules, and retaining the nucleic acid duplexes; contacting the nucleic acid duplexes of step (e) with a second plurality of polymerases, wherein the contacting is conducted under a condition suitable for binding the second plurality of polymerases to the nucleic acid duplexes, thereby forming a second plurality of complexed polymerases comprising a second polymerase bound to a nucleic acid duplex; and contacting the second plurality of complexed polymerases with a plurality of nucleotides, wherein the contacting is conducted under a condition suitable for binding complementary nucleotides from the plurality of nucleotides to at least two of the second complexed polymerases, thereby forming a plurality of nucleotide-complexed polymerases.

[0073] In some embodiments, the nucleotides are labeled with a detectable reporter moiety, and the method comprises: detecting the complementary nucleotides which are incorporated into the sequencing primers of the nucleotide-complexed polymerases, and identifying the bases of the complementary nucleotides.

[0074] In some embodiments, nucleotides in the plurality comprise chain terminating moieties, and the method comprises: removing the chain terminating moieties from the incorporated nucleotides.

[0075] In some embodiments, the method comprises repeating steps (a)-(j) at least once.

[0076] In some embodiments, the sequencing at step (h) comprises contacting a plurality of polymerases, a plurality of sequencing primers, a plurality of multivalent molecules and the plurality of concatemer molecules under conditions suitable to: bind a first portion of a concatemer molecule with a polymerase, a sequencing primer and a first nucleotide moiety of a multivalent molecule, thereby forming a first binding complex, wherein the first nucleotide moiety of the first multivalent molecule binds to the first polymerase, and bind a second portion of the concatemer molecule with a second polymerase and a second nucleotide moiety of the multivalent molecule, thereby forming a second binding complex, wherein the second nucleotide moiety of the multivalent molecule binds to the second polymerase, thereby forming an avidity complex.

[0077] In some embodiments, the method comprises: detecting the first and second binding complexes on the same concatemer molecule; and identifying the first nucleotide moiety, thereby determining the sequence of the first portion of the concatemer molecule, and identifying the second nucleotide moiety, thereby determining the sequence of the second portion of the concatemer molecule.

[0078] In some embodiments, the method comprises: dissociating the plurality of polymerases and plurality of multivalent molecules, incorporating nucleotides into 3’ ends of sequencing primers bound to the concatemer molecules, and repeating steps (a)-(d) at least once.

[0079] In some embodiments, the sequencing primers hybridize to the universal primer binding site for the surface capture primer (210) or to a universal primer binding site for a surface pinning primer (220).

[0080] In some embodiments, at least one multivalent molecule comprises: (1) a core; and (2) a plurality of nucleotide arms, individual nucleotide arms comprising (i) a core attachment moiety, (ii) a spacer comprising a PEG moiety, (iii) a linker, and (iv) a nucleotide moiety, wherein the core is attached to the plurality of nucleotide arms, wherein the spacer is attached to the linker, and wherein the linker is attached to the nucleotide moiety.

[0081] In some embodiments, the plurality of nucleotide arms comprises the same type of a nucleotide moiety, and wherein the type of nucleotide moiety is selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

[0082] In some embodiments, the plurality of multivalent molecules comprises a mixture of two or more types of multivalent molecules, each type of multivalent molecules comprising one or more nucleotide moiety types selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

[0083] In some embodiments, the plurality of multivalent molecules comprises at least one fluorophore-labeled multivalent molecule.

[0084] In some embodiments, the sequencing of step (h) comprises sequencing by binding.

[0085] In some embodiments, the sequencing of step (h) comprises using phosphate- chain labeled nucleotides.DESCRIPTION OF THE DRAWINGS

[0086] The features of the present disclosure are set forth with particularity in the appended claims. A better understanding of the features and advantages of the present disclosure will be obtained by reference to the following detailed description that sets forth illustrative embodiments, in which the principles of the disclosure are utilized, and the accompanying drawings of which:

[0087] FIG. 1 is a schematic of an exemplary low binding support comprising a glass substrate and alternating layers of hydrophilic coatings which are covalently or non- covalently adhered to the glass, and which further comprises chemically-reactive functional groups that serve as attachment sites for oligonucleotide primers (e.g., capture oligonucleotides and circularization oligonucleotides). In an alternative embodiment, the support can be made of any material such as glass, plastic or a polymer material.

[0088] FIG. 2 is a schematic of various exemplary configurations of multivalent molecules. Left (Class I): schematics of multivalent molecules having a “starburst” or “helter-skelter” configuration. Center (Class II): a schematic of a multivalent molecule having a dendrimer configuration. Right (Class III): a schematic of multiple multivalent molecules formed by reacting streptavidin with 4-arm or 8-arm PEG-NHS with biotin and dNTPs. Nucleotide moieties are designated ‘N’, biotin is designated ‘B’, and streptavidin is designated ‘SA’.

[0089] FIG. 3 is a schematic of an exemplary multivalent molecule comprising a generic core attached to a plurality of nucleotide-arms.

[0090] FIG. 4 is a schematic of an exemplary multivalent molecule comprising a dendrimer core attached to a plurality of nucleotide-arms.

[0091] FIG. 5 is a schematic of an exemplary multivalent molecule comprising a core attached to a plurality of nucleotide-arms, where the nucleotide arms comprise a core attachment moiety, a spacer, a linker, and a nucleotide moiety.

[0092] FIG. 6 is a schematic of an exemplary nucleotide-arm of a multivalent molecule, wherein the nucleotide arm comprises a core attachment moiety, a spacer, a linker, and a nucleotide moiety e.g., a nucleotide unit).

[0093] FIG. 7 shows the chemical structure of an exemplary spacer (Top), and the chemical structures of various exemplary linkers, including an 11 -atom Linker, 16-atom Linker, 23-atom Linker and an N3 Linker (Bottom).

[0094] FIG. 8 shows the chemical structures of various exemplary linkers, including Linkers 1-9.

[0095] FIG. 9 shows the chemical structures of various exemplary linkers joined / attached to nucleotide moieties.

[0096] FIG. 10 shows the chemical structures of various exemplary linkers joined / attached to nucleotide moieties.

[0097] FIG. 11 shows the chemical structures of various exemplary linkers joined / attached to nucleotide moieties.

[0098] FIG. 12 shows the chemical structures of various exemplary linkers joined / attached to nucleotide moieties.

[0099] FIG. 13 shows the chemical structure of an exemplary biotinylated nucleotide-arm. In this example, the nucleotide moiety is connected to the linker via a propargyl amine attachment at the 5 position of a pyrimidine base or the 7 position of a purine base.

[0100] FIG. 14 is a schematic of a guanine tetrad (e.g., G-tetrad).

[0101] FIG. 15 is a schematic of an exemplary intramolecular G-quadruplex structure.

[0102] FIG. 16 is a schematic of an exemplary nucleic acid fragment circularization workflow, which comprises contacting a linear double stranded nucleic acid fragment (100) with a partial double stranded splint adaptor (200) to form a library-splint complex (300). The partial double stranded splint adaptor (200) can comprise a first, second and third oligonucleotide hybridized together. The first oligonucleotide can comprise a universal primer binding site for a surface capture primer (210), a universal primer binding site for a surface pinning primer (220), and a sample index sequence (230). The sample index sequence (230) can include or lack a short random sequence (e.g., NNN). The second oligonucleotide (211) can comprise a sequence that can hybridize to a portion of the first oligonucleotide. For example, the second oligonucleotide (211) can hybridize to at least a portion of the universal primer binding site for the surface capture primer (210). The third oligonucleotide comprises a sequence that can hybridize to a portion of the first oligonucleotide. For example, the third oligonucleotide comprises a sequence (221) that can hybridize to a portion of the universal primer binding site for a surface pinning primer site (220) of the first oligonucleotide. The third oligonucleotide can comprise a portion (XXX) that can hybridize or bind to the short random sequence (e.g., NNN) of the first oligonucleotide. The third oligonucleotide can comprise a sequence (231) that can hybridize to the sample index sequence (230) of the first oligonucleotide. The first, second and third oligonucleotides can hybridize together to form a partially double stranded splint adaptor having blunt ends at both ends. In the library-splint complex (300), the ends of the linear double stranded nucleic acid fragment (100) and the ends of the partial double stranded splint adaptor (200) can form double stranded nicks, orgaps, which are ligatable. The solid black triangles indicate the double stranded nicks or gaps. The example library-splint complex (300) shown in FIG. 16 comprises two blunt-ended double stranded nicks.

[0103] FIG. 17 is a schematic of an exemplary nucleic acid fragment circularization workflow which comprises contacting a linear double stranded nucleic acid fragment (100) with a partial double stranded splint adaptor (200) to form a library-splint complex (300). The partial double stranded splint adaptor (200) can comprise a first, second and third oligonucleotide hybridized together. The first oligonucleotide can comprise a universal primer binding site for a surface capture primer (210), a universal primer binding site for a surface pinning primer (220), and a sample index sequence (230). The sample index sequence can include or lack a short random sequence (e.g., NNN). The second oligonucleotide (211) can comprise a sequence that can hybridize to a portion of the first oligonucleotide. For example, the second oligonucleotide (211) can hybridize to at least a portion of the universal primer binding site for a surface capture primer (210). The third oligonucleotide comprises a sequence that can hybridize to a portion of the first oligonucleotide. For example, the third oligonucleotide comprises a sequence (221) that can hybridize to a portion of the universal primer binding site for the surface pinning primer site (220) of the first oligonucleotide. The third oligonucleotide comprises a portion (XXX) that can hybridize or bind to the short random sequence (e.g., NNN) of the first oligonucleotide. The third oligonucleotide can comprise a sequence (231) that can hybridize to the sample index sequence (230) of the first oligonucleotide. The first, second and third oligonucleotides can hybridize together to form a partially double stranded splint adaptor having a 3’ overhang end at one or both ends, or having a 5’ overhang end at one or both ends. In the library-splint complex (300), the ends of the linear double stranded nucleic acid molecule or fragment (100) and the ends of the partial double stranded splint adaptor (200) form double stranded nicks which are ligatable. The solid black triangles indicate the double stranded nicks. The library-splint complex (300) shown in FIG. 17 comprises two 3’ overhang double stranded nicks.

[0104] FIG. 18 is a schematic of an exemplary workflow for generating a single stranded closed circular library molecule (500). A library-splint complex (300) (e.g., from FIG. 16 or 17) can be subjected to enzymatic ligation to ligate the ends of the linear double stranded nucleic acid fragment (100) to the ends of the partial double stranded splint adaptor (200) to generate a covalently closed circular library molecule (400) which is partially double stranded (FIG. 18, top). The covalently closed circular library molecule (400) can besubjected to denaturation (e.g., using NaOH) to generate a single stranded covalently closed circular library molecule (500) (FIG. 18, bottom).

[0105] FIG. 19 is a schematic of an exemplary workflow for generating a concatemer molecule which is immobilized to a support. A single stranded covalently closed circular library molecule (500) can be hybridized to a capture primer which is immobilized to a support wherein the single stranded covalently closed circular library molecule (500) comprises a universal sequence that can hybridize to at least a portion of the immobilized capture primer. The terminal 3’ end of the immobilized capture primer is extendible. The terminal 3’ end of the immobilized capture primer can be used to initiate a rolling circle amplification reaction to generate a concatemer molecule which is immobilized to the support. The concatemer molecule comprises tandem repeat sequences of the single stranded covalently closed circular library molecule (500) including any insert sequence and any adaptor sequences present in the single stranded covalently closed circular library molecule (500). The immobilized concatemer molecule can be sequenced. At least a portion of the immobilized concatemer molecule can be sequenced using soluble sequencing primers (solid arrows) that hybridize to a region of the concatemer molecule that is located 5’ (e.g., upstream) of the short random sequence (NNN) and the sample index (230). The short random sequence (NNN), the sample index (230) and the insert region (110) can be sequenced to generate a plurality of first sequencing read products (dashed arrows) (e.g., forward sequence read products). At least a portion of the immobilized concatemer molecule can be subjected to forward sequencing reactions as indicated by the encircled numeral “1”. The immobilized concatemer molecule can be subjected to a pairwise sequencing workflow by replacing the forward sequencing read products by conducting a primer extension reaction which generates a strand that is complementary to the immobilized concatemer molecule. At least a portion of the complementary strand can be sequenced using soluble sequencing primers (solid arrows) that hybridize to a region of the complementary strand that is located 5’ (e.g., upstream) of the insert region (110). In some embodiments, the insert region (110) can be sequenced to generate a plurality of second sequencing read products (dashed arrows) (e.g., reverse sequence read products). At least a portion of the complementary strand can be subjected to reverse sequencing reactions as indicated by the encircled numeral “2”.

[0106] FIG. 20 is a schematic showing an exemplary support having a surface capture primer and a surface pinning primer immobilized thereon. A concatemer can be generated by hybridizing a single stranded covalently closed library molecule (500) to a surface capture primer immobilized to a support, and conducting rolling circle amplification therebygenerating an immobilized concatemer molecule. A portion of the immobilized concatemer molecule can hybridize to the immobilized surface pinning primer. The immobilized concatemer molecule has two or more copies of a universal binding sequence for an immobilized surface pinning primer.

[0107] FIG. 21 is a graph showing the nucleotide base diversity of a sample index sequence which includes a short 3-mer random sequence (NNN). The graph shows a nucleotide diversity of the 3-mer random sequence (NNN) of approximately 30% for A and T base calls, and approximately 20% for C and G base calls.

[0108] FIG. 22 is a graph showing the nucleotide base diversity of a sample index sequence which lacks a short 3-mer random sequence (NNN). The graph shows a nucleotide diversity of approximately 40% for A and T base calls, approximately 15% for C base calls, and approximately 5% for G base calls.DETAILED DESCRIPTIONDefinitions:

[0109] The headings provided herein are not limitations of the various aspects of the disclosure, which aspects can be understood by reference to the specification as a whole.

[0110] Unless defined otherwise, technical and scientific terms used herein have meanings that are commonly understood by those of ordinary skill in the art unless defined otherwise. Generally, terminologies pertaining to techniques of molecular biology, nucleic acid chemistry, protein chemistry, genetics, microbiology, transgenic cell production, and hybridization described herein are those well-known and commonly used in the art. Techniques and procedures described herein are generally performed according to conventional methods well known in the art and as described in various general and more specific references that are cited and discussed throughout the instant specification. For example, see Sambrook et al.. Molecular Cloning: A Laboratory Manual (Third ed., Cold Spring Harbor Laboratory Press, Cold Spring Harbor, N.Y. 2000). See also Ausubel et al., Current Protocols in Molecular Biology, Greene Publishing Associates (1992). The nomenclatures utilized in connection with, and the laboratory procedures and techniques described herein are those well-known and commonly used in the art.

[0111] Unless otherwise required by context herein, singular terms shall include pluralities, and plural terms shall include the singular. Singular forms “a”, “an” and “the”, and singular use of any word, include plural referents, unless expressly and unequivocally limited on one referent.

[0112] It is understood the use of the alternative term (e.g., “or”) is taken to mean either one or both or any combination thereof of the alternatives.

[0113] The term “and / or” used herein is to be taken mean specific disclosure of each of the specified features or components with or without the other. For example, the term “and / or” as used in a phrase such as “A and / or B” herein is intended to include: “A and B”; “A or B”; “A” (A alone); and “B” (B alone). In a similar manner, the term “and / or” as used in a phrase such as “A, B, and / or C” is intended to encompass each of the following aspects: “A, B, and C”; “A, B, or C”; “A or C”; “A or B”; “B or C”; “A and B”; “B and C”; “A and C”; “A” (A alone); “B” (B alone); and “C” (C alone).

[0114] As used herein and in the appended claims, terms “comprising”, “including”, “having” and “containing”, and their grammatical variants, as used herein are intended to be non-limiting so that one item or multiple items in a list do not exclude other items that can be substituted or added to the listed items. It is understood that wherever aspects are described herein with the language “comprising,” otherwise analogous aspects described in terms of “consisting of’ and / or “consisting essentially of’ are also provided.

[0115] As used herein, the terms “about” and “approximately” refer to a value or composition that is within an acceptable error range for the particular value or composition as determined by one of ordinary skill in the art, which will depend in part on how the value or composition is measured or determined, i.e., the limitations of the measurement system. For example, “about” or “approximately” can mean within one or more than one standard deviation per the practice in the art. Alternatively, “about” or “approximately” can mean a range of up to 10% i.e., ±10%) or more depending on the limitations of the measurement system. For example, about 5 mg can include any number between 4.5 mg and 5.5 mg. Furthermore, and particularly with respect to biological systems or processes, the terms can mean up to an order of magnitude or up to 5-fold of a value. When particular values or compositions are provided in the instant disclosure, unless otherwise stated, the meaning of “about” or “approximately” should be assumed to be within an acceptable error range for that particular value or composition. Also, where ranges and / or subranges of values are provided, the ranges and / or subranges can include the endpoints of the ranges and / or subranges.

[0116] The terms “peptide”, “polypeptide” and “protein” and other related terms used herein are used interchangeably and refer to a polymer of amino acids and are not limited to any particular length. Polypeptides may comprise natural and non-natural amino acids. Polypeptides can include recombinant or chemically-synthesized forms. Polypeptides can also include precursor molecules that have not yet been subjected to post-translationmodification, such as proteolytic cleavage, cleavage due to ribosomal skipping, hydroxylation, methylation, lipidation, acetylation, SUMOylation, ubiquitination, glycosylation, phosphorylation and / or disulfide bond formation. These terms encompass native and artificial proteins, protein fragments and polypeptide analogs (such as muteins, variants, chimeric proteins and fusion proteins) of a protein sequence as well as post- translationally, or otherwise covalently or non-covalently, modified proteins.

[0117] The term “cellular biological sample” refers to a single cell, a plurality of cells, a tissue, an organ, an organism, or section of any of these cellular biological samples. The cellular biological sample can be extracted (e.g., biopsied) from an organism, or can be obtained from a cell culture grown in liquid or in a culture dish. The cellular biological sample can comprise a sample that is fresh, frozen, fresh frozen, or archived (e.g., formalin- fixed paraffin-embedded; “FFPE”). The cellular biological sample can be embedded in a wax, resin, epoxy or agar. The cellular biological sample can be fixed, for example, in any one or any combination of two or more of acetone, ethanol, methanol, formaldehyde, paraformaldehyde-Triton or glutaraldehyde. The cellular biological sample can be sectioned or non-sectioned. The cellular biological sample can be stained, de-stained, or non-stained.

[0118] Nucleic acids of interest can be extracted from cells or cellular biological samples using any of a number of techniques known to those of skill in the art. For example, a typical DNA extraction procedure comprises (i) collection of the cellular sample or tissue sample from which DNA is to be extracted, (ii) disruption of cell membranes (i.e., cell lysis) to release DNA and other cytoplasmic components, (iii) treatment of the lysed sample with a concentrated salt solution to precipitate proteins, lipids, and RNA, followed by centrifugation to separate out precipitated proteins, lipids, and RNA, and (iv) purification of DNA from the supernatant to remove detergents, proteins, salts, or other reagents used during the cell membrane lysis. A variety of suitable commercial nucleic acid extraction and purification kits known in the art are consistent with the methods of the disclosure herein. Examples include, but are not limited to, the QIAamp® kits (for isolation of genomic DNA from human samples) and DNAeasy® kits (for isolation of genomic DNA from animal or plant samples) from Qiagen® (Germantown, MD), or the Maxwell® and ReliaPrep™ series of kits from Promega® (Madison, WI).

[0119] The term “polymerase” and its variants, as used herein, comprises an enzyme comprising a domain that binds a nucleotide (or nucleoside) where the polymerase can form a complex having a template nucleic acid and a complementary nucleotide. The polymerase can have one or more activities including, but not limited to, base analog detection activities,DNA polymerization activity, reverse transcriptase activity, DNA binding, strand displacement activity, and nucleotide binding and recognition. A polymerase can be any enzyme that can catalyze polymerization of nucleotides (including analogs thereof) into a nucleic acid strand. Typically, but not necessarily such nucleotide polymerization can occur in a template-dependent fashion. Typically, a polymerase comprises one or more active sites at which nucleotide binding and / or catalysis of nucleotide polymerization can occur. In some embodiments, a polymerase includes other enzymatic activities, such as for example, 3' to 5' exonuclease activity or 5' to 3' exonuclease activity. In some embodiments, a polymerase has strand displacing activity. A polymerase can include, without limitation, naturally occurring polymerases and any subunits and truncations thereof, mutant polymerases, variant polymerases, recombinant, fusion or otherwise engineered polymerases, chemically modified polymerases, synthetic molecules or assemblies, and any analogs, derivatives or fragments thereof that retain the ability to catalyze nucleotide polymerization (e.g., catalytically active fragment). Polymerases can include catalytically inactive polymerases, catalytically active polymerases, reverse transcriptases, and other enzymes comprising a nucleotide binding domain. In some embodiments, a polymerase can be isolated from a cell, or generated using recombinant DNA technology or chemical synthesis methods. In some embodiments, a polymerase can be expressed in prokaryote, eukaryote, viral, or phage organisms. In some embodiments, a polymerase can be a post-translationally modified protein or fragment, e.g., a functional fragment, thereof. A polymerase can be derived from a prokaryote, eukaryote, virus or phage. A polymerase can comprise DNA-directed DNA polymerase and RNA- directed DNA polymerase.

[0120] The term “strand displacing” refers to the ability of a polymerase to locally separate strands of double-stranded nucleic acids and synthesize a new strand in a templatebased manner. Strand displacing polymerases displace a complementary strand from a template strand and catalyze new strand synthesis. Strand displacing polymerases include mesophilic and thermophilic polymerases. Strand displacing polymerases include wild type enzymes, and variants including exonuclease minus mutants, mutant versions, chimeric enzymes and truncated enzymes. Examples of strand displacing polymerases include phi29 DNA polymerase, large fragment of Bst DNA polymerase, large fragment of Bsu DNA polymerase (exo-), Bea DNA polymerase (exo-), KI enow fragment of E. coli DNA polymerase, T5 polymerase, M-MuLV reverse transcriptase, HIV viral reverse transcriptase, Deep Vent DNA polymerase and KOD DNA polymerase. The phi29 DNA polymerase can be wild type phi29 DNA polymerase (e.g., MagniPhi® from Expedeon®), or variantEquiPhi29 DNA polymerase (e.g., from Thermo Fisher Scientific®), or chimeric QualiPhi® DNA polymerase (e.g., from 4basebio®).

[0121] The terms “nucleic acid”, “polynucleotide” and “oligonucleotide” and other related terms used herein are used interchangeably and refer to polymers of nucleotides and are not limited to any particular length. Nucleic acids include recombinant and chemically- synthesized forms. Nucleic acids can be isolated. Nucleic acids include DNA molecules (e.g., cDNA or genomic DNA), RNA molecules (e.g., mRNA), analogs of the DNA or RNA generated using nucleotide analogs (e.g., peptide nucleic acids and non-naturally occurring nucleotide analogs), and chimeric forms containing DNA and RNA. Nucleic acids can be single-stranded or double-stranded. Nucleic acids comprise polymers of nucleotides, where the nucleotides include natural or non-natural bases and / or sugars. Nucleic acids comprise naturally-occurring internucleosidic linkages, for example phosphodiester linkages. Nucleic acids comprise non-natural intemucleoside linkages, including phosphorothioate, phosphorothiolate, or peptide nucleic acid (PNA) linkages. In some embodiments, nucleic acids comprise one type of polynucleotides or a mixture of two or more different types of polynucleotides.

[0122] The term “operably linked” and “operably joined” or related terms as used herein refers to juxtaposition of components. The juxtapositioned components can be linked together covalently. For example, two nucleic acid components can be enzymatically ligated together, where the linkage that joins together the two components comprises a phosphodiester linkage. A first and second nucleic acid component can be linked together, where the first nucleic acid component can confer a function on a second nucleic acid component. For example, a linkage between a primer binding sequence and a sequence of interest forms a nucleic acid library molecule having a portion that can bind to a primer. In another example, a transgene (e.g., a nucleic acid encoding a polypeptide or a nucleic acid sequence of interest) can be ligated to a vector, where the linkage permits expression or functioning of the transgene sequence contained in the vector. In some embodiments, a transgene is operably linked to a host cell regulatory sequence (e.g., a promoter sequence) that affects expression of the transgene. In some embodiments, the vector comprises at least one host cell regulatory sequence, including a promoter sequence, enhancer, transcription and / or translation initiation sequence, transcription and / or translation termination sequence, polypeptide secretion signal sequences, and the like. In some embodiments, the host cell regulatory sequence controls expression of the level, timing and / or location of the transgene.

[0123] The terms “linked”, “joined”, “attached”, “appended” and variants thereof comprise any type of fusion, bond, adherence or association between any combination of compounds or molecules that is of sufficient stability to withstand use in a particular procedure. The procedure can include, but is not limited to: nucleotide binding; nucleotide incorporation; de-blocking (e.g., removal of a chain-terminating moiety); washing; removing; flowing; detecting; imaging and / or identifying. Such linkage can comprise, for example, covalent, ionic, hydrogen, dipole-dipole, hydrophilic, hydrophobic, or affinity bonding, bonds or associations involving van der Waals forces, mechanical bonding, and the like. In some embodiments, such linkage occurs intramolecularly, for example, linking together the ends of a single-stranded or double-stranded linear nucleic acid molecule to form a circular molecule. In some embodiments, such linkage can occur between a combination of different molecules, or between a molecule and a non-molecule, including but not limited to: linkage between a nucleic acid molecule and a solid surface; linkage between a protein and a detectable reporter moiety; linkage between a nucleotide and detectable reporter moiety; and the like. Some examples of linkages can be found, for example and without limitation, in Hermanson, G., “Bioconjugate Techniques”, Second Edition (2008); Aslam, M., Dent, A., “Bioconjugation: Protein Coupling Techniques for the Biomedical Sciences”, London: Macmillan (1998); Aslam, M., Dent, A., “Bioconjugation: Protein Coupling Techniques for the Biomedical Sciences”, London: Macmillan (1998).

[0124] The term “primer” and related terms used herein refers to an oligonucleotide that is capable of hybridizing with a DNA and / or RNA polynucleotide template to form a duplex molecule. Primers can be single-stranded along their entire length or have single-stranded and double-stranded portions. Primers comprise natural nucleotides and / or nucleotide analogs. Primers can be recombinant nucleic acid molecules. Primers may have any length, but typically range from 4-50 nucleotides. A typical primer comprises a 5’ end and 3’ end. The 3’ end of the primer can include a 3’ OH moiety which serves as a nucleotide polymerization initiation site in a polymerase-catalyzed primer extension reaction. Alternatively, the 3’ end of the primer can lack a 3’ OH moiety, or can include a terminal 3’ blocking group that inhibits nucleotide polymerization in a polymerase-catalyzed reaction. Any one nucleotide, or more than one nucleotide, along the length of the primer can be labeled with a detectable reporter moiety. A primer can be in solution (e.g., a soluble primer) or can be immobilized to a support (e.g., a capture primer).

[0125] The term “template nucleic acid”, “template polynucleotide”, “target nucleic acid” “target polynucleotide”, “template strand” and other variations refer to a nucleic acid strandthat serves as the basis nucleic acid molecule for any of the amplification and / or sequencing methods describe herein. The template nucleic acid can be single-stranded or doublestranded, or the template nucleic acid can have single-stranded or double-stranded portions. The template nucleic acid can be obtained from a naturally-occurring source, recombinant form, or chemically synthesized to include any type of nucleic acid analog. The template nucleic acid can be linear, concatemeric, circular, or other forms.

[0126] As used herein, with respect to a nucleotide sequence, “upstream” refers to sequence located 5’ of a particular reference feature in the nucleotide sequence. Similarly, “downstream” refers to sequence located 3’ of the particular reference feature. “Immediately” upstream or downstream refers to a nucleotide or sequence that is approximately 1-10 nucleotides (e.g., about 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10) upstream or downstream of the reference feature.

[0127] As used herein, the term “sequencing read product” refers to a primer extension product generated by conducting a sequencing reaction using a sequencing primer hybridized to a template molecule to be sequenced (e.g., a concatemer molecule), a sequencing polymerase and a plurality of nucleotides. In some embodiments, the sequencing polymerase catalyzes nucleotide incorporation using the 3’ end of the sequencing primer as an initiation site and generates an extension product comprising a sequence that is complementary to the template molecule. In some embodiments, a nucleotide incorporation reaction extends the sequencing primer by one nucleotide. In some embodiments, the number of nucleotide incorporation reactions that are conducted will dictate the length of the sequencing read product. For example, conducting eleven nucleotide incorporation reactions will generate a sequencing primer that is extended by eleven nucleotides. In some embodiments, one cycle of a sequencing reaction comprises: conducting one nucleotide incorporation reaction using a sequencing polymerase and a nucleotide thereby extending the sequencing primer by one nucleotide. In some embodiments, one cycle of a sequencing reaction comprises: (i) binding a multivalent molecule to the 3’ end of a first sequencing primer and a sequencing polymerase under a condition that inhibits polymerase-catalyzed nucleotide incorporation where the multivalent molecule comprises a plurality of nucleotide arms attached to a core; (ii) removing the multivalent molecule and the sequencing polymerase while retaining the template molecule hybridized to the sequencing primer; and (iii) conducting one nucleotide incorporation reaction using a second sequencing polymerase and a nucleotide thereby extending the sequencing primer by one nucleotide.

[0128] When used in reference to nucleic acid molecules, the terms “hybridize” or “hybridizing” or “hybridization” or other related terms refers to hydrogen bonding between two different nucleic acids to form a duplex nucleic acid. Hybridization also includes hydrogen bonding between two different regions of a single nucleic acid molecule to form a self-hybridizing molecule having a duplex region. Hybridization can comprise Watson-Crick or Hoogstein binding to form a duplex double-stranded nucleic acid, or a double-stranded region within a nucleic acid molecule. The double-stranded nucleic acid, or the two different regions of a single nucleic acid, may be wholly complementary, or partially complementary. Complementary nucleic acid strands need not hybridize with each other across their entire length. The complementary base pairing can be standard A-T or C-G base pairing, or can be other forms of base-pairing interactions. Duplex nucleic acids can include mismatched basepaired nucleotides.

[0129] When used in reference to nucleic acids, the terms “extend”, “extending”, “extension” and other variants, refers to incorporation of one or more nucleotides into a nucleic acid molecule. Nucleotide incorporation comprises polymerization of one or more nucleotides into the terminal 3’ OH end of a nucleic acid strand, resulting in extension of the nucleic acid strand. Nucleotide incorporation can be conducted with natural nucleotides and / or nucleotide analogs. Typically, but not necessarily, nucleotide incorporation occurs in a template-dependent fashion. Any suitable method of extending a nucleic acid molecule as known in the art may be used, including but not limited to primer extension catalyzed by a DNA polymerase or RNA polymerase.

[0130] The term “nucleotides” and related terms refers to a molecule comprising an aromatic base, a five-carbon sugar (e.g., ribose or deoxyribose), and at least one phosphate group. Canonical or non-canonical nucleotides are consistent with use of the term. In some embodiments, the nucleotide comprises a monophosphate, diphosphate, triphosphate, or corresponding phosphate analog. The term “nucleoside” refers to a molecule comprising an aromatic base and a sugar. Nucleotides and nucleosides can be non-labeled, or labeled with a detectable reporter moiety.

[0131] Nucleotides (and nucleosides) typically comprise a hetero cyclic base including substituted or unsubstituted nitrogen-containing parent heteroaromatic ring which are commonly found in nucleic acids, including naturally-occurring, substituted, modified, or engineered variants, or analogs of the same. The base of a nucleotide (or nucleoside) is capable of forming Watson-Crick and / or Hoogstein hydrogen bonds with an appropriate complementary base. Exemplary bases include, but are not limited to, purines andpyrimidines such as: 2-aminopurine, 2,6-diaminopurine, adenine (A), ethenoadenine, N6-A2- isopentenyladenine (6iA), N6-A2-isopentenyl-2-methylthioadenine (2ms6iA), N6- methyladenine, guanine (G), isoguanine, N2-dimethylguanine (dmG), 7-methylguanine (7mG), 2-thiopyrimidine, 6-thioguanine (6sG), hypoxanthine and O6-methylguanine; 7- deaza-purines such as 7-deazaadenine (7-deaza-A) and 7-deazaguanine (7-deaza-G); pyrimidines such as cytosine (C), 5-propynylcytosine, isocytosine, thymine (T), 4- thiothymine (4sT), 5,6-dihydrothymine, O4-methylthymine, uracil (U), 4-thiouracil (4sU) and 5,6-dihydrouracil (dihydrouracil; D); indoles such as nitroindole and 4-methylindole; pyrroles such as nitropyrrole; nebularine; inosines; hydroxymethylcytosines; 5 -methy cytosines; base (Y); as well as methylated, glycosylated, and acylated base moieties; and the like. Additional exemplary bases can be found in Fasman, 1989, in “Practical Handbook of Biochemistry and Molecular Biology”, pp. 385-394, CRC Press, Boca Raton, Fla.

[0132] Nucleotides (and nucleosides) typically comprise a sugar moiety, such as carbocyclic moiety (Ferraro and Gotor 2000 Chem. Rev. 100: 4319-48), acyclic moieties (Martinez, et al., 1999 Nucleic Acids Research 27: 1271-1274; Martinez, et al., 1997 Bioorganic & Medicinal Chemistry Letters vol. 7: 3013-3016), and other sugar moieties (Joeng, et al., 1993 J. Med. Chem. 36: 2627-2638; Kim, et al., 1993 J. Med. Chem. 36: 30-7; Eschenmosser 1999 Science 284:2118-2124; and U.S. Pat. No. 5,558,991). The sugar moiety comprises: ribosyl; 2'-deoxyribosyl; 3 '-deoxyribosyl; 2', 3 '-dideoxyribosyl; 2', 3'- didehydrodideoxyribosyl; 2'-alkoxyribosyl; 2'-azidoribosyl; 2'-aminoribosyl; 2'-fluororibosyl; 2'-mercaptoriboxyl; 2'-alkylthioribosyl; 3 '-alkoxyribosyl; 3 '-azidoribosyl; 3 '-aminoribosyl; 3 '-fluororibosyl; 3'-mercaptoriboxyl; 3 '-alkylthioribosyl carbocyclic; acyclic or other modified sugars.

[0133] In some embodiments, nucleotides comprise a chain of one, two or three phosphorus atoms where the chain is typically attached to the 5’ carbon of the sugar moiety via an ester or phosphoramide linkage. In some embodiments, the nucleotide is an analog having a phosphorus chain in which the phosphorus atoms are linked together with intervening O, S, NH, methylene or ethylene. In some embodiments, the phosphorus atoms in the chain include substituted side groups including O, S or BH3. In some embodiments, the chain includes phosphate groups substituted with analogs including phosphoramidate, phosphorothioate, phosphorodithioate, and O-methylphosphoroamidite groups.

[0134] The term “rolling circle amplification” generally refers to an amplification method that employs a circularized nucleic acid template molecule containing a target sequence of interest, an amplification primer binding sequence, and optionally one or more adaptorsequences such as a sequencing primer binding sequence and / or a sample index sequence. The rolling circle amplification reaction can be conducted under isothermal amplification conditions, and includes the circularized nucleic acid template molecule, an amplification primer, a strand-displacing polymerase and a plurality of nucleotides, to generate a concatemer containing tandem repeat sequences of the circular template molecule and any adaptor sequences present in the original circularized nucleic acid template molecule. Optionally, the concatemer can self-collapse to form a nucleic acid nanoball. The shape and size of the nanoball can be further compacted by including a pair of inverted repeat sequences in the circular template molecule, or by conducting the rolling circle amplification reaction with one or more compaction oligonucleotides. One of the advantages of using rolling circle amplification to generate clonal amplicons for a sequencing workflow, is that the repeat copies of the target sequence in the nanoball can be simultaneously sequenced to increase signal intensity. In some embodiments, the rolling circle amplification reaction can be conducted in the presence of a plurality of compaction oligonucleotides having at least four consecutive guanines. The rolling circle amplification reaction can generate concatemers comprising repeat copies of the universal binding sequence for the compaction oligonucleotide. At least one compaction oligonucleotide can form a guanine tetrad and hybridize to the universal binding sequences for the compaction oligonucleotide, and the resulting concatemer can fold to form an intramolecular G-quadruplex structure. The concatemers can self-collapse to form compact nanoballs. Without wishing to be bound by theory, it is hypothesized that formation of the guanine tetrads and G-quadruplexes in the nanoballs may increase the stability of the nanoballs to retain their compact size and shape which can withstand repeated flows of reagents for conducting any of the sequencing workflows described herein.

[0135] When used in reference to nucleic acids, the terms “amplify”, “amplifying”, “amplification”, and other related terms include producing multiple copies of an original polynucleotide template molecule, where the copies comprise a sequence that is complementary to the template sequence, and / or the copies comprise a sequence that is the same as the template sequence. In some embodiments, the copies comprise a sequence that is substantially identical to a template sequence, and / or is substantially identical to a sequence that is complementary to the template sequence.

[0136] The term “reporter moiety”, “reporter moieties” or related terms refers to a compound that generates, or causes to generate, a detectable signal. A reporter moiety is sometimes called a “label”. Any suitable reporter moiety may be used, includingluminescent, photoluminescent, electroluminescent, bioluminescent, chemiluminescent, fluorescent, phosphorescent, chromophore, radioisotope, electrochemical, mass spectrometry, Raman, hapten, affinity tag, atom, or an enzyme. A reporter moiety can generate a detectable signal resulting from a chemical or physical change (e.g., heat, light, electrical, pH, salt concentration, enzymatic activity, or proximity events). A proximity event can include two reporter moieties approaching each other, or associating with each other, or binding each other. It is well known to one skilled in the art to select reporter moieties so that individual moieties absorb excitation radiation and / or emit fluorescence at a wavelength distinguishable from the other reporter moieties to permit monitoring the presence of different reporter moieties in the same reaction or in different reactions. Two or more different reporter moieties can be selected having spectrally distinct emission profiles, or having minimal overlapping spectral emission profiles. Reporter moieties can be linked (e.g., operably linked) to nucleotides, nucleosides, nucleic acids, enzymes (e.g., polymerases or reverse transcriptases), or support (e.g., surfaces).

[0137] A reporter moiety (or label) comprises a fluorescent label or a fluorophore. Exemplary fluorescent moieties which may serve as fluorescent labels or fluorophores include, but are not limited to fluorescein and fluorescein derivatives such as carboxyfluorescein, tetrachlorofluorescein, hexachlorofluorescein, carboxynapthofluorescein, fluorescein isothiocyanate, NHS-fluorescein, iodoacetamidofluorescein, fluorescein maleimide, SAMSA-fluorescein, fluorescein thiosemicarbazide, carbohydrazinomethylthioacetyl-amino fluorescein, rhodamine and rhodamine derivatives such as TRITC, TMR, lissamine rhodamine, Texas Red, rhodamine B, rhodamine 6G, rhodamine 10, NHS-rhodamine, TMR-iodoacetamide, lissamine rhodamine B sulfonyl chloride, lissamine rhodamine B sulfonyl hydrazine, Texas Red sulfonyl chloride, Texas Red hydrazide, coumarin and coumarin derivatives such as AMCA, AMCA-NHS, AMCA-sulfo- NHS, AMCA-HPDP, DCIA, AMCE-hydrazide, BODIPY and derivatives such as BODIPY FL C3-SE, BODIPY 530 / 550 C3, BODIPY 530 / 550 C3-SE, BODIPY 530 / 550 C3 hydrazide, BODIPY 493 / 503 C3 hydrazide, BODIPY FL C3 hydrazide, BODIPY FL IA, BODIPY 530 / 551 IA, Br-BODIPY 493 / 503, Cascade Blue and derivatives such as Cascade Blue acetyl azide, Cascade Blue cadaverine, Cascade Blue ethylenediamine, Cascade Blue hydrazide, Lucifer Yellow and derivatives such as Lucifer Yellow iodoacetamide, Lucifer Yellow CH, cyanine and derivatives such as indolium based cyanine dyes, benzo-indolium based cyanine dyes, pyridium based cyanine dyes, thiozolium based cyanine dyes, quinolinium based cyanine dyes, imidazolium based cyanine dyes, Cy 3, Cy5, lanthanide chelates andderivatives such as BCPDA, TBP, TMT, BHHCT, BCOT, Europium chelates, Terbium chelates, Alexa Fluor® dyes, DyLight® dyes, Atto™ dyes, LightCycler® Red dyes, CAL Flour dyes, JOE and derivatives thereof, Oregon Green™ dyes, WellRED dyes, IRD dyes, phycoerythrin and phycobilin dyes, Malachite green, stilbene, DEG dyes, NR dyes, nearinfrared dyes and others known in the art such as those described in Haugland, Molecular Probes Handbook, (Eugene, Oreg.) 6th Edition; Lakowicz, Principles of Fluorescence Spectroscopy, 2nd Ed., Plenum Press New York (1999), or Hermanson, Bioconjugate Techniques, 2nd Edition, or derivatives thereof, or any combination thereof. Cyanine dyes may exist in either sulfonated or non-sulfonated forms, and consist of two indolenin, benzo- indolium, pyridium, thiozolium, and / or quinolinium groups separated by a polymethine bridge between two nitrogen atoms. Commercially available cyanine fluorophores include, for example, Cy3, (which may comprise l-[6-(2,5-dioxopyrrolidin-l-yloxy)-6-oxohexyl]-2- (3-{ l-[6-(2,5-dioxopyrrolidin-l-yloxy)-6-oxohexyl]-3,3-dimethyl-l,3-dihydro-2H-indol-2- ylidenejprop- 1 -en- 1 -yl)-3 ,3 -dimethyl-3H-indolium or 1 - [6-(2, 5-dioxopyrrolidin- 1 -yloxy)-6- oxohexyl]-2-(3-{ l-[6-(2,5-dioxopyrrolidin-l-yloxy)-6-oxohexyl]-3,3-dimethyl-5-sulfo-l,3- dihydro-2H-indol-2-ylidene}prop-l-en-l-yl)-3,3-dimethyl-3H-indolium-5-sulfonate), Cy5 (which may comprise l-(6-((2,5-dioxopyrrolidin-l-yl)oxy)-6-oxohexyl)-2-((lE,3E)-5-((E)-l- (6-((2,5-dioxopyrrolidin-l-yl)oxy)-6-oxohexyl)-3,3-dimethyl-5-indolin-2-ylidene)penta-l,3- dien- 1 -yl)-3 ,3 -dimethyl-3H-indol- 1 -ium or 1 -(6-((2, 5-dioxopyrrolidin- 1 -yl)oxy)-6- oxohexyl)-2-((lE,3E)-5-((E)-l-(6-((2,5-dioxopyrrolidin-l-yl)oxy)-6-oxohexyl)-3,3-dimethyl- 5-sulfoindolin-2-ylidene)penta-l,3-dien-l-yl)-3,3-dimethyl-3H-indol-l-ium-5-sulfonate), and Cy7 (which may comprise l-(5-carboxypentyl)-2-[(lE,3E,5E,7Z)-7-(l-ethyl-l,3-dihydro-2H- indol-2-ylidene)hepta-l,3,5-trien-l-yl]-3H-indolium or l-(5-carboxypentyl)-2- [(lE,3E,5E,7Z)-7-(l-ethyl-5-sulfo-l,3-dihydro-2H-indol-2-ylidene)hepta-l,3,5-trien-l-yl]- 3H-indolium-5-sulfonate), where “Cy” stands for 'cyanine', and the first digit identifies the number of carbon atoms between two indolenine groups. Cy2, which is an oxazole derivative rather than indolenin, and the benzo-derivatized Cy3.5, Cy5.5 and Cy7.5, are exceptions to this rule. Additional fluorophores are described in WO 2024 / 124008, the contents of which are incorporated by reference in their entirety herein.

[0138] In some embodiments, the reporter moiety can be a fluorescence resonance energy transfer (FRET) pair, such that multiple classifications can be performed under a single excitation and imaging step. As used herein, FRET may comprise excitation exchange (Forster) transfers, or electron-exchange (Dexter) transfers.

[0139] The term “support” as used herein refers to a substrate that is designed for deposition of biological molecules or biological samples for assays and / or analyses. Examples of biological molecules to be deposited onto a support can include nucleic acids (e.g., DNA, RNA), polypeptides, saccharides, lipids, a single cell or multiple cells. Examples of biological samples include, but are not limited to, saliva, phlegm, mucus, blood, plasma, serum, urine, stool, sweat, tears and fluids from tissues or organs.

[0140] In some embodiments, the support is solid, semi-solid, or a combination of both. In some embodiments, the support is porous, semi-porous, non-porous, or any combination of porosity. In some embodiments, the support can be substantially planar, concave, convex, or any combination thereof. In some embodiments, the support can be cylindrical, for example comprising a capillary or interior surface of a capillary.

[0141] In some embodiments, the surface of the support can be substantially smooth. In some embodiments, the support can be regularly or irregularly textured, including bumps, etched, pores, three-dimensional scaffolds, or any combination thereof.

[0142] In some embodiments, the support comprises a bead having any shape, including but not limited to, spherical, hemi- spherical, cylindrical, barrel-shaped, toroidal, disc-shaped, rod-like, conical, triangular, cubical, polygonal, tubular or wire-like.

[0143] The support can be fabricated from any material, including but not limited to glass, fused-silica, silicon, a polymer (e.g., polystyrene (PS), macroporous polystyrene (MPPS), polymethylmethacrylate (PMMA), polycarbonate (PC), polypropylene (PP), polyethylene (PE), high density polyethylene (HDPE), cyclic olefin polymers (COP), cyclic olefin copolymers (COC), polyethylene terephthalate (PET)), or any combination thereof. Various compositions of both glass and plastic substrates are contemplated.

[0144] The present disclosure provides a plurality (e.g., two or more) of nucleic acid template molecules immobilized to a support. In some embodiments, the immobilized plurality of nucleic acid template molecules has the same sequence or have different sequences. In some embodiments, individual nucleic acid template molecules in the plurality of nucleic acid template molecules are immobilized to a different site on the support. In some embodiments, two or more individual nucleic acid template molecules in the plurality of nucleic acid templates are immobilized to a site on the support.

[0145] The term “array” refers to a support comprising a plurality of sites located at predetermined locations on the support to form an array of sites. The sites can be discrete and separated by interstitial regions. In some embodiments, the pre-determined sites on the support can be arranged in one dimension in a row or a column, or arranged in twodimensions in rows and columns. In some embodiments, the plurality of pre-determined sites is arranged on the support in an organized fashion. In some embodiments, the plurality of pre-determined sites is arranged in any organized pattern, including rectilinear, hexagonal patterns, grid patterns, patterns having reflective symmetry, patterns having rotational symmetry, or the like. The pitch between different pairs of sites can be that same or can vary. In some embodiments, the support comprises at least 102sites, at least 103sites, at least 104sites, at least 105sites, at least 106sites, at least 107sites, at least 108sites, at least 109sites, at least IO10sites, at least 1011sites, at least 1012sites, at least 1013sites, at least 1014sites, at least 1015sites, or more, where the sites are located at pre-determined locations on the support. In some embodiments, a plurality of pre-determined sites on the support (e.g., 102- 1015sites, or more) are immobilized with nucleic acid template molecules to form a nucleic acid template array. In some embodiments, the nucleic acid template molecules that are immobilized at a plurality of pre-determined sites by hybridization to immobilized surface capture primers, or the nucleic acid template molecules are covalently attached to the surface capture primers. In some embodiments, the nucleic acid template molecules are immobilized at a plurality of pre-determined sites, for example, immobilized at 102- 1015sites, or more. In some embodiments, the immobilized nucleic acid template molecules are clonally-amplified to generate immobilized nucleic acid clusters at the plurality of pre-determined sites. In some embodiments, individual immobilized nucleic acid clusters comprise linear clusters, or comprise single-stranded or double-stranded concatemers.

[0146] In some embodiments, a support comprising a plurality of sites located at random locations on the support is referred to herein as a support having randomly located sites thereon. The location of the randomly located sites on the support are not pre-determined. The plurality of randomly-located sites is arranged on the support in a disordered and / or unpredictable fashion. In some embodiments, the support comprises at least 102sites, at least 103sites, at least 104sites, at least 105sites, at least 106sites, at least 107sites, at least 108sites, at least 109sites, at least IO10sites, at least 1011sites, at least 1012sites, at least 1013sites, at least 1014sites, at least 1015sites, or more, where the sites are randomly located on the support. In some embodiments, a plurality of randomly located sites on the support e.g., 102- 1015sites or more) are immobilized with nucleic acid template molecules. In some embodiments, the nucleic acid template molecules are immobilized at a plurality of randomly located sites by hybridization to immobilized surface capture primers, or the nucleic acid template molecules are covalently attached to the surface capture primers. In some embodiments, the nucleic acid templates that are immobilized at a plurality of randomlylocated sites, for example, immobilized at 102- 1015sites or more. In some embodiments, the immobilized nucleic acid templates are clonally-amplified to generate immobilized nucleic acid clusters at the plurality of randomly located sites. In some embodiments, individual immobilized nucleic acid clusters comprise linear clusters, or comprise single-stranded or double-stranded concatemers.

[0147] In some embodiments, the plurality of immobilized surface capture primers on the support (e.g., located at pre-determined or random locations on the support) are in fluid communication with each other to permit flowing a solution of reagents (e.g., nucleic acid template molecules, soluble primers, enzymes, nucleotides, divalent cations, buffers, and the like) onto the support so that the plurality of immobilized surface capture primers on the support can be essentially simultaneously reacted with the reagents in a massively parallel manner. In some embodiments, the fluid communication of the plurality of immobilized surface capture primers can be used to conduct nucleic acid amplification reactions (e.g., RCA, MDA, PCR and bridge amplification) essentially simultaneously on the plurality of immobilized surface capture primers.

[0148] In some embodiments, the plurality of immobilized nucleic acid clusters on the support are in fluid communication with each other to permit flowing a solution of reagents (e.g., enzymes, nucleotides, divalent cations, and the like) onto the support so that the plurality of immobilized nucleic acid clusters on the support can be essentially simultaneously reacted with the reagents in a massively parallel manner. In some embodiments, the fluid communication of the plurality of immobilized nucleic acid clusters can be used to conduct nucleotide binding assays and / or conduct nucleotide polymerization reactions (e.g., primer extension or sequencing) essentially simultaneously on the plurality of immobilized nucleic acid clusters, and optionally to conduct detection and imaging for massively parallel sequencing.

[0149] In some embodiments, the term “immobilized” and related terms refer to nucleic acid molecules that are attached to a support through covalent bond or non-covalent interaction, or attached to a coating on the support, or buried within a matrix formed by a coating on the support, where the nucleic acid molecules include surface capture primers, nucleic acid template molecules and extension products of capture primers. Extension products of capture primers can include concatemers (e.g., nucleic acid clusters). The nucleic acid molecules can be immobilized at pre-determined or random locations on the support. The nucleic acid molecules can be immobilized at pre-determined or random locations on or within a coating passivated on the support.

[0150] In some embodiments, the term “immobilized” and related terms refer to enzymes (e.g., polymerases) that are attached to a support through covalent bond or non-covalent interaction, or attached to a coating on the support, or buried within a matrix formed by a coating on the support. The enzymes can be immobilized at pre-determined or random locations on the support. The enzymes can be immobilized at pre-determined or random locations on or within a coating passivated on the support.

[0151] In some embodiments, one or more nucleic acid template molecules are immobilized on the support, for example immobilized at the sites on the support. In some embodiments, the one or more nucleic acid template molecules are clonally-amplified. In some embodiments, the one or more nucleic acid template molecules are clonally-amplified off the support (e.g., in-solution) and then deposited onto the support and immobilized on the support. In some embodiments, the clonal amplification reaction of the one or more nucleic acid template molecules is conducted on the support resulting in immobilization on the support. In some embodiments, the one or more nucleic acid template molecules are clonally-amplified (e.g., in solution or on the support) using a nucleic acid amplification reaction, including any one or any combination of: polymerase chain reaction (PCR), multiple displacement amplification (MDA), transcription-mediated amplification (TMA), nucleic acid sequence-based amplification (NASBA), strand displacement amplification (SDA), real-time SDA, bridge amplification, isothermal bridge amplification, rolling circle amplification (RCA), circle-to-circle amplification, helicase-dependent amplification, recombinase-dependent amplification, and / or single-stranded binding (SSB) proteindependent amplification.

[0152] The term “surface primer” and related terms refers to single-stranded oligonucleotides that are immobilized to a support and comprise a sequence that can hybridize to at least a portion of a nucleic acid template molecule. Surface capture primers can be used to immobilize template molecules to a support via hybridization. Surface capture primers can be immobilized to a support in a manner that resists primer removal during flowing, washing, aspirating, and changes in temperature, pH, salts, chemical and / or enzymatic conditions. Typically, but not necessarily, the 5’ end of a surface capture primer can be immobilized to a support or to a coating on the support (or embedded in a coating on the support). Alternatively, an interior portion or the 3’ end of a surface capture primer can be immobilized to a support.

[0153] The sequence of surface capture primers can be wholly or partially complementary along their length to at least a portion of the nucleic acid template molecule.A support can include a plurality of immobilized surface capture primers having the same sequence, or having two or more different sequences. Surface capture primers can be any length, for example, 4-50 nucleotides, or 50-100 nucleotides, or 100-150 nucleotides, or longer lengths.

[0154] A surface capture primer can have a terminal 3’ nucleotide having a sugar 3’ OH moiety which is extendible for nucleotide polymerization (e.g., polymerase catalyzed polymerization). A surface capture primer can have a terminal 3’ nucleotide having the 3’ sugar position linked to a chain-terminating moiety that inhibits nucleotide polymerization. The 3’ chain-terminating moiety can be removed (e.g., de-blocked) to convert the 3’ end to an extendible 3’ OH end using a de-blocking agent. Examples of chain terminating moi eties include alkyl group, alkenyl group, alkynyl group, allyl group, aryl group, benzyl group, azide group, amine group, amide group, keto group, isocyanate group, phosphate group, thio group, disulfide group, carbonate group, urea group, acetal group or silyl group. Azide type chain terminating moieties including azide, azido and azidomethyl groups. Examples of deblocking agents include a phosphine compound, such as Tris(2-carboxyethyl)phosphine (TCEP) and bis-sulfo triphenyl phosphine (BS-TPP), for chain-terminating groups azide, azido and azidomethyl groups. Examples of de-blocking agents include tetrakis(triphenylphosphine)palladium(0) (Pd(PPh3)4) with piperidine, or with 2,3-Dichloro- 5,6-dicyano-l,4-benzo-quinone (DDQ), for chain-terminating groups alkyl, alkenyl, alkynyl and allyl. Examples of a de-blocking agent include, without limitation, Pd / C for chainterminating groups aryl and benzyl. Examples of de-blocking agents include, without limitation, phosphine, beta-mercaptoethanol or dithiothritol (DTT), for chain-terminating groups amine, amide, keto, isocyanate, phosphate, thio and disulfide. Examples of deblocking agents include potassium carbonate (K2CO3) in MeOH, triethylamine in pyridine, and Zn in acetic acid (AcOH), for carbonate chain-terminating groups. Examples of deblocking agents include, without limitation, tetrabutylammonium fluoride, pyridine-HF, with ammonium fluoride, and triethylamine trihydrofluoride, for chain-terminating groups urea and silyl.

[0155] The term “sequencing” and related terms refers to a method for obtaining nucleotide sequence information from a nucleic acid molecule, typically by determining the identity of at least some nucleotides (including their nucleobase components) within the nucleic acid molecule. In some embodiments, the sequence information of a given region of a nucleic acid molecule includes identifying each and every nucleotide within a region that is sequenced. In some embodiments, sequencing information determines only some of thenucleotides a region, while the identity of some nucleotides remains undetermined or incorrectly determined. Any suitable method of sequencing as known in the art may be used. In an exemplary embodiment, sequencing can include label-free or ion based sequencing methods. In some embodiments, sequencing can include labeled or dye-containing nucleotide or fluorescent based nucleotide sequencing methods. In some embodiments, sequencing can include polony-based sequencing or bridge sequencing methods. In some embodiments, the sequencing employs polymerases and multivalent molecules for generating at least one avidity complex, wherein individual multivalent molecules comprise a plurality of nucleotide moieties tethered to a core. In some embodiments, the sequencing employs polymerases and free nucleotides for performing sequencing-by-synthesis. In some embodiments, the sequencing employs a ligase enzyme and a plurality of sequence-specific oligonucleotides for performing sequence-by-ligation.

[0156] In some aspects, the present disclosure provides various reagents, and methods that employ the reagents for conducting nucleic acid denaturation (de-hybridization) and sequencing. The various reagents can include at least one pH buffering agent. The full names of exemplary pH buffering agents are listed herein.

[0157] The term “Tris” refers to a pH buffering agent Tris(hydroxymethyl)- aminomethane. The term “Tris-HQ” refers to a pH buffering agent Tris(hydroxymethyl)- aminomethane hydrochloride. The term “Tris-acetate” refers to a pH buffering agent comprising an acetate salt of Tris (hydroxymethyl)-aminom ethane.

[0158] The term “Tricine” refers to a pH buffering agent N- [tris(hydroxymethyl)methyl]glycine.

[0159] The term “Bicine” refers to a pH buffering agent N,N-bis(2hydroxyethyl)glycine.

[0160] The term “Bis-Tris propane” refers to a pH buffering agent 1,3Bis[tris(hydroxymethyl)methylamino]propane.

[0161] The term “HEPES” refers to a pH buffering agent 4-(2-hy droxy ethyl)- 1- piperazineethanesulfonic acid.

[0162] The term “MES” refers to a pH buffering agent 2-(A-morpholino)ethanesulfonic acid).

[0163] The term “MOPS” refers to a pH buffering agent 3-(N- morpholino)propanesulfonic acid.

[0164] The term “MOPSO” refers to a pH buffering agent 3-(N-morpholino)-2- hydroxypropanesulfonic acid.

[0165] The term “BES” refers to a pH buffering agent N,N-bis(2-hydroxyethyl)-2- aminoethanesulfonic acid.

[0166] The term “TES” refers to a pH buffering agent 2-[(2-Hydroxy- l,lbis(hydroxymethyl)ethyl)amino]ethanesulfonic acid).

[0167] The term “CAPS” refers to a pH buffering agent 3 -(cyclohexylamino)- 1- propanesuhinic acid.

[0168] The term “TAPS” refers to a pH buffering agent N-[Tris(hydroxymethyl)methyl]- 3 -amino propane sulfonic acid.

[0169] The term “TAPSO” refers to a pH buffering agent N- [Tris(hydroxymethyl)methyl]-3-amino-2-hyidroxypropansulfonic acid.

[0170] The term “ACES” refers to a pH buffering agent 7V-(2-Acetamido)-2- aminoethanesulfonic acid.

[0171] The term “PIPES” refers to a pH buffering agent piperazine-l,4-bis(2- ethanesulfonic acid.

[0172] The term “ethanolamine” refers to a pH buffering agent that is also known as 2- aminoethanol.IntroductionPartial Double-Stranded Splint Adaptors and Library-Splint Complexes

[0173] The present disclosure provides compositions comprising nucleic acid partial double-stranded splint adaptors, including kits, and methods that employ the double-stranded splint adaptors.

[0174] The partial double-stranded splint adaptors (200) can be used to append one or more universal adaptor sequences the ends of double stranded nucleic acid fragments. Individual partial double stranded splint adaptors (200) can comprise a first, second and third oligonucleotide hybridized together to form a nucleic acid molecule having single stranded and double stranded portions. In some embodiments, the partial double-stranded splint adaptors comprise blunt ends at one or both ends, or comprise 3’ overhang ends at one or both ends, or comprise 5’ overhang ends at one or both ends, (e.g., see FIGs. 16 and 17). In some embodiments, individual partial double stranded splint adaptors (200) comprise 3’ overhangs at both ends. In some embodiments, individual partial double stranded splint adaptors (200) comprise 5’ overhangs at both ends.

[0175] In some embodiments, the first oligonucleotide comprises a universal primer binding site for a surface capture primer (210), a universal primer binding site for a surface pinning primer (220), and a sample index sequence (230). In some embodiments, the sample index sequence includes or lacks a short random sequence (e.g., NNN) wherein the short random sequence can be 3-6 nucleotides in length. In some embodiments, the 5’ end of the first oligonucleotide can be phosphorylated or non-phosphorylated. In some embodiments, the 3’ end of the first oligonucleotide comprises a terminal thymine base (“T”) which can be used for T / A cloning or ligation (e.g., see FIGs. 16 and 17). In some embodiments, the first oligonucleotide can be 30-150 nucleotides in length, or 60-100 nucleotides in length, or 70- 90 nucleotides in length. In some embodiments, the first oligonucleotide comprises one or more phosphorothioate linkage at the 5’ and / or 3’ ends to confer exonuclease resistance. In some embodiments, the first oligonucleotide comprises one or more phosphorothioate linkage at an internal position to confer endonuclease resistance. In some embodiments, the first oligonucleotide comprises one or more 2’-O-methylcytosine bases at the 5’ and / or 3’ end, or at an internal position. In some embodiments, the first oligonucleotide comprises single stranded DNA, RNA, chimeric DNA / RNA, or analogs thereof. In some embodiments, the first oligonucleotide comprises at least one ribonucleoside residue. Various embodiments of the sequences of the universal primer binding site for a surface capture primer (210) and the universal primer binding site for a surface pinning primer (220) are listed in Table 1. In some embodiments, the sequences of the universal primer binding site for a surface capture primer (210) and / or the universal primer binding site for a surface pinning primer (220) can be complementary to any of the sequences listed in Table 1.

[0176] In some embodiments, the second oligonucleotide (211) comprises a sequence that can hybridize to a portion of the first oligonucleotide. In some embodiments, the second oligonucleotide (211) can hybridize to at least a portion of the universal primer binding site for a surface capture primer (210). In some embodiments, the 3’ end of the second oligonucleotide comprises a terminal thymine base (“T”) which can be used for T / A cloning or ligation (e.g., see FIGs. 16 and 17). In some embodiments, the second oligonucleotide can be 5-75 nucleotides in length, or 15-50 nucleotides in length, or 20-35 nucleotides in length. In some embodiments, the second oligonucleotide comprises one or more phosphorothioate linkage at the 5’ and / or 3’ ends to confer exonuclease resistance. In some embodiments, the second oligonucleotide comprise one or more phosphorothioate linkage at an internal position to confer endonuclease resistance. In some embodiments, the second oligonucleotide comprises one or more 2’-O-methylcytosine bases at the 5’ and / or 3’ end, or at an internalposition. In some embodiments, the second oligonucleotide comprises single stranded DNA, RNA, chimeric DNA / RNA, or analogs thereof. In some embodiments, the second oligonucleotide comprises at least one ribonucleoside residue.

[0177] In some embodiments, the third oligonucleotide comprises a sequence that can hybridize to a portion of the first oligonucleotide. In some embodiments, the third oligonucleotide comprises a sequence (221) that can hybridize to a portion of the universal primer binding site for the surface pinning primer (220) of the first oligonucleotide. In some embodiments, the third oligonucleotide comprises a portion (XXX) that can hybridize or bind to the short random sequence (e.g., NNN) of the first oligonucleotide. In some embodiments, the portion (XXX) of the third oligonucleotide comprises a sequence that can hybridize with the short random sequence (e.g., NNN) of the first oligonucleotide. In some embodiments, the portion (XXX) of the third oligonucleotide comprises at least one deoxyinosine. In some embodiments, the portion (XXX) of the third oligonucleotide comprises a spacer. In some embodiments, the spacer comprises an 18-carbon spacer (e.g., comprising a hexaethyleneglycol spacer), multiple C3 spacer phosphoramidites, or a spacer 9 comprising a trimethylene glycol spacer, e.g., a synthetic flexible 9 atom spacer (6 carbon, 3 oxygen) . In some embodiments, the spacer comprises a polyethylene glycol spacer, including a PEG2, PEG3 or PEG4 spacer. In some embodiments, the PEG2, PEG3 and PEG4 spacer arms comprise linear PEG spacer arms comprising 2, 3 or 4 ethylene glycol units, respectively. In some embodiments, the third oligonucleotide comprises a sequence (231) that can hybridize to the sample index sequence (230) of the first oligonucleotide. In some embodiments, the 5’ end of the third oligonucleotide can be phosphorylated or non-phosphorylated. In some embodiments, the third oligonucleotide can be 5-75 nucleotides in length, or 15-50 nucleotides in length, or 20-35 nucleotides in length. In some embodiments, the third oligonucleotide comprises one or more phosphorothioate linkage at the 5’ and / or 3’ ends to confer exonuclease resistance. In some embodiments, the third oligonucleotide comprise one or more phosphorothioate linkage at an internal position to confer endonuclease resistance. In some embodiments, the third oligonucleotide comprises one or more 2’-O-methylcytosine bases at the 5’ and / or 3’ end, or at an internal position. In some embodiments, the third oligonucleotide comprises single stranded DNA, RNA, chimeric DNA / RNA, or analogs thereof. In some embodiments, the third oligonucleotide comprises at least one ribonucleoside residue.

[0178] In some embodiments, the partial double stranded splint adaptor (200) comprises a first double stranded region, e.g., double-stranded end, formed by hybridization of the firstand third oligonucleotides, wherein the first double stranded region, e.g., double-stranded end, can be ligated to a linear double stranded nucleic acid fragment (100).

[0179] In some embodiments, the partial double stranded splint adaptor (200) comprises a second double stranded region, e.g., double-stranded end, formed by hybridization of the first and second oligonucleotides, wherein the second double stranded region, e.g., doublestranded end, can be ligated to a linear double stranded nucleic acid fragment (100).

[0180] In some embodiments, the ends of individual partial double-stranded splint adaptors can be ligated to the ends of a double stranded nucleic acid fragment to generate a covalently closed circular library molecule, thereby appending universal adaptor sequences to the ends of the double stranded nucleic acid fragment (e.g., see FIGs. 16-18).

[0181] Thus, the partial double-stranded splint adaptors and the methods described herein can be advantageously used to convert any linear nucleic acid fragment into a covalently closed circular molecule. Introduction of the universal primer binding site for the surface capture primer (210) and the universal primer binding site for the surface pinning primer (220) can enable binding of the single stranded covalently closed circular molecule (500) to a support having a plurality of surface capture primers and surface pinning primers immobilized thereon (e.g., FIG. 20). The new universal adaptor sequence(s) facilitate use of the single stranded covalently closed circular molecule (500) in amplification and sequencing workflows.

[0182] Additionally, the partial double-stranded splint adaptors are simple in design, and lack additional (separate) universal binding sites for a forward sequencing primer and a reverse sequencing primer. The universal primer binding site for the surface capture primer (210) can bind a surface capture primer or can bind a soluble sequencing primer. The universal primer binding site for the surface pinning primer (220) can bind a surface pinning primer or can bind a soluble sequencing primer. Thus, the partial double-stranded splint adaptors append two universal binding sites to the double stranded nucleic acid fragments, and the resulting single stranded covalently closed circular molecule (500), or a molecule having a complementary sequence of the single stranded covalently closed circular molecule (500), can bind to four different universal primer sequences.

[0183] The methods described herein can also offer the advantage of employing a ligation reaction, rather than a gap fill-in reaction, to introduce the new adaptor sequences. One benefit of the ligation reaction is that it gives a high efficiency circularization with as little as 0.25 pmol library molecules.

[0184] Tables 1-4 below list various exemplary embodiments of universal adaptor sequences in the partial double stranded splint adaptor (200), sequences of immobilized surface primers, and sequences of the immobilized pinning primers.

[0185] In some embodiments, any of the universal adaptor sequences which are listed in any of Tables 1-4 can be truncated at the 5’ end and / or the 3’ end, where the truncation can be 1-12 nucleotides. In some embodiments, the truncation can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 or 12 nucleotides in length.

[0186] In some embodiments, a sequencing primer comprises a sequence that is complementary to any of the sequences listed in Table 1.

[0187] In some embodiments, a sequencing primer comprises a sequence that is complementary to any of the sequences listed in Table 1, wherein the sequencing primer is truncated at the 5’ end and / or the 3’ end, and wherein the truncation can be 1-12 nucleotides. In some embodiments, the truncation can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 or 12 nucleotides in length.

[0188] In some embodiments, a sequencing primer comprises a sequence that is complementary to any of the sequences of the universal primer binding site for the surface pinning primer or surface capture primer listed in Table 1, wherein the sequencing primer is truncated at the 5’ end and / or the 3’ end, and wherein the truncation can be 1-12 nucleotides. In some embodiments, the truncation can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 or 12 nucleotides in length.TABLE 1:TABLE 2:TABLE 3:TABLE 4:Library-Splint Complexes

[0189] In some aspects, the present disclosure provides a library-splint complex (300) comprising: (i) a linear double stranded nucleic acid fragment (100); and (ii) a partial double stranded splint adaptor (200) which includes a first, second and third oligonucleotide hybridized together to form a nucleic acid molecule having single stranded and double stranded portions (e.g., see FIGs. 16 and 17). In some embodiments, the linear double stranded nucleic acid fragment (100) comprises blunt ends at one or both ends, or comprise 3’ overhang ends at one or both ends, or comprise 5’ overhang ends at one or both ends. In some embodiments, the partial double stranded splint adaptor (200) comprises blunt ends at one or both ends, or comprise 3’ overhang ends at one or both ends, or comprise 5’ overhang ends at one or both ends.

[0190] In some embodiments, any of the library-splint complexes (300) described herein comprise a plurality of library-splint complexes (300), wherein the linear double strandednucleic acid fragments (100) of individual library-splint complexes (300) in the plurality comprise the same sequence of interest or different sequences of interest.

[0191] In some embodiments, in the library-splint complex (300), the 5’ end of the linear double stranded nucleic acid fragment (100) is phosphorylated or lacks a phosphate group. In some embodiments, the 3’ end of the double-stranded nucleic acid fragment includes a terminal 3’ OH group or a terminal 3’ blocking group.

[0192] In some embodiments, in the library-splint complex (300), the 3’ end of one or both strands of the linear double stranded nucleic acid fragment (100) comprises a terminal adenine base (“A”) which can be used for T / A cloning or ligation (e.g., see FIGs. 16 and 17). An A-tailing reaction, such as the addition of the terminal adenine base, is an enzymatic method for adding a non-templated nucleotide to the 3' end of a blunt-ended, double-stranded DNA molecule. The A-tailing reaction may prepare double-stranded DNA for use in T / A cloning. “T / A cloning” is a rapid method utilizing stabilization of the single-base 3’ extension ( / .< ., adenosine) produced by Taq polymerase by the complementary terminal T-base (i.e., thymidine) of the partial double-stranded adaptors prior to ligation.

[0193] The present disclosure also provides a reaction mixture comprising a plurality of any of the library-splint complexes (300) described herein. In some embodiments, the reaction mixture comprises a plurality of any of the library-splint complexes (300) described herein, and a T4 polynucleotide kinase. In some embodiments, the reaction mixture comprises a plurality of any of the library-splint complexes (300) described herein, and lacks a T4 polynucleotide kinase. In some embodiments, the reaction mixture comprises a plurality of any of the library-splint complexes (300) described herein, and a ligase enzyme. In some embodiments, the reaction mixture comprises a plurality of any of the library-splint complexes (300) described herein, and a T4 polynucleotide kinase and a ligase enzyme. In some embodiments, the reaction mixture comprises a plurality of any of the library-splint complexes (300) described herein and a ligase enzyme and lacks a T4 polynucleotide kinase. In some embodiments, the ligase enzyme comprises T7 DNA ligase, T3 ligase, T4 ligase, or Taq ligase.

[0194] Blunt-end ligation refers to a ligation reaction in which the blunt ends of two fragments are joined, while sticky-end ligation refers to a ligation reaction in which complementary single-stranded overhangs at the ends of two fragments are joined. Depending on the configuration of the ends of the partial double stranded splint adaptor (200) and the double stranded nucleic acid fragments (100), e.g. blunt or comprising overhangs, the partial double stranded splint adaptors (200) can be ligated to the double stranded nucleicacid fragments (100) using either sticky-ended or blunt-end ligation. For example, when both the partial double stranded splint adaptor (200) and the double stranded nucleic acid fragments (100) comprise blunt ends (FIG. 16), the ligation can be blunt end ligation. Alternatively, the partial double stranded splint adaptor (200) and the double stranded nucleic acid fragments (100) comprise overhands (FIG. 17), the ligation can be sticky-ended ligation.Covalently Closed Circular Molecules

[0195] In some aspects, the present disclosure provides a covalently closed circular library molecule (400) which is partially double stranded. In some embodiments, the covalently closed circular library molecule (400) can be generated by enzymatic ligation of a linear double stranded nucleic acid fragment (100) to a partial double-stranded splint adaptor (400) (e.g., see FIG. 18 (top)). In some embodiments, the covalently closed circular library molecule (400) comprises: a single stranded covalently closed circular library molecule comprising (i) an insert region (110) of one strand of the double-stranded nucleic acid fragment hybridized to an insert region (111) of the other strand of the double-stranded nucleic acid fragment; (ii) a universal primer binding site for a surface capture primer (210) which is hybridized to a second oligonucleotide (211); (iii) a universal primer binding site for a surface pinning primer (220) which is hybridized to a sequence (221) of the third oligonucleotide; (iv) a short random sequence (e.g., NNN); and (v) a sample index sequence (230) which is hybridized to a sequence (231) of the third oligonucleotide (e.g., see FIG. 18 (top)).

[0196] The present disclosure provides a single stranded covalently closed circular library molecule (500). In some embodiments, the single stranded covalently closed circular library molecule (500) can be generated by treating the covalently closed circular library molecule (400) with a nucleic acid denaturation conditions (e.g., heat or NaOH) to denature and remove the linear single stranded molecule carrying the second oligonucleotide (211), the insert region (111), and the third oligonucleotide (e.g., see FIG. 18 (bottom)).

[0197] In some embodiments, in the single stranded covalently closed circular library molecule (500), one end of the insert region (110) is covalently linked to a universal primer binding site for a surface capture primer (210) which is which is covalently linked to a universal primer binding site for a surface pinning primer (220) which is covalently linked to a short random sequence (e.g., NNN) which is covalently linked to a sample index sequence (230) which is covalently linked to the other end of the insert region (110) (e.g., see FIG. 18 (bottom)).

[0198] In some embodiments, any of the single stranded covalently closed circular library molecules (500) described herein can further comprise a plurality of single stranded covalently closed circular library molecules (500), wherein the sequence of interest (110) of individual single stranded covalently closed circular library molecules (500) in the plurality comprise the same sequence of interest. In some embodiments, the sequence of interest (110) of individual covalently closed circular library molecules (500) in the plurality comprise different sequences of interest.

[0199] Multiplex workflows as described herein are enabled by preparing single stranded covalently closed circular library molecules (500) which are sample-indexed using partial double-stranded splint adaptors carrying at least one sample index sequence. The sample index sequence can be employed to prepare separate batches of single stranded covalently closed circular library molecules (500) which are sample-indexed using input double stranded nucleic acid fragments isolated from different sources. The sample-indexed covalently closed circular library molecules (500) can be pooled together to generate a multiplex single stranded covalently closed circular library molecule (500) mixture, and the pooled single stranded covalently closed circular library molecules (500) can then be amplified and / or sequenced. The sequences of the sequence of interest (110) (also referred to herein as the insert region (110)) along with the sample index sequence can be used to identify the source of the input nucleic acids. In some embodiments, any number of batches of single stranded covalently closed circular library molecules (500) which are sample-indexed can be pooled together, for example, 2-10, or 10-50, or 50-100, or 100-200, or more than 200 batches of single-stranded covalently closed circular library molecules (500) which are sample indexed can be pooled. Exemplary double stranded nucleic acid fragment sources can include naturally-occurring, recombinant, or chemically-synthesized sources. Exemplary double stranded nucleic acid fragments can be isolated from single cells, a plurality of cells, tissue, biological fluid, environmental sample or whole organism. Exemplary double stranded nucleic acid fragments can be isolated from any type of cell, cells or tissue including fresh, frozen, fresh-frozen or archived sources (e.g., formalin-fixed paraffin-embedded; “FFPE”). The skilled artisan will recognize that the double stranded nucleic acid fragments can be isolated from many other sources.Kits Comprising Partial Double-Stranded Splint Adaptors

[0200] In some aspects, the present disclosure provides a kit for appending one or more universal adaptor sequences to double stranded nucleic acid fragments using any of thepartial double-stranded splint adaptors described herein. In some embodiments, the kit can be used to generate single stranded covalently closed circular library molecules (500) having a sequence of interest (110) (e.g., insert) flanked on one side by a universal adaptor sequence for a universal primer binding site for a surface capture primer (210) and flanked on the other side by a sample index sequence with or without a short random sequence (e.g., NNN). In some embodiments, the single stranded covalently closed circular library molecules (500) can be subjected to a rolling circle amplification (RCA) reaction to generate concatemers. The concatemers can be immobilized to a support for massively parallel sequencing.

[0201] The present disclosure further provides kits comprising a plurality of partial double stranded splint adaptors (200). In some embodiments, individual partial double stranded splint adaptors (200) comprise a first, second and third oligonucleotide hybridized together to form a nucleic acid molecule having single stranded and double stranded portions. In some embodiments, the partial double-stranded splint adaptors comprise blunt ends at one or both ends, or comprise 3’ overhang ends at one or both ends, or comprise 5’ overhang ends at one or both ends, (e.g., see FIGs. 16 and 17).

[0202] In some embodiments, the kit comprises first, second and third oligonucleotides that are separate and are not hybridized together to form the plurality of partial double stranded splint adaptors (200). In some embodiments, the kit includes instructions for hybridizing the first, second and third oligonucleotides to form the plurality of partial double stranded splint adaptors (200).

[0203] In some embodiments, the kit comprises first, second and third oligonucleotides that are pre-hybridized together to form the plurality of partial double stranded splint adaptors (200).

[0204] In some embodiments, in the kit, the first oligonucleotide comprises a universal primer binding site for a surface capture primer (210), a universal primer binding site for a surface pinning primer (220), and a sample index sequence (230). In some embodiments, the sample index sequence includes or lacks a short random sequence (e.g., NNN) wherein the short random sequence can be 3-6 nucleotides in length. In some embodiments, the 5’ end of the first oligonucleotide can be phosphorylated or non-phosphorylated. In some embodiments, the 3’ end of the first oligonucleotide comprises a terminal thymine base (“T”) which can be used for T / A cloning or ligation (e.g., see FIGs. 16 and 17). In some embodiments, the first oligonucleotide can be 30-150 nucleotides in length, or 60-100 nucleotides in length, or 70-90 nucleotides in length. In some embodiments, the first oligonucleotide comprises one or more phosphorothioate linkage at the 5’ and / or 3’ ends toconfer exonuclease resistance. In some embodiments, the first oligonucleotide comprises one or more phosphorothioate linkage at an internal position to confer endonuclease resistance. In some embodiments, the first oligonucleotide comprises one or more 2’-O-methylcytosine bases at the 5’ and / or 3’ end, or at an internal position. In some embodiments, the first oligonucleotide comprises single stranded DNA, RNA, chimeric DNA / RNA, or analogs thereof. In some embodiments, the first oligonucleotide comprises at least one ribonucleoside residue. Various embodiments of the sequences of the universal primer binding site for a surface capture primer (210) and the universal primer binding site for a surface pinning primer (220) are listed in Table 1.

[0205] In some embodiments, in the kit, the second oligonucleotide (211) comprises a sequence that can hybridize to a portion of the first oligonucleotide. In some embodiments, the second oligonucleotide (211) can hybridize to at least a portion of the universal primer binding site for a surface capture primer (210). In some embodiments, the 3’ end of the second oligonucleotide comprises a terminal thymine base (“T”) which can be used for T / A cloning or ligation (e.g., see FIGs. 16 and 17). In some embodiments, the second oligonucleotide can be 5-75 nucleotides in length, or 15-50 nucleotides in length, or 20-35 nucleotides in length. In some embodiments, the second oligonucleotide comprises one or more phosphorothioate linkage at the 5’ and / or 3’ ends to confer exonuclease resistance. In some embodiments, the second oligonucleotide comprise one or more phosphorothioate linkage at an internal position to confer endonuclease resistance. In some embodiments, the second oligonucleotide comprises one or more 2’-O-methylcytosine bases at the 5’ and / or 3’ end, or at an internal position. In some embodiments, the second oligonucleotide comprises single stranded DNA, RNA, chimeric DNA / RNA, or analogs thereof. In some embodiments, the second oligonucleotide comprises at least one ribonucleoside residue.

[0206] In some embodiments, in the kit, the third oligonucleotide comprises a sequence that can hybridize to a portion of the first oligonucleotide. In some embodiments, the third oligonucleotide comprises a sequence (221) that can hybridize to a portion of the universal binding site for the surface pinning primer (220) of the first oligonucleotide. In some embodiments, the third oligonucleotide comprises a portion (XXX) that can hybridize or bind to the short random sequence (e.g., NNN) of the first oligonucleotide. In some embodiments, the portion (XXX) of the third oligonucleotide comprises a sequence that can hybridize with the short random sequence (e.g., NNN) of the first oligonucleotide. In some embodiments, the portion (XXX) of the third oligonucleotide comprises at least one deoxyinosine. In some embodiments, the portion (XXX) of the third oligonucleotide comprises a spacer. In someembodiments, the spacer comprises an 18-carbon spacer (e.g., comprising a hexaethyleneglycol spacer), multiple C3 spacer phosphoramidites, or a spacer 9 comprising a trimethylene glycol spacer. In some embodiments, the spacer comprises a polyethylene glycol spacer, including a PEG2, PEG3 or PEG4 spacer. In some embodiments, the PEG2, PEG3 and PEG4 spacer arms comprise linear PEG spacer arms comprising 2, 3 or 4 ethylene glycol units, respectively. In some embodiments, the third oligonucleotide comprises a sequence (231) that can hybridize to the sample index sequence (230) of the first oligonucleotide. In some embodiments, the 5’ end of the third oligonucleotide can be phosphorylated or non-phosphorylated. In some embodiments, the third oligonucleotide can be 5-75 nucleotides in length, or 15-50 nucleotides in length, or 20-35 nucleotides in length. In some embodiments, the third oligonucleotide comprises one or more phosphorothioate linkage at the 5’ and / or 3’ ends to confer exonuclease resistance. In some embodiments, the third oligonucleotide comprise one or more phosphorothioate linkage at an internal position to confer endonuclease resistance. In some embodiments, the third oligonucleotide comprises one or more 2’-O-methylcytosine bases at the 5’ and / or 3’ end, or at an internal position. In some embodiments, the third oligonucleotide comprises single stranded DNA, RNA, chimeric DNA / RNA, or analogs thereof. In some embodiments, the third oligonucleotide comprises at least one ribonucleoside residue.

[0207] In some embodiments, in the kit, the partial double stranded splint adaptor (200) comprises a first double stranded region, e.g., double-stranded end, formed by hybridization of the first and third oligonucleotides, wherein the first double stranded region, e.g., double stranded end, can be ligated to a linear double stranded nucleic acid fragment (100).

[0208] In some embodiments, in the kit, the partial double stranded splint adaptor (200) comprises a second double stranded end formed by hybridization of the first and second oligonucleotides, wherein the second double stranded end can be ligated to a linear double stranded nucleic acid fragment (100).

[0209] In some embodiments, the ends of individual partial double-stranded splint adaptors can be ligated to the ends of a double stranded nucleic acid fragment to generate a covalently closed circular library molecule, thereby appending universal adaptor sequences to the ends of the double stranded nucleic acid fragment (e.g., see FIGs. 16-18).

[0210] In some embodiments, the kit comprises a plurality of at least one type of sequencing primers.

[0211] In some embodiments, in the kit, the first, second and third oligonucleotides, and the plurality of sequencing primers, comprise any of the sequences listed in Tables 1-4.

[0212] Tables 1-4 herein list various embodiments of universal adaptor sequences in the partial double stranded splint adaptor (200), sequences of immobilized surface primers, and sequences of the immobilized pinning primers.

[0213] In some embodiments, in the kit, any of the universal adaptor sequences which are listed in any of Tables 1-4 can be truncated at the 5’ end and / or the 3’ end, where the truncation can be 1-12 nucleotides. In some embodiments, the truncation can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 or 12 nucleotides in length.

[0214] In some embodiments, a sequencing primer comprises a sequence that is complementary to any of the sequences listed in Table 1.

[0215] In some embodiments, a sequencing primer comprises a sequence that is complementary to any of the sequences listed in Table 1, wherein the sequencing primer is truncated at the 5’ end and / or the 3’ end, and wherein the truncation can be 1-12 nucleotides. In some embodiments, the truncation can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 or 12 nucleotides in length.

[0216] In some embodiments, a sequencing primer comprises a sequence that is complementary to any of the sequences for the universal primer binding site for the surface pinning primer (220) listed in Table 1, wherein the sequencing primer is truncated at the 5’ end and / or the 3’ end, and wherein the truncation can be 1-12 nucleotides. In some embodiments, the truncation can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 or 12 nucleotides in length.

[0217] In some embodiments, the kit comprises partial double stranded splint adaptors (200) and further comprises a T4 polynucleotide kinase. In some embodiments, the kit further comprises a ligase enzyme, wherein the ligase enzyme comprises T7 DNA ligase, T3 ligase, T4 ligase, or Taq ligase. In some embodiments, the kit further comprises at least one endonuclease, which comprises any one or any combination of two or more of exonuclease I, thermolabile exonuclease I and / or T7 exonuclease.

[0218] In some embodiments, the kit comprises at least one buffer for hybridizing the plurality of the partial double stranded splint adaptors (200) and the plurality of linear double stranded nucleic acid fragments (100).

[0219] In some embodiments, the kit comprises one or more containers that contain any of the partial double stranded splint adaptors (200) described herein. The kit can further comprise one or more containers that contain a T4 polynucleotide kinase, at least one ligase and / or at least one exonuclease. The kit can comprise any of these components in any combination. The kit, or components of the kit, can be contained in a single container, or can be contained in separate container, or any combination thereof.

[0220] The kit can further include instructions for use of the kit, e.g., for conducting reactions to introduce one or more new adaptor sequences into linear nucleic acid library molecules.Methods for Forming a Plurality of Library-Splint Complexes

[0221] In some aspects, the present disclosure provides methods for forming a plurality of library-splint complexes (300) comprising step (a): providing a plurality of partial double stranded splint adaptors (200) wherein individual partial double stranded splint adaptors (200) in the plurality comprise a first, second and third oligonucleotide hybridized together to form a nucleic acid molecule having single stranded and double stranded portions. In some embodiments, the partial double-stranded splint adaptors comprise blunt ends at one or both ends. In some embodiments, the partial double-stranded splint adaptors comprise 3’ overhang ends at one or both ends. In some embodiments, the partial double-stranded splint adaptors comprise 5’ overhang ends at one or both ends.

[0222] In some embodiments, in the methods for forming a plurality of library-splint complexes (300), the first oligonucleotide comprises a universal primer binding site for a surface capture primer (210), a universal primer binding site for a surface pinning primer (220), and a sample index sequence (230). In some embodiments, the sample index sequence includes or lacks a short random sequence (e.g., NNN) wherein the short random sequence can be 3-6 nucleotides in length. In some embodiments, the 5’ end of the first oligonucleotide can be phosphorylated or non-phosphorylated. In some embodiments, the 3’ end of the first oligonucleotide comprises a terminal thymine base (“T”) which can be used for T / A cloning or ligation (e.g., see FIGs. 16 and 17). In some embodiments, the first oligonucleotide can be 30-150 nucleotides in length, or 60-100 nucleotides in length, or 70-90 nucleotides in length. In some embodiments, the first oligonucleotide comprises one or more phosphorothioate linkage at the 5’ and / or 3’ ends to confer exonuclease resistance. In some embodiments, the first oligonucleotide comprises one or more phosphorothioate linkages at an internal position, e.g., to confer endonuclease resistance. In some embodiments, the first oligonucleotide comprises one or more 2’-O-methylcytosine bases at the 5’ and / or 3’ end, or at an internal position. In some embodiments, the first oligonucleotide comprises single stranded DNA, RNA, chimeric DNA / RNA, or analogs thereof. In some embodiments, the first oligonucleotide comprises at least one ribonucleoside residue. Various exemplary embodiments of the sequences of the universal primer binding site for a surface captureprimer (210) and the universal primer binding site for a surface pinning primer (220) are listed in Table 1.

[0223] In some embodiments, in the methods for forming a plurality of library-splint complexes (300), the second oligonucleotide (211) comprises a sequence that can hybridize to a portion of the first oligonucleotide. In some embodiments, the second oligonucleotide (211) can hybridize to at least a portion of the universal primer binding site for a surface capture primer (210). In some embodiments, the 3’ end of the second oligonucleotide comprises a terminal thymine base (“T”) which can be used for T / A cloning or ligation (e.g., see FIGs. 16 and 17). In some embodiments, the second oligonucleotide can be 5-75 nucleotides in length, or 15-50 nucleotides in length, or 20-35 nucleotides in length. In some embodiments, the second oligonucleotide comprises one or more phosphorothioate linkage at the 5’ and / or 3’ ends to confer exonuclease resistance. In some embodiments, the second oligonucleotide comprises one or more phosphorothioate linkages at an internal position, e.g., to confer endonuclease resistance. In some embodiments, the second oligonucleotide comprises one or more 2’-O-methylcytosine bases at the 5’ and / or 3’ end, or at an internal position. In some embodiments, the second oligonucleotide comprises single stranded DNA, RNA, chimeric DNA / RNA, or analogs thereof. In some embodiments, the second oligonucleotide comprises at least one ribonucleoside residue.

[0224] In some embodiments, in the methods for forming a plurality of library-splint complexes (300), the third oligonucleotide comprises a sequence that can hybridize to a portion of the first oligonucleotide. In some embodiments, the third oligonucleotide comprises a sequence (221) that can hybridize to a portion of the universal primer binding site surface pinning primer (220) of the first oligonucleotide. In some embodiments, the third oligonucleotide comprises a portion (XXX) that can hybridize or bind to the short random sequence (e.g., NNN) of the first oligonucleotide. In some embodiments, the portion (XXX) of the third oligonucleotide comprises a sequence that can hybridize with the short random sequence (e.g., NNN) of the first oligonucleotide. In some embodiments, the portion (XXX) of the third oligonucleotide comprises at least one deoxyinosine. In some embodiments, the portion (XXX) of the third oligonucleotide comprises a spacer. In some embodiments, the spacer comprises an 18-carbon spacer (e.g., comprising a hexa-ethyleneglycol spacer), multiple C3 spacer phosphoramidites, or a spacer 9 comprising a trimethylene glycol spacer. In some embodiments, the spacer comprises a polyethylene glycol spacer, including a PEG2, PEG3 or PEG4 spacer. In some embodiments, the PEG2, PEG3 and PEG4 spacer arms comprise linear PEG spacer arms comprising 2, 3 or 4 ethylene glycol units, respectively. Insome embodiments, the third oligonucleotide comprises a sequence (231) that can hybridize to the sample index sequence (230) of the first oligonucleotide. In some embodiments, the 5’ end of the third oligonucleotide can be phosphorylated or non-phosphorylated. In some embodiments, the third oligonucleotide can be 5-75 nucleotides in length, or 15-50 nucleotides in length, or 20-35 nucleotides in length. In some embodiments, the third oligonucleotide comprises one or more phosphorothioate linkage at the 5’ and / or 3’ ends to confer exonuclease resistance. In some embodiments, the third oligonucleotide comprise one or more phosphorothioate linkage at an internal position to confer endonuclease resistance. In some embodiments, the third oligonucleotide comprises one or more 2’-O-methylcytosine bases at the 5’ and / or 3’ end. In some embodiments, the third oligonucleotide comprises one or more 2’-O-methylcytosine bases at an internal position. In some embodiments, the third oligonucleotide comprises single stranded DNA, RNA, chimeric DNA / RNA, or analogs thereof. In some embodiments, the third oligonucleotide comprises at least one ribonucleoside residue.

[0225] In some embodiments, in the methods for forming a plurality of library-splint complexes (300), the partial double stranded splint adaptor (200) comprises a first double stranded end formed by hybridization of the first and third oligonucleotides, wherein the first double stranded end can be ligated to a linear double stranded nucleic acid fragment (100).

[0226] In some embodiments, in the methods for forming a plurality of library-splint complexes (300), the partial double stranded splint adaptor (200) comprises a second double stranded end formed by hybridization of the first and second oligonucleotides, wherein the second double stranded end can be ligated to a linear double stranded nucleic acid fragment (100).

[0227] In some embodiments, the ends of individual partial double stranded splint adaptors (200) can be ligated to the ends of a double stranded nucleic acid fragment to generate a covalently closed circular library molecule, thereby appending universal adaptor sequences to the ends of the double stranded nucleic acid fragment (e.g., see FIGs. 16-18).

[0228] Exemplary partial double stranded splint adaptors (200) are shown in FIGs. 16 and 17.

[0229] The methods for forming a plurality of library-splint complexes (300) can further comprise step (b): contacting the plurality of partial double stranded splint adaptors (200) with a plurality of linear double stranded nucleic acid fragments (100) (e.g., FIGs. 16 and 17). In some embodiments, individual linear double stranded nucleic acid fragments (100) in the plurality comprise a first nucleic acid strand comprising a phosphorylated 5’ end, a terminaladenine base (“A”) at the 3’ end and a first insert sequence (110). In some embodiments, individual linear double-stranded nucleic acid fragments (100) in the plurality comprise a second nucleic acid strand a phosphorylated 5’ end, a terminal adenine base (“A”) at the 3’ end and a second insert sequence (111). In some embodiments, the first insert sequence (110) is complementary to the second insert sequence (111). In some embodiments, the contacting is conducted under a condition suitable for hybridizing the terminal adenine at one end of the first nucleic acid strand with the thymine at one end of the first oligonucleotide thereby forming a first nick, and the condition suitable for hybridizing the terminal adenine at one end of the second nucleic acid strand with the thymine at one end of the second oligonucleotide thereby forming a second nick (e.g., FIGS. 16 and 17). In some embodiments, the first and second nicks are enzymatically ligatable. In some embodiments, the contacting of step (b) is conducted under a condition suitable for forming a plurality of library-splint complexes (300). In some embodiments, enzymatically ligatable nicks are ligated, e.g., by sticky-end ligation.

[0230] In some embodiments, the methods for forming a plurality of library-splint complexes (300) further comprise step (c): contacting the plurality of library-splint complexes (300) with an enzyme having a ligase activity (e.g., a ligase enzyme) under a condition suitable to enzymatically ligate the first and second nicks or gaps, thereby generating a plurality of covalently closed circular library molecules (400) which are partially double stranded. In some embodiments, the ligase enzyme comprises a T7 DNA ligase, a T3 DNA ligase, a T4 DNA ligase, or a Taq ligase. In some embodiments, individual covalently closed circular library molecules (400) in the plurality comprise: a single stranded covalently closed circular library molecule comprising (i) an insert region (110) hybridized to an insert region (111); (ii) a universal primer binding site for a surface capture primer (210) which is hybridized to a second oligonucleotide (211); (iii) a universal primer binding site for a pinning primer (220) which is hybridized to a sequence (221) of the third oligonucleotide; (iv) a short random sequence (e.g., NNN); and (v) a sample index sequence (230) which is hybridized to a sequence (231) of the third oligonucleotide (e.g., see FIG. 18 (top)). In some embodiments, the ligase activity of step (c) generates linear single stranded molecules each carrying the second oligonucleotide, the insert region (111), and the third oligonucleotide (e.g, see FIG. 18 (top)).

[0231] In some embodiments, the methods for forming a plurality of library-splint complexes (300) further comprise step (d): denaturing the plurality of plurality of covalently closed circular library molecules (400) which are partially double stranded to remove thelinear single stranded molecules each carrying the second oligonucleotide, the insert region (111), and the third oligonucleotide. In some embodiments, the denaturing of step (d) generates a plurality of single stranded covalently closed circular library molecules (500) each being single stranded. In some embodiments, the denaturing of step (d) comprises contacting the plurality of covalently closed circular library molecules (400) which are partially double stranded with heat or an alkaline condition (e.g., NaOH). Alternately, the linear single stranded molecules can be removed by contacting the plurality of covalently closed circular library molecules (400) which are partially double stranded with at least one exonuclease enzyme to degrade the linear single stranded molecules and retain the plurality of single stranded covalently closed circular library molecules (500). Suitable exonucleases are known in the art, and include, for example Exonuclease I, exonuclease III, T7 exonuclease, exonuclease Vlll-truncated and lambda exonuclease.

[0232] In some embodiments, individual single stranded covalently closed circular library molecules (500) comprise: one end of the insert region (110) is covalently linked to a universal primer binding site for a surface capture primer (210) which is which is covalently linked to a universal primer binding site for a pinning primer (220) which is covalently linked to a short random sequence (e.g., NNN) which is covalently linked to a sample index sequence (230) which is covalently linked to the other end of the insert region (110) (e.g., see FIG. 18 (bottom)).

[0233] Multiplex workflows can be enabled by preparing sample-indexed single stranded covalently closed circular library molecules (500) using partial double stranded splint adaptors (200) carrying at least one sample index sequence (230). The sample index sequence can be employed to prepare separate batches of single stranded covalently closed circular library molecules (500) which are sample-indexed using input double stranded nucleic acid fragments isolated from different sources. The sample-indexed single stranded covalently closed circular library molecules (500) can be pooled together to generate a multiplex single stranded covalently closed circular library molecule (500) mixture, and the pooled mixture can be amplified and / or sequenced. The sequences of the insert region (110) along with the sample index sequence (230) can be used to identify the source of the input nucleic acid fragments. In some embodiments, any number of batches of sample-indexed single stranded covalently closed circular library molecules (500) can be pooled together, for example, 2-10, or 10-50, or 50-100, or 100-200, or more than 200 batches of sample-indexed single stranded covalently closed circular library molecules (500) can be pooled. Exemplary nucleic acid fragment sources include, without limitation, naturally-occurring, recombinant, orchemically-synthesized sources. Exemplary nucleic acid fragment sources can include single cells, a plurality of cells, tissue, biological fluid, environmental sample or whole organism. Exemplary nucleic acid fragment sources include fresh, frozen, fresh-frozen or archived sources (e.g., formalin-fixed paraffin-embedded; “FFPE”). The skilled artisan will recognize that the nucleic acid fragments can be isolated from many other sources.Methods for Rolling Circle Amplification

[0234] In some aspects, the present disclosure provides methods for conducting rolling circle amplification reaction on the single stranded covalently closed circular library molecules (500). In some embodiments, the single stranded covalently closed circular library molecules (500) can be distributed onto a support having a plurality of capture primers immobilized thereon, and then can be subjected to rolling circle amplification reaction. In some embodiments, the single stranded covalently closed circular library molecules (500) can be subjected to rolling circle amplification reaction in-solution and then distributed onto a support having a plurality of capture primers immobilized thereon.On-Support Rolling Circle Amplification

[0235] In some embodiments, the methods for conducting rolling circle amplification reaction on a plurality of single stranded covalently closed circular library molecules (500) comprise step (a): distributing the plurality of single stranded covalently closed circular library molecules (500) onto a support having a plurality of the surface capture primers immobilized on the support, under a condition suitable for hybridizing individual single stranded covalently closed circular library molecules (500) to individual immobilized surface capture primers thereby immobilizing the plurality of single stranded covalently closed circular library molecules (500) to the support (e.g., see FIG. 19). In some embodiments, the plurality of the surface capture primers comprises any one of the sequences listed in Table 4 or a complementary sequence thereof.

[0236] Individual surface capture primers can hybridize to a single stranded covalently closed circular library molecule (500) having a universal binding sequence for the surface capture primer (210) or a complementary sequence thereof.

[0237] In some embodiments, the methods for conducting rolling circle amplification reaction further comprises step (b): contacting the plurality of single stranded covalently closed circular library molecules (500) with a plurality of strand-displacing polymerases anda plurality of nucleotides, under a condition suitable to conduct a rolling circle amplification reaction on the support using the plurality of surface capture primers as immobilized amplification primers and the plurality of single stranded covalently closed circular library molecules (500) as template molecules, thereby generating a plurality of concatemer molecules immobilized to the surface capture primers. In some embodiments, the plurality of nucleotides comprises any combination of two or more of dATP, dGTP, dCTP, dTTP and / or dUTP. In some embodiments, individual immobilized concatemers are covalently joined to individual surface capture primers. In some embodiments, individual single stranded covalently closed circular library molecules (500) in the plurality comprise universal binding sequences for a surface capture primer and a surface pinning primer so that the rolling circle amplification reaction generates concatemer molecules having multiple, e.g., two or more, tandem copies of sequences carried by the single stranded covalently closed circular library molecules (500) including universal binding sequences for a surface capture primer and a surface pinning primer. In some embodiments, the support further comprises a plurality of surface pinning primers. In some embodiments, the immobilized surface pinning primers serve to pin down at least one portion of the concatemer molecules to the support (e.g., FIG. 20). In some embodiments, the immobilized surface pinning primers have a non-extendible 3’ end and cannot be used to initiate rolling circle amplification. In some embodiments, the plurality of the surface pinning primers comprises any one of the sequences listed in Table 4 or a complementary sequence thereof. In some embodiments, the immobilized concatemers can be subjected to sequencing reactions. In some embodiments, the rolling circle amplification reaction can be conducted in the presence or absence of a plurality of compaction oligonucleotides.

[0238] In some embodiments, in the methods for conducting rolling circle amplification reaction, the plurality of single stranded covalently closed circular library molecules (500) can be distributed onto a support that is coated with one or more compounds to produce a passivated layer on the support (e.g., FIG. 1). In some embodiments, the passivated layer forms a porous or semi-porous layer. In some embodiments, one or more types of surface primers, concatemer template molecules and / or polymerases, can be attached to the passivated layer for immobilization to the support. In some embodiments, the support comprises a low non-specific binding surface that enable improved nucleic acid hybridization and amplification performance on the support. In general, the support may comprise one or more layers of a covalently or non-covalently attached low-binding, chemical modification layers, e.g, silane layers, polymer films, and one or more covalently or non-covalentlyattached oligonucleotides that can be used for immobilizing a plurality of concatemer molecules to the support. In some embodiments, the support can comprise a functionalized polymer coating layer covalently bound at least to a portion of the support via a chemical group on the support, a primer grafted to the functionalized polymer coating, and a water- soluble protective coating on the primer and the functionalized polymer coating. In some embodiments, the functionalized polymer coating comprises a poly(N-(5- azidoacetamidylpentyl)acrylamide-co-acrylamide (PAZAM). In some embodiments, the support comprises a surface coating having at least one hydrophilic polymer coating layer and at least one layer of a plurality of oligonucleotides. The hydrophilic polymer coating layer can comprise polyethylene glycol (PEG). The hydrophilic polymer coating layer can comprise branched PEG having at least 4 branches. In some embodiments, the low nonspecific binding coating has a degree of hydrophilicity which can be measured as a water contact angle, where the water contact angle is no more than 45 degrees. In some embodiments, the density of the covalently closed circular library molecules (600) immobilized to the support or immobilized to the coating on the support is about 102- 106per mm2, or about 106- 109per mm2, or about 109- 1012per mm2. In some embodiments, the plurality of covalently closed circular library molecules (600) is immobilized to the support or immobilized to the coating on the support at pre-determined sites on the support (or the coating on the support), or immobilized to the coating on the support at random sites on the support (or the coating on the support).In-Solution Rolling Circle Amplification Using Soluble Amplification Primers

[0239] In some embodiments, the methods for conducting rolling circle amplification reaction on a plurality of single stranded covalently closed circular library molecules (500) comprises: (a) hybridizing in solution a plurality of single stranded covalently closed circular library molecules (500) and a plurality of soluble forward amplification primers; and (b) conducting a first rolling circle amplification reaction by contacting the plurality of single stranded covalently closed circular library molecules (500) with a plurality of stranddisplacing polymerases and a plurality of nucleotides, under a condition suitable to conduct a rolling circle amplification reaction in solution using the plurality of forward amplification primers and the plurality of single stranded covalently closed circular library molecules (500) as template molecules, thereby generating a plurality of nascent concatemer molecules having a portion which are still hybridized to their single stranded covalently closed circular library molecules (500). In some embodiments, the soluble forward amplification primers of step (a)can bind at least a portion of the single stranded covalently closed circular library molecules (500) including the universal primer binding site for a surface capture primer (210) or the universal primer binding site for a surface pinning primer (220). In some embodiments, the in-solution rolling circle amplification reaction can be conducted in the presence of a plurality of compaction oligonucleotides. In some embodiments, the in-solution rolling circle amplification reaction can be conducted in the absence of a plurality of compaction oligonucleotides.

[0240] In some embodiments, the methods for conducting rolling circle amplification reaction further comprises step (c): distributing the plurality of nascent concatemer molecules onto a support having a plurality of the surface capture primers immobilized thereon, under a condition suitable for hybridizing at least a portion of the nascent concatemers to the plurality of the immobilized surface capture primers thereby immobilizing the plurality of concatemer molecules. Individual immobilized nascent concatemer molecules are still hybridized to a single stranded covalently closed circular library molecule (500).

[0241] In some embodiments, the methods for conducting rolling circle amplification reaction further comprises step (d): contacting the immobilized plurality of nascent concatemer molecules with a plurality of strand-displacing polymerases and a plurality of nucleotides, under a condition suitable to conduct a second rolling circle amplification reaction on the support using the plurality of single stranded covalently closed circular library molecules (500) as template molecules, thereby extending the plurality of immobilized nascent concatemer molecules. In some embodiments, the first and / or the second rolling circle amplification reactions can be conducted with a plurality of nucleotides which comprise any combination of two or more of dATP, dGTP, dCTP, dTTP and / or dUTP. In some embodiments, individual immobilized concatemers are hybridized to individual surface capture primers. In some embodiments, individual single stranded covalently closed circular library molecules (500) in the plurality comprise universal binding sequences for a surface capture primer and a surface pinning primer so that the in-solution rolling circle amplification reaction generates concatemer molecules having multiple, e.g., two or more, tandem copies of sequences carried by the single stranded covalently closed circular library molecules (500) including universal binding sequences for a surface capture primer and a surface pinning primer. In some embodiments, the support further comprises a plurality of surface pinning primers. In some embodiments, the immobilized surface pinning primers serve to pin down at least one portion of the concatemer molecules to the support (e.g., FIG. 20). In some embodiments, the immobilized surface pinning primers have a non-extendible 3’ end andcannot be used to initiate rolling circle amplification. In some embodiments, the immobilized concatemers can be subjected to sequencing reactions. In some embodiments, the soluble forward amplification primers have the same sequence as the surface capture primers. In some embodiments, the plurality of the surface capture primers comprises any one of the sequences listed in Table 4 or a complementary sequence thereof. In some embodiments, the plurality of the surface pinning primers comprises any one of the sequences listed in Table 4 or a complementary sequence thereof. In some embodiments, the on-support rolling circle amplification reaction can be conducted in the presence or absence of a plurality of compaction oligonucleotides.

[0242] In some embodiments, the plurality of in-solution generated concatemer molecules of step (c) can be distributed onto a support that is coated with one or more compounds to produce a passivated layer on the support (e.g., FIG. 1). In some embodiments, the passivated layer forms a porous or semi-porous layer. In some embodiments, the one or more types of surface primers, concatemer template molecules and / or polymerases, can be attached to the passivated layer for immobilization to the support. In some embodiments, the support comprises a low non-specific binding surface that enable improved nucleic acid hybridization and amplification performance on the support. In general, the support may comprise one or more layers of a covalently or non-covalently attached low-binding, chemical modification layers, e.g., silane layers, polymer films, and one or more covalently or non-covalently attached oligonucleotides that can be used for immobilizing a plurality of concatemer molecules to the support. In some embodiments, the support can comprise a functionalized polymer coating layer covalently bound at least to a portion of the support via a chemical group on the support, a primer grafted to the functionalized polymer coating, and a water-soluble protective coating on the primer and the functionalized polymer coating. In some embodiments, the functionalized polymer coating comprises a poly(N-(5- azidoacetamidylpentyl)acrylamide-co-acrylamide (PAZAM). In some embodiments, the support comprises a surface coating having at least one hydrophilic polymer coating layer and at least one layer of a plurality of oligonucleotides. The hydrophilic polymer coating layer can comprise polyethylene glycol (PEG). The hydrophilic polymer coating layer can comprise branched PEG having at least 4 branches. In some embodiments, the low nonspecific binding coating has a degree of hydrophilicity which can be measured as a water contact angle, where the water contact angle is no more than 45 degrees. In some embodiments, the density of the concatemer molecules immobilized to the support or immobilized to the coating on the support is about 102- 106per mm2, or about 106- 109permm2, or about 109-l 012per mm2. In some embodiments, the plurality of the concatemer molecules is immobilized to the support or immobilized to the coating on the support at predetermined sites on the support (or the coating on the support), or immobilized to the coating on the support at random sites on the support (or the coating on the support).Compaction Oligonucleotides

[0243] In some aspects, the present disclosure provides compositions and methods for conducting rolling circle amplification in the presence, or in the absence, of a plurality of compaction oligonucleotides. Exemplary compaction oligonucleotides are described in W02024040058, the contents of which are incorporated by reference in their entirety herein. Compaction oligonucleotides are single-stranded and include a 5’ region, an optional internal region, and a 3’ region. The 5’ and 3’ regions of the compaction oligonucleotide can hybridize to the concatemer to pull together distal portions of the concatemer causing compaction of the concatemer to form a nanostructure. For example, the 5’ region of the compaction oligonucleotide can be designed to hybridize to a first portion (e.g., a first universal adaptor sequence) of the concatemer molecule, and the 3’ region of the compaction oligonucleotide can be designed to hybridized to a second portion (e.g., a second universal adaptor sequence) of the same concatemer molecule. Inclusion of compaction oligonucleotides during rolling circle amplification can promote formation of nanostructures having tighter size and shape compared to concatemers generated in the absence of the compaction oligonucleotides. The compact and stable characteristics of the nucleic acid nanostructures improves sequencing accuracy by increasing signal intensity and they retain their shape and size during multiple sequencing cycles. In some embodiments, the terminal 3’ ends of individual compaction oligonucleotides comprise a blocking moiety that can inhibit polymerase-catalyzed primer extension. In some embodiments, the compaction oligonucleotides comprise 3’ non-extendible ends.

[0244] In some embodiments, the compaction oligonucleotides are single stranded oligonucleotides comprising DNA, RNA, or a combination of DNA and RNA. The compaction oligonucleotides can be any length, including 20-150 nucleotides, or 30-100 nucleotides, or 40-80 nucleotides in length.

[0245] In some embodiments, the compaction oligonucleotide comprises a 5’ region and a 3’ region, and optionally an intervening region between the 5’ and 3’ regions. The intervening region can be any length, for example about 2-20 nucleotides in length. In someembodiments, the intervening region comprises a homopolymer having consecutive identical bases (e.g., AAA, GGG, CCC, TTT or UUU). In some embodiments, the intervening region comprises a non-homopolymer sequence.

[0246] In some embodiments, the 5’ region of the compaction oligonucleotides can be wholly complementary or partially complementary along its length to a first portion of a concatemer molecule. For example, the 5’ region of the compaction oligonucleotide can comprise a sequence that can hybridize to a universal adaptor sequence, e.g., listed in Table 1, including a surface capture primer binding site, or a surface pinning primer binding site.

[0247] In some embodiments, the 3’ region of the compaction oligonucleotides can be wholly complementary or partially complementary along its length to a second portion of a concatemer molecule. For example, the 3’ region of the compaction oligonucleotide can comprise a sequence that can hybridize to a universal adaptor sequence, e.g., listed in Table 1, including a surface capture primer binding site, or a surface pinning primer binding site.

[0248] The 5’ region of the compaction oligonucleotides can hybridize to a first universal sequence portion of a concatemer molecule. The 3’ region of the compaction oligonucleotides can hybridize to a second universal sequence portion of a concatemer molecule. The 5’ and 3’ regions of the compaction oligonucleotide can then hybridize to the concatemer to pull together distal portions of the concatemer, causing compaction of the concatemer to form a nanostructure.

[0249] In some embodiments, the 5’ region of the compaction oligonucleotide can have the same sequence as the 3’ region. In some embodiments, the 5’ region of the compaction oligonucleotide can have a sequence different from the 3’ region. In some embodiments, the 3’ region of the compaction oligonucleotide can have a sequence that is a reverse sequence of the 5’ region.

[0250] In some embodiments, the compaction oligonucleotides comprise one or more modified bases or linkages at their 5’ or 3’ ends to confer certain functionalities. In some embodiments, the compaction oligonucleotides comprise at least one phosphorothioate linkage at their 5’ and / or 3’ ends to confer exonuclease resistance. In some embodiments, at least one nucleotide at or near the 3’ end comprises a 2’ fluoro base, which confers exonuclease resistance. In some embodiments, the 3’ end of the compaction oligonucleotides comprise at least one 2’-O-methyl RNA base which blocks polymerase-catalyzed extension. In some embodiments, the compaction oligonucleotides comprise a 3’ inverted dT at their 3’ ends which blocks polymerase-catalyzed extension. In some embodiments, the compaction oligonucleotides comprise 3’ phosphorylation, which blocks polymerase-catalyzed extension.In some embodiments, the internal region of the compaction oligonucleotides comprises at least one locked nucleic acid (LNA). Without wishing to be bound by theory, it is hypothesized that the at least one LNA increases the thermal stability of duplexes formed by hybridizing a compaction oligonucleotide to a concatemer molecule.

[0251] The compaction oligonucleotides can include at least one region having consecutive guanines. For example, the compaction oligonucleotides can include at least one region having 2, 3, 4, 5, 6 or more consecutive guanines. In some embodiments, the compaction oligonucleotides comprise four consecutive guanines, which can form a guanine tetrad structure. The guanine tetrad structure can be stabilized via Hoogsteen hydrogen bonding. The guanine tetrad structure can be stabilized by a central cation, e.g., potassium, sodium, lithium, rubidium or cesium.

[0252] The rolling circle amplification reaction can be conducted in the presence of a plurality of compaction oligonucleotides having at least four consecutive guanines. The resulting concatemers comprise repeat copies of the universal binding sequence for the compaction oligonucleotide. At least one compaction oligonucleotide can form a guanine tetrad (e.g., FIG. 14) and hybridize to the universal binding sequences for the compaction oligonucleotide, and the resulting concatemer can fold to form an intramolecular G- quadruplex structure (e.g., FIG. 15). The concatemers can self-collapse to form compact nanostructures. Formation of the guanine tetrads and G-quadruplexes in the nanostructures may increase the stability of the nanostructures to retain their compact size and shape which can withstand changes in pH, temperature and / or repeated flows of reagents.Methods for Sequencing

[0253] In some aspects, the present disclosure further provides methods for sequencing any of the concatemer molecules described herein. Suitable methods for sequencing the concatemer molecules described herein are described, for example in WO2022266470 and WO2024159166, the contents of which are incorporated by reference in their entireties herein. Any of the methods for conducting on-support or in-solution rolling circle amplification reaction described herein can be used to generate a plurality of concatemer molecules immobilized to a support, and the immobilized concatemers can then be subjected to sequencing reactions. In some embodiments, the sequencing reactions employ detectably labeled nucleotide analogs. In some embodiments, the sequencing reactions employ a two- stage sequencing reaction comprising binding detectably labeled multivalent molecules, andincorporating nucleotide analogs. The terms “concatemer molecule” and “template molecule” are used interchangeably herein.

[0254] In some embodiments, any of the rolling circle amplification reaction (“RCA”) methods described herein (e.g., RCA conducted on-support or in-solution) can be used to generate immobilized concatemers, individual immobilized concatemers containing tandem repeat units of the sequence-of-interest and any adaptor sequences present in the covalently closed circular library molecules (600).

[0255] In some embodiments, an exemplary tandem repeat unit comprises: (i) a universal primer binding site for a surface capture primer (210); (ii) an insert region (110); (iii) a sample index sequence (230); (iv) a short random sequence (e.g., NNN); and (v) a universal primer binding site for a pinning primer (e.g., FIG. 19). The immobilized concatemer can self-collapse into a compact nucleic acid nanoball. Inclusion of one or more compaction oligonucleotides during the RCA reaction can further compact the size and / or shape of the nanoball. An increase in the number of tandem repeat units in a given concatemer can increase the number of sites along the concatemer for hybridizing to multiple sequencing primers (e.g., sequencing primers having a universal sequence) which serve as multiple initiation sites for polymerase-catalyzed sequencing reactions. When the sequencing reaction employs detectably labeled nucleotides and / or detectably labeled multivalent molecules (e.g., having nucleotide moieties), the signals emitted by the nucleotides or nucleotide moieties that participate in the parallel sequencing reactions along the concatemer yields an increased signal intensity for each concatemer. Multiple portions of a given concatemer can be simultaneously sequenced. Furthermore, a plurality of binding complexes can form along a particular concatemer molecule, each binding complex comprising a sequencing polymerase bound to a multivalent molecule wherein the plurality of binding complexes remains stable without dissociation resulting in increased persistence time which increases signal intensity and reduces imaging time.Sequencing Methods Using Sequencing Polymerases and Nucleotide Reagents

[0256] In some aspects, the present disclosure provides concatemer molecules (also referred to herein as “concatemer template molecules,” “nucleic acid template molecules” and the like) that can be sequenced using any nucleic acid sequencing method that employs sequencing polymerases and a plurality of nucleotide reagents which comprise nucleotides, nucleotide analogs, labeled or non-labeled nucleotides and / or multivalent molecules. In some embodiments, the nucleotide reagents comprise labeled or non-labeled chain terminatingnucleotides, where the chain terminating nucleotides include a 3’-O-azido group (or 3’-O- methylazido group) or any other type of bulky blocking group at the sugar 3’ position. In some embodiments, the concatemer molecules can be sequenced using a sequencing-by- avidity method (SB A) using a two-stage sequencing method which employs nucleotide reagents comprising labeled multivalent molecules and non-labeled chain terminating nucleotides. In some embodiments, the concatemer molecules can be sequenced using a sequencing-by-synthesis (SBS) method which employs nucleotide reagents comprising labeled chain-terminating nucleotides. In some embodiments, the concatemer molecules can be sequenced using a sequencing-by-binding method (SBB) which employ nucleotide reagents comprising non-labeled chain-terminating nucleotides. In some embodiments, the concatemer molecules can be sequenced using nucleotide reagents comprising phosphate- chain labeled nucleotides.Methods for Sequencing using Nucleotide Analogs

[0257] In some aspects, the present disclosure provides methods for sequencing a concatemer wherein the concatemer is generated using any of the partial double-stranded splint adaptors and methods described herein (e.g., see FIGs. 16-19).

[0258] The present disclosure further provides methods for sequencing, comprising step (a): contacting a sequencing polymerase to (i) a concatemer molecule and (ii) a nucleic acid primer, wherein the contacting is conducted under a condition suitable to bind the sequencing polymerase to the concatemer molecule which is hybridized to the nucleic acid primer, wherein the concatemer molecule hybridized to the nucleic acid primer forms the nucleic acid duplex. In some embodiments, the sequencing polymerase comprises a recombinant mutant sequencing polymerase. In some embodiments, the primer comprises a 3’ extendible end.

[0259] In some embodiments, the methods for sequencing further comprise step (b): contacting the sequencing polymerase with a plurality of nucleotides under a condition suitable for binding at least one nucleotide to the sequencing polymerase which is bound to the nucleic acid duplex and suitable for polymerase-catalyzed nucleotide incorporation. In some embodiments, the sequencing polymerase is contacted with the plurality of nucleotides in the presence of at least one catalytic cation comprising magnesium and / or manganese. In some embodiments, the plurality of nucleotides comprises at least one nucleotide analog having a chain terminating moiety at the sugar 2’ or 3’ position. In some embodiments, the plurality of nucleotides comprises at least one nucleotide that lacks a chain terminating moiety.

[0260] In some embodiments, the methods for sequencing further comprise step (c): incorporating at least one nucleotide into the 3’ end of the extendible primer under a condition suitable for incorporating the at least one nucleotide. In some embodiments, the suitable conditions for nucleotide binding the polymerase and for incorporation the nucleotide can be the same or different. In some embodiments, conditions suitable for incorporating the nucleotide comprise inclusion of at least one catalytic cation comprising magnesium and / or manganese. In some embodiments, the at least one nucleotide binds the sequencing polymerase and incorporates into the 3’ end of the extendible primer. In some embodiments, the incorporating the nucleotide into the 3’ end of the primer in step (c) comprises a primer extension reaction.

[0261] In some embodiments, the methods for sequencing further comprise step (d): repeating the incorporating at least one nucleotide into the 3 ’ end of the extendible primer of step (c) at least once. In some embodiments, the plurality of nucleotides comprises a plurality of nucleotides labeled with detectable reporter moiety. The detectable reporter moiety comprises a fluorophore. In some embodiments, the fluorophore is attached to the nucleotide base. In some embodiments, the fluorophore is attached to the nucleotide base with a linker which is cleavable / removable from the base. In some embodiments, at least one of the nucleotides in the plurality is not labeled with a detectable reporter moiety. In some embodiments, a particular detectable reporter moiety (e.g., fluorophore) that is attached to the nucleotide can correspond to the nucleotide base (e.g., dATP, dGTP, dCTP, dTTP or dUTP) to permit detection and identification of the nucleotide base. In some embodiments, the method further comprises detecting the at least one incorporated nucleotide at step (c) and / or (d). In some embodiments, the method further comprises identifying the at least one incorporated nucleotide at step (c) and / or (d). In some embodiments, the sequence of the concatemer molecule can be determined by detecting and identifying the nucleotide that binds the sequencing polymerase, thereby determining the sequence of the concatemer molecule. In some embodiments, the sequence of the concatemer molecule can be determined by detecting and identifying the nucleotide that incorporates into the 3’ end of the primer, thereby determining the sequence of the concatemer molecule.

[0262] In some embodiments, in the methods for sequencing, the plurality of sequencing polymerases that are bound to the nucleic acid duplexes comprise a plurality of complexed polymerases, having at least a first and second complexed polymerase, wherein (a) the first complexed polymerases comprises a first sequencing polymerase bound to a first nucleic acid duplex comprising a first nucleic acid template sequence which is hybridized to a first nucleicacid primer, (b) the second complexed polymerases comprises a second sequencing polymerase bound to a second nucleic acid duplex comprising a second nucleic acid template sequence which is hybridized to a second nucleic acid primer, (c) the first and second nucleic acid template sequences comprise the same or different sequences, (d) the first and second concatemers are clonally-amplified, (e) the first and second primers comprise extendible 3’ ends or non-extendible 3’ ends, and (f) the plurality of complexed polymerases are immobilized to a support. In some embodiments, the density of the plurality of complexed polymerases is about 102- 1015complexed polymerases per mm2that are immobilized to the support.Two-Stage Methods for Nucleic Acid Sequencing

[0263] In some aspects, the present disclosure provides methods for sequencing a concatemer molecule wherein the concatemer molecule is generated using any of the partial double-stranded splint adaptors and methods described herein (e.g., see FIGs. 16-19).

[0264] The present disclosure further provides a two-stage method for sequencing nucleic acid molecules (e.g., concatemer molecules). In some embodiments, the first stage generally comprises binding multivalent molecules to complexed polymerases to form multivalent- complexed polymerases, and detecting the multivalent-complexed polymerases.

[0265] In some embodiments, the first stage comprises step (a): contacting a plurality of a first sequencing polymerase to (i) a plurality of concatemer molecules and (ii) a plurality of nucleic acid primers, wherein the contacting is conducted under a condition suitable to bind the plurality of first sequencing polymerases to the plurality of concatemer molecules and the plurality of nucleic acid primers thereby forming a plurality of first complexed polymerases each comprising a first sequencing polymerase bound to a nucleic acid duplex wherein the nucleic acid duplex comprises a concatemer molecule hybridized to a nucleic acid primer. In some embodiments, the first polymerase comprises a recombinant mutant sequencing polymerase.

[0266] In some embodiments, in the methods for sequencing concatemer molecules, the primer comprises a 3’ extendible end or a 3’ non-extendible end. In some embodiments, the plurality of concatemer molecules comprise amplified template molecules (e.g., clonally amplified template molecules). In some embodiments, the plurality of concatemer molecules comprise one copy of a target sequence of interest. In some embodiments, the plurality of nucleic acid molecules comprises two or more tandem copies of a target sequence of interest(e.g., concatemers). In some embodiments, the concatemer molecules in the plurality of concatemer molecules comprise the same target sequence of interest or different target sequences of interest. In some embodiments, the plurality of concatemer molecules and / or the plurality of nucleic acid primers are in solution or are immobilized to a support. In some embodiments, when the plurality of concatemer molecules and / or the plurality of nucleic acid primers are immobilized to a support, the binding with the first sequencing polymerase generates a plurality of immobilized first complexed polymerases. In some embodiments, the plurality of concatemer molecules and / or nucleic acid primers are immobilized to 102- 1015different sites on a support. In some embodiments, the binding of the plurality of concatemer molecules and nucleic acid primers with the plurality of first sequencing polymerases generates a plurality of first complexed polymerases immobilized to 102- 1015different sites on the support. In some embodiments, the plurality of immobilized first complexed polymerases on the support are immobilized to pre-determined or to random sites on the support. In some embodiments, the plurality of immobilized first complexed polymerases is in fluid communication with each other to permit flowing a solution of reagents (e.g., enzymes including sequencing polymerases, multivalent molecules, nucleotides, and / or divalent cations) onto the support so that the plurality of immobilized complexed polymerases on the support are reacted with the solution of reagents in a massively parallel manner.

[0267] In some embodiments, the methods for sequencing further comprise step (b): contacting the plurality of first complexed polymerases with a plurality of multivalent molecules to form a plurality of multival ent-complexed polymerases (e.g., binding complexes). In some embodiments, individual multivalent molecules in the plurality of multivalent molecules comprise a core attached to multiple nucleotide arms and each nucleotide arm is attached to a nucleotide moiety (e.g., FIGs. 2-6). In some embodiments, the contacting of step (b) is conducted under a condition suitable for binding complementary nucleotide moieties of the multivalent molecules to at least two of the plurality of first complexed polymerases thereby forming a plurality of multivalent-complexed polymerases. In some embodiments, the condition is suitable for inhibiting polymerase-catalyzed incorporation of the complementary nucleotide moieties into the primers of the plurality of multivalent-complexed polymerases. In some embodiments, the plurality of multivalent molecules comprises at least one multivalent molecule having multiple nucleotide arms (e.g., FIGs. 2-6) each attached with a nucleotide analog (e.g., nucleotide analog unit), where the nucleotide analog includes a chain terminating moiety at the sugar 2’ and / or 3’ position. Insome embodiments, the plurality of multivalent molecules comprises at least one multivalent molecule comprising multiple nucleotide arms each attached with a nucleotide moiety that lacks a chain terminating moiety. In some embodiments, at least one of the multivalent molecules in the plurality of multivalent molecules is labeled with a detectable reporter moiety. Any portion of the multivalent molecule can be labeled including the core, nucleotide arm or nucleo-base. In some embodiments, the detectable reporter moiety comprises a fluorophore. In some embodiments, the contacting of step (b) is conducted in the presence of at least one non-catalytic cation comprising strontium, barium and / or calcium.

[0268] In some embodiments, the methods for sequencing further comprise step (c): detecting the plurality of multivalent-complexed polymerases. In some embodiments, the detecting includes detecting the multivalent molecules that are bound to the complexed polymerases, where the complementary nucleotide moieties of the multivalent molecules are bound to the primers, but incorporation of the complementary nucleotide moieties is inhibited. In some embodiments, the multivalent molecules are labeled with a detectable reporter moiety to permit detection. In some embodiments, the labeled multivalent molecules comprise a fluorophore attached to the core, linker and / or nucleotide moiety of the multivalent molecules.

[0269] In some embodiments, the methods for sequencing further comprise step (d): identifying the base of the complementary nucleotide moieties that are bound to the plurality of first complexed polymerases, thereby determining the sequence of the concatemer molecule. In some embodiments, the multivalent molecules are labeled with a detectable reporter moiety that corresponds to the particular nucleotide moieties attached to the nucleotide arms, to permit identification of the complementary nucleotide moieties (e.g., nucleotide base adenine, guanine, cytosine, thymine or uracil) that are bound to the plurality of first complexed polymerases.

[0270] In some embodiments, the second stage of the two-stage sequencing method generally comprises nucleotide incorporation. In some embodiments, the methods for sequencing further comprise step (e): dissociating the plurality of multivalent-complexed polymerases and removing the plurality of first sequencing polymerases and their bound multivalent molecules, and retaining the plurality of nucleic acid duplexes.

[0271] In some embodiments, the methods for sequencing further comprises step (f): contacting the plurality of the retained nucleic acid duplexes of step (e) with a plurality of second sequencing polymerases, wherein the contacting is conducted under a condition suitable for binding the plurality of second sequencing polymerases to the plurality of theretained nucleic acid duplexes, thereby forming a plurality of second complexed polymerases each comprising a second sequencing polymerase bound to a nucleic acid duplex. In some embodiments, the second sequencing polymerase comprises a recombinant mutant sequencing polymerase.

[0272] In some embodiments, the plurality of first sequencing polymerases of step (a) has an amino acid sequence that is 100% identical to the amino acid sequence as the plurality of the second sequencing polymerases of step (f). In some embodiments, individual first sequencing polymerases in the plurality of first sequencing polymerases of step (a) have an amino acid sequence that differs from the amino acid sequence of individual second sequencing polymerases in the plurality of the second sequencing polymerases of step (f).

[0273] In some embodiments, the methods for sequencing further comprise step (g): contacting the plurality of second complexed polymerases with a plurality of nucleotides, wherein the contacting is conducted under a condition suitable for binding complementary nucleotides from the plurality of nucleotides to at least two of the second complexed polymerases thereby forming a plurality of nucleotide-complexed polymerases. In some embodiments, the contacting of step (g) is conducted under a condition that is suitable for promoting polymerase-catalyzed incorporation of the bound complementary nucleotides into the primers of the nucleotide-complexed polymerases thereby forming a plurality of nucleotide-complexed polymerases. In some embodiments, the incorporating the nucleotide into the 3’ end of the primer in step (g) comprises a primer extension reaction. In some embodiments, the contacting of step (g) is conducted in the presence of at least one catalytic cation comprising magnesium and / or manganese. In some embodiments, the contacting of step (g) is conducted in the presence of magnesium and / or manganese. In some embodiments, the plurality of nucleotides comprises native nucleotides (e.g., non-analog nucleotides) or nucleotide analogs. In some embodiments, the plurality of nucleotides comprises a 2’ and / or 3’ chain terminating moiety which is removable or is not removable. In some embodiments, the plurality of nucleotides comprises a plurality of nucleotides labeled with detectable reporter moiety. The detectable reporter moiety comprises a fluorophore. In some embodiments, the fluorophore is attached to the nucleotide base. In some embodiments, the fluorophore is attached to the nucleotide base with a linker which is cleavable / removable from the base or is not removable from the base. In some embodiments, a particular detectable reporter moiety (e.g., fluorophore) that is attached to the nucleotide can correspond to the nucleotide base (e.g., dATP, dGTP, dCTP, dTTP or dUTP) to permit detection and identification of the nucleotide base. In some embodiments, at least one of the nucleotides inthe plurality is not labeled with a detectable reporter moiety. In some embodiments, the plurality of nucleotides is not labeled with a detectable reporter moiety.

[0274] In some embodiments, the methods for sequencing further comprise step (h): when the nucleotides of step (g) are labeled with a detectable reporter moiety, then step (h) comprises detecting the complementary nucleotides which are incorporated into the primers of the nucleotide-complexed polymerases. In some embodiments, the plurality of nucleotides is labeled with a detectable reporter moiety to permit detection. In some embodiments, in the methods for sequencing concatemer molecules, when the nucleotides of step (g) are nonlabeled then the detecting of step (h) is omitted.

[0275] In some embodiments, the methods for sequencing further comprise step (i): when the nucleotides of step (g) are labeled with a detectable reporter moiety, then step (i) comprises identifying the bases of the complementary nucleotides which are incorporated into the primers of the nucleotide-complexed polymerases. In some embodiments, the identification of the incorporated complementary nucleotides in step (i) can be used to confirm the identity of the complementary nucleotides of the multivalent molecules that are bound to the plurality of first complexed polymerases in step (d). In some embodiments, the identifying of step (i) can be used to determine the sequence of the concatemer molecules. In some embodiments, in the methods for sequencing concatemer molecules, when the nucleotides of step (g) are non-labeled then the identifying of step (i) is omitted.

[0276] In some embodiments, the methods for sequencing further comprise step (j): removing the chain terminating moiety from the incorporated nucleotide when step (g) is conducted by contacting the plurality of second complexed polymerases with a plurality of nucleotides that comprise at least one nucleotide having a 2’ and / or 3’ chain terminating moiety.

[0277] In some embodiments, the methods for sequencing further comprise step (k): repeating steps (a) - (j) at least once. In some embodiments, the sequence of the concatemer molecules can be determined by detecting and identifying the multivalent molecules that bind the sequencing polymerases but do not incorporate into the 3 ’ end of the primer at steps (c) and (d). In some embodiments, the sequence of the concatemer molecule can be determined (or confirmed) by detecting and identifying the nucleotide that incorporates into the 3’ end of the primer at steps (h) and (i).

[0278] In some embodiments, in any of the methods for sequencing nucleic acid molecules, the binding of the plurality of first complexed polymerases with the plurality of multivalent molecules forms at least one avidity complex, the method comprising the steps:(a) binding a first nucleic acid primer, a first sequencing polymerase, and a first multivalent molecule to a first portion of a concatemer molecule thereby forming a first binding complex, wherein a first nucleotide moiety of the first multivalent molecule binds to the first sequencing polymerase; and (b) binding a second nucleic acid primer, a second sequencing polymerase, and the first multivalent molecule to a second portion of the same concatemer molecule thereby forming a second binding complex, wherein a second nucleotide moiety of the first multivalent molecule binds to the second sequencing polymerase, wherein the first and second binding complexes which include the same multivalent molecule forms an avidity complex. In some embodiments, the first sequencing polymerase comprises any wild type or mutant polymerase described herein. In some embodiments, the second sequencing polymerase comprises any wild type or mutant polymerase described herein. The concatemer molecule comprises tandem repeat sequences of a sequence of interest and at least one universal sequencing primer binding site. The first and second nucleic acid primers can bind to a sequencing primer binding site along the concatemer molecule. Exemplary multivalent molecules are shown in FIGs. 2-6.

[0279] In some embodiments, in any of the methods for sequencing nucleic acid molecules, wherein the method includes binding the plurality of first complexed polymerases with the plurality of multivalent molecules to form at least one avidity complex, the method comprises the steps: (a) contacting the plurality of sequencing polymerases and the plurality of nucleic acid primers with different portions of a concatemer molecule to form at least first and second complexed polymerases on the same concatemer molecule; (b) contacting a plurality of multivalent molecules to the at least first and second complexed polymerases on the same concatemer molecule, under conditions suitable to bind a single multivalent molecule from the plurality to the first and second complexed polymerases, wherein at least a first nucleotide moiety of the single multivalent molecule is bound to the first complexed polymerase which includes a first primer hybridized to a first portion of the concatemer molecule thereby forming a first binding complex (e.g., first ternary complex), and wherein at least a second nucleotide moiety of the single multivalent molecule is bound to the second complexed polymerase which includes a second primer hybridized to a second portion of the concatemer molecule thereby forming a second binding complex (e.g., second ternary complex), wherein the contacting is conducted under a condition suitable to inhibit polymerase-catalyzed incorporation of the bound first and second nucleotide moieties in the first and second binding complexes, and wherein the first and second binding complexes which are bound to the same multivalent molecule forms an avidity complex; and (c)detecting the first and second binding complexes on the same concatemer molecule, and (d) identifying the first nucleotide moiety in the first binding complex thereby determining the sequence of the first portion of the concatemer molecule, and identifying the second nucleotide moiety in the second binding complex thereby determining the sequence of the second portion of the concatemer molecule. In some embodiments, the plurality of sequencing polymerases comprise any wild type or mutant sequencing polymerase described herein. The concatemer molecule can comprise tandem repeat sequences of a sequence of interest and at least one universal sequencing primer binding site. The plurality of nucleic acid primers can bind to a sequencing primer binding site along the concatemer molecule. Exemplary multivalent molecules are shown in FIGs. 2-6.Sequencing-by-Binding

[0280] In some aspects, the present disclosure provides methods for sequencing a concatemer wherein the concatemer is generated using any of the partial double-stranded splint adaptors and methods described herein (e.g., see FIGs. 16-19).

[0281] The present disclosure further provides methods for sequencing any of the immobilized concatemer molecules described herein, wherein the sequencing methods comprise a sequencing-by-binding (SBB) procedure which employs non-labeled chainterminating nucleotides. In some embodiments, the sequencing-by-binding (SBB) method comprises the steps of (a) sequentially contacting a primed template nucleic acid with at least two separate mixtures under ternary complex stabilizing conditions, wherein the at least two separate mixtures each include a polymerase and a nucleotide, whereby the sequentially contacting results in the primed template nucleic acid being contacted, under the ternary complex stabilizing conditions, with nucleotide cognates for first, second and third base type base types in the template; (b) examining the at least two separate mixtures to determine whether a ternary complex formed; and (c) identifying the next correct nucleotide for the primed template nucleic acid molecule, wherein the next correct nucleotide is identified as a cognate of the first, second or third base type if ternary complex is detected in step (b), and wherein the next correct nucleotide is imputed to be a nucleotide cognate of a fourth base type based on the absence of a ternary complex in step (b); (d) adding a next correct nucleotide to the primer of the primed template nucleic acid after step (b), thereby producing an extended primer; and (e) repeating steps (a) through (d) at least once on the primed template nucleic acid that comprises the extended primer. Exemplary sequencing-by-bindingmethods are described in U.S. patent Nos. 10,246,744 and 10,731,141 (where the contents of both patents are hereby incorporated by reference in their entireties).Methods for Sequencing using Phosphate-Chain Labeled Nucleotides

[0282] In some aspects, the present disclosure provides methods for sequencing a concatemer wherein the concatemer is generated using any of the partial double-stranded splint adaptors and methods described herein (e.g., see FIGs. 16-19).

[0283] The present disclosure further provides methods for sequencing using phosphate chain-labeled nucleotides, comprising step (a): contacting (i) a plurality of sequencing polymerases, (ii) a plurality of concatemer molecules immobilized to a support and (iii) a plurality of nucleic acid sequencing primers, where the contacting is conducted under a condition suitable to form a plurality of sequencing polymerase complexes each complex comprising a sequencing polymerase bound to a nucleic acid duplex wherein the nucleic acid duplex comprises a portion of a concatemer molecule hybridized to a nucleic acid sequencing primer. In some embodiments, the sequencing polymerases comprise a recombinant mutant sequencing polymerase that can bind and incorporate nucleotide analogs. In some embodiments, the sequencing primers comprise 3’ extendible ends or 3’ blocked end that can be converted into a 3’ extendible end.

[0284] In some embodiments, the methods for sequencing concatemer molecules further comprise step (b): contacting the plurality of sequencing polymerase complexes with a plurality of phosphate chain-labeled nucleotides under a condition suitable for binding at least one phosphate chain-labeled nucleotide to one of the sequencing polymerase complexes, and the condition is suitable for promoting polymerase-catalyzed nucleotide incorporation. In some embodiments, the sequencing polymerase complex is contacted with the plurality of nucleotides in the presence of at least one catalytic cation comprising magnesium and / or manganese. In some embodiments, individual phosphate chain-labeled nucleotides in the plurality comprise an aromatic base, a five-carbon sugar (e.g., ribose or deoxyribose), and phosphate chain comprising 3-20 phosphate groups, where the terminal phosphate group is linked to a detectable reporter moiety (e.g., a fluorophore). The first, second and third phosphate groups can be referred to as alpha, beta and gamma phosphate groups. In some embodiments, a particular detectable reporter moiety which is attached to the terminal phosphate group corresponds to the nucleotide base (e.g., dATP, dGTP, dCTP, dTTP or dUTP) to permit detection and identification of the nucleo-base. In some embodiments, the sequencing polymerases are capable of binding a complementary phosphate chain labelednucleotide and incorporating the complementary nucleotide opposite a nucleotide in a template molecule. In some embodiment, the polymerase-catalyzed nucleotide incorporation reaction cleaves between the alpha and beta phosphate groups thereby releasing a multiphosphate chain linked to the detectable reporter moiety. In some embodiments, the plurality of phosphate chain-labeled nucleotides comprises one type or a mixture of any two or more types of nucleotides comprising dATP, dGTP, dCTP, dTTP and / or dUTP.

[0285] In some embodiments, the sequencing method further comprises step (c): detecting the fluorescent signal emitted by the phosphate chain labeled nucleotide that is bound by the sequencing polymerase, and incorporated into the terminal end of the sequencing primer. In some embodiments, step (c) further comprises identifying the phosphate chain labeled nucleotide that is bound by the sequencing polymerase, and incorporated into the terminal end of the sequencing primer.

[0286] In some embodiments, the sequencing method further comprises step (d): repeating steps (b) - (c) at least once. In some embodiments, sequencing methods that employ phosphate chain labeled nucleotides can be conducted according to the methods described in U.S. Patent Nos. 7,170,050; 7,302,146; and / or 7,405,281, which are incorporated by reference in their entireties.

[0287] In some embodiments, in step (a), the plurality of concatemer molecules is immobilized to a support which comprises a plurality of separate compartments. In some embodiments, the plurality of sequencing polymerases is in solution in a compartment. In some embodiments, at least one sequencing polymerase is immobilized to the bottom of individual compartments. In some embodiments, the separate compartments comprise a silica bottom through which light can penetrate. In some embodiments, the separate compartments comprise a silica bottom configured with a nanophotonic confinement structure comprising a hole in a metal cladding film (e.g., aluminum cladding film). In some embodiments, the hole in the metal cladding has a small aperture, for example, approximately 70 nm. In some embodiments, the height of the nanophotonic confinement structure is approximately 100 nm. In some embodiments, the nanophotonic confinement structure comprises a zero-mode waveguide (ZMW). In some embodiments, the nanophotonic confinement structure contains a liquid.Sample Indexes for Improved Base Calling

[0288] Generally, it is desirable to prepare nucleic acid libraries that will be distributed onto a support (e.g., a coated flow cell), where the library molecules are converted into template molecules that are immobilized at a high density to the support for massively parallel sequencing. For template molecules (e.g., concatemer molecules) that are immobilized at high densities at random locations on the support, the challenge of resolving high density fluorescent images for accurate base calling during sequencing runs becomes challenging.

[0289] The nucleotide diversity of a population of immobilized template molecules generally refers to the relative proportion of nucleotides A, G, C and T that are present in each sequencing cycle. An optimal high diversity template molecule will generally include sequence-of-interest (insert) regions having approximately equal proportions of all four nucleotides represented in each cycle of a sequencing run. Low diversity template molecules will generally include sequence-of-interest (insert) regions having a high proportion of certain nucleotides and low proportion of other nucleotides. To overcome the problem of low diversity template molecules, a small amount of a high diversity molecules prepared from PhiX bacteriophage can be mixed with the template molecules-of-interest (e.g., PhiX spike-in library) and sequenced together on the same flow cell. While the PhiX spike-in library provides nucleotide diversity, it also occupies space on the flow cell, thereby replacing template molecules carrying the sequence-of-interest and reducing the amount of sequencing data obtainable from the template molecule (e.g., reducing sequencing throughput). Another method to overcome the problem of low diversity template molecules is to prepare template molecules having at least one sample index sequence that is designed to be color-balanced. However, it may be desirable to design a large number of sample index sets, for example, a set of single index sample sequences or paired index sample sequences for 16-plex, 24-plex, 96-plex or larger plexy levels. It is challenging to design sample index sequences, as a single or paired sample indexes, for large sample index sets where all sample index sequences are color-balanced (e.g., see FIGs. 21 and 22).

[0290] An alternative method to overcome the challenges of sequencing low diversity template molecules (e.g., at high density on the support) is to prepare template molecules having at least one sample index sequence comprising a short random sequence (e.g., NNN) linked directly to a sample index sequence, where the short random sequence (e.g., NNN) provides nucleotide diversity and color balance. In some embodiments, a sample index sequence includes a short random sequence (e.g., NNN) linked directly to a sample index sequence. In some embodiments, the short random sequence (e.g., NNN) is upstream ordownstream of the sample index sequence. Some exemplary sample index sequences include, but are not limited to: NNNGTAGGAGCC; NNNCCGCTGCTA; NNNAACAACAAG; NNNGGTGGTCTA; NNNTTGGCCAAC; NNNCAGGAGTGC; and NNNATCACACTA (e.g., see Table 3).

[0291] The skilled artisan will recognize that a universal sample index can be any length and have any sequence that can be used to distinguish sequences of interest obtained from different sample sources in a multiplex assay. In a population of a given sample index, for example, NNNGTAGGAGCC, the population contains a mixture of individual sample index molecules each carrying the same universal sample index sequence (e.g., GTAGGAGCC) and a different short random sequence (e.g., NNN) where up to 64 different short random sequences may be present in the population of the given sample index.

[0292] In a population of sample-indexed template molecules, the short random sequence (e.g., NNN) of the sample index provides high nucleotide diversity which includes approximately equal proportions of all four nucleotides (e.g., A, G, C, T and / or U) that will be represented in each cycle of a sequencing run (see FIGs. 21 and 22). The high nucleotide diversity of the short random sequence (e.g., NNN) also provides color balance during each cycle of the sequencing run. The advantage of designing sample indexes to include a short random sequence (e.g., NNN) is that, in a low-plex population of template molecules (e.g., 2- plex or 4-plex), the universal sample index sequences that identify the two or four different samples need not exhibit nucleotide diversity (e.g., see FIGs. 21 and 22). Additionally, the nucleotide diversity of the short random sequence (e.g., NNN) can obviate the need to include a PhiX spike-in library, or permits use of a reduced amount of PhiX spike-in library to be distributed onto the flow cell and sequenced.

[0293] The concatemer template molecules can include a first sample index sequence, which includes a short random sequence (e.g., NNN), and a second sample index sequence, which lacks a short random sequence (e.g., NNN). In some embodiments, the sequencing data from only the sample index sequence with the short random sequence (e.g., NNN) is used for polony mapping and template registration because the short random sequence (e.g., NNN) provides sufficient nucleotide diversity and color balance. Both types of sample indexes can be used to distinguish sequences of interest obtained from different sample sources in a multiplex assay.

[0294] The order of sequencing the sequence-of-interest region and the sample index region(s) can also be used to improve the challenges of sequencing low diversity template molecules. For example, the sample index region can be sequenced first before sequencingthe sequence-of-interest region, and the sample index sequence can be associated with the sequence-of-interest region. For example, the sample index region can be sequenced first, including sequencing the short random sequence (e.g., NNN) and optionally sequencing at least a portion of the universal sample index), and then sequencing the sequence-of-interest region. In a population of sample indexed template molecules, the short random sequence (e.g., NNN) can provide nucleotide diversity which may not be provided by the sequence-of- interest regions of the template molecules. The sequence of the sample index thus provides improved nucleotide diversity and color balance for polony mapping and template registration.

[0295] In some embodiments, when sequencing the sample index region first, the length of the sequenced sample index region is relatively short (e.g., less than 30 nucleotides in length) so that de-hybridization of the product of the sequenced sample index region is more complete. Gentler de-hybridization conditions can be used to remove most or all of the product of the sequenced sample index region, which reduces the level of residual signals from any sequencing products remaining hybridized to the template molecules. By contrast, the sequence-of-interest region is typically much longer than the sample index region (e.g., more than 100 nucleotides in length). When the sequence-of-interest region is sequenced before the sample index region, the product of the sequenced sequence-of-interest region must be subjected to harsher de-hybridization conditions to remove any products remaining hybridized to the template molecules, which may damage the template molecules.

[0296] In some aspects, the present disclosure provides template molecules each comprising at least one sample index sequence that can be used to distinguish sequences of interest obtained from different sample sources in a multiplex assay, where the at least one sample index sequence comprises a short random sequence (e.g., NNN) linked to a universal sample index sequence. The at least one sample index sequence can include sequence diversity, e.g., for improved base calling. The at least one sample index sequence can be used to improve base calling accuracy.

[0297] In some embodiments, the short random sequence (e.g., NNN) is positioned upstream of the universal sample index sequence, so that during a sequencing run the short random sequence portion is sequenced before the universal sample index sequence. In some embodiments, the short random sequence (e.g., NNN) is positioned downstream of the universal sample index sequence, so that during a sequencing run the short random sequence portion is sequenced after the universal sample index sequence.

[0298] In some embodiments, in the short random sequence (e.g., NNN) each base “N” at a given position is independently selected from A, G, C, T or U. In some embodiments, the random sequence lacks consecutive repeat sequences having 2 or 3 of the same nucleo-base, for example, AA, TT, CC, GG, UU, AAA, TTT, CCC, GGG or UUU. In some embodiments, in a population of template molecules the universal sample index sequences include a short random sequence (e.g., NNN) having a high diversity sequence which includes approximately equal proportions of all four nucleotides (e.g., A, G, C, T and / or U) that will be represented in each cycle of a sequencing run.

[0299] In some embodiments, the short random sequence (e.g., NNN) comprises 3-20 nucleotides, or 3-10 nucleotides, or 3-8 nucleotides, or 3-6 nucleotides, or 3-5 nucleotides, or 3-4 nucleotides.

[0300] In some embodiments, the short random sequence (e.g., NNN) includes, but is not limited to, AGC, AGT, GAC, GAT, CAT, CAG, TAG, TAC. The skilled artisan will recognize that many more random sequences can be prepared (e.g., 64 possible combinations) where each base “N” at a given position in the random sequence is independently selected from A, G, C, T or U.

[0301] In some embodiments, the universal sample index sequence comprises 5-20 nucleotides, or 7-18 nucleotides, or 9-16 nucleotides.

[0302] In some embodiments, individual sample index sequences in a population of sample indexes comprise a universal sample index sequence and a short random sequence (e.g., NNN). In some embodiments, the short random sequences (e.g., NNN) in the population of sample index sequences have an overall base composition of about 25% or about 20-30% of all four nucleotide bases (e.g., A, G, C and T / U) to provide nucleotide diversity at each sequencing cycle during sequencing the short random sequence (e.g., NNN).

[0303] In some embodiments, in the population of sample index sequences the proportion of adenine (A) at any given position in the short random sequence (e.g., NNN) is about 20- 30%, or about 15-35%, or about 10-40%. In some embodiments, in the population of sample index sequences the proportion of guanine (G) at any given position in the short random sequence (e.g., NNN) is about 20-30%, or about 15-35%, or about 10-40%. In some embodiments, in the population of sample index sequences the proportion of cytosine (C) at any given position in the short random sequence (e.g., NNN) is about 20-30%, or about 15- 35%, or about 10-40%. In some embodiments, in the population of sample index sequences the proportion of thymine (T) or uracil (U) at any given position in the short random sequence (e.g., NNN) is about 20-30%, or about 15-35%, or about 10-40%.

[0304] In some embodiments, in the population of sample index sequences the proportion of adenine (A) and thymine (T), or the proportion of adenine (A) and uracil (U), at any given position in the short random sequence (e.g., NNN) is about 10-65%, or any range therebetween. In some embodiments, in the population of sample index sequences the proportion of guanine (G) and cytosine (C) at any given position in the short random sequence (e.g., NNN) is about 10-65%, or any range therebetween.

[0305] In some embodiments, in the population of sample index sequences the sequence diversity of the short random sequences (e.g., NNN) ensures that no sequencing cycle is presented with fewer than four different nucleotide bases during sequencing at least the short random sequence (e.g., NNN).

[0306] In some embodiments, the random sequence (e.g., NNN) provides a balanced ratio of nucleo-bases adenine, cytosine, guanine, thymine and / or uracil (see FIG. 21). In some embodiments, in a population of sample-indexed template molecules, the random sequence (e.g., NNN) together with at least a portion of the universal sample index sequence provide a balanced ratio of nucleo-bases adenine, cytosine, guanine, thymine and / or uracil represented in each cycle of a sequencing run.

[0307] In some embodiments, a sequencing reaction includes use of polymerases and nucleotides (e.g., nucleotide analogs) that are labeled with a different fluorophore that corresponds to the nucleo-base. In some embodiments, sequencing the random sequence (e.g., NNN) using labeled nucleotides provides a balanced ratio of fluorescent colors that correspond to the nucleo-bases adenine, cytosine, guanine, thymine and / or uracil in each cycle of a sequencing run. In some embodiments, sequencing the random sequence (e.g., NNN) and at least a portion of the universal sample index sequence using labeled nucleotides provides a balanced ratio of fluorescent colors that correspond to nucleo-bases adenine, cytosine, guanine, thymine and / or uracil (e.g., see FIG. 21). The labeled nucleotides emit fluorescent signals during the sequencing reactions. In some embodiments, the sequencing reaction is conducted on a sequencing apparatus having a detector that captures fluorescent images from sequencing reactions on the immobilized template molecules. The sequencing apparatus can be configured to relay the fluorescent imaging data captured by the detector to a computer system that is programmed to determine the location (e.g., mapping) of the immobilized template molecules on the flow cell. The computer system can generate a map of the locations of the immobilized template molecules based on the fluorescent imaging data of only the random sequence (e.g., NNN), or based on the random sequence (e.g., NNN) and at least a portion the universal sample index sequence. Thus, the few numbers of sequencingcycles used to sequence the random sequence (e.g., NNN) and optionally a portion of the universal sample index sequence can be used to generate a map of the location of the immobilized template molecules. The computer system can be configured to extract the fluorescent color and intensity of only the random sequence (e.g. , NNN), or the random sequence (e.g., NNN) and at least a portion of the universal sample index sequence. The computer system can be configured to use the location of a given immobilized template molecule and the fluorescent color and intensity associated with the given template molecule (which were established while sequencing the random sequence) for base calling while sequencing the insert region (110). The computer system can be configured to detect phasing and pre-phasing while sequencing the random sequence (e.g., NNN) and the universal sample index sequence, and the insert region (110). In some embodiments, the balanced ratio of fluorescent colors provided by the random sequence (e.g., NNN) at each sequencing cycle can improve the quality of the data which is processed from the fluorescent images captured by the detector, and can in turn improve the capability by the computer system to determine the location of the immobilized template molecules on the flow cell, and the color and intensity, all of which can improve base calling accuracy and quality scores of the sequenced insert region (110).

[0308] In some embodiments, a sequencing reaction includes use of polymerases and multivalent molecules that are labeled with a different fluorophore that corresponds to the nucleo-base (e.g., adenine, guanine, cytosine, thymine or uracil) of the nucleotide moietiesthat are attached to the nucleotide arms in a given multivalent molecule. In some embodiments, the core of individual multivalent molecules is attached to a fluorophore which corresponds to the nucleotide moieties(e.g., adenine, guanine, cytosine, thymine or uracil) that are attached to the nucleotide arms in a given multivalent molecule (e.g., see FIGs. 2-6). In some embodiments, at least one of the nucleotide arms of the multivalent molecule comprises a linker and / or nucleotide base that is attached to a fluorophore, and wherein the fluorophore which is attached to a given linker or nucleotide base corresponds to the nucleotide base (e.g., adenine, guanine, cytosine, thymine or uracil) of the nucleotide arm. In some embodiments, sequencing the random sequence (e.g., NNN) using labeled multivalent molecules provides a balanced ratio of fluorescent colors that correspond to the nucleo-bases adenine, cytosine, guanine, thymine and / or uracil in each cycle of a sequencing run. In some embodiments, sequencing the random sequence (e.g., NNN) and at least a portion of the universal sample index sequence using labeled multivalent molecules provides a balanced ratio of fluorescent colors that correspond to nucleo-bases adenine, cytosine, guanine,thymine and / or uracil (e.g., see FIG. 21). The labeled multivalent molecules can emit fluorescent signals during the sequencing reactions. In some embodiments, the sequencing reaction is conducted on a sequencing apparatus having a detector that captures fluorescent images from sequencing reactions on the immobilized template molecules. The sequencing apparatus can be configured to relay the fluorescent imaging data captured by the detector to a computer system that is programmed to determine the location (e.g., mapping) of the immobilized template molecules (polonies) on the flow cell. The computer system can generate a map of the locations of the immobilized template molecules based on the fluorescent imaging data of only the random sequence (e.g., NNN), or based on the random sequence (e.g., NNN) and at least a portion of the universal sample index sequence. Thus, the few numbers of sequencing cycles used to sequence the random sequence (e.g., NNN) and optionally a portion of the universal sample index sequence can be used to generate a map of the location of the immobilized template molecules. The computer system can be configured to extract the fluorescent color and intensity of only the random sequence (e.g., NNN) or the random sequence (e.g., NNN) and the universal sample index sequence. The computer system can be configured to use the location of a given immobilized template molecule and the fluorescent color and intensity associated with the given template molecule (which were established while sequencing the random sequence) for base calling while sequencing the insert region (110). The computer system can be configured to detect phasing and prephasing while sequencing the random sequence (e.g., NNN) and the universal sample index sequence, and the insert region (110) . In some embodiments, the balanced ratio of fluorescent colors provided by the random sequence (e.g., NNN) at each sequencing cycle can improve the quality of the data which is processed from the fluorescent images captured by the detector, and can in turn improve the capability by the computer system to determine the location of the immobilized template molecules on the flow cell, and the color and intensity, all of which can improve base calling accuracy and quality scores of the sequenced insert region (110).Sequencing Sample Index Sequences

[0309] In some embodiments, a single stranded covalently closed circular library molecule (500) comprises: (i) a universal primer binding site for a surface capture primer (210); (ii) an insert region (110); (iii) a sample index sequence (230); (iv) a short random sequence (e.g., NNN); and (v) a universal primer binding site for a pinning primer (e.g., see FIG. 19). In some embodiments, a plurality of single stranded covalently closed circularlibrary molecules (500) are subjected to rolling circle amplification by hybridizing the plurality of single stranded covalently closed circular library molecules (500) to a plurality of surface capture primers immobilized to a support where the terminal 3 ’ ends of the surface capture primers initiate amplification thereby generating a plurality of immobilized concatemers each having tandem repeat sequences of its cognate single stranded covalently closed circular library molecule (500). In some embodiments, the rolling circle amplification is conducted in the presence of a plurality of compaction oligonucleotides which can hybridize to the concatemers at their universal binding sequence for a surface pinning primer or universal binding sequence for a surface capture primer. In some embodiments, the plurality of immobilized capture primers lacks uracil bases. In some embodiments, the rolling circle amplification reaction includes a plurality of nucleotides including dATP, dGTP, dCTP, dTTP and dUTP, to generate a plurality of immobilized concatemers wherein individual concatemer molecules comprise randomly-distributed uracil bases. In some embodiments, at least a portion of the immobilized concatemer molecule is sequenced.

[0310] In some embodiments, the order of sequencing comprises: (1) sequencing the short random sequence (e.g., NNN), the sample index sequence (230) and the insert region (110) of the concatemers, wherein the sequencing of step (1) employs soluble sequencing primers (e.g., solid arrows pointing left in FIG. 19) that can hybridize to the universal primer binding site for surface pinning primers (220) on the concatemer molecule and the sequencing reactions can generate forward sequencing read products (e.g. , dashed arrows pointing left in FIG. 19) . In some embodiments, the order of sequencing further comprises: (2) conducting a pairwise turn reaction so that the immobilized concatemer molecule is replaced with an immobilized second strand that is complementary to the concatemer molecule; and (3) sequencing the insert region (110) on the second strand, wherein the sequencing of step (3) employs soluble sequencing primers that can hybridize to the universal primer binding sites for surface capture primers (210) on the concatemer molecule (e.g, see FIG. 19). In some embodiments, the sequencing of step (1) generates forward sequencing read products which are indicated by the encircled numeral “1”. In some embodiments, the sequencing of step (3) generated reverse sequencing read products which are indicated by the encircled numeral “2”. In some embodiments, sequencing the short random sequence (e.g, NNN) and the sample index sequence (230) may provide sufficient nucleotide diversity and color balance for polony mapping and concatemer registration.

[0311] In some embodiments, methods for sequencing the concatemer molecules immobilized to the support comprises step (a): hybridizing the immobilized concatemermolecules with a plurality of soluble forward sequencing primers that hybridize to at least a portion of the universal primer binding site for the surface capture primer (210) (e.g., solid arrows pointing left in FIG. 19) and sequencing the short random sequence (e.g., NNN), the universal sample index sequence (230) and the insert region (110) of the concatemer thereby generating a plurality of forward sequencing read products that are hybridized to the immobilized concatemer molecules (e.g., dashed arrows pointing left in FIG. 19). In some embodiments, individual immobilized concatemer molecules comprise at least one uracil base at random locations throughout the concatemer molecule.

[0312] In some embodiments, the methods for sequencing further comprise step (b): removing the forward sequencing read products and retaining the immobilized concatemer molecules.

[0313] In some embodiments, the methods for sequencing further comprise step (c): replacing the plurality of forward sequencing read products that are hybridized to the immobilized concatemer molecules by conducting a primer extension reaction using stranddisplacing polymerases and a plurality of nucleotides to generate second strand extension products that are hybridized to the immobilized concatemer molecules including the immobilized capture primer.

[0314] In some embodiments, the methods for sequencing further comprise step (d): removing the immobilized concatemer molecules by generating abasic sites in the immobilized concatemer molecules at the uracil sites and generating gaps at the abasic sites thereby generating gap-containing concatemer molecules while retaining the second strand extension products that were generated in step (c) where individual second strand extension products are retained by hybridization to an immobilized capture primer. In some embodiments, pairwise turn is achieved by conducting steps (c) and (d).

[0315] In some embodiments, the methods for sequencing further comprise step (e): hybridizing the retained second strand extension products with a plurality of soluble reverse sequencing primers that hybridize to the universal primer binding sites for a surface pinning primer (220) on the retain second strand extension products (e.g., solid arrows pointing right in FIG. 19) and sequencing at least of portion of the insert region (110) thereby generating a plurality of reverse sequencing read products (e.g., dashed arrows pointing right in FIG. 19).

[0316] In some embodiments, the methods for sequencing further comprise: assigning the sequence of (i) the insert region (110) to (ii) the sample index sequence (230), thereby identifying the insert region as being obtained from a particular source.

[0317] In some embodiments, the removing of the forward sequencing read products of step (b) can be conducted using a denaturation reagent comprising SSC (e.g., saline-sodium citrate) buffer with or without formamide, at a temperature that promotes nucleic acid denaturation such as for example 50 - 90 °C. In some embodiments, the removing of the plurality of forward sequencing read products of step (b) can be conducted using a dehybridization reagent at a temperature that promotes nucleic acid denaturation such as for example 50 - 90 °C. In some embodiments, the de-hybridization reagent comprises a pH buffering agent, a reducing agent, a monovalent salt and a crowding agent. In some embodiments, the de-hybridization reagent further comprises a chaotropic agent.

[0318] In some embodiments, the sequencing of steps (a) and (e) include conducting any of the sequencing methods described herein that employ sequencing polymerases and detectably labeled nucleotide analogs. In some embodiments, the sequencing of steps (a) and (e) include conducting any of the two-stage sequencing methods described herein that employ sequencing polymerases, detectably labeled multivalent molecules, and labeled nucleotide analogs or non-labeled nucleotide analogs. In some embodiments, the sequencing of steps (a) and (e) include conducting any of the sequencing-by-binding methods or any of the sequencing methods that employ phosphate-chain labeled nucleotides described herein.

[0319] In some embodiments, the density of the plurality of concatemer molecules immobilized to the support is about 102- 1015per mm2. In some embodiments, the plurality of concatemer molecules is immobilized at random locations on the support. In some embodiments, the plurality of concatemer molecules is immobilized on the support in a predetermined pattern.De-Hybridization Reagents

[0320] In some aspects, the present disclosure provides one or more nucleic acid de- hybridization reagents that can promote nucleic acid denaturation between any two nucleic acid strands. In some embodiments, the de-hybridization reagents can promote nucleic acid denaturation between a nucleic acid template molecule and a nucleic acid extension product. In some embodiments, the de-hybridization reagents can promote nucleic acid denaturation between concatemer molecules and the plurality of sample index extension products while retaining the immobilized concatemer molecules. In some embodiments, the de-hybridization reagents can promote nucleic acid denaturation between concatemer molecules and the plurality of insert extension products while retaining the immobilized concatemer molecules.In some embodiments, the de-hybridization reagents can promote nucleic acid denaturation between second strand molecules and the plurality of insert extension products while retaining the immobilized second strand molecules.

[0321] The present disclosure further provides one or more nucleic acid de-hybridization reagents (e.g., denaturation reagent), and methods that employ the nucleic acid de- hybridization reagents where the methods comprise any of the order of sequencing workflows. For example, the order of sequencing workflows can include those described above, e.g., methods comprising removing the plurality of sample index extension products from the immobilized concatemer molecules, removing the plurality of insert extension products from the immobilized concatemer molecules and / or removing the plurality of insert extension products from the immobilized second strand molecules.

[0322] In some embodiments, the de-hybridization reagent comprises a pH buffering agent, a reducing agent, a monovalent salt and a crowding agent. In some embodiments, the de-hybridization reagent further comprises a chaotropic agent. In some embodiments, the de- hybridization reagent is at a pH range of about 5 - 5.25, or a pH range of about 5.25 - 5.5, or a pH range of about 5.5 - 5.75, or a pH range of about 5.75 - 6.

[0323] In some embodiments, any of the de-hybridization reagents described herein can include a pH buffering agent which can maintain the pH of the reagent in a range that is suitable for nucleic acid hybridization. The pH buffering agent can comprise any one or any combination of two or more of Tris, Tris-HCl, Tris-acetate, Tricine, Bicine, Bis-Tris propane, HEPES, MES, MOPS, MOPSO, BES, TES, CAPS, TAPS, TAPSO, ACES, PIPES, ethanolamine (i.e., 2-amino methanol; MEA), a citrate compound, a citrate mixture, NaOH and / or KOH. In some embodiments, the pH buffering agent can be present in any of the de- hybridization reagents described herein at a concentration of about 1-100 mM, or about 10-50 mM, or about 10-25 mM. In some embodiments, the pH of the pH buffering agent which is present in any of the reagents described here in can be adjusted to a pH of about 4-9.5, or a pH of about 5-9, or a pH of about 5-8, or a pH of about 5.5-7.

[0324] In some embodiments, any of the de-hybridization reagents described herein can include at least one reducing agent comprising DTT (dithiothreitol), 2-beta mercaptoethanol, TCEP, (tris(2- carboxyethyl)phosphine), formamide, DMSO (dimethyl sulfoxide), sodium dithionite (Na2S2O4), glutathione, methionine, betaine, Tris(3-hydroxypropyl)phosphine (THPP) and / or N-acetyl cysteine. The de-hybridization reagents can include the reducing agent at a concentration of about 0.1-0.5 M, or about 0.5-1 M, or about 1-2 M. The de- hybridization reagents can include the reducing agent at a concentration of about 0.01-0.1mM, or about 0.1-1 mM, or about 1-2.5 mM, or about 2.5-5 mM, or about 5-7.5 mM, or about 7.5-9 mM, or about 9-12 mM, or about 12-25 mM, or about 25-50 mM. The dehybridization reagents can include the reducing agent at a concentration of about l%-5%, or about 5%- 10%, or about 10%-20%, or about 20%-30%, or about 30%-40%, or about 40%- 50%.

[0325] In some embodiments, any of the de-hybridization reagents described herein can include at least one monovalent salt comprising NaCl, KC1, NH2SO4 and / or potassium glutamate. The de-hybridization reagents can include the monovalent salt at a concentration of about 25-500 mM, or about 50-250 mM, or about 100-200 mM, or about 500 mM - 750 mM, or about 750 mM - 1 M, or about 1 M - 1.5 M.

[0326] In some embodiments, any of the de-hybridization reagents described herein can include a crowding agent that increases molecular crowding. In some embodiments, the crowding agent comprises polyethylene glycol (PEG, e.g., 1-50K molecular weight), dextran, dextran sulfate, hydroxypropyl methyl cellulose (HPMC), hydroxyethyl methyl cellulose (HEMC), hydroxybutyl methyl cellulose, hydroxypropyl cellulose, methycellulose, and hydroxyl methyl cellulose. The crowding agent can be present in the de-hybridization reagent at about 1-10%, or about 10-25%, or about 25-50%, or higher percentages by volume based on the total volume of the hybridization reagent.

[0327] In some embodiments, any of the de-hybridization reagents described herein can include a chaotropic agent that can disrupt non-covalent bonds such as hydrogen bonds or van der Waals forces. In some embodiments, the chaotropic agent comprises SDS (sodium dodecyl sulfate), urea, thiourea, guanidinium chloride, guanidine hydrochloride, guanidine thiocyanate, guanidine isothiocyanate, guanidine isothionate, potassium thiocyanate, lithium chloride, sodium iodide or sodium perchlorate. The de-hybridization reagents can include a chaotropic agent at a concentration of about 0.5-1 M, 0.1-1 M, or about 1-2 M, or about 2-3 M, or about 3-4 M, or about 4-5 M.Kits Comprising De-Hybridization Reagents

[0328] In some aspects, the present disclosure provides a kit for conducting any of the order of sequencing workflows described above, for example, methods comprising removing the plurality of sample index extension products from the immobilized concatemer molecules, removing the plurality of insert extension products from the immobilized concatemer molecules and / or removing the plurality of insert extension products from the immobilized second strand molecules. In some embodiments, the kit comprises a de-hybridization reagent comprising a pH buffering agent, a reducing agent, a monovalent salt and a crowding agent. In some embodiments, the de-hybridization reagent further comprises a chaotropic agent. In some embodiments, the kit further comprises any one or any combination of two or more of: a plurality of forward sequencing primers which can hybridize to the universal primer binding site for the surface pinning primer (220) on a concatemer molecule, a plurality of reverse sequencing primers which can hybridize to the universal primer binding site for the surface capture primer (210) on a concatemer molecule, a plurality of sequencing polymerases, plurality of detectably labeled nucleotide analogs, a plurality of non-labeled nucleotide analogs, a plurality of detectably labeled multivalent molecules and / or a cleaving reagent that can remove a chain terminating moiety (e.g., blocking moiety) from the 2’ sugar position or 3’ sugar position of a nucleotide analog.Sequencing 3-mer Random Sequences to Generate a Polony Map

[0329] In some aspects, the present disclosure provides methods for sequencing nucleic acids comprising: (a) providing a plurality of concatemer molecules immobilized on a support (e.g., immobilized at random or pre-determined locations) using the methods described herein, wherein individual template molecules comprise an insert sequence region and one sample index, wherein each sample index comprises a 3-mer random sequence (e.g., a short random sequence, e.g., NNN) joined to a sample index sequence (230) (e.g., a universal sample index sequence) which identifies the sample source of the insert sequence, wherein different concatemer molecules have a different 3-mer random sequence and the same sample index sequence (230), and wherein the concatemer molecules have different insert sequences; (b) conducting three cycles of polymerase-mediated sequencing reactions of the 3-mer random sequence (e.g., NNN) of the plurality of concatemer molecules using a plurality of detectably labeled nucleotide reagents comprising a mixture of different types of nucleo-bases A, G, C and T / U, wherein the nucleotide reagents comprise a different detectable color label that corresponds with each different type of nucleo-base, wherein the three cycles of sequencing include detecting and imaging the optical color signals emitted from the detectably labeled nucleotide reagents that are bound to the concatemer molecules thereby determining the sequences of the 3-mer random sequences in individual concatemer molecules of the plurality of concatemer molecules, and wherein a balanced diversity of nucleo-bases of A, G, C and T / U is detected and imaged in each of the first, second and third sequencing cycles among the plurality of concatemer molecules; and (c) generating a map of the locations of the plurality of concatemer molecules using the images obtained in step (b),wherein the sequence of the insert region is not used to generate the map. In some embodiments, the plurality of concatemer molecules immobilized to the support comprise a plurality of immobilized concatemer molecules.

[0330] In some embodiments, in the methods for sequencing nucleic acids, the balanced diversity of step (b) is about 5-85%, or about 5-60%, or about 10-50%, or about 15-55%, or about 25-75% of each of the nucleo-bases A, G, C and T / U that are detected and imaged in each of the first, second and third sequencing cycles.

[0331] In some embodiments, in the methods for sequencing nucleic acids, the method further comprises: (a) sequencing the sample index sequence (230) (e.g., the universal sample index sequence) of the plurality of concatemer molecules; (b) sequencing the insert region (110) of the plurality of concatemer molecules; and (c) assigning the insert sequence of a given concatemer molecule obtained in step (b) with the universal sample index sequence from the same given concatemer molecule obtained in step (a), thereby identifying the sample source of the given insert sequence.

[0332] In some aspects, the present disclosure provides methods for sequencing nucleic acids comprising: (a) providing a plurality of concatemer molecules immobilized on a support (e.g., immobilized at random or pre-determined locations) using the methods described herein, wherein individual concatemer molecules comprise an insert sequence region and one sample index sequence (230) (e.g., a universal sample index sequence), wherein each sample index comprises a 3-mer random sequence (e.g., a short random sequence, e.g., NNN) joined to a sample index sequence (230) which identifies the sample source of the insert sequence, wherein the universal sample index sequence comprises 3-20 nucleotides, wherein different concatemer molecules have a different 3-mer random sequence (e.g., NNN) and the same universal sample index sequence, and wherein the concatemer molecules have different insert sequences; (b) conducting four cycles of polymerase- mediated sequencing reactions of the 3-mer random sequence (e.g., NNN) and the first base position of the sample index sequence (230) of the plurality of concatemer molecules using a plurality of detectably labeled nucleotide reagents comprising a mixture of different types of nucleo-bases A, G, C and T / U, wherein the nucleotide reagents comprise a different detectable color label that corresponds with each different type of nucleo-base, wherein the four cycles of sequencing include detecting and imaging the optical color signals emitted from the detectably labeled nucleotide reagents that are bound to the concatemer molecules thereby determining the sequences of the 3-mer random sequences and the first base position of the universal sample index sequences in individual concatemer molecules of the pluralityof concatemer molecules, and wherein a balanced diversity of nucleo-bases of A, G, C and T / U is detected and imaged in each of the first, second, third and fourth sequencing cycles among the plurality of concatemer molecules; and (c) generating a map of the locations of the plurality of concatemer molecules using the images of the four cycles of polymerase- mediated sequencing reactions obtained in step (b), wherein the sequence of the insert region is not used to generate the map. In some embodiments, the plurality of concatemer molecules immobilized to the support comprise a plurality of immobilized concatemer molecules.

[0333] In some embodiments, in the methods for sequencing nucleic acids, the balanced diversity of step (b) is about 5-85%, or about 5-60%, or about 10-50%, or about 15-55%, or about 25-75% of each of the nucleo-bases A, G, C and T / U that are detected and imaged in each of the first, second, third and fourth sequencing cycles.

[0334] In some embodiments, in the methods for sequencing nucleic acids, the method further comprises: (a) sequencing the remaining base positions of the 1 sample index sequence (230) (e.g., a universal sample index sequence) of the plurality of concatemer molecules; (b) sequencing the insert sequence region (110) of the plurality of concatemer molecules; and (c) assigning the insert sequence of a given template molecule obtained in step (b) with the universal sample index sequence from the same given concatemer molecule obtained in step (a), thereby identifying the sample source of the given insert sequence.

[0335] In some embodiments, in any of the methods for sequencing nucleic acids, the support comprises a glass or plastic substrate. In some embodiments, the support is configured on a flow cell channel, a flow cell, or a capillary lumen. In some embodiments, the support is passivated with at least one hydrophilic polymer coating having a water contact angle of not more than 45 degrees. In some embodiments, the at least one hydrophilic polymer coating comprises a molecule selected from a group consisting of polyethylene glycol (PEG), poly(vinyl alcohol) (PVA), poly(vinyl pyridine), poly(vinyl pyrrolidone) (PVP), poly(acrylic acid) (PAA), polyacrylamide, poly(N-isopropylacrylamide) (PNIPAM), poly(methyl methacrylate) (PMA), poly(2-hydroxylethyl methacrylate) (PHEMA), poly(oligo(ethylene glycol) methyl ether methacrylate) (POEGMA), polyglutamic acid (PGA), poly-lysine, poly-glucoside, streptavidin, and dextran. In some embodiments, the at least one hydrophilic polymer coating comprises branched hydrophilic polymer molecules having at least four branches. In some embodiments, the at least one hydrophilic polymer coating comprises polymer molecules having a molecular weight of at least 1000 Daltons.

[0336] In some embodiments, in any of the methods for sequencing nucleic acids, the concatemer molecules comprise a plurality of tandem repeat sequences of the insertsequence and the one sample index. In some embodiments, the concatemer template molecules comprise a plurality of different clustered template molecules having one copy of the insert sequence and one copy of the one sample index, wherein the clustered template molecules are generated via bridge amplification. In some embodiments, the density of the template molecules positioned at random or pre-determined locations on the support is 104- 108per mm2. In some embodiments, the sample source of the insert sequences is genomic DNA, double-stranded cDNA or cell free circulating DNA.

[0337] In some embodiments, in any of the methods for sequencing nucleic acids, the detectably labeled nucleotide reagents comprise nucleotides each comprising an aromatic nucleo-base, a five-carbon sugar moiety, 1-10 phosphate groups, and a fluorophore. In some embodiments, the detectably labeled nucleotide reagents comprise nucleotides each comprising an aromatic nucleo-base, a five-carbon sugar moiety having a chain terminating group at the 3’ carbon sugar position, 1-10 phosphate groups, and a fluorophore. In some embodiments, the detectably labeled nucleotide reagents comprise multivalent molecules each comprising (1) a core, (2) a plurality of nucleotide arms, and (3) at least one fluorophore, wherein individual nucleotide arms comprise (i) a core attachment moiety, (ii) a spacer comprising a PEG moiety, (iii) a linker, and (iv) a nucleotide moiety, wherein the core is attached to the plurality of nucleotide arms, wherein the spacer is attached to the linker, wherein the linker is attached to the nucleotide moiety.

[0338] In some embodiments, in any of the methods for sequencing nucleic acids, the detectably labeled nucleotide reagents that are bound to the concatemer template molecules in step (b) comprise individual template molecules hybridized to a sequencing primer to form a duplex, and the duplex is bound to a polymerase to form a complexed polymerase, and the complexed polymerase is bound to a detectably labeled nucleotide reagent. In some embodiments, the complexed polymerase is bound to a detectably labeled nucleotide reagent under a condition suitable for binding the detectably labeled nucleotide reagent to the complexed polymerase and incorporating the detectably labeled nucleotide into the hybridized sequencing primer, wherein the detectably labeled nucleotide reagent comprises an aromatic nucleo-base, a five-carbon sugar moiety, 1-10 phosphate groups, and a fluorophore. In some embodiments, the complexed polymerase is bound to a detectably labeled nucleotide reagent under a condition suitable for binding the detectably labeled nucleotide reagent to the complexed polymerase and incorporating the detectably labeled nucleotide into the hybridized sequencing primer, wherein the detectably labeled nucleotide reagent comprises an aromatic nucleo-base, a five carbon sugar moiety having a chainterminating group at the 3’ carbon sugar position, 1-10 phosphate groups, and a fluorophore. In some embodiments, the complexed polymerase is bound to a detectably labeled nucleotide reagent under a condition suitable for binding the detectably labeled nucleotide reagent to the complexed polymerase and the condition is suitable for inhibiting nucleotide incorporation, wherein the detectably labeled nucleotide reagent comprises a multivalent molecule which includes (1) a core, (2) a plurality of nucleotide arms, and (3) at least one fluorophore, wherein individual nucleotide arms comprise (i) a core attachment moiety, (ii) a spacer comprising a PEG moiety, (iii) a linker, and (iv) a nucleotide moiety, wherein the core is attached to the plurality of nucleotide arms, wherein the spacer is attached to the linker, wherein the linker is attached to the nucleotide moiety (e.g., FIGs. 2-6).

[0339] In some embodiments, in any of the methods for sequencing nucleic acids, the template molecule comprises an immobilized concatemer molecule which is hybridized to a plurality of sequencing primers to form at least a first and second duplex on the same concatemer molecule, wherein the first duplex is bound to a first polymerase and the second duplex is bound to a second polymerase to form first and second complexed polymerases, and wherein the method comprises: (a) contacting a plurality of multivalent molecules to the first and second complexed polymerases on the same concatemer template molecule, wherein individual multivalent molecules include (1) a core, (2) a plurality of nucleotide arms, and (3) at least one fluorophore, wherein individual nucleotide arms comprise (i) a core attachment moiety, (ii) a spacer comprising a PEG moiety, (iii) a linker, and (iv) a nucleotide moiety, wherein the core is attached to the plurality of nucleotide arms, and the spacer is attached to the linker, and the linker is attached to the nucleotide moiety e.g., FIGs. 2-6), wherein the contacting is conducted under conditions suitable to bind a single multivalent molecule from the plurality to the first and second complexed polymerases, wherein a first nucleotide moiety of the single multivalent molecule is bound to the first complexed polymerase which includes the first sequencing primer hybridized to a first portion of the concatemer template molecule thereby forming a first binding complex, and wherein a second nucleotide moiety of the single multivalent molecule is bound to the second complexed polymerase which includes the second sequencing primer hybridized to a second portion of the concatemer template molecule thereby forming a second binding complex, wherein the first and second binding complexes which are bound to the same multivalent molecule forms an avidity complex, and wherein the contacting is conducted under a condition suitable to inhibit polymerase- catalyzed incorporation of the bound first and second nucleotide moieties in the first and second binding complexes; (b) detecting the first and second binding complexes on the sameconcatemer template molecule; (c) imaging the optical color signals emitted from the detectably labeled multivalent molecule which forms the first and second binding complexes on the same concatemer template molecule; and (d) identifying the first nucleotide moiety in the first binding complex thereby determining the sequence of the first portion of the concatemer template molecule, and identifying the second nucleotide moiety in the second binding complex thereby determining the sequence of the second portion of the concatemer template molecule.Sources of Nucleic Acid Fragments

[0340] In some aspects, the present disclosure provides linear double stranded nucleic acid fragments (100) from any source including a biological sample (e.g., fresh or live sample) such as a single cell, a plurality of cells or tissue. The linear double stranded nucleic acid fragments (100) can be isolated from healthy or diseases cells or tissues. The linear double stranded nucleic acid fragments (100) can be obtained from an archived sample such as a fresh frozen paraffin embedded (“FFPE”) sample, or from needle biopsies, circulating tumor cells, cell free circulating DNA (e.g., from tumor cells or a fetus). Cells or tissues are typically treated with a lysis buffer to release their DNA and RNA, and the desired nucleic acid is separated from non-desired macromolecules such as proteins.

[0341] The linear double stranded nucleic acid fragments (100) can be isolated in any form, including chromosomal, genomic (e.g., whole genomic), organellar (e.g., mitochondrial, chloroplast or ribosomal), recombinant molecules, cloned or amplified. The linear double stranded nucleic acid fragments (100) can be methylated or non-methylated.

[0342] The linear double stranded nucleic acid fragments (100) can be isolated from any organism including, without limitation, viruses, fungi, prokaryotes or eukaryotes. The insert region can be isolated from any organism including human, simian, ape, canine, feline, bovine, equine, murine, porcine, caprine, lupine, ranine, piscine, plant, insect or bacteria. The insert region can be isolated from organisms borne in air, water, soil or food.

[0343] The linear double stranded nucleic acid fragments (100) can be isolated from any biological fluid, including, without limitation, blood, urine, serum, lymph, tumor, saliva, anal secretions, vaginal secretions, amniotic samples, perspiration, semen, environmental samples or culture samples. The insert region can be isolated from any organ, including head, neck, brain, breast, ovary, cervix, colon, rectum, endometrium, gallbladder, intestines, bladder, prostate, testicles, liver, lung, kidney, esophagus, pancreas, thyroid, pituitary, thymus, skin, heart, larynx, or other organs.

[0344] The linear double stranded nucleic acid fragments (100) can be prepared using recombinant nucleic acid technology including, but not limited to, any combination of vector cloning, transgenic host cell preparation, host cell culturing and / or PCR amplification.

[0345] The double stranded nucleic acid molecules can be in fragmented or unfragmented form. Fragmented nucleic acids can be obtained, for example, by mechanical force, enzymatic or chemical fragmentation methods. The fragmented nucleic acids can be generated using procedures that yield a population of fragments having overlapping sequences or non-overlapping sequences.

[0346] Mechanical fragmentation typically generates randomly fragmented nucleic acid molecules. Mechanical fragmentation methods include mechanical shearing such as fluid shear, constant shear and pulsatile shear. Mechanical fragmentation methods also include mechanical stress including sonication, nebulization and acoustic cavitation. In some embodiments focused acoustic energy can be used to randomly fragment nucleic acid molecules. A commercially-available apparatus (e.g., CORVARIS) can be used to fragment nucleic acid molecules using focused acoustic energy.

[0347] Enzymatic fragmentation procedures can be conducted under conditions suitable to generate randomly or non-randomly fragmented nucleic acid molecules. For example, restriction endonuclease enzyme digestion can be conducted to completion to generate non- randomly fragmented nucleic acid molecule. Alternatively, partial or incomplete restriction enzyme digestion can be conducted to generate randomly-fragmented nucleic acid molecules. Enzymatic fragmentation using restriction endonuclease enzymes includes any one or any combination of two or more restriction enzymes selected from a group consisting of type I, type II, type Ils, type IIB, type III, or type IV restriction enzymes. Enzymatic fragmentation generally includes digestion of the nucleic acid with a rare-cutting restriction enzyme, e.g., Not I, Asc I, Bae I, AspC I, Pac I, Fse I, Sap I, Sfi I or Psr I. Enzymatic fragmentation include use of any combination of a nicking restriction endonuclease, endonuclease and / or exonuclease. Enzymatic fragmentation can be achieved by conducting a nick translation reaction.

[0348] In some embodiments, enzymatic fragmentation can be achieved by reacting nucleic acids with an enzyme mixture, for example an enzyme that generates single- stranded nicks and another enzyme that catalyzes double-stranded cleavage. An exemplary enzyme mixture is FRAGMENTASE (e.g., from New England Biolabs).

[0349] Fragmented nucleic acids can be generated with PCR using sequence-specific primers that hybridize to target regions in the input DNA samples to generate insert regions having known fragment lengths and sequences.

[0350] Targeted fragmentation methods using CRISPR / Cas9 can be used to generate fragmented insert regions from genomic DNA or other sources of input DNA.

[0351] Fragmented nucleic acids can also be generated using a transposase-based tagmentation method using NEXTERA (from Epicentre).

[0352] In some embodiments, input DNA can be fragmented using a Tn5 transposase- based workflow that employs a transposon end sequence comprising a double-stranded DNA having sequences that can bind a transposase enzyme to form a DNA-transposase complex (e.g. , a transpososome), where the complex can transpose / insert the transposon end sequences into DNA in an in vitro tagmentation reaction. The transposon end sequence comprises a first and second DNA strand. In some embodiments, the first DNA strand comprises a 19 base transfer end sequence 5 'AG AT GT GT AT A AG AG AC AG 3' (SEQ ID NO:31). The second DNA strand comprises a 19 base non-transfer end sequence 5' CTGTCTCTTATACACATCT 3' (SEQ ID NO:32) which can be phosphorylated at its 5’ end.

[0353] When it is desirable to fragment input DNA and append adaptors using the Tn5 transposase-based workflow (e.g., tagmentation workflow), the first transposon DNA strand further comprises a first strand of an adaptor sequence. In some embodiments, the second transposon DNA strand further comprises a second strand of an adaptor sequence. In some embodiments, the first and second adaptor sequences are fully complementary along their lengths thereby forming a linear double-stranded transposon-end-adaptor molecule. In some embodiments, the first and second adaptor sequences are partially complementary along their lengths thereby forming a Y-shaped double-stranded transposon-end-adaptor molecule. In some embodiments, the Y-shaped double-stranded transposon-end-adaptor molecule can be full length or stubby Y-shaped adaptors.

[0354] In some embodiments, a plurality of Tn5 transposases and a plurality of doublestranded transposon-end-adaptor molecules can be mixed together under conditions suitable to bind / load the double-stranded transposon-end-adaptor molecules onto the transposase enzymes to form a plurality of DNA-transposase complexes (e.g., transpososomes).

[0355] In some embodiments, input DNA (e.g., double-stranded DNA) can be mixed with a plurality of transpososomes under a condition suitable for transposing / inserting the transposon end sequences into random sites in the input DNA which fragments the input DNA and covalently attaches the transferred end sequence to the 5’ end of one strand of theinput DNA, and the non-transferred end sequence is hybridized to the transferred end sequence with a gap (e.g., 9 base gap) at the 3’ end of the complementary input DNA strand. The gap can be subjected to a polym erase-catalyzed fill-in reaction and enzymatic ligation to generate tagmented double-stranded DNA with no gaps and carrying adaptors at both ends. The transposase-based tagmentation workflow can be conducted using any of the methods described in U.S. Patent Nos. 10,184,122, 10,287,574, 11,028,438, and published U.S. application No. 2019 / 0194737, the contents of each of which are incorporated by reference in their entireties.

[0356] In some embodiments, any of the fragmentation methods described above can be used to generate DNA fragments having one or both ends that are blunt-ended, or have a 5’ overhang end, or have a 3 ’ overhang end, or any combination thereof.

[0357] In some embodiments, the fragmented nucleic acids can be subjected to enzymatic reactions for end-repair and / or A-tailing. One or both ends of the fragmented nucleic acids can be subjected to an enzymatic tailing reaction to generate a non-template A tail by employing a terminal transferase reaction as described herein. The fragmented nucleic acids can be contacted with a plurality of enzymes under a condition suitable to generate nucleic acid fragments having blunt ended 5’ phosphorylated ends. In some embodiments, the plurality of enzymes generates blunt-ended fragments having a non-template A-tail at their 3’ ends. The plurality of enzymes comprises two or more enzymes that can catalyze nucleic acid end-repair, phosphorylation and / or A-tailing. The end-repair enzymes include a DNA polymerase (e.g., T4 DNA polymerase) and KI enow fragment. The 5’ end phosphorylation enzyme comprises T4 polynucleotide kinase. The A-tailing enzyme includes a Taq polymerase (e.g., non-proof-reading polymerase) and dATP. In some embodiments, the fragmenting, end-repair, phosphorylation and A-tailing can be conducted in a one-pot reaction using a mixture of enzymes. The ends of the fragmented nucleic acids can be compatible for joining to at least one adaptor.

[0358] The fragmented nucleic acids can be any length, for example about 50-250, or about 250-500, or about 500-750, or about 750-1000 bases or base pairs in length. The fragmented nucleic acids can be 50-5000 bases or base pairs in length.

[0359] The linear fragmented nucleic acids (100) (the “fragments”) containing the insert region can be subjected to a size selection process. Alternatively, the fragments are not size selected. For example, the fragments can be size selected by gel electrophoresis and gel slice extraction. The fragments can be size selected using a solid phase adherence / immobilization method which typically employs micro paramagnetic beads coated with a chemical functionalgroup that interacts with nucleic acids under certain ionic strength conditions with or without polyethylene glycol or polyalkylene glycol. Commercially-available solid phase adherence beads include SPRI (Solid Phase Reversible Immobilization) beads from Beckman Coulter (AMPUR XP paramagnetic beads, catalog No. B23318), MAGNA PURE magnetic glass particles (Roche Diagnostics, catalog No. 03003990001), MAGNASIL paramagnetic beads from Promega (catalog No. MD1360), MAGTRATION paramagnetic beads and system from Precision System Science (catalog Nos. Al 120 and A1060), MAG-BIND from Omega Bio- Tek (catalog No. M1378-01), MAGPREP silica from Millapore (catalog No. 101193), SNARE DNA purification systems from Bangs Laboratories (catalog Nos. BP691, BP692 and BP693), and CHEMAGEN M-PVA beads from Perkin Elmer (catalog No. CMG-200).Supports with Low Non-Specific Binding Coatings

[0360] In some aspects, the present disclosure provides compositions and methods for sequencing, which employ a support having a plurality of surface primers immobilized thereon. In some embodiments, the support is passivated with a low non-specific binding coating. The surface coatings described herein can exhibit very low non-specific binding to reagents typically used for nucleic acid capture, amplification and sequencing workflows, such as dyes, nucleotides, enzymes, and nucleic acid primers. The surface coatings exhibit low background fluorescence signals or high contrast-to-noise (CNR) ratios compared to conventional surface coatings.

[0361] In general, the supports can comprise a substrate (or support structure), one or more layers of a covalently or non-covalently attached low-binding, chemical modification layers, e.g., silane layers, polymer films, and one or more covalently or non-covalently attached primer sequences that may be used for tethering single-stranded target nucleic acid(s) to the support surface. In some embodiments, the formulation of the surface, e.g., the chemical composition of one or more layers, the coupling chemistry used to cross-link the one or more layers to the support surface and / or to each other, and the total number of layers, may be varied such that non-specific binding of proteins, nucleic acid molecules, and other hybridization and amplification reaction components to the support surface is minimized or reduced relative to a comparable monolayer. Often, the formulation of the surface may be varied such that non-specific hybridization on the support surface is minimized or reduced relative to a comparable monolayer. The formulation of the surface may be varied such that non-specific amplification on the support surface is minimized or reduced relative to a comparable monolayer. The formulation of the surface may be varied such that specificamplification rates and / or yields on the support surface are maximized. Amplification levels suitable for detection are generally achieved in no more than 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, or more than 30 amplification cycles in methods disclosed herein.

[0362] The substrate or support structure that comprises the one or more chemically- modified layers, e.g., layers of a low non-specific binding polymer, may be independent or integrated into another structure or assembly. For example, in some embodiments, the substrate or support structure may comprise one or more surfaces within an integrated or assembled microfluidic flow cell. The substrate or support structure may comprise one or more surfaces within a microplate format, e.g., the bottom surface of the wells in a microplate. In some embodiments, the substrate or support structure comprises the interior surface (such as the lumen surface) of a capillary. In some embodiments, the substrate or support structure comprises the interior surface (such as the lumen surface) of a capillary etched into a planar chip.

[0363] The attachment chemistry used to graft a first chemically-modified layer to a surface will generally be dependent on both the material from which the surface is fabricated and the chemical nature of the layer. In some embodiments, the first layer may be covalently attached to the surface. In some embodiments, the first layer may be non-covalently attached, e.g., adsorbed to the surface through non-covalent interactions such as electrostatic interactions, hydrogen bonding, or van der Waals interactions between the surface and the molecular components of the first layer. In some embodiments, the substrate surface may be treated prior to attachment or deposition of the first layer. Any of a variety of surface preparation techniques known to those of skill in the art may be used to clean or treat the surface. For example, glass or silicon surfaces may be acid-washed using a Piranha solution (a mixture of sulfuric acid (H2SO4) and hydrogen peroxide (H2O2)), base treatment in KOH and NaOH, and / or cleaned using an oxygen plasma treatment method.

[0364] Silane chemistries constitute one non-limiting approach for covalently modifying the silanol groups on glass or silicon surfaces to attach more reactive functional groups (e.g., amines or carboxyl groups), which may then be used in coupling linker molecules (e.g, linear hydrocarbon molecules of various lengths, such as C6, C12, C18 hydrocarbons, or linear polyethylene glycol (PEG) molecules) or layer molecules (e.g, branched PEG molecules or other polymers) to the surface. Examples of suitable silanes that may be used in creating any of the disclosed low binding surfaces include, but are not limited to, (3 -Aminopropyl) trimethoxy silane (APTMS), (3 -Aminopropyl) tri ethoxy silane (APTES), any of a variety of PEG-silanes (e.g., comprising molecular weights of IK, 2K, 5K, 10K, 20K, etc.), amino-PEGsilane (i.e., comprising a free amino functional group), maleimide-PEG silane, biotin-PEG silane, and the like.

[0365] Any of a variety of molecules known to those of skill in the art including, but not limited to, amino acids, peptides, nucleotides, oligonucleotides, other monomers or polymers, or combinations thereof may be used in creating the one or more chemically-modified layers on the surface, where the choice of components used may be varied to alter one or more properties of the surface, e.g., the surface density of functional groups and / or tethered oligonucleotide primers, the hydrophilicity / hydrophobicity of the surface, or the three three- dimensional nature (i.e., “thickness”) of the surface. Examples of preferred polymers that may be used to create one or more layers of low non-specific binding material in any of the disclosed surfaces include, but are not limited to, polyethylene glycol (PEG) of various molecular weights and branching structures, streptavidin, polyacrylamide, polyester, dextran, poly-lysine, and poly-lysine copolymers, or any combination thereof. Examples of conjugation chemistries that may be used to graft one or more layers of material (e.g. polymer layers) to the surface and / or to cross-link the layers to each other include, but are not limited to, biotin-streptavidin interactions (or variations thereof), his tag - Ni / NTA conjugation chemistries, methoxy ether conjugation chemistries, carboxylate conjugation chemistries, amine conjugation chemistries, NHS esters, maleimides, thiol, epoxy, azide, hydrazide, alkyne, isocyanate, and silane.

[0366] The low non-specific binding surface coating may be applied uniformly across the substrate. Alternately, the surface coating may be patterned, such that the chemical modification layers are confined to one or more discrete regions of the substrate. For example, the surface may be patterned using photolithographic techniques to create an ordered array or random pattern of chemically-modified regions on the surface. Alternately or in combination, the substrate surface may be patterned using, e.g., contact printing and / or ink-jet printing techniques. In some embodiments, an ordered array or random patter of chemically-modified regions may comprise at least 1, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, or 10,000 or more discrete regions.

[0367] In order to achieve low nonspecific binding surfaces, hydrophilic polymers may be nonspecifically adsorbed or covalently grafted to the surface. Typically, passivation is performed utilizing poly(ethylene glycol) (PEG, also known as polyethylene oxide (PEO) or polyoxyethylene) or other hydrophilic polymers with different molecular weights and end groups that are linked to a surface using, for example, silane chemistry. The end groups distalfrom the surface can include, but are not limited to, biotin, methoxy ether, carboxylate, amine, NHS ester, maleimide, and bis-silane. In some embodiments, two or more layers of a hydrophilic polymer, e.g., a linear polymer, branched polymer, or multi -branched polymer, may be deposited on the surface. In some embodiments, two or more layers may be covalently coupled to each other or internally cross-linked to improve the stability of the resulting surface. In some embodiments, oligonucleotide primers with different base sequences and base modifications (or other biomolecules, e.g., enzymes or antibodies) may be tethered to the resulting surface layer at various surface densities. In some embodiments, for example, both surface functional group density and oligonucleotide concentration may be varied to target a certain primer density range. Additionally, primer density can be controlled by diluting oligonucleotide with other molecules that carry the same functional group. For example, amine-labeled oligonucleotide can be diluted with amine-labeled polyethylene glycol in a reaction with an NHS-ester coated surface to reduce the final primer density. Primers with different lengths of linker between the hybridization region and the surface attachment functional group can also be applied to control surface density. Examples of suitable linkers include poly-T and poly- A strands at the 5’ end of the primer (e.g., 0 to 20 bases), PEG linkers (e.g., 3 to 20 monomer units), and carbon-chain (e.g., C6, C12, C18, etc.). To measure the primer density, fluorescently-labeled primers may be tethered to the surface and a fluorescence reading then compared with that for a dye solution of known concentration.

[0368] In order to scale primer surface density and add additional dimensionality to hydrophilic or amphoteric surfaces, surfaces comprising multi-layer coatings of PEG and other hydrophilic polymers have been developed. By using hydrophilic and amphoteric surface layering approaches that include, but are not limited to, the polymer / co-polymer materials described below, it is possible to increase primer loading density on the surface significantly. Traditional PEG coating approaches use monolayer primer deposition, which have been generally reported for single molecule applications, but do not yield high copy numbers for nucleic acid amplification applications. As described herein “layering” can be accomplished using traditional crosslinking approaches with any compatible polymer or monomer subunits such that a surface comprising two or more highly crosslinked layers can be built sequentially. Examples of suitable polymers include, but are not limited to, streptavidin, poly acrylamide, polyester, dextran, poly-lysine, and copolymers of poly-lysine and PEG. In some embodiments, the different layers may be attached to each other through any of a variety of conjugation reactions including, but not limited to, biotin-streptavidinbinding, azide-alkyne click reaction, amine-NHS ester reaction, thiol-maleimide reaction, and ionic interactions between positively charged polymer and negatively charged polymer. In some embodiments, high primer density materials may be constructed in solution and subsequently layered onto the surface in multiple steps.

[0369] As noted, the low non-specific binding coatings of the present disclosure exhibit reduced non-specific binding of proteins, nucleic acids, and other components of the hybridization and / or amplification formulation used for solid-phase nucleic acid amplification. The degree of non-specific binding exhibited by a given support surface may be assessed either qualitatively or quantitatively. For example, in some embodiments, exposure of the surface to fluorescent dyes (e.g., cyanine dyes such as Cy3, or Cy5, etc., fluoresceins, coumarins, rhodamines, etc., or other dyes disclosed herein), fluorescently- labeled nucleotides, fluorescently-labeled oligonucleotides, and / or fluorescently-labeled proteins (e.g., polymerases) under a standardized set of conditions, followed by a specified rinse protocol and fluorescence imaging may be used as a qualitative tool for comparison of non-specific binding on supports comprising different surface formulations. In some embodiments, exposure of the surface to fluorescent dyes, fluorescently-labeled nucleotides, fluorescently-labeled oligonucleotides, and / or fluorescently-labeled proteins (e.g., polymerases) under a standardized set of conditions, followed by a specified rinse protocol and fluorescence imaging may be used as a quantitative tool for comparison of non-specific binding on supports comprising different surface formulations - provided that care has been taken to ensure that the fluorescence imaging is performed under a condition where fluorescence signal is linearly related (or related in a predictable manner) to the number of fluorophores on the support surface (e.g., under a condition where signal saturation and / or self-quenching of the fluorophore is not an issue) and suitable calibration standards are used. In some embodiments, other techniques known to those of skill in the art, for example, radioisotope labeling and counting methods, may be used for quantitative assessment of the degree to which non-specific binding is exhibited by the different support surface formulations of the present disclosure.

[0370] Some surfaces disclosed herein exhibit a ratio of specific to nonspecific binding of a fluorophore such as Cy3 of at least 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 25, 30, 35, 40, 50, 75, 100, or greater than 100, or any intermediate value spanned by the range herein. Some surfaces disclosed herein exhibit a ratio of specific to nonspecific fluorescence of a fluorophore such as Cy3 of at least 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,15, 16, 17, 18, 19, 20, 25, 30, 35, 40, 50, 75, 100, or greater than 100, or any intermediate value spanned by the range herein.

[0371] As noted, in some embodiments, the degree of non-specific binding exhibited by the disclosed low-binding supports may be assessed using a standardized protocol for contacting the surface with a labeled protein (e.g., bovine serum albumin (BSA), streptavidin, a DNA polymerase, a reverse transcriptase, a helicase, a single-stranded binding protein (SSB), etc., or any combination thereof), a labeled nucleotide, a labeled oligonucleotide, etc., under a standardized set of incubation and rinse conditions, followed be detection of the amount of label remaining on the surface and comparison of the signal resulting therefrom to an appropriate calibration standard. In some embodiments, the label may comprise a fluorescent label. In some embodiments, the label may comprise a radioisotope. In some embodiments, the label may comprise any other detectable label known to one of skill in the art. In some embodiments, the degree of non-specific binding exhibited by a given support surface formulation may thus be assessed in terms of the number of non-specifically bound protein molecules (or other molecules) per unit area. In some embodiments, the low-binding supports of the present disclosure may exhibit non-specific protein binding (or non-specific binding of other specified molecules, (e.g., cyanine dyes such as Cy3, or Cy5, etc., fluoresceins, coumarins, rhodamines, etc. or other dyes disclosed herein)) of less than 0.001 molecule per pm2, less than 0.01 molecule per pm2, less than 0.1 molecule per pm2, less than 0.25 molecule per pm2, less than 0.5 molecule per pm2, less than 1 molecule per pm2, less than 10 molecules per pm2, less than 100 molecules per pm2, or less than 1,000 molecules per pm2. Those of skill in the art will realize that a given support surface of the present disclosure may exhibit non-specific binding falling anywhere within this range, for example, of less than 86 molecules per pm2. For example, some modified surfaces disclosed herein exhibit nonspecific protein binding of less than 0.5 molecule / pm2following contact with a 1 pM solution of Cy3 labeled streptavidin (GE Amersham®) in phosphate buffered saline (PBS) buffer for 15 minutes, followed by 3 rinses with deionized water. Some modified surfaces disclosed herein exhibit nonspecific binding of Cy3 dye molecules of less than 0.25 molecules per pm2. In independent nonspecific binding assays, 1 pM labeled Cy3 SA (ThermoFisher), 1 pM Cy5 SA dye (ThermoFisher), 10 pM Aminoallyl-dUTP - ATTO-647N (Jena Biosciences), 10 pM Aminoallyl-dUTP - ATTO-Rhol l (Jena Biosciences), 10 pM Aminoallyl-dUTP - ATTO-Rho 11 (Jena Biosciences), 10 pM 7-Propargylamino-7-deaza- dGTP - Cy5 (Jena Biosciences, and 10 pM 7-Propargylamino-7-deaza-dGTP - Cy3 (Jena Biosciences) were incubated on the low binding substrates at 37°C for 15 minutes in a 384well plate format. Each well was rinsed 2-3 x with 50 uL deionized RNase / DNase Free water and 2-3 x with 25 mM ACES buffer pH 7.4. The 384 well plates were imaged on a GE Typhoon instrument using the Cy3, AF555, or Cy5 filter sets (according to dye test performed) as specified by the manufacturer at a PMT gain setting of 800 and resolution of 50-100 pm. For higher resolution imaging, images were collected on an Olympus 1X83 microscope (Olympus Corp., Center Valley, PA) with a total internal reflectance fluorescence (TIRF) objective (100X, 1.5 NA, Olympus), a CCD camera (e.g., an Olympus EM-CCD monochrome camera, Olympus XM-10 monochrome camera, or an Olympus DP80 color and monochrome camera), an illumination source (e.g., an Olympus 100W Hg lamp, an Olympus 75W Xe lamp, or an Olympus U-HGLGPS fluorescence light source), and excitation wavelengths of 532 nm or 635 nm. Dichroic mirrors were purchased from Semrock (IDEX Health & Science, LLC, Rochester, New York), e.g., 405, 488, 532, or 633 nm dichroic reflectors / beamsplitters, and band pass filters were chosen as 532 LP or 645 LP concordant with the appropriate excitation wavelength. Some modified surfaces disclosed herein exhibit nonspecific binding of dye molecules of less than 0.25 molecules per pm2.

[0372] In some embodiments, the surfaces disclosed herein exhibit a ratio of specific to nonspecific binding of a fluorophore such as Cy3 of at least 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 25, 30, 35, 40, 50, 75, 100, or greater than 100, or any intermediate value spanned by the range herein. In some embodiments, the surfaces disclosed herein exhibit a ratio of specific to nonspecific fluorescence signals for a fluorophore such as Cy3 of at least 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 25, 30, 35, 40, 50, 75, 100, or greater than 100, or any intermediate value spanned by the range herein.

[0373] The low-background surfaces consistent with the disclosure herein may exhibit specific dye attachment (e.g., Cy3 attachment) to non-specific dye adsorption (e.g., Cy3 dye adsorption) ratios of at least 4:1, 5: 1, 6: 1, 7: 1, 8: 1, 9: 1, 10: 1, 15: 1, 20: 1, 30: 1, 40: 1, 50: 1, or more than 50 specific dye molecules attached per molecule nonspecifically adsorbed. Similarly, when subjected to an excitation energy, low-background surfaces consistent with the disclosure herein to which fluorophores, e.g., Cy3, have been attached may exhibit ratios of specific fluorescence signal (e.g., arising from Cy3-labeled oligonucleotides attached to the surface) to non-specific adsorbed dye fluorescence signals of at least 4: 1, 5: 1, 6: 1, 7: 1, 8: 1, 9: 1, 10: 1, 15: 1, 20: 1, 30: 1, 40: 1, 50: 1, or more than 50:1.

[0374] In some embodiments, the degree of hydrophilicity (or “wettability” with aqueous solutions) of the disclosed support surfaces may be assessed, for example, through themeasurement of water contact angles in which a small droplet of water is placed on the surface and its angle of contact with the surface is measured using, e.g., an optical tensiometer. In some embodiments, a static contact angle may be determined. In some embodiments, an advancing or receding contact angle may be determined. In some embodiments, the water contact angle for the hydrophilic, low-binding support surface disclosed herein may range from about 0 degrees to about 30 degrees. In some embodiments, the water contact angle for the hydrophilic, low-binding support surfaced disclosed herein may no more than 50 degrees, 40 degrees, 30 degrees, 25 degrees, 20 degrees, 18 degrees, 16 degrees, 14 degrees, 12 degrees, 10 degrees, 8 degrees, 6 degrees, 4 degrees, 2 degrees, or 1 degree. In many cases the contact angle is no more than 40 degrees. Those of skill in the art will realize that a given hydrophilic, low-binding support surface of the present disclosure may exhibit a water contact angle having a value of anywhere within this range.

[0375] In some embodiments, the hydrophilic surfaces disclosed herein facilitate reduced wash times for bioassays, often due to reduced nonspecific binding of biomolecules to the low-binding surfaces. In some embodiments, adequate wash steps may be performed in less than 60, 50, 40, 30, 20, 15, 10, or less than 10 seconds. For example, in some embodiments adequate wash steps may be performed in less than 30 seconds.

[0376] The low-binding surfaces of the present disclosure exhibit significant improvement in stability or durability to prolonged exposure to solvents and elevated temperatures, or to repeated cycles of solvent exposure or changes in temperature. For example, in some embodiments, the stability of the disclosed surfaces may be tested by fluorescently labeling a functional group on the surface, or a tethered biomolecule (e.g., an oligonucleotide primer) on the surface, and monitoring fluorescence signal before, during, and after prolonged exposure to solvents and elevated temperatures, or to repeated cycles of solvent exposure or changes in temperature. In some embodiments, the degree of change in the fluorescence used to assess the quality of the surface may be less than 1%, 2%, 3%, 4%, 5%, 10%, 15%, 20%, or 25% over a time period of 1 minute, 2 minutes, 3 minutes, 4 minutes, 5 minutes, 10 minutes, 20 minutes, 30 minutes, 40 minutes, 50 minutes, 60 minutes, 2 hours, 3 hours, 4 hours, 5 hours, 6 hours, 7 hours, 8 hours, 9 hours, 10 hours, 15 hours, 20 hours, 25 hours, 30 hours, 35 hours, 40 hours, 45 hours, 50 hours, or 100 hours of exposure to solvents and / or elevated temperatures (or any combination of these percentages as measured over these time periods). In some embodiments, the degree of change in the fluorescence used to assess the quality of the surface may be less than 1%, 2%, 3%, 4%, 5%, 10%, 15%, 20%, or 25% over 5 cycles, 10 cycles, 20 cycles, 30 cycles, 40 cycles, 50 cycles, 60 cycles,70 cycles, 80 cycles, 90 cycles, 100 cycles, 200 cycles, 300 cycles, 400 cycles, 500 cycles, 600 cycles, 700 cycles, 800 cycles, 900 cycles, or 1,000 cycles of repeated exposure to solvent changes and / or changes in temperature (or any combination of these percentages as measured over this range of cycles).

[0377] In some embodiments, the surfaces disclosed herein may exhibit a high ratio of specific signal to nonspecific signal or other background. For example, when used for nucleic acid amplification, some surfaces may exhibit an amplification signal that is at least 4, 5, 6, 7, 8, 9, 10, 15, 20, 30, 40, 50, 75, 100, or greater than 100-fold greater than a signal of an adjacent unpopulated region of the surface. Similarly, some surfaces exhibit an amplification signal that is at least 4, 5, 6, 7, 8, 9, 10, 15, 20, 30, 40, 50, 75, 100, or greater than 100-fold greater than a signal of an adjacent amplified nucleic acid population region of the surface.

[0378] In some embodiments, fluorescence images of the disclosed low background surfaces when used in nucleic acid hybridization or amplification applications to create clusters of hybridized or clonally-amplified nucleic acid molecules (e.g., that have been directly or indirectly labeled with a fluorophore) exhibit contrast-to-noise ratios (CNRs) of at least 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 20, 210, 220, 230, 240, 250, or greater than 250.

[0379] One or more types of primer (e.g., capture oligonucleotides and / or circularization oligonucleotides) may be attached or tethered to the support surface. In some embodiments, the one or more types of adapters or primers may comprise spacer sequences, adapter sequences for hybridization to adapter-ligated target library nucleic acid sequences, forward amplification primers, reverse amplification primers, sequencing primers, and / or molecular barcoding sequences, or any combination thereof. In some embodiments, 1 primer or adapter sequence may be tethered to at least one layer of the surface. In some embodiments, at least 2, 3, 4, 5, 6, 7, 8, 9, 10, or more than 10 different primer or adapter sequences may be tethered to at least one layer of the surface.

[0380] In some embodiments, the tethered adapter and / or primer sequences may range in length from about 10 nucleotides to about 100 nucleotides. In some embodiments, the tethered adapter and / or primer sequences may be at least 10, at least 20, at least 30, at least 40, at least 50, at least 60, at least 70, at least 80, at least 90, or at least 100 nucleotides in length. In some embodiments, the tethered adapter and / or primer sequences may be at most 100, at most 90, at most 80, at most 70, at most 60, at most 50, at most 40, at most 30, at most 20, or at most 10 nucleotides in length. Any of the lower and upper values described in thisparagraph may be combined to form a range included within the present disclosure, for example, in some embodiments the length of the tethered adapter and / or primer sequences may range from about 20 nucleotides to about 80 nucleotides. Those of skill in the art will recognize that the length of the tethered adapter and / or primer sequences may have any value within this range, e.g., about 24 nucleotides.

[0381] In some embodiments, the resultant surface density of primers on the low binding support surfaces of the present disclosure may range from about 100 primer molecules per pm2to about 100,000 primer molecules per pm2. In some embodiments, the resultant surface density of primers on the low binding support surfaces of the present disclosure may range from about 100,000 primer molecules per pm2to about 1015primer molecules per pm2. In some embodiments, the surface density of primers may be at least 1,000, at least 10,000, at least 100,000, or at least 1015primer molecules per pm2. In some embodiments, the surface density of primers may be at most 10,000, at most 100,000, at most 1,000,000, or at most 1015primer molecules per pm2. Any of the lower and upper values described in this paragraph may be combined to form a range included within the present disclosure, for example, in some embodiments the surface density of primers may range from about 10,000 molecules per pm2to about 1015molecules per pm2. Those of skill in the art will recognize that the surface density of primer molecules may have any value within this range, e.g., about 455,000 molecules per pm2. In some embodiments, the surface density of target library nucleic acid sequences initially hybridized to adapter or primer sequences on the support surface may be less than or equal to that indicated for the surface density of tethered primers. In some embodiments, the surface density of clonally-amplified target library nucleic acid sequences hybridized to adapter or primer sequences on the support surface may span the same range as that indicated for the surface density of tethered primers.

[0382] Local densities as listed above do not preclude variation in density across a surface, such that a surface may comprise a region having an oligo density of, for example, 500,000 per pm2, while also comprising at least a second region having a substantially different local density.

[0383] The low non-specific binding coating comprise one or more layers of a multilayered surface coating may comprise a branched polymer or may be linear. Examples of suitable branched polymers include, but are not limited to, branched PEG, branched poly(vinyl alcohol) (branched PVA), branched poly(vinyl pyridine), branched poly(vinyl pyrrolidone) (branched PVP), branched ), poly(acrylic acid) (branched PAA), branched polyacrylamide, branched poly(N-isopropylacrylamide) (branched PNIPAM), branchedpoly(methyl methacrylate) (branched PMA), branched poly(2 -hydroxylethyl methacrylate) (branched PHEMA), branched poly(oligo(ethylene glycol) methyl ether methacrylate) (branched POEGMA), branched polyglutamic acid (branched PGA), branched poly-lysine, branched poly-glucoside, and dextran.

[0384] In some embodiments, the branched polymers used to create one or more layers of any of the multi-layered surfaces disclosed herein may comprise at least 4 branches, at least 5 branches, at least 6 branches, at least 7 branches, at least 8 branches, at least 9 branches, at least 10 branches, at least 12 branches, at least 14 branches, at least 16 branches, at least 18 branches, at least 20 branches, at least 22 branches, at least 24 branches, at least 26 branches, at least 28 branches, at least 30 branches, at least 32 branches, at least 34 branches, at least 36 branches, at least 38 branches, or at least 40 branched.

[0385] Linear, branched, or multi-branched polymers used to create one or more layers of any of the multi-layered surfaces disclosed herein may have a molecular weight of at least 500, at least 1,000, at least 2,000, at least 3,000, at least 4,000, at least 5,000, at least 10,000, at least 15,000, at least 20,000, at least 25,000, at least 30,000, at least 35,000, at least 40,000, at least 45,000, or at least 50,000 daltons.

[0386] In some embodiments, e.g., wherein at least one layer of a multi-layered surface comprises a branched polymer, the number of covalent bonds between a branched polymer molecule of the layer being deposited and molecules of the previous layer may range from about one covalent linkage per molecule to about 32 covalent linkages per molecule. In some embodiments, the number of covalent bonds between a branched polymer molecule of the new layer and molecules of the previous layer may be at least 1, at least 2, at least 3, at least 4, at least 5, at least 6, at least 7, at least 8, at least 9, at least 10, at least 12, at least 14, at least 16, at least 18, at least 20, at least 22, at least 24, at least 26, at least 28, at least 30, or at least 32 covalent linkages per molecule.

[0387] Any reactive functional groups that remain following the coupling of a material layer to the surface may optionally be blocked by coupling a small, inert molecule using a high yield coupling chemistry. For example, in the case that amine coupling chemistry is used to attach a new material layer to the previous one, any residual amine groups may subsequently be acetylated or deactivated by coupling with a small amino acid such as glycine.

[0388] The number of layers of low non-specific binding material, e.g., a hydrophilic polymer material, deposited on the surface, may range from 1 to about 10. In some embodiments, the number of layers is at least 1, at least 2, at least 3, at least 4, at least 5, atleast 6, at least 7, at least 8, at least 9, or at least 10. In some embodiments, the number of layers may be at most 10, at most 9, at most 8, at most 7, at most 6, at most 5, at most 4, at most 3, at most 2, or at most 1. Any of the lower and upper values described in this paragraph may be combined to form a range included within the present disclosure, for example, in some embodiments the number of layers may range from about 2 to about 4. In some embodiments, all of the layers may comprise the same material. In some embodiments, each layer may comprise a different material. In some embodiments, the plurality of layers may comprise a plurality of materials. In some embodiments at least one layer may comprise a branched polymer. In some embodiment, all of the layers may comprise a branched polymer.

[0389] One or more layers of low non-specific binding material may in some cases be deposited on and / or conjugated to the substrate surface using a polar protic solvent, a polar or polar aprotic solvent, a nonpolar solvent, or any combination thereof. In some embodiments the solvent used for layer deposition and / or coupling may comprise an alcohol (e.g., methanol, ethanol, propanol, etc.), another organic solvent (e.g., acetonitrile, dimethyl sulfoxide (DMSO), dimethyl formamide (DMF), etc.), water, an aqueous buffer solution (e.g., phosphate buffer, phosphate buffered saline, 3-(N-morpholino)propanesulfonic acid (MOPS), etc.), or any combination thereof. In some embodiments, an organic component of the solvent mixture used may comprise at least 1%, 5%, 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, 50%, 55%, 60%, 70%, 75%, 80%, 85%, 90%, 95%, 98%, or 99% of the total, with the balance made up of water or an aqueous buffer solution. In some embodiments, an aqueous component of the solvent mixture used may comprise at least 1%, 5%, 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, 50%, 55%, 60%, 70%, 75%, 80%, 85%, 90%, 95%, 98%, or 99% of the total, with the balance made up of an organic solvent. The pH of the solvent mixture used may be less than 6, about 6, 6.5, 7, 7.5, 8, 8.5, 9, or greater than pH 9.

[0390] Fluorescence imaging may be performed using any of a variety of fluorophores, fluorescence imaging techniques, and fluorescence imaging instruments known to those of skill in the art. Examples of suitable fluorescence dyes that may be used (e.g., by conjugation to nucleotides, oligonucleotides, or proteins) include, but are not limited to, fluorescein, rhodamine, coumarin, cyanine, and derivatives thereof, including the cyanine derivatives Cyanine dye-3 (Cy3), Cyanine dye-5 (Cy5), Cyanine dye-7 (Cy7), etc. Examples of fluorescence imaging techniques that may be used include, but are not limited to, fluorescence microscopy imaging, fluorescence confocal imaging, two-photon fluorescence, and the like. Examples of fluorescence imaging instruments that may be used include, butare not limited to, fluorescence microscopes equipped with an image sensor or camera, confocal fluorescence microscopes, two-photon fluorescence microscopes, or custom instruments that comprise a suitable selection of light sources, lenses, mirrors, prisms, dichroic reflectors, apertures, and image sensors or cameras, etc. A non-limiting example of a fluorescence microscope equipped for acquiring images of the disclosed low-binding support surfaces and clonally-amplified colonies (polonies) of template nucleic acid sequences hybridized thereon is the Olympus 1X83 inverted fluorescence microscope equipped with ) 20x, 0.75 NA, a 532 nm light source, a bandpass and dichroic mirror filter set optimized for 532 nm long-pass excitation and Cy3 fluorescence emission filter, a Semrock 532 nm dichroic reflector, and a camera (Andor sCMOS, Zyla 4.2) where the excitation light intensity is adjusted to avoid signal saturation. Often, the support surface may be immersed in a buffer (e.g., 25 mM ACES, pH 7.4 buffer) while the image is acquired.

[0391] In some instances, the performance of nucleic acid hybridization and / or amplification reactions using the disclosed reaction formulations and low non-specific binding supports may be assessed using fluorescence imaging techniques, where the contrast- to-noise ratio (CNR) of the images provides a key metric in assessing amplification specificity and non-specific binding on the support. CNR is commonly defined as: CNR = (Signal - Background) / Noise. The background term is commonly taken to be the signal measured for the interstitial regions surrounding a particular feature (diffraction limited spot, DLS) in a specified region of interest (ROI). While signal-to-noise ratio (SNR) is often considered to be a benchmark of overall signal quality, it can be shown that improved CNR can provide a significant advantage over SNR as a benchmark for signal quality in applications that require rapid image capture (e.g., sequencing applications for which cycle times must be minimized), as shown in the example below. The surfaces of the instant disclosure are also provided in co-pending International Application Serial No. PCT / US2019 / 061556, which is hereby incorporated by reference in its entirety.

[0392] In most ensemble-based sequencing approaches, the background term is typically measured as the signal associated with ‘interstitial’ regions. In addition to “interstitial” background (Binter), “intrastitial” background (Bintra) exists within the region occupied by an amplified DNA colony. The combination of these two background signals dictates the achievable CNR, and subsequently directly impacts the optical instrument requirements, architecture costs, reagent costs, run- times, cost / genome, and ultimately the accuracy and data quality for cyclic array -based sequencing applications. The Binter background signal arises from a variety of sources; a few examples include auto-fluorescence from consumableflow cells, non-specific adsorption of detection molecules that yield spurious fluorescence signals that may obscure the signal from the ROI, the presence of non-specific DNA amplification products (e.g., those arising from primer dimers). In typical next generation sequencing (NGS) applications, this background signal in the current field-of-view (FOV) is averaged over time and subtracted. The signal arising from individual DNA colonies (i.e., (S) - Binterin the FOV) yields a discernable feature that can be classified. In some instances, the intrastitial background (Bintra) can contribute a confounding fluorescence signal that is not specific to the target of interest, but is present in the same ROI thus making it far more difficult to average and subtract.

[0393] The implementation of nucleic acid amplification on the low-binding substrates of the present disclosure may decrease the Binter background signal by reducing non-specific binding, may lead to improvements in specific nucleic acid amplification, and may lead to a decrease in non-specific amplification that can impact the background signal arising from both the interstitial and intrastitial regions. In some instances, the disclosed low-binding support surfaces, optionally used in combination with the disclosed hybridization buffer formulations, may lead to improvements in CNR by a factor of 2, 5, 10, 100, or 1000-fold over those achieved using conventional supports and hybridization, amplification, and / or sequencing protocols. Although described here in the context of using fluorescence imaging as the read-out or detection mode, the same principles apply to the use of the disclosed low non-specific binding supports and nucleic acid hybridization and amplification formulations for other detection modes as well, including both optical and non-optical detection modes.

[0394] The disclosed low-binding supports, optionally used in combination with the disclosed hybridization and / or amplification protocols, yield solid-phase reactions that exhibit: (i) negligible non-specific binding of protein and other reaction components (thus minimizing substrate background), (ii) negligible non-specific nucleic acid amplification product, and (iii) provide tunable nucleic acid amplification reactions.

[0395] In some embodiments, fluorescence images of the disclosed low background surfaces when used in nucleic acid hybridization or amplification applications to create polonies of hybridized or clonally-amplified nucleic acid molecules (e.g., that have been directly or indirectly labeled with a fluorophore) exhibit contrast-to-noise ratios (CNRs) of at least 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 20, 210, 220, 230, 240, 250, or greater than 250.

[0396] In some embodiments, a fluorescence image of the surface exhibits a contrast-to- noise ratio (CNR) of at least 20 when a sample nucleic acid molecule or complementarysequences thereof are labeled with a Cyanine dye-3 (Cy3) fluorophore, and when the fluorescence image is acquired using an inverted fluorescence microscope (e.g., Olympus 1X83) with a 20 x 0.75 NA objective, a 532 nm light source, a bandpass and dichroic mirror filter set optimized for 532 nm excitation and Cy3 fluorescence emission, and a camera (e.g., Andor sCMOS, Zyla 4.2) under non-signal saturating conditions while the surface is immersed in a buffer (e.g., 25 mM ACES, pH 7.4 buffer).Sequencing Polymerases

[0397] The present disclosure provides methods for sequencing nucleic acid molecules, where any of the sequencing methods described herein employ at least one type of sequencing polymerase and a plurality of nucleotides, or employ at least one type of sequencing polymerase and a plurality of nucleotides and a plurality of multivalent molecules. In some embodiments, the sequencing polymerase(s) is / are capable of incorporating a complementary nucleotide opposite a nucleotide in a concatemer template molecule. In some embodiments, the sequencing polymerase(s) is / are capable of binding a complementary nucleotide moiety of a multivalent molecule opposite a nucleotide in a concatemer template molecule. In some embodiments, the plurality of sequencing polymerases comprises recombinant mutant polymerases.

[0398] Examples of suitable polymerases for use in sequencing with nucleotides and / or multivalent molecules include but are not limited to: Klenow DNA polymerase; Thermits aquaticus DNA polymerase I (Taq polymerase); KlenTaq polymerase; Candidates altiarchaeales archaeon; Candidates Hadarchaeum Yellow stonense; Hadesarchaea archaeon; Euryarchaeota archaeon; Thermoplasmata archaeon; Thermococcus polymerases such as Thermococcus litoralis, bacteriophage T7 DNA polymerase; human alpha, delta and epsilon DNA polymerases; bacteriophage polymerases such as T4, RB69 and phi29 bacteriophage DNA polymerases; Pyrococcus furiosus DNA polymerase (Pfu polymerase); Bacillus subtilis DNA polymerase III; E. coli DNA polymerase III alpha and epsilon; 9 degree N polymerase; reverse transcriptases such as HIV type M or O reverse transcriptases; avian myeloblastosis virus reverse transcriptase; Moloney Murine Leukemia Virus (MMLV) reverse transcriptase; or telomerase. Further non-limiting examples of DNA polymerases include those from various Archaea genera, such as, Aeropyrum, Archaeglobus, Desulfurococcus, Pyrobaculum, Pyrococcus, Pyrolobus, Pyrodictium, Staphylothermus, Stetteria, Sulfolobus, Thermococcus, and Vulcanisaeta and the like or variants thereof,including such polymerases as are known in the art such as 9 degrees N, VENT, DEEP VENT, THERMINATOR, Pfu, KOD, Pfx, Tgo and RB69 polymerases. The phi29 DNA polymerase can be wild type phi29 DNA polymerase (e.g., MAGNIPHI from Expedeon), or variant EQUIPHI29 DNA polymerase (e.g., from ThermoFisher Scientific), or chimeric QUALIPHI DNA polymerase (e.g., from 4basebio). Additional polymerases are described in U.S. Patent No. 11,859,241, the contents of which are incorporated by reference in their entirety herein.Nucleotides

[0399] The present disclosure provides methods for sequencing nucleic acid molecules using nucleotides, wherein at least one nucleotide in the plurality of nucleotides comprise a base, sugar and at least one phosphate group. In some embodiments, at least one nucleotide in the plurality comprises an aromatic base, a five-carbon sugar (e.g., ribose or deoxyribose), and one or more phosphate groups (e.g, 1-10 phosphate groups). The plurality of nucleotides can comprise at least one type of nucleotide selected from a group consisting of dATP, dGTP, dCTP, dTTP and dUTP. The plurality of nucleotides can comprise at a mixture of any combination of two or more types of nucleotides selected from a group consisting of dATP, dGTP, dCTP, dTTP and / or dUTP. In some embodiments, at least one nucleotide in the plurality is not a nucleotide analog. In some embodiments, at least one nucleotide in the plurality comprises a nucleotide analog.

[0400] In some embodiments, in any of the methods for sequencing nucleic acid molecules described herein, at least one nucleotide in the plurality of nucleotides comprise a chain of one, two or three phosphorus atoms where the chain is typically attached to the 5’ carbon of the sugar moiety via an ester or phosphoramide linkage. In some embodiments, at least one nucleotide in the plurality is an analog having a phosphorus chain in which the phosphorus atoms are linked together with intervening O, S, NH, methylene or ethylene. In some embodiments, the phosphorus atoms in the chain include substituted side groups including O, S or BH3. In some embodiments, the chain includes phosphate groups substituted with analogs including phosphoramidate, phosphorothioate, phosphorodithioate, and O-methylphosphoramidite groups.

[0401] In some embodiments, in any of the methods for sequencing nucleic acid molecules described herein, at least one nucleotide in the plurality of nucleotides comprises a terminator nucleotide analog having a chain terminating moiety (e.g, blocking moiety) at theI l lsugar 2’ position, at the sugar 3’ position, or at the sugar 2’ and 3’ position. In some embodiments, the chain terminating moiety can inhibit polymerase-catalyzed incorporation of a subsequent nucleotide moiety or free nucleotide in a nascent strand during a primer extension reaction. In some embodiments, the chain terminating moiety is attached to the 3’ sugar hydroxyl position where the sugar comprises a ribose or deoxyribose sugar moiety. In some embodiments, the chain terminating moiety is removable / cleavable from the 3’ sugar hydroxyl position to generate a nucleotide having a 3 ’OH sugar group which is extendible with a subsequent nucleotide in a polymerase-catalyzed nucleotide incorporation reaction. In some embodiments, the chain terminating moiety comprises an alkyl group, alkenyl group, alkynyl group, allyl group, aryl group, benzyl group, azide group, amine group, amide group, keto group, isocyanate group, phosphate group, thio group, disulfide group, carbonate group, urea group, acetal group or silyl group. In some embodiments, the chain terminating moiety is cleavable / removable from the nucleotide, for example by reacting the chain terminating moiety with a chemical agent, pH change, light or heat. In some embodiments, the chain terminating moieties alkyl, alkenyl, alkynyl and allyl are cleavable with tetrakis(triphenylphosphine)palladium(0) (Pd(PPh3)4) with piperidine, or with 2,3-Dichloro- 5,6-dicyano-l,4-benzo-quinone (DDQ). In some embodimen...

Claims

WHAT IS CLAIMED:

1. A method for forming a plurality of concatemer molecules immobilized to a support, comprising: a) providing a plurality of linear double stranded nucleic acid fragments (100), wherein a3’ end of both strands of an individual linear double-stranded nucleic acid fragment (100) comprises a terminal adenine base (“A”); b) providing a plurality of partial double stranded splint adaptors (200), wherein individual partial double stranded splint adaptors (200) in the plurality comprise a first, second and third oligonucleotide hybridized together to form a nucleic acid molecule having single stranded and double stranded portions, o wherein individual partial double stranded splint adaptors (200) comprise a first double stranded region formed by hybridization of the first and third oligonucleotides, wherein the first double stranded region can be ligated to a first end of a linear double stranded nucleic acid fragment (100), o wherein individual partial double stranded splint adaptors (200) comprise a second double stranded region formed by hybridization of the first and second oligonucleotides, wherein the second double stranded region can be ligated to a second end of the same double stranded nucleic acid fragment (100); o wherein the first oligonucleotide comprises a universal primer binding site for a surface capture primer (210)and wherein a 3’ end of the first oligonucleotide comprises a terminal thymine base (“T”); o wherein a 3’ end of the second oligonucleotide comprises a terminal thymine base (“T”); c) contacting the plurality of partial double stranded splint adaptors (200) with a plurality of linear double-stranded nucleic acid fragments (100), wherein the contacting is conducted under a condition suitable for hybridizing the terminal adenine base at the 3’ end of both strands of the linear double-stranded nucleic acid fragments (100) with the terminal thymine base at the 3’ end of the first oligonucleotide and the terminal thymine base at the 3’ end of the second oligonucleotide, thereby circularizing the double stranded nucleic acid fragments and forming a plurality of library-splint complexes (300), individuallibrary-splint complexes (300) having a first nick or gap and a second nick or gap which are enzymatically ligatable; d) contacting the plurality of library-splint complexes (300) with a plurality of DNA ligase enzymes under a condition suitable to enzymatically ligate the first and second nicks or gaps, thereby generating a plurality of covalently closed circular library molecules (400) which are partially double stranded; e) contacting the covalently closed circular library molecules (400) with an alkaline condition to generate a plurality of single stranded covalently close circular library molecules (500); f) distributing the plurality of single stranded covalently closed circular library molecules (500) onto a support having a plurality of surface capture primers immobilized on the support, wherein the distributing is conducted under a condition suitable for hybridizing individual single stranded covalently closed circular library molecules (500) to individual immobilized surface capture primers, thereby immobilizing the plurality of single stranded covalently closed circular library molecules (500) to the support; g) contacting the plurality of single stranded covalently closed circular library molecules (500) with a plurality of strand-displacing polymerases, a plurality of nucleotides and a plurality of compaction oligonucleotides, under a condition suitable to conduct a rolling circle amplification reaction on the support using the plurality of surface capture primers as amplification primers and the plurality of single stranded covalently closed circular library molecules (500) as template molecules, thereby generating the plurality of concatemer molecules immobilized to the support; and h) sequencing the plurality of concatemer molecules.

2. The method of claim 1, wherein the first double stranded region is at a first end of the partial double-stranded splint adaptor.

3. The method of claim 1 or 2, wherein the second double stranded region is at a second end of the partial double-stranded splint adaptor that is opposite the first end.

4. The method of claim 1, wherein a first end of the partial double-stranded splint adaptor comprises a 5’ overhang followed by the first double-stranded region.

5. The method of claim 1, wherein the first end of the partial double-stranded splint adaptor comprises a 3’ overhang followed by the first double-stranded region.

6. The method of claim 1, wherein the first end of the partial double-stranded splint adaptor comprises a blunt end followed by the first double-stranded region.

7. The method of claim 4, wherein a second end of the partial double-stranded splint adaptor comprises a 5’ overhang followed by the second double-stranded region, wherein the second end is opposite the first end.

8. The method of claim 4, wherein a second end of the partial double-stranded splint adaptor comprises a 3’ overhang followed by the second double-stranded region, wherein the second end is opposite the first end.

9. The method of claim 4, wherein a second end of the partial double-stranded splint adaptor comprises a blunt end followed by the second double-stranded region, wherein the second end is opposite the first end.

10. The method of any one of claims 1-9, wherein a 5’ end of the first and / or third oligonucleotide is phosphorylated.

11. The method of any one of claims 1-10, wherein the first oligonucleotide comprises a sample index sequence (230).

12. The method of any one of claims 1-11, wherein the support comprises a plurality of surface pinning primers immobilized thereon, and wherein the first oligonucleotide comprises a universal primer binding site for a surface pinning primer (220).

13. The method of any one of claims 1-12, wherein the first oligonucleotide comprises a short random sequence.

14. The method of claim 13, wherein the short random sequence is 3-6 nucleotides in length, optionally wherein the short random sequence is 3 nucleotides in length (NNN).

15. The method of claim 13 or 14, wherein the third oligonucleotide comprises a portion that can hybridize to the short random sequence of the first oligonucleotide.

16. The method of claim 15, wherein the portion of the third oligonucleotide that can hybridize to the short random sequence comprises an 18-carbon spacer, multiple C3 spacer phosphoramidites, a trimethylene glycol spacer, or a polyethylene glycol spacer.

17. The method of claim 16, wherein the 18-carbon spacer comprises a hexa-ethyleneglycol spacer.

18. The method of any one of claims 1-17, wherein a portion of the second oligonucleotide hybridizes to a portion of the first oligonucleotide.

19. The method of claim 18, wherein the portion of the second oligonucleotide that hybridizes to the portion of the first oligonucleotide hybridizes to at least a portion of the universal primer binding site for the surface capture primer (210).

20. The method of any one of claims 1-19, wherein a portion of the third oligonucleotide hybridizes to a portion of the first oligonucleotide.

21. The method of claim 20, wherein the first oligonucleotide comprises a universal primer binding site for a surface pinning primer (220), and wherein the portion of the third oligonucleotide that hybridizes to the portion of the first oligonucleotide hybridizes to a portion of the universal primer binding site for the surface pinning primer (220).

22. The method of any one of claims 1-21, wherein the third oligonucleotide comprises a sequence (231) that hybridizes to a sample index sequence (230) of the first oligonucleotide.

23. The method of any one of claims 1-22, wherein the first oligonucleotide comprises, from 5’ to 3’ : a. the universal primer binding site for the surface capture primer (210), b. a universal primer binding site for a surface pinning primer (220), c. a short random sequence, d. a sample index sequence (230), and e. a 3’ terminal thymine.

24. The method of any one of claims 1-23, wherein the second oligonucleotide comprises, from 5’ to 3’ : a. a sequence that hybridizes to at least a portion of a universal primer binding site for the surface capture primer (210), and b. a 3’ terminal thymine.

25. The method of any one of claims 1-24, wherein the third oligonucleotide comprises, from 5’ to 3’ : a. a sequence (231) that hybridizes to a sample index sequence (230) of the first oligonucleotide, b. a spacer, optionally wherein the spacer comprises an 18-carbon spacer, multiple C3 spacer phosphoramidites, a trimethylene glycol spacer, or a polyethylene glycol spacer, and c. a sequence (221) that hybridizes to a portion of a universal primer binding site for a surface pinning primer (220) of the first oligonucleotide.

26. The method of any one of claims 1-25, wherein individual linear double stranded nucleic acid fragments (100) comprise an insert sequence and the terminal adenine base at the 3’ ends of both strands.

27. The method of claim 26, wherein individual linear double stranded nucleic acid fragments (100) in the plurality comprise the same insert sequence, or comprise different insert sequences.

28. The method of any one of claims 1-27, wherein the terminal thymine bases of the first and second oligonucleotides hybridize to the terminal adenine bases at the 3’ ends of the linear double stranded nucleic acid fragments (100).

29. The method of any one of claims 1-28, wherein enzymatically ligating at step (d) comprises ligating the first and second ends of the partial double stranded splint adaptors (200) to both ends of individual linear double stranded nucleic acid fragments (100).

30. The method of claim 29, wherein individual partial double stranded splint adaptors (200) comprise 5’ overhangs at both ends, and enzymatically ligating at step (d) comprises sticky-end ligation.

31. The method of claim 29, wherein individual partial double stranded splint adaptors (200) comprise double stranded regions at both ends, and enzymatically ligating at step (d) comprises blunt-end ligation.

32. The method of any one of claims 1-31, wherein partial double-stranded splint adaptors do not include additional universal binding sites for a forward sequencing primer and a reverse sequencing primer.

33. The method of any one of claims 11-32, wherein individual sample index sequences in the plurality of partial double stranded splint adaptors (200) comprise the same sequence, or comprise different sequences.

34. The method of any one of claims 1-33, wherein individual covalently closed circular molecules comprise: a. a first insert region (110) on a first strand which is hybridized to a second insert region on a second strand (111); b. a universal primer binding site for a capture primer (210) which is hybridized to at least a portion of the second oligonucleotide (211); c. a universal primer binding site for a pinning primer (220) which is hybridized to a sequence (221) of the third oligonucleotide; d. a short random sequence; and e. a sample index sequence (230) which is hybridized to a sequence (231) of the third oligonucleotide.

35. The method of any one of claims 1-34, wherein individual concatemer molecules comprise two or more copies of: a. a universal primer binding site for a capture primer (210), b. a first insert region (110), c. a sample index sequence (230), d. a short random sequence, and e. a universal primer binding site for a surface pinning primer (220), wherein (a)-(e) can be arranged in any order.

36. The method of any one of claims 1-35, wherein the covalently closed circular library molecules are denatured at step (e), thereby generating single stranded covalently closed circular library molecules.

37. The method of any one of claims 1-36, wherein the plurality of surface capture primers is located at random and non-predetermined positions on the support, or wherein the plurality of surface capture primers is located at predetermined positions on the support.

38. The method of any one of claims 1-37, wherein a plurality of surface pinning primers is located at random and non-predetermined positions on the support, or wherein the plurality of surface pinning primers is located at predetermined positions on the support.

39. The method of any one of claims 1-38, wherein the rolling circle amplification reaction comprises a plurality of compaction oligonucleotides.

40. The method of claim 39, wherein 5’ and 3’ regions of individual compaction oligonucleotides hybridize to a concatemer molecule to pull together distal portions of the concatemer molecule, thereby causing the concatemer molecule to form a compact DNA nanoball.

41. The method of any one of claims 1-40, wherein the support is configured on a flow cell, or an interior of a capillary lumen.

42. The method of any one of claims 1-41, wherein the support comprises at least one hydrophilic polymer coating layer, and the plurality of surface capture primers are immobilized to the at least one hydrophilic polymer coating layer, and wherein the at least one hydrophilic polymer coating layer has a water contact angle of no more than 45 degrees.

43. The method of claim 42, wherein the at least one hydrophilic polymer coating layer comprises polyethylene glycol (PEG), poly(vinyl alcohol) (PVA), poly(vinylpyridine), poly(vinyl pyrrolidone) (PVP), poly(acrylic acid) (PAA), polyacrylamide, poly(N-isopropylacrylamide) (PNIPAM), poly(methyl methacrylate) (PMA), poly(2- hydroxylethyl methacrylate) (PHEMA), poly(oligo(ethylene glycol) methyl ether methacrylate) (POEGMA), polyglutamic acid (PGA), poly-lysine, poly-glucoside, streptavidin, or dextran.

44. The method of claim 42 or 43, wherein the at least one hydrophilic polymer coating layer comprises polymer molecules having a molecular weight of at least 1000 Daltons.

45. The method of any one of claims 42-44, wherein the at least one hydrophilic polymer coating layer comprises branched polymer molecules having 4-8 branches.

46. The method of any one of claims 42-45, wherein the support comprises: a) a first coating layer comprising a first monolayer of hydrophilic polymer molecules tethered to the support; b) a second coating layer comprising a second monolayer of hydrophilic polymer molecules tethered to the first monolayer; and c) a third coating layer comprising a third monolayer of hydrophilic polymer molecules tethered to the second monolayer, and wherein the hydrophilic polymer molecules of the first layer, second layer or third layer comprise branched polymer layers.

47. The method of any one of claims 42-46, wherein one or more of the at least one hydrophilic polymer coating layers comprise the plurality of surface capture primers at a surface density of least 1000 / pm2.

48. The method of any one of claims 1-47, wherein the sequencing at step (h) comprises contacting the plurality of concatemer molecules with (i) a first plurality of sequencing primers, (ii) a plurality of sequencing polymerases, and (iii) a plurality of nucleotide reagents, under conditions suitable for hybridizing sequencing primers to individual concatemer molecules to generate a plurality of nucleic acid duplexes on the individual concatemer molecules, and wherein the conditions are suitable for binding nucleic acid duplexes with sequencing polymerases and nucleotide reagents.

49. The method of claim 48, wherein the first plurality of sequencing primers is soluble.

50. The method of claim 48 or 49, wherein the first plurality of sequencing primers hybridizes to the universal primer binding site for the surface capture primer (210) or to a universal primer binding site for a surface pinning primer (220).

51. The method of any one of claims 48-50, wherein individual nucleotide reagents in the plurality of nucleotide reagents comprise an aromatic base, a five-carbon sugar and 1- 10 phosphate groups.

52. The method of any one of claims 48-51, wherein the plurality of nucleotide reagents comprises one or more types of nucleotide reagent selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

53. The method of any one of claims 48-51, wherein the plurality of nucleotide reagents comprises a combination of two or more types of nucleotide reagent selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

54. The method of any one of claims 48-53, wherein at least one nucleotide reagent in the plurality of nucleotide reagents lacks a detectable reporter moiety.

55. The method of any one of claims 48-54, wherein at least one nucleotide reagent in the plurality of nucleotide reagents is labeled with a detectable reporter moiety.

56. The method of any one of claims 48-55, wherein individual nucleotide reagents in the plurality of nucleotide reagents comprise at least one chain terminating nucleotide comprising (i) an aromatic base, (ii) a sugar having a 3’ chain terminating moiety that inhibits polymerase-catalyzed nucleotide incorporation, and (iii) 1-10 phosphate groups.

57. The method of claim 56, wherein the at least one chain terminating nucleotide comprises a removable chain terminating moiety at the 3' sugar group, and wherein the removable chain terminating moiety comprises an alkyl group, alkenyl group, alkynyl group, allyl group, aryl group, benzyl group, azide group, azido group, O- azidomethyl group, amine group, amide group, keto group, isocyanate group, phosphate group, thio group, disulfide group, carbonate group, urea group, or silyl group.

58. The method of claim 57, wherein the at the at least one chain terminating nucleotide comprises a removable chain terminating moiety at the 3' sugar group, and wherein the removable chain terminating moiety comprises a 3’-O-amino group, a 3’-O- aminom ethyl group, a 3’-O-methylamino group, or derivatives thereof.

59. The method of any one of claims 56-58, wherein the at least one chain terminating moiety is cleavable or removable with a chemical compound to generate an extendible 3' OH moiety on the sugar group.

60. The method of any one of claims 48-59, wherein the plurality of nucleotide reagents comprises at least one multivalent molecule, wherein the at least one multivalent molecule comprises: (1) a core; and (2) a plurality of nucleotide arms, individual nucleotide arms comprising (i) a core attachment moiety, (ii) a spacer comprising a PEG moiety, (iii) a linker, and (iv) a nucleotide moiety.

61. The method of any one of claims 1-47, wherein sequencing the plurality of concatemer molecules at step (h) comprises: a) contacting the plurality of concatemer molecules with (i) a first plurality of sequencing polymerases and (ii) a plurality of first sequencing primers, and wherein the contacting is conducted under conditions suitable to form a plurality of complexed polymerases comprising a sequencing polymerase bound to a nucleic acid duplex, wherein the nucleic acid duplex comprises a portion of an individual concatemer molecule hybridized to an individual first sequencing primer; b) contacting the plurality of complexed sequencing polymerases with a plurality of nucleotides under conditions suitable for binding at least one nucleotide to a complexed polymerase, wherein the nucleotides in the plurality are labeled with a detectable reporter moiety, optionally wherein the detectable reporter moiety comprises a fluorophore; c) incorporating at least one nucleotide into a 3’ end of the first sequencing primers, thereby generating a plurality of first sequencing read products by extending the first nucleic acid sequencing primers; and d) detecting the at least one nucleotide and identifying the nucleobase of the at least one nucleotide.

62. The method of claim 60, wherein the first sequencing primers are soluble.

63. The method of claim 60 or 61, wherein individual first sequencing primers hybridize to the universal primer binding site for the surface capture primer (210) or to a universal primer binding site for a surface pinning primer (220).

64. The method of any one of claims 61-63, comprising repeating steps (a)-(d) at least once.

65. The method of any one of claims 1-47, wherein the sequencing at step (h) comprises: a. contacting a first plurality of polymerases with (i) the plurality of concatemer molecules and (ii) a plurality of sequencing primers, wherein the contacting is conducted under a condition suitable to bind the first plurality of polymerases with the plurality of concatemer molecules and the plurality of sequencing primers, thereby forming a plurality of first complexed polymerases comprising a polymerase bound to a nucleic acid duplex, wherein the nucleic acid duplex comprises a concatemer molecule hybridized to a sequencing primer;b. contacting the plurality of first complexed polymerases with a plurality of multivalent molecules to form a plurality of multivalent-complexed polymerases under a condition suitable for binding complementary nucleotide moieties of the multivalent molecules to at least two of the plurality of first complexed polymerases thereby forming a plurality of multivalent-complexed polymerases, wherein at least one of the multivalent molecules in the plurality of multivalent molecules is labeled with a detectable reporter moiety, and wherein individual multivalent molecules in the plurality comprises: (1) a core; and (2) a plurality of nucleotide arms, individual nucleotide arms comprising (i) a core attachment moiety, (ii) a spacer comprising a PEG moiety, (iii) a linker, and (iv) a nucleotide moiety; c. detecting the plurality of multivalent-complexed polymerases; and d. identifying the base of the complementary nucleotide moieties that are bound to the plurality of first complexed polymerases, thereby determining sequences of the plurality of concatemer molecules.

66. The method of claim 65, wherein the sequencing primers hybridize to the universal primer binding site for the surface capture primer (210) or to a universal primer binding site for a surface pinning primer (220).

67. The method of claim 65 or 66, comprising: e. dissociating the plurality of multivalent-complexed polymerases and removing the plurality of first sequencing polymerases and their bound multivalent molecules, and retaining the nucleic acid duplexes; f. contacting the nucleic acid duplexes of step (e) with a second plurality of polymerases, wherein the contacting is conducted under a condition suitable for binding the second plurality of polymerases to the nucleic acid duplexes, thereby forming a second plurality of complexed polymerases comprising a second polymerase bound to a nucleic acid duplex; and g. contacting the second plurality of complexed polymerases with a plurality of nucleotides, wherein the contacting is conducted under a condition suitable for binding complementary nucleotides from the plurality of nucleotides to at least two of the second complexed polymerases, thereby forming a plurality of nucleotide-complexed polymerases.

68. The method of claim 67, wherein the nucleotides are labeled with a detectable reporter moiety, and the method comprises:h. detecting the complementary nucleotides which are incorporated into the sequencing primers of the nucleotide-complexed polymerases, and i. identifying the bases of the complementary nucleotides.

69. The method of claim 68, wherein nucleotides in the plurality comprise chain terminating moieties, and the method comprises: j . removing the chain terminating moieties from the incorporated nucleotides.

70. The method of claim 69, comprising repeating steps (a)-(j) at least once.

71. The method of any one of claims 1-47, wherein the sequencing at step (h) comprises contacting a plurality of polymerases, a plurality of sequencing primers, a plurality of multivalent molecules and the plurality of concatemer molecules under conditions suitable to: a. bind a first portion of a concatemer molecule with a polymerase, a sequencing primer and a first nucleotide moiety of a multivalent molecule, thereby forming a first binding complex, wherein the first nucleotide moiety of the first multivalent molecule binds to the first polymerase, and b. bind a second portion of the concatemer molecule with a second polymerase and a second nucleotide moiety of the multivalent molecule, thereby forming a second binding complex, wherein the second nucleotide moiety of the multivalent molecule binds to the second polymerase, thereby forming an avidity complex.

72. The method of claim 71, comprising: c. detecting the first and second binding complexes on the same concatemer molecule; and d. identifying the first nucleotide moiety, thereby determining the sequence of the first portion of the concatemer molecule, and identifying the second nucleotide moiety, thereby determining the sequence of the second portion of the concatemer molecule.

73. The method of claim 72, comprising: e. dissociating the plurality of polymerases and plurality of multivalent molecules, f. incorporating nucleotides into 3’ ends of sequencing primers bound to the concatemer molecules, and g. repeating steps (a)-(d) at least once.

74. The method of any one of claims 71-73, wherein the sequencing primers hybridize to the universal primer binding site for the surface capture primer (210) or to a universal primer binding site for a surface pinning primer (220).

75. The method of claim any one of claims 65-74, wherein at least one multivalent molecule comprises: (1) a core; and (2) a plurality of nucleotide arms, individual nucleotide arms comprising (i) a core attachment moiety, (ii) a spacer comprising a PEG moiety, (iii) a linker, and (iv) a nucleotide moiety, wherein the core is attached to the plurality of nucleotide arms, wherein the spacer is attached to the linker, and wherein the linker is attached to the nucleotide moiety.

76. The method of claim 75, wherein the plurality of nucleotide arms comprises the same type of a nucleotide moiety, and wherein the type of nucleotide moiety is selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

77. The method of any one of claims 65-76, wherein the plurality of multivalent molecules comprises a mixture of two or more types of multivalent molecules, each type of multivalent molecules comprising one or more nucleotide moiety types selected from the group consisting of dATP, dGTP, dCTP, dTTP and dUTP.

78. The method of any one of claims 65-77, wherein the plurality of multivalent molecules comprises at least one fluorophore-labeled multivalent molecule.

79. The method of any one of claims 1-47, wherein the sequencing of step (h) comprises sequencing by binding.

80. The method of any one of claims 1-47, wherein the sequencing of step (h) comprises using phosphate-chain labeled nucleotides.

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