High-throughput nucleic acid sequencing with single-molecule sensor arrays

Abstract

Embodiments of single molecule array sequencing (SMAS) devices and systems are disclosed herein. Each sensor in the sensor array of the SMAS device is capable of detecting a label attached to a nucleotide incorporated into a single nucleic acid chain bound to a respective binding site. Each sensor can detect a single label (e.g., fluorescent, magnetic, organic metal, charged molecule, etc.) attached to the incorporated nucleotide. Also disclosed are methods for highly adjustable nucleic acid (e.g., DNA) sequencing based on synthetic sequencing (SBS) of multiple examples of cloned amplified DNA fixed on such a SMAS device using a SMAS device and system. Also disclosed are error correction methods that mitigate errors (e.g., detection or non-detection of erroneous labels) generated in sequencing individual nucleic acid chains.

Description

[0001] CROSS REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Provisional Application No. 63 / 013,236, filed on April 21, 2020 and entitled “HIGH-THROUGHPUT DNA SEQUENCING WITH SINGLE-MOLECULE SENSOR-ARRAYS” (Agent File No. ROA-1002P-US / P36083-US), and this application hereby incorporates the contents of U.S. Provisional Application No. 63 / 013,236 by reference in its entirety. This application also incorporates by reference for all purposes PCT Application No. PCT / US20 / 27290, filed on April 8, 2020, entitled “NUCLEIC ACID SEQUENCING BY SYNTHESIS USING MAGNETIC SENSOR ARRAYS” (Attorney Docket No. ROA-1000-WO / P35097-WO), which was published on October 15, 2020 as WO 2020 / 210370, and PCT Application No. PCT / US20 / 27290, filed on April 8, 2020, entitled “NUCLEIC ACID SEQUENCING BY SYNTHESIS USING MAGNETIC SENSOR ARRAYS” (Attorney Docket No. ROA-1000-WO / P35097-WO), which was published on October 15, 2020 as WO 2020 / 210370, and PCT Application No. PCT / US20 / 27290, filed on March 7, 2021, entitled “MAGNETIC SENSOR ARRAYS FOR NUCLEIC ACID SEQUENCING AND METHODS OF MAKING AND USING PCT Application No. PCT / US2021 / 021274 (hereinafter referred to as “THEM”) (Agent File No. ROA-1001-WO / P35967-WO) is incorporated herein by reference. Background Art

[0003] Commercially successful DNA sequencing methods involve the synthesis and analysis of clonal deoxyribonucleic acid (DNA) clusters or the detection of individual DNA molecules. Although cluster sequencers exhibit sufficiently low error rates for diagnostic applications, their read lengths are greatly limited due to the nature of error propagation in molecular ensembles. Single-molecule sequencers can produce significantly longer reads, but typically exhibit static and dynamic heterogeneity that results in errors that are too large for high-precision diagnostics.

[0004] Therefore, there is a need to improve DNA sequencing, and nucleic acid sequencing in general, to achieve longer reads with lower error rates. Summary of the invention

[0005] This Summary represents non-limiting embodiments of the present disclosure.

[0006] Embodiments of single molecule array sequencing (SMAS) devices and systems are disclosed herein. Each sensor of a plurality of sensors within a sensor array of a SMAS device detects a label attached to a nucleotide incorporated into a single nucleic acid strand bound to a respective binding site. Each sensor can detect a single label (e.g., fluorescent, magnetic, organic metal, charged molecule, etc.) attached to the incorporated nucleotide. Also disclosed are methods for highly tunable nucleic acid (e.g., DNA) sequencing based on synthetic sequencing (SBS) of multiple instances of clonally amplified DNA immobilized on such a SMAS device using a SMAS device and system. Also disclosed are error correction methods that mitigate errors (e.g., detection or non-detection of erroneous labels) generated in sequencing individual nucleic acid strands.

[0007] In some embodiments, a device for sequencing nucleic acids includes a fluid chamber, a plurality of S magnetic sensors configured to detect a tag present in the fluid chamber, and at least one processor. The fluid chamber includes a plurality of S binding sites, each of which is configured to bind no more than one nucleic acid chain. Each of the S magnetic sensors senses a separate chain of nucleic acids bound to a separate binding site of the S binding sites. The at least one processor is configured to execute one or more machine-executable instructions, which, when executed, cause at least one processor to obtain a separate characteristic of a separate magnetic sensor in each of a plurality of M query steps of a sequencing program and for each of the S magnetic sensors (a), wherein the separate characteristic indicates the presence or absence of at least one tag, and (b) at least partially based on the obtained separate characteristic, determine whether the separate magnetic sensor detects the presence or absence of at least one tag during the query step.

[0008] In some embodiments, a system comprises a plurality of S binding sites, each of the S binding sites being configured to bind no more than one nucleic acid strand, a plurality of S sensors (e.g., magnetic, optical sensors, etc.) configured to detect a label, and at least one processor. Each of the S sensors is configured to sense a respective strand of nucleic acid bound to a respective binding site of the S binding sites. The at least one processor is configured to execute one or more machine executable instructions, which when executed cause the at least one processor to (a) obtain a respective characteristic of the respective sensor for each of the S sensors in each of the M query steps of a sequencing procedure, wherein the respective characteristic indicates the presence or absence of at least one label, and (b) determine whether the respective sensor detected the presence or absence of the at least one label during the query step based at least in part on the obtained respective characteristic. Additionally, when executed, the one or more machine executable instructions further cause the at least one processor to perform an error correction procedure on at least one record, the at least one record comprising the results of the sequencing procedure for at least one subset of the S sensors in each of the M query steps.

[0009] In some embodiments, a method for sequencing multiple S nucleic acid chains using a SMAS device includes (a) binding the S nucleic acid chains to S binding sites, (b) performing a sequencing procedure including M query steps to generate S records, each of the S records capturing M detection results of a respective one of the S sensors, each of the M detection results indicating whether a respective one of the S sensors detected at least one marker in a fluid chamber during a respective one of the M query steps, and (c) applying an error correction procedure to at least one subset of the S records to estimate the nucleic acid sequence of at least one of the S nucleic acid chains.

[0010] Some embodiments are a method of mitigating errors in sequencing data generated by a nucleic acid sequencing procedure using a single molecule sensor array, wherein the single molecule sensor array has a plurality of sensors, each of the plurality of sensors being associated with a respective binding site of a plurality of binding sites, each of the plurality of binding sites being configured to bind no more than one nucleic acid strand to be sequenced. In some such embodiments, the method includes (a) identifying multiple records in sequencing data, each of the multiple records capturing a respective sequencing result for a respective instance of a first chain of nucleic acid, each of the multiple records having multiple entries, each of the multiple entries indicating a respective step of a plurality of query steps for a nucleic acid sequencing procedure, (i) detection of a tag by a respective sensor associated with a respective instance of the first chain of nucleic acid, or (ii) no detection of the tag by a respective sensor associated with a respective instance of the first chain of nucleic acid; (b) determining multiple candidate sequences of the first chain of nucleic acid based on the multiple records, each of the multiple candidate sequences estimating at least a portion of the nucleic acid sequence of the first chain of nucleic acid; and (c) identifying a specific candidate sequence among the multiple candidate sequences as at least a portion of the nucleic acid sequence of the first chain of nucleic acid, the specific candidate sequence being the most likely correct from among the multiple candidate sequences.

[0011] Compared to cluster-based approaches, the disclosed sequencing and error correction apparatus, systems, and methods are expected to achieve higher throughput, lower error rates, and longer read lengths. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The objects, features and advantages of the present invention will be readily apparent from the following description of certain embodiments taken in conjunction with the accompanying drawings, in which:

[0013] Figure 1 A portion of a magnetic sensor according to some embodiments is described.

[0014] Figure 2A and 2B The resistance of a magnetoresistive (MR) sensor is described, which may be used in accordance with some embodiments.

[0015] Figure 3A A spin torque oscillator (STO) sensor is described, which may be used in accordance with some embodiments.

[0016] Figure 3B Shows the experimental response of STO under example conditions.

[0017] Figure 3C and 3D Short nanosecond field pulses of STO are described, which may be used according to some embodiments.

[0018] Figure 4AA single sensor of a cluster sequencing device is illustrated for sensing a number of N clonally amplified DNA strands in its vicinity.

[0019] Figure 4B An exemplary plurality of S single-molecule sensors is illustrated, wherein each sensor is used to monitor a respective single-stranded DNA (ssDNA) via a SMAS device according to some embodiments.

[0020] Figure 5A is a block diagram showing components of an exemplary SMAS device for nucleic acid sequencing according to some embodiments.

[0021] Figure 5B , 5C 5D illustrate portions of an exemplary SMAS device for nucleic acid sequencing according to some embodiments.

[0022] Figure 5E A square grid (or lattice) pattern of a sensor is illustrated in accordance with some embodiments.

[0023] Fig. 6A A sensor, a DNA strand in a helical state, and a label are illustrated according to some embodiments.

[0024] Figure 6B Exemplary dimensions of sensors, elongated DNA strands, and labels are illustrated according to some embodiments.

[0025] Fig. 7A An exemplary geometric arrangement for estimating sensor array packaging limits of a SMAS device is described in accordance with some embodiments.

[0026] Figure 7B The sensors of a SMAS device are illustrated arranged in a square grid, according to some embodiments.

[0027] Fig. 8A and 8B Sensors of a SMAS device are illustrated arranged in a hexagonal pattern according to some embodiments.

[0028] Fig. 9A An exemplary geometric arrangement for estimating sensor array packaging limits of a SMAS device is described in accordance with some embodiments.

[0029] Fig. 9B Sensors of a SMAS device are illustrated arranged in a hexagonal lattice, according to some embodiments.

[0030] Fig.10 The density of the exemplary SMAS implementation is compared to the current state-of-the-art cluster sequencing devices.

[0031] Fig.11An exemplary method for sequencing multiple nucleic acid strands using a SMAS device according to some embodiments is described.

[0032] Fig.12 is a flow chart of a sequencing procedure using an additive approach according to some embodiments.

[0033] Fig.13 An additive sequencing scheme according to some embodiments is described.

[0034] Fig.14 is a flow chart of a sequencing procedure using a subtractive approach according to some embodiments.

[0035] Fig.15 A subtractive sequencing scheme according to some embodiments is described.

[0036] Fig.16 is a flow chart of a sequencing procedure using a modified additive method according to some embodiments.

[0037] Fig.17 An improved additive sequencing scheme according to some embodiments is described.

[0038] Fig.18A Illustration of failed nucleotide incorporation (FNI) of a cluster sequencer.

[0039] Fig.18B Describe the FNI of the SMAS device.

[0040] Fig.18C Describes failed mark removal (FLR) of the cluster sequencer.

[0041] Fig.18D Demonstrating the FLR of the SMAS device.

[0042] Fig.18E Illustration of failed nucleotide removal (FNR) of a cluster sequencing device.

[0043] Fig.18F The FNR of the SMAS device is described.

[0044] Figure 18G Illustration of failed nucleotide deletion (FLD) of cluster sequencing apparatus.

[0045] Fig.18H The FLD of the SMAS device is illustrated.

[0046] Fig.19 is a flow chart of an exemplary sequencing procedure using the modified additive method with FLR and FNI error detection according to some embodiments.

[0047] Fig. 20 Displays instance records with FNI and FLR errors.

[0048] Fig.21 Illustrate expected signal levels detected by cluster sequencer sensors that capture the behavior of molecular collectives during the sequencing procedure.

[0049] Fig. 22 Describes how SMAS devices provide better accuracy when using error correction techniques according to some embodiments.

[0050] Fig.23 FNI error correction by deleting strings of four "not detected marker" entries in the record of detection results from a sequencer is described in accordance with some embodiments.

[0051] Fig.24 The results of an exemplary SBS reaction according to some embodiments are illustrated.

[0052] Fig.25 The effect of larger cluster size on base-calling accuracy of cluster sequencers is illustrated.

[0053] Fig.26 Deterministic error correction of FLR and FNI errors according to some embodiments is described.

[0054] Fig. 27 Explain the FNI, FLR and FNR errors in the detection data.

[0055] Fig.28 FLR error correction and base calling of data generated by a SMAS device according to some embodiments is described.

[0056] Fig.29 FNI error correction and base calling of data generated by a SMAS device according to some embodiments is described.

[0057] Fig.30 Error correction and base calling of data generated by a SMAS device according to some embodiments is described.

[0058] Fig.31 Illustrate FNI, FLR, FNR, and FLD errors in exemplary detection results from a SMAS device.

[0059] Fig.32 The application of an error correction procedure to data captured by a SMAS device during SBS in accordance with some embodiments is described.

[0060] Fig.33 A flow chart illustrating an error correction process according to some embodiments.

[0061] Fig.34AIllustrate the average signal intensity at the query step, where the label should be detected because a matching nucleotide was introduced and successfully incorporated.

[0062] Fig.34B Illustrate the functional fit of the measured intensities from the cluster model.

[0063] Fig.35 Plot the probability function of the cluster sequencer.

[0064] Fig.36 Describe the discrete probability function of the cluster sequencer.

[0065] Fig.37A Intensity curve illustrating the cluster sequencing device.

[0066] Fig.37B Describe the probability distribution function of the cluster sequencer.

[0067] Fig.38A and 38B Plot the probability function of the cluster sequencer.

[0068] Fig.39 Illustrate the Nr parameter space of the cluster sequencer under various conditions.

[0069] Fig.40A The calculated probabilities of cluster sequencing devices along the Q30 contour are shown for various Nr combinations.

[0070] Fig.40B The calculated cumulative error probability of a cluster sequencer is shown.

[0071] Fig.41 Describing the Nr parameter space for a cluster sequencer, wherein the cumulative probability of an incorrect base call at position 150 is less than or equal to 1 in 100 1 in 1,000 1 in 10,000 and 1 in 100,000

[0072] Fig.42 Calculation results for the Kr parameter space for a SMAS device are illustrated, where the probability of incorrect base calling at each query step is less than 1 in 100 (Q20), 1 in 1,000 (Q30), 1 in 10,000 (Q40), and 1 in 100,000 (Q50) according to some embodiments.

[0073] Fig.43A and 43B The cumulative probability of incorrect base calls at position 150 is shown for a cluster sequencing device and a SMAS device according to some embodiments.

[0074] Fig.44 and 45 An exemplary sample preparation and loading process according to some embodiments is described.

[0075] Fig.46A , 46B and 46C illustrate simulation test results of an exemplary SMAS device according to some embodiments.

[0076] Fig.47 Description According to some embodiments of the invention Fig.46A , 46B and how the detection data in 46C can be rearranged to identify the bases and show the positions of the different DNA strands.

[0077] Fig.48A and 48B Plotted are the calculated probabilities of incorrect base calls as a function of the number of query steps C and the chemical failure rate r.

[0078] Fig.49 Depicted is the use of barcodes in sample preparation and DNA loading according to some embodiments.

[0079] Fig.50 An exemplary system 160 is described in accordance with some embodiments.

[0080] For ease of understanding, the same reference numerals are used where possible to represent the same components common to the figures. It is contemplated that components disclosed in one embodiment may be beneficially used in other embodiments without specific description. In addition, the description of a component in the context of one figure may be applied to other figures illustrating the component. DETAILED DESCRIPTION

[0081] Some of the description and examples herein are in the context of DNA sequencing, but it should be understood that the disclosure is generally applicable to nucleic acid sequencing.

[0082] Terminology and Notes

[0083] As used herein, the term "strand" refers to a single nucleic acid chain (eg, ssDNA). When referring to nucleic acids, the terms "strand" and "fragment" are used interchangeably.

[0084] As used herein, the term "plurality" means two or more, but not necessarily all. Thus, a plurality of sensors only means at least two sensors, but not necessarily all sensors in a sensor array or a sequencing device / system. Similarly, a plurality of binding sites only means at least two binding sites, but not necessarily all binding sites in a sequencing device / system.

[0085] As used herein, the term "instance" when referring to a nucleic acid strand means a template nucleic acid strand or a copy thereof (e.g., produced by an amplification or replication process). Ideally, a copy of a template nucleic acid strand is identical to the template strand, but as is known in the art, copies are not necessarily identical due to replication / amplification errors. It should be understood that even if errors are introduced by the amplification procedure, the duplicates produced by amplification are still considered copies of the original nucleic acid strand. Therefore, all instances of a strand are ideally identical to each other but may not be identical.

[0086] As used herein, the term "query cycle" refers to a single cycle of a nucleic acid sequencing program during which all possible nucleotides are introduced to determine which, if any, are introduced into the sequenced strand. For example, for a DNA sequencing program, all adenines (A), thymines (T), cytosines (C), and guanines (G) are tested in a certain (arbitrary) order (which need not be the same for each query cycle). As described in detail below, more than one label may be detected per strand during a single sequencing cycle, depending on the sequencing program selected.

[0087] As used herein, the term "query step" refers to a step or set of steps of a sequencing procedure during which a determination is made whether one or more sensors of a sequencer are detecting a tag. For a DNA sequencing cycle across all A, T, C, and G, there are four query steps per query cycle (one for each nucleotide). For a sensor in use, each query step produces a single determination whether the sensor is detecting a tag.

[0088] As used herein, the term "detection result" refers to a value indicating that (a) a marker was detected during a query step or (b) a marker was not detected during a query step. In some embodiments, the detection result is a binary value (e.g., 0 or 1). The detection result can be derived from other data (e.g., a signal representing resistance, frequency, intensity, etc.; a measurement of resistance, frequency, intensity, etc.).

[0089] As used herein, the term "record" refers to a stored representation of the detection results of a single sensor. If the selected sequencer has M query steps, then after the sequencer is completed, each record has M detection results. The records of the S sensors can be stored in a single file (e.g., in a table with S rows and M columns, or S columns and M rows), or separate files can be created for the records of each individual sensor.

[0090] As used herein, with respect to test results contained in a record, the term "string" means a consecutive sequence of identical values.

[0091] The terms "sensor" and "sensing component" are used interchangeably herein.

[0092] The variable S is used herein to refer to the number of sensors in the plurality of sensors. The S sensors may be instances sensing the same chain, or they may be instances sensing different chains.

[0093] The variable K is used herein to refer to the number of sensors in a plurality of sensors that all sense instances of the same chain.

[0094] mark

[0095] The methods for nucleic acid sequencing described herein use labeled nucleotide precursors comprising cleavable labels. These cleavable labels can be, for example, magnetic, fluorescent, organometallic or charged molecules.

[0096] Each label may comprise, for example, a magnetic nanoparticle, such as, for example, a molecule, a superparamagnetic nanoparticle, or a ferromagnetic particle. The magnetic label may be a nanoparticle with high magnetic anisotropy. Examples of nanoparticles with high magnetic anisotropy include, but are not limited to, Fe3O4, FePt, FePd, and CoPt. In order to facilitate chemical binding to nucleotides, the particles may be synthesized and coated with SiO2. See, for example, M. Aslam, L. Fu, S. Li, and VP Dravid, "Silica encapsulation and magnetic properties of FePt nanoparticles", Journal of Colloid and Interface Science, Vol. 290, No. 2, Oct. 15, 2005, pp. 444-449. Because magnetic markers of this size have a permanent magnetic moment whose direction fluctuates randomly on very short time scales, some embodiments described further below rely on sensitive sensing schemes that detect fluctuations in the magnetic field due to the presence of the magnetic marker.

[0097] Each label may comprise, for example, a fluorophore. Fluorescent labels are well known in the art and are suitable for use with the present disclosure.

[0098] The label may comprise, for example, an organometallic compound. As is understood, an organometallic compound is any member of a class of substances comprising at least one metal-carbon bond, wherein the carbon is part of an organic group. Examples of organometallic compounds include Gilman reagent (which comprises lithium and copper), Grinard reagent (which comprises magnesium), nickel tetracarbonyl and ferrocene (which comprises a transition metal), organolithium compounds such as n-butyllithium (n-BuLi), organozinc compounds such as diethylzinc (Et2Zn), organotin compounds such as tributyltin hydride (Bu3SnH)), organoborane compounds such as triethylborane (Et3B) and organoaluminum compounds such as trimethylaluminum (Me3Al)

[0099] Labels may comprise, for example, charged molecules.

[0100] There are a variety of methods by which a label can be attached to a nucleotide precursor and cleaved after incorporation into the nucleotide precursor. For example, a label can be attached to a base, in which case it can be chemically cleaved. As another example, a label can be attached to a phosphate, in which case it can be cleaved by a polymerase, or if attached via a linker, by cleaving the linker.

[0101] In some embodiments, the label is attached to a nitrogenous base (e.g., A, C, T, G, or derivatives) of a nucleotide precursor. After incorporation of the nucleotide precursor and detection by a sequencing device (e.g., as described in further detail below), the label is cleaved from the incorporated nucleotide.

[0102] In some embodiments, the label is attached via a cleavable linker. Cleaved linkers are known in the art and have been described, for example, in U.S. Pat. Nos. 7,057,026, 7,414,116, and continuations and improvements thereof. In some embodiments, the label is attached to the 5 position in a pyrimidine or the 7 position in a purine via a linker comprising an allyl or azido group. In other embodiments, the linker comprises a disulfide bond, an indole, or a Sieber group. The linker may further comprise one or more selected from alkyl (C 1-6 ) or alkoxy (C 1-6), nitro, cyano, fluorine groups or substituents of groups with similar properties. In simple terms, the linker can be cleaved by a water-soluble phosphine or a catalyst containing a phosphine transition metal. Other linkers and linker cleavage mechanisms are known in the art. For example, linkers comprising trityl, p-alkoxybenzyl esters and p-alkoxybenzyl amides and tert-butyloxycarbonyl (Boc) groups and acetal systems can be cleaved by proton-releasing cleavage agents under acidic conditions. Thioacetals or other sulfur-containing linkers can be cleaved using sulfur-philic metals (such as nickel, silver or mercury). Cleaved protecting groups can also be considered for the preparation of suitable linker molecules. Ester-containing linkers and disulfide-containing linkers can be cleaved under reducing conditions. Linkers containing triisopropylsilane (TIPS) or tert-butyldimethylsilane (TBDMS) can be cleaved in the presence of F ions. Photocleavable linkers that can be cleaved by wavelengths that do not affect other components of the reaction mixture include linkers containing O-nitrobenzyl groups. Linkers containing benzyloxycarbonyl groups can be cleaved by catalysts based on Pd.

[0103] In some embodiments, the nucleotide precursor comprises a label attached to a phosphate moiety, such as described in, for example, U.S. Pat. Nos. 7,405,281 and 8,058,031. In short, the nucleotide precursor comprises a chain of nucleoside moieties and 3 or more phosphate groups, wherein one or more of the oxygen atoms are optionally substituted, for example, by S. The label may be attached directly or via a linker to an α, β, γ or higher phosphate group (if present). In some embodiments, the label is attached to a phosphate group via a non-covalent linker, such as described in, for example, U.S. Pat. No. 8,252,910. In some embodiments, the linker is a hydrocarbon selected from the following: substituted or unsubstituted alkyl, substituted or unsubstituted heteroalkyl, substituted or unsubstituted aryl, substituted or unsubstituted heteroaryl, substituted or unsubstituted cycloalkyl, and substituted or unsubstituted heterocycloalkyl; see, for example, U.S. Pat. No. 8,367,813. The linker may also comprise a nucleic acid chain; see, for example, U.S. Pat. No. 9,464,107.

[0104] In embodiments where the label is attached to a phosphate group, the nucleotide precursor is incorporated into the nascent chain by a nucleic acid polymerase that also cleaves and releases the detectable label. In some embodiments, the label is removed by cleaving the linker, for example, as described in U.S. Pat. No. 9,587,275.

[0105] In some embodiments, the nucleotide precursor is a non-extendable "terminator" nucleotide, that is, a nucleotide whose 3' end is blocked by a blocking "terminator" group and cannot add the next nucleotide. The blocking group is a reversible terminator, which can be removed to continue the chain synthesis process as described herein. It is known in the art to attach a removable blocking group to a nucleotide precursor. See, for example, U.S. Pat. Nos. 7,541,444 and 8,071,739 and their continuations and improvements. In short, the blocking group may include an allyl group, which can be cleaved by reacting with a metal-allyl complex in the presence of a phosphine or nitrogen-phosphine ligand in an aqueous solution. Other examples of reversible terminator nucleotides for use in synthetic sequencing include modified nucleotides described in International Application No. PCT / US2019 / 066670, filed on December 16, 2019, and entitled “3’-protected Nucleotides,” which was published as WO / 2020 / 131759.

[0106] sensor

[0107] The characteristics and capabilities of the sensors used in the nucleic acid sequencing devices, systems, and methods described herein depend on the choice of the label used. The sensor may be, for example, a magnetic sensor (to detect, for example, magnetic nanoparticles, organometallic compounds, etc.) or an optical sensor (to detect, for example, fluorophores). It should be understood that other types of sensors may be suitable for detecting various types of labels, and the examples described herein are not intended to be limiting. In general, the disclosed devices, systems, and methods may use any type of label that can be detected by a selected type of sensor, and conversely, the disclosed devices, systems, and methods may use any type of sensor that can detect the presence (and absence) of a selected type of label.

[0108] Reference numeral 105 is used herein generically for single molecule sensors, regardless of the type of those single molecule sensors (and regardless of the type of label they detect). Reference numeral 15 is used for sensors that sense nucleic acid clusters.

[0109] Magnetic Sensor

[0110] Some embodiments disclosed herein use magnetic sensors to detect the presence of magnetic labels (eg, magnetic nanoparticles, organometallic complexes, charged molecules, etc.) coupled to nucleotide precursors. Figure 1 A portion of a magnetic sensor 105 is illustrated according to some embodiments. Figure 1An exemplary magnetic sensor 105 of has a bottom surface 108 and a top surface 109 and includes three layers, such as two ferromagnetic layers 106A, 106B separated by a nonmagnetic spacer layer 107. The nonmagnetic spacer layer 107 can be, for example, a metallic material such as, for example, copper or silver, in which case the structure is called a spin valve (SV), or it can be an insulator such as, for example, aluminum oxide or magnesium oxide, in which case the structure is called a magnetic tunnel junction (MTJ). Suitable materials for use in the ferromagnetic layers 106A, 106B include, for example, alloys of Co, Ni, and Fe (sometimes mixed with other elements). In some embodiments, the ferromagnetic layers 106A, 106B are engineered so that their magnetic moments are oriented in the plane of the film or perpendicular to the plane of the film. Additionally, the materials can be shown in Figure 1 Although the three layers 106A, 106B, and 107 in the magnetic sensor 105 are deposited below and above the three layers 106A, 106B, and 107 in the magnetic sensor 105 for purposes such as interface smoothing, texturing, and protection from processing for patterning a device in which the sensor 105 is incorporated, the active area of ​​the magnetic sensor 105 is located in this three-layer structure. Therefore, a component in contact with the magnetic sensor 105 may be in contact with one of the three layers 106A, 106B, or 107, or it may be in contact with another portion of the magnetic sensor 105.

[0111] like Figure 2A and 2B As shown in Figure 1, the resistance of the MR sensor is proportional to 1-cos(θ), where θ is the value shown in Figure 1. Figure 1 The angle between the magnetic moments of the two ferromagnetic layers 106A, 106B in the sensor 105. In order to maximize the signal generated by the magnetic field and provide a linear response of the magnetic sensor 105 to the applied magnetic field, the magnetic sensor 105 can be designed so that the magnetic moments of the two ferromagnetic layers 106A, 106B are oriented at π / 2 radians or 90 degrees relative to each other in the absence of a magnetic field. This orientation can be achieved by many methods known in the art. For example, one solution is to use an antiferromagnet to "fix" the magnetization direction of one of the ferromagnetic layers (106A or 106B, designated as "FM1") through an effect called exchange bias and then coat the sensor with a double layer having an insulating layer and a permanent magnet. The insulating layer avoids electrical shorting of the magnetic sensor 105, and the permanent magnet provides a "hard bias" magnetic field perpendicular to the fixed direction of FM1, which then causes the second ferromagnet (106B or 106A, designated as "FM2") to rotate and produce the desired configuration. The magnetic field parallel to FM1 then causes FM2 to rotate about this 90 degree configuration, and the change in resistance results in a voltage signal that can be calibrated to measure the magnetic field acting on the magnetic sensor 105. In this way, the magnetic sensor 105 acts as a magnetic field to voltage converter.

[0112] It should be noted that although the example discussed immediately above describes the use of ferromagnets whose magnetic moments are oriented at 90 degrees relative to each other in the plane of the film, a perpendicular configuration can alternatively be achieved by orienting the magnetic moment of one of the ferromagnetic layers 106A, 106B out of the plane of the film, which orientation can be achieved using what is known as perpendicular magnetic anisotropy (PMA).

[0113] In some embodiments, the magnetic sensor 105 uses a quantum mechanical effect called spin transfer torque. In such a device, a current passing through one ferromagnetic layer 106A (or 106B) in a SV or MTJ preferentially allows electrons with a spin parallel to the magnetic moment of the layer to be transmitted through, while electrons with antiparallel spins are more likely to be reflected. In this way, the current becomes spin-polarized, with more electrons of one spin type than another spin type. This spin-polarized current then interacts with the second ferromagnetic layer 106B (or 106A), thereby exerting a torque on the magnetic moment of the layer. This torque can, in different circumstances, cause the magnetic moment of the second ferromagnetic layer 106B (or 106A) to precess around the effective magnetic field when acting on the ferromagnet, or it can cause the magnetic moment to reversibly switch between two orientations defined by the uniaxial anisotropy induced in the system. The resulting spin torque oscillator (STO) is frequency-tunable by changing the magnetic field acting on it. Therefore, it has the ability to act as a magnetic field and frequency (or phase) converter (thereby generating an AC signal with a frequency), such as Figure 3A , which illustrates the concept of using an STO sensor. Figure 3B The experimental response of an STO through a delayed detection circuit is shown when an AC magnetic field with a frequency of 1 GHz and a peak-to-peak amplitude of 5 mT is applied across the STO. This result is similar to those shown in the case of short nanosecond field pulses. Figure 3C and 3D The results in show how these oscillators can be used as nanoscale magnetic field detectors. Further details can be found in T. Nagasawa, H. Suto, K. Kudo, T. Yang, K. Mizushima, and R. Sato, "Delay detection of frequency modulation signal from a spin-torque oscillator under a nanosecond-pulsed magnetic field", Journal of Applied Physics, Vol. 111, 07C908 (2012).

[0114] Optical Sensors

[0115] Some nucleic acid sequencing methods use fluorescent labels. In such methods, the sequenced nucleic acid molecules are fixed on a solid support, and the binding of fluorescently labeled target molecules (e.g., nucleotides) to the molecules is monitored. Optical instruments (e.g., excitation and reading devices for fluorescence) provide light of a certain wavelength to excite the fluorescent labels and detect fluorescence emitted from the labels at slightly different wavelengths. Because the beam path (light path) of the excitation light must be at least partially different from the beam path (light path) of the fluorescence, excitation and emission filters (whose spectra do not overlap significantly) can be used to achieve spectral separation, and / or vertical or side illumination can be used.

[0116] Optical sensors and sequencing devices and methods using fluorescent labels such as fluorophores are well known in the art.

[0117] Amplification / replication

[0118] Nucleic acid sequencing devices generally rely on an amplification (or replication) process to produce a large number of nucleic acid instances from a single nucleic acid strand (e.g., instances of a single-sided DNA strand (ssDNA) from a DNA molecule). The polymerase chain reaction (PCR) is a well-known method for amplifying double-stranded DNA, which enables the replication of large amounts of DNA from small initial amounts.

[0119] Cluster Sequencer

[0120] Some sequencing devices (referred to herein as cluster (CLUS) devices) use amplification techniques to form local clusters of many DNA chains. For example, a DNA chain is used as a template, and PCR amplification generates thousands or millions of DNA sequence instances in a local area. At least a portion of the PCR primers is fixed to a solid support, which allows the generated DNA molecules to be fixed to local clusters to form distinguishable "pure lines". The generated DNA clusters may include ssDNA. Examples of clonal amplification techniques include bridge PCR and emulsion PCR, including emulsion PCR based on microbeads. For bridge amplification, primers attached to a solid surface (such as a glass slide) are used to amplify single DNA molecules by in situ PCR to form DNA clusters. Each DNA cluster is a physically separated "pure line" composed of instances of a DNA chain. For clonal amplification based on emulsion PCR, a single DNA molecule is cloned and amplified in an emulsion droplet. In some methods, a DNA chain is attached to a microbead inside a droplet. The clonal amplification of a single molecule can also be performed in a separate microwell.

[0121] As used herein, the term "cluster" refers to a localized cluster of nucleic acid chains, ideally having the same sequence, that is produced by clonal amplification. When the nucleic acid is DNA, the cluster comprises the same DNA chain (or fragment) attached (ideally) to a solid support. For example, the cluster can be produced on a spot on a slide or attached to a microbead, microwell, or other microparticle.

[0122] The use of CLUS devices for fluorescence-based DNA sequencing is well known.

[0123] A sequencing device for nucleic acid sequencing using clusters using a magnetic sensor array is described, for example, in PCT application No. PCT / US2021 / 021274, filed on March 7, 2021 and entitled “MAGNETIC SENSORARRAYS FOR NUCLEIC ACID SEQUENCING AND METHODS OF MAKING AND USING THEM” (Agent File No. ROA-1001-WO / P35967-WO).

[0124] Figure 4A A single sensor 15 of a CLUS device is illustrated for sensing some N clonally amplified DNA strands 101 in its vicinity. The sensor 15 may be, for example, a magnetic sensor to sense magnetic labels attached to incorporated nucleotides. For convenience, Figure 4A Chain 101 is shown in contact with sensor 15, but it should be appreciated that there may be a barrier (e.g., an insulating layer) between sensor 15 and chain 100. Sensor 15 may be a magnetic sensor, for example, as described in PCT Application No. PCT / US2021 / 021274 referenced above.

[0125] Current state-of-the-art commercial CLUS devices (such as those sensing fluorescent markers) can use hundreds of millions of sensors 15, each sensing many instances of individually amplified DNA chains 101. One drawback of some CLUS devices is that achieving optimal cluster density can be critical for high-quality sequencing. Specifically, the use of large clusters tends to provide higher data quality, but reduces data output, while the use of small clusters can lead to run failures, poor run performance, lower Q30 scores, introduction of sequencing artifacts, and reduced overall data output. To alleviate these problems, newer CLUS devices use patterned flow cells with different nanopores for cluster generation. These nanopores are organized into a hexagonal arrangement to more efficiently use the flow cell surface area.

[0126] Single-molecule array sequencing device

[0127] The single-molecule array sequencing device (referred to herein as a "SMAS device") is an alternative to the CLUS device. In contrast to the CLUS device, which senses and sequences local clusters of multiple instances of a single nucleic acid chain, the SMAS device uses sensors that sense and sequence individual chains of nucleic acids individually. Generally speaking, in a SMAS device, no sensor senses more than one physical nucleic acid chain, but different sensors sense instances of the same chain. In other words, there are multiple instances of nucleic acid chains, but each sensed chain is sensed by a different individual sensor. Depending on the amplification technology used, the individual chains may be randomly distributed in the fluid chamber of the SMAS device, or they may be located in more local areas. As discussed in the following advances, the location of instances of a particular chain can be identified, and an error correction program can be applied to the detection results corresponding to the instance before identifying the base to improve the accuracy of sequencing relative to the CLUS device. In addition, relative to the CLUS device, for a reasonable chemical failure rate, the SMAS device requires fewer instances of each nucleic acid chain to be sequenced to achieve accurate sequencing results.

[0128] Figure 4B An exemplary plurality of S single-molecule sensors 105 are illustrated, each of which is used to monitor a respective single-stranded DNA (ssDNA) 101 through a SMAS device. Each of the plurality of S sensors 105 can be, for example, a magnetic sensor, an optical sensor, etc. Figure 4B Five single molecule sensors 105A, 105B, 105C, 105D, and 105E are illustrated, each of which senses a respective DNA strand 101 (which may be instances of the same DNA strand, or instances of different DNA strands). Each sensor 105 may be, for example, a nanoscale sensor that is so small that only a single DNA strand 101 can bind to a binding site associated with the sensor 105. (For convenience, Figure 4B The strand 101 is shown in contact with a sensor 105, but as further described below, in some embodiments, the strand 100 is attached to individual binding sites, each of which is associated with a respective sensor 105.

[0129] Consider clonally amplified DNA bound to a solid surface comprising an array of densely packed sensors 105, such as Figure 4B 105E. The DNA may be replicated by solid phase amplification (SPA) to create monoclonal DNA clusters, each strand intended to be sensed by a different sensor 105, or the DNA may be amplified in bulk and then immobilized on the surface of the SMAS device. If the DNA is amplified on the surface of the fluid chamber of the SMAS device (e.g., by SPA), the sensors 105A, 105B, 105C, 105D, 105E may sense instances of clonal DNA. Alternatively, if the DNA is amplified in bulk outside the device and added to the fluid chamber of the SMAS device, the amplified DNA strands 101 may be more randomly distributed in the sensors 105.

[0130] Figure 5A 1 is a block diagram showing components of an exemplary SMAS device 100 for nucleic acid sequencing according to some embodiments. As shown, the device 100 includes a sensor array 110, which is coupled to a circuit 120, which is coupled to at least one processor 130. The sensor array 110 includes a plurality of sensors 105 (e.g., magnetic sensors, optical sensors, etc.), which can be arranged in any suitable manner, as further described below. The characteristics and properties of the sensors 105 in the sensor array 110 depend on the type of label used for sequencing.

[0131] The circuit 120 may include, for example, one or more wires that allow the sensors 105 in the sensor array 110 to be interrogated by the at least one processor 130 (e.g., with the aid of other components known in the art, such as current sources, etc.). For example, in operation, the processor 130 may cause the circuit 120 to apply a current to such wires to detect a characteristic of at least one of the plurality of sensors 105 in the sensor array 110, wherein the characteristic indicates the presence of a tag or the absence of any tag within the range of the sensor 105. In other words, the characteristic (e.g., resistance, frequency, voltage, signal level, etc.) indicates that the sensor 105 has detected at least one tag or has not detected any tag. For example, the at least one processor 130 may assess the value of the characteristic (e.g., frequency, wavelength, magnetic field, resistance, noise level, intensity, color of light, etc.) and determine that a tag is detected (or not detected) based on a comparison of the characteristic value to a threshold value (e.g., by determining whether the characteristic value of the sensor 105 meets or exceeds the threshold value) or a baseline value. As another example, the at least one processor 130 may compare the obtained characteristic of the sensor 105 with a previously detected characteristic value (e.g., a baseline value of the sensor 105) and base the determination of whether a marker is detected or not detected on a change in the characteristic value (e.g., a change in magnetic field, resistance, noise level, frequency, wavelength, intensity, color of light, etc.). For example, as described below in Fig.19 As further described in the discussion of , the at least one processor 130 may evaluate a characteristic obtained from the sensor 105 to detect whether a sensor 105 that detected a marker during a first query step of a sequencing procedure still detects the marker after a cutting step that should have removed the marker. Similarly, the at least one processor 130 may evaluate a change in a characteristic from one query step to the next query step to determine whether the sensor 105 (a) did not detect the marker during any query step, (b) detected the marker during both query steps, (c) did not detect the marker during the first query step but detected the marker during a subsequent query step, and / or (d) detected the marker during the first query step but did not detect the marker during a subsequent query step.

[0132] The characteristic detected depends on the type of label used in the sequencing procedure. The label may be, for example, fluorescent, in which case the sensor 105 may be an optical detector that can detect, for example, the wavelength, frequency, modulation frequency, color, or intensity of light emitted by the fluorescent label. Optical sensors suitable for detecting fluorescent labels are well known in the art. In the case where the label used in the nucleic acid sequencing procedure is fluorescent, in some embodiments, the circuit 120 allows the at least one processor 130 to detect deviations or fluctuations in the light (or electromagnetic energy) detected by some or all of the sensors 105 in the sensor array 110.

[0133] The label may be, for example, magnetic (e.g., magnetic nanoparticles, organometallic compounds, charged molecules, etc.), in which case the sensor 105 may be a magnetic sensor that can detect magnetic properties. Magnetic sensors have been described in applicant's previously filed patent applications, including, for example, PCT Application No. PCT / US20 / 27290, entitled "NUCLEIC ACID SEQUENCING BY SYNTHESIS USING MAGNETICSENSOR ARRAYS" (Attorney Docket No. ROA-1000-WO / P35097-WO), filed on April 8, 2020, and published as WO2020 / 210370 on October 15, 2020. In some embodiments where the label is magnetic, the sensor 105 is a magnetoresistive (MR) sensor that can detect, for example, a magnetic field or resistance, a change in a magnetic field or a change in resistance, or a noise level. In some embodiments, each of the sensors 105 of the sensor array 110 is a thin film device that uses the MR effect to detect magnetic labels attached to nucleotides incorporated into a single strand of nucleic acid bound to a respective binding site. The sensor 105 can be used as a potentiometer whose resistance changes as the strength and / or direction of the sensed magnetic field changes. In some embodiments using magnetic labels, the sensor 105 includes a magnetic oscillator (e.g., a spin torque oscillator (STO)), and the characteristic indicating whether at least one label is detected is the frequency of a signal associated with or generated by the magnetic oscillator, or a change in the frequency of the signal.

[0134] In the case where the marker used in the nucleic acid sequencing procedure is magnetic, in some embodiments, the at least one processor 130 detects deviations or fluctuations in the magnetic environment of some or all sensors 105 in the sensor array 110 with the help of the circuit 120. For example, compared with the sensor 105 with the presence of the magnetic marker, the MR type sensor 105 without the magnetic marker should have relatively small noise above a certain frequency, because the field fluctuations from the magnetic marker will cause the fluctuations of the magnetic moment of the sensing ferromagnet. These fluctuations can be assessed using heterodyne detection (e.g., by measuring the noise power density) or by directly measuring the voltage of the sensor 105 and using a comparator circuit to compare with another sensor component that does not sense the binding site. In the case where the sensor 105 includes an STO component, due to the instantaneous change in frequency, the fluctuating magnetic field from the magnetic marker will cause a phase jump of the sensor 105, which can be detected using a phase detection circuit. Another option is to design the STO so that it oscillates only within a small magnetic field range, so the presence of the magnetic marker will shut down the oscillation.

[0135] It should be understood that the examples of labels and sensors 105 provided above are exemplary only. In general, any type of label that can label a nucleotide precursor can be used with an array 110 of any type of sensor 105 that can detect that type of label.

[0136] Figure 5B , 5C 5D and 5D illustrate portions of an exemplary SMAS device 100 for nucleic acid sequencing according to some embodiments. The exemplary SMAS device 100 uses magnetic labels and magnetic sensors 105. Figure 5B is a top view of the device 100 .

[0137] Figure 5C It is by Figure 5B A cross-sectional view at the position indicated by the long dashed line marked as "5C" in FIG. Figure 5D It is by Figure 5B A cross-sectional view at the position indicated by the long dashed line labeled “5D”.

[0138] Shown in Figure 5B , 5C The exemplary device 100 in FIG. 5D includes a sensor array 110 for sensing magnetic markers within a fluid chamber 115. The sensor array 110 includes a plurality of magnetic sensors 105, wherein Figure 5B Sixteen sensors 105 are shown in the array 110 of FIG. 1. It should be appreciated that implementations of the SMAS device 100 may include many sensors 105 (e.g., hundreds, thousands, or millions of sensors 105). To avoid obscuring the drawings, Figure 5BOnly seven of the marker sensors 105 are shown, that is, sensors 105A, 105B, 105C, 105D, 105E, 105F, and 105G. As described above, the magnetic sensors 105 detect the presence or absence of magnetic markers. In other words, each of the magnetic sensors 105 detects whether there is at least one magnetic marker in its vicinity.

[0139] Reference Figure 5C and 5D Combination Figure 5B , each sensor 105 is illustrated in the exemplary embodiment of the device 100 as having a cylindrical shape. However, it should be appreciated that, in general, the sensors 105 may have any suitable shape. For example, the sensors 105 may be rectangular parallelepipeds in three dimensions. Furthermore, different sensors 105 may have different shapes (e.g., some may be rectangular parallelepipeds and others may be cylindrical, etc.). It should be appreciated that the figures are exemplary only.

[0140] like Figure 5C and 5D As shown in , the device 100 includes a fluid chamber 115. The fluid chamber 115 includes a plurality of binding sites 116 (e.g., three binding sites 116). In some embodiments, the fluid chamber 115 contains fluids (e.g., nucleotide precursors and other fluids) used during the nucleic acid sequencing procedure. However, it should be understood that embodiments in which the fluid chamber 115 does not contain fluids are contemplated and within the scope of the disclosure herein. For example, the binding site 116 may be arranged on a removable (or movable) portion (e.g., a panel, a plate, a slide, etc.), which may be immersed in reagents and other fluids after the nucleic acid chain has been attached to the binding site 116 and then placed so that the sensor 105 can detect the label. Therefore, although the name of the fluid chamber 115 shows that it contains fluids, it is not required that the fluid chamber 115 contains fluids.

[0141] like Figure 5B , 5C As shown in 5D and 5D, each of the sensors 105 is associated with a respective binding site 116. (For simplicity, this document generally refers to a binding site by the reference numeral 116. Individual binding sites are given the reference numeral 116 followed by a letter.) In other words, the sensors 105 and binding sites 116 are in a one-to-one relationship. Figure 5BAs shown in FIG. 1 , sensor 105A is associated with binding site 116A, sensor 105B is associated with binding site 116B, sensor 105C is associated with binding site 116C, sensor 105D is associated with binding site 116D, sensor 105E is associated with binding site 116E, sensor 105F is associated with binding site 116F, and sensor 105G is associated with binding site 116G. Figure 5B Each of the other unlabeled sensors 105 in is also associated with a respective binding site 116. Figure 5B , 5C 5D, each sensor 105 is shown disposed below its respective binding site 116, but it should be appreciated that the binding site 116 may be located at other positions relative to its respective sensor 105. For example, the binding site 116 may be located to the side of its respective sensor 105.

[0142] Each of the binding sites 116 is configured to allow no more than one nucleic acid strand (e.g., ssDNA) to bind to the fluid chamber 115 of the SMAS device 100. In other words, each binding site 116 has properties and / or features that allow one and only one strand of nucleic acid to bind thereto for sensing (and for sequencing) by the respective sensor 105. Thereafter, the respective sensor 105 can detect the label attached to the nucleotide incorporated into the nucleic acid strand bound to the binding site 116 during the nucleic acid sequencing procedure, as further discussed below. In some embodiments, the binding site 116 has a structure (or multiple structures) configured to anchor the nucleic acid to the binding site 116. For example, the structure (or structures) may include a cavity or a ridge. Figure 5C and 5D The binding sites 116 are illustrated as extending from the surface of the fluid chamber 115 , but it should be appreciated that the binding sites 116 may be flush with or etched into the surface of the fluid chamber 115 .

[0143] The binding sites 116 may have any suitable size and shape that facilitates the attachment of one and only one strand of nucleic acid to each binding site 116. For example, the shape of the binding site may be similar or identical to the shape of the sensor 105 (e.g., if the sensor 105 is a cylinder in three dimensions, the binding site 116 may also be a cylinder that protrudes from the surface of the fluid chamber 115 or forms a fluid container within the surface of the fluid chamber 115, and whose radius may be larger, smaller, or the same size as the radius of the respective sensor 105; if the sensor 105 is a cuboid in three dimensions, the binding site 116 may also be a cuboid whose surface is larger, smaller, or the same size as the closest portion of the sensor 105, etc.). In general, the binding sites 116 and the surface of the fluid chamber 115 may have any shape and characteristics that facilitate the attachment of a single nucleic acid strand to each binding site 116 and allow the sensor 105 to detect a label attached to an incorporated nucleotide at its respective binding site 116.

[0144] Figure 5C and 5D A closed fluid chamber 115 having a top portion extending in the xy plane is illustrated, but the fluid chamber 115 need not be closed. In some embodiments, the surface of the fluid chamber 115 has properties and characteristics that protect the sensor 105 from any fluid in the fluid chamber 115, while still allowing the nucleic acid strand to bind to the binding site 116 and allowing the sensor 105 to detect the label attached to the nucleotide incorporated into the nucleic acid strand attached to the binding site 116. The material of the fluid chamber 115 (and possibly the material of the binding site 116) may be an insulator or include an insulator. In some embodiments, the surface of the fluid chamber 115 includes an organic polymer, a metal, or a silicate. The fluid chamber 115 may include, for example, a metal oxide, silicon dioxide, polypropylene, gold, glass, or silicon. The thickness of the surface of the fluid chamber 115 may be selected so that the sensor 105 can detect the magnetic label attached to the nucleotide incorporated into the nucleic acid strand bound to the binding site 116 within the fluid chamber 115. In some embodiments, the surface is about 3 to 20 nm thick such that each sensor 105 is between about 5 nm and about 50 nm from any label attached to a nucleotide incorporated into a nucleic acid strand that binds to a corresponding binding site 116 of the sensor 105. It should be understood that these values ​​are exemplary only. It should be understood that embodiments may have fluid chambers 115 with thicker or thinner surfaces.

[0145] The circuit 120 of the device 100 may include one or more wires 125. In some embodiments, each of the plurality of sensors 105 is coupled to at least one wire 125. Figure 5B , 5C5D, the device 100 includes eight wires 125A, 125B, 125C, 125D, 125E, 125F, 125G, and 125H. (For simplicity, this document generally refers to wires by reference numeral 125. Individual wires are given reference numerals 125 followed by a letter.) The wires 125 can be used to access (e.g., interrogate) individual sensors 105. In the example shown in FIG. Figure 5B , 5C In the exemplary embodiment of 5D and 5D, each sensor 105 of the sensor array 110 is coupled to two lines 125. For example, sensor 105A is coupled to lines 125A and 125H; sensor 105B is coupled to lines 125B and 125H; sensor 105C is coupled to lines 125C and 125H; sensor 105D is coupled to lines 125D and 125H; sensor 105E is coupled to lines 125D and 125E; sensor 105F is coupled to lines 125D and 125F; and sensor 105G is coupled to lines 125D and 125G. Figure 5B , 5C In the exemplary embodiments of FIGS. 5A and 5D , display lines 125A, 125B, 125C, and 125D are located below the magnetic sensor 105 , and display lines 125E, 125F, 125G, and 125H are located above the magnetic sensor 105 . Figure 5C Sensor 105E is shown with respect to lines 125D and 125E, sensor 105F is shown with respect to lines 125D and 125F, sensor 105G is shown with respect to lines 125D and 125G, and sensor 105D is shown with respect to lines 125D and 125H. Figure 5D Sensor 105D is shown with respect to lines 125D and 125H, sensor 105C is shown with respect to lines 125C and 125H, sensor 105B is shown with respect to lines 125B and 125H, and sensor 105A is shown with respect to lines 125A and 125H.

[0146] Figure 5B , 5C The sensors 105 of the exemplary SMAS device 100 of 5D and 5D are arranged in a rectangular pattern sensor array 110. (It should be understood that a square pattern is a special case of a rectangular pattern.) Each of the lines 125 identifies a row or column of the sensor array 110. For example, each of the lines 125A, 125B, 125C, and 125D identifies a different row of the sensor array 110, and each of the lines 125E, 125F, 125G, and 125H identifies a different column of the sensor array 110. Figure 5C, each of lines 125E, 125F, 125G, and 125H is in contact with one of the sensors 105 along the cross section (that is, line 125E is in contact with the top of sensor 105E, line 125F is in contact with the top of sensor 105F, line 125G is in contact with the top of sensor 105G, and line 125H is in contact with the top of sensor 105D), and line 125D is in contact with the bottom of each of sensors 105E, 105F, 105G, and 105D. Similarly, and as Figure 5D As shown in , each of lines 125A, 125B, 125C and 125D contacts the bottom of one of the sensors 105 along the cross section (that is, line 125A contacts the bottom of sensor 105A, line 125B contacts the bottom of sensor 105B, line 125C contacts the bottom of sensor 105C, and line 125D contacts the bottom of sensor 105D), and line 125H contacts the top of each of sensors 105D, 105C, 105B and 105A.

[0147] Figure 5B The sensor 105 and the portion of the wire 125 connected to the sensor array 110 are depicted using dashed lines to indicate that they may be embedded within the device 100. As described above, the sensor 105 may be protected (e.g., by an insulator) from the contents of the fluid chamber 115, which itself may be sealed. Thus, it should be understood that the various illustrated components (e.g., wire 125, sensor 105, binding site 116, etc.) are not necessarily visible in the physical instantiation of the device 100 (e.g., they may be embedded in or covered by a protective material such as an insulator).

[0148] In some embodiments, some or all of the binding sites 116 reside in nanopores or grooves in the wire 125 that passes through the sensor 105. For example, Figure 5D As shown in the example of FIG. 1 , line 125H can be thinner on sensor 105 than it is between sensors 105. For example, line 125H has a first thickness over sensor 105D, a second, larger thickness between sensors 105D and 105C, and a first thickness over sensor 105C. This configuration can be advantageously fabricated using conventional thin film fabrication methods (e.g., by depositing material, applying a mask to the deposited material, and removing (e.g., by etching) some of the deposited material in accordance with the mask). Binding sites 116 and, if present, nanopores can both be fabricated using conventional techniques.

[0149] To simplify the explanation, Figure 5B , 5C5D illustrate an exemplary device 100 having only sixteen sensors 105, only sixteen individual binding sites 116, and eight wires 125 in the sensor array 110. It should be appreciated that the device 100 may have fewer or more sensors 105 in the sensor array 110, and therefore, may have more or fewer binding sites 116. Similarly, embodiments including wires 125 may have more or fewer wires 125. In general, any configuration of sensors 105 and binding sites 116 may be used that allows the sensor 105 to detect a tag attached to a nucleotide incorporated into a single nucleic acid strand attached to the binding site 116. Similarly, any configuration of one or more wires 125 or some other mechanism that allows for determining whether a sensor 105 has sensed one or more tags may be used. The examples presented herein are not intended to be limiting.

[0150] As explained above, the Figure 5B , 5C 5D may be a magnetic sensor 105. Thus, the sensor 105 is in close proximity to the binding site 116, and therefore, it is also in close proximity to the nucleic acid strand that binds to the binding site 116. It will be appreciated that the appropriate location of the sensor array 110 relative to the binding site 116 depends in part on the type of label used, and therefore on the type of sensor 105 used. For example, if the label is a fluorophore, and the sensor 105 is an optical sensor, then it may be appropriate for the sensor array 110 to be located away from the binding site 116 (e.g., located above the binding site 116).

[0151] although Figure 5B , 5C 5D (and other figures herein) illustrate sensors 105 and binding sites 116 in a one-to-one relationship, but it should be understood that each binding site 116 can be sensed by more than one sensor 105. A characteristic that distinguishes the SMAS device 100 from the CLUS device is that the sensors 105 of the SMAS device 100 do not sense more than one instance of a nucleic acid strand. If the SMAS device 100 has more sensors 105 than binding sites 116, it may be feasible to sense at least some nucleic acid strands by multiple sensors 105 (e.g., to improve the accuracy of marker detection).

[0152] Shown and described in Figure 5B , 5C The exemplary sensor array 110 in the context of 5D is a rectangular array in which the sensors 105 are arranged in rows and columns. In other words, the plurality of sensors 105 of the sensor array 110 are arranged in a rectangular grid pattern. In some embodiments, adjacent rows and columns of the rectangular grid pattern are equidistant from each other, which results in the sensors 105 being arranged in a square grid (or lattice) pattern, such as Figure 5EIn an embodiment where the sensors 105 are arranged in a square grid pattern, each sensor 105 has up to four nearest neighbors. For example, Figure 5E As shown in FIG. 1 , sensor 105A has four nearest neighbors, labeled 105B, 105C, 105D, and 105E. Figure 5E , the closest sensor 105 is a nearest neighbor distance 112. Thus, each of sensors 105B, 105C, 105D, and 105E is a distance 112 from sensor 105A.

[0153] A commercially viable SMAS device 100 can use high-precision nanoscale fabrication of densely packed nanoscale sensors 105 capable of identifying individual tags. The size of the functionalized binding sites 116 can be similar to the size of, for example, the DNA to which the tags are attached, so that multiple strands cannot bind to the same binding site 116 or be sensed by the same sensor 105. A recognized metric for evaluating the commercial competitiveness of a sequencer is the degree of density with which the DNA strands are packed together in the fluid chamber 115.

[0154] A suitable value for the nearest neighbor distance 112 can be determined based on the properties of the sensor 105, the length of the nucleic acid strands that the device 100 is intended to sequence, and the properties of the labels used, which can then be used to determine the size of the SMAS device 100 and / or the maximum number of sensors 105 that can be assembled within a SMAS device 100 of a selected size. For example, the combined length of the nucleic acid strands and the size of the labels to be used can provide a physical limit on how close two sensors 105 in a SMAS device 100 can be positioned. In some embodiments, the size of the sensor 105 can be limited by the nanoscale patterning capabilities of the process used to manufacture the SMAS device 100. For example, using the technology available at the time of writing, the size of each magnetic sensor 105 (e.g., the diameter of the sensor 105 in the xy plane, assuming a cylindrical sensor 105) can be about 20nm. Assuming that the type of nucleic acid to be sequenced is DNA, and that it is desired to sequence fragments up to 150 base pairs (bp) in length, the maximum length of the DNA chain 101 to be sequenced in the elongated state is about 50 nm, although the ssDNA conformation can vary between the elongated and helical forms, such as Fig. 6A As shown in , it depends on the ionic strength of the buffer. Because the marker 102 participates in the unimolecular reaction, the marker 102 should have a molecular size. For the SMAS device 100 using the magnetic sensor 105, the marker 102 can be, for example, a superparamagnetic nanoparticle, an organic metal compound, or any other functional molecular group that can be detected by the nanoscale magnetic sensor 105. Therefore, it is assumed that each marker 102 has a size no greater than about 10 nm. Under these assumptions, Figure 6BThe relative sizes of the magnetic sensor 105, the DNA strand 101 in an elongated state, and the magnetic label 102 are shown.

[0155] The actual SMAS device 100 using magnetic sensors 105 to detect magnetic nanoparticles used as markers 102 can be implemented using existing technology. For the sake of demonstration, it is assumed that only markers 102 within 20nm of the edge of the sensor 105 are detected. The detection range of each sensor 105 is small because the magnetic markers 102 (e.g., superparamagnetic nanoparticles, organometallic compounds, etc.) that can be selected for nucleic acid sequencing applications do not produce significant disturbances to the detected magnetic field. Although the markers 102 attached to the nucleotides incorporated into the ssDNA bound to the binding site 116 of a particular sensor 105 can temporarily reside outside the range of the individual sensors 105 because the ssDNA assumes various conformational states during the detection process, it is expected that the markers are not allowed to reach the sensitive space (detection area) of the adjacent sensor 105 when the ssDNA assumes its fully elongated state.

[0156] The sensor packing limit of a practical SMAS device 100 can be derived, for example, assuming that the markers are superparamagnetic nanoparticles (e.g., iron oxide, iron platinum, etc.), and that the sensor array 110 of the SMAS device 100 is a rectangular (e.g., square) array of magnetic tunnel junctions (MTJs) similar to those used in non-volatile data storage applications. In this case, an area of ​​each nanoscale sensor 105 or its immediate vicinity can be functionalized to serve as a respective binding site 116. A simple geometric arrangement for estimating the sensor array packing limit of the SMAS device 100 is shown in Fig. 7A , which shows two sensors 105A, 105B. Each sensor 105A, 105B (assumed to have a cylindrical shape for convenience only) is assumed to have a diameter of about 20 nm (as described above) and is assumed to be able to detect any mark within 20 nm from its edge. The sensing area boundary 111 is shown in Fig. 7A101A, 101B. The maximum reaches of the labels 102A, 102B when attached to nucleotides incorporated into the chains 101A, 101B (e.g., when a DNA chain having 150 bases is in its fully non-helical state) are shown by the outer dotted circle 103. In order to make the sequencing results accurate, it is desirable that each sensor 105 detects only the labels 102 attached to the nucleotides incorporated into the DNA chain 101 bound to the respective binding site 116 of the sensor 105. Therefore, under the assumptions described above, the minimum nearest neighbor distance 112 between the sensors 105 to avoid crosstalk (e.g., detecting labels 102 attached to nucleotides incorporated into the nucleic acid chain 101 bound to the binding site 116 of another sensor 105) is about 100 nm.

[0157] In some embodiments of the SMAS device 100, the sensors 105 (eg, MTJs) are arranged in a square grid that is compatible with existing cross-point MRAM sensor geometries, such as Figure 7B The area of ​​the unit cell 114 is 10 4 nm 2 , which allows each DNA strand 101 to extend through approximately 10 4 nm 2 area, which yields a DNA surface density of approximately 10 10 Chains / cm 2 Assuming that at least ten instances of each chain 101 are used in the sensor array 110, approximately 10 9 Unique chains / cm 2 , generating 150Gbase (1 billion×150bp DNA strand length) of information per square centimeter of sensor array 110. Under ideal conditions (e.g., when the chemical failure rate is low and only three DNA samples are needed, as discussed further below), approximately 3.3×10 9 Different chains / cm 2 , and each square centimeter of the sensor array 110 can generate approximately 500Gbase data.

[0158] As a specific example, a SMAS device 100 having a configuration similar to a single Toshiba 4Gbit density STT-MRAM chip first introduced at the International Electron Devices Meeting (IEDM) in 2016 can potentially produce about 600Gbase of high quality data. The minimum distance 112 between sensors 105 of the Toshiba platform is 90nm, which is only slightly lower than the estimated minimum distance 112 of 100nm derived above. Therefore, crosstalk using a configuration similar to the Toshiba platform may still be low even for ssDNA of 150 bases in length, but shorter fragments can be sequenced to reduce crosstalk even further.

[0159] It should be understood that the sensor 105 is arranged in a grid pattern (e.g., as shown in FIG. Figure 7B The arrangement of the sensors 105 in a square grid is one of many possible arrangements. One of ordinary skill in the art will appreciate that other arrangements of the sensors 105 are possible and within the scope of the disclosure herein. For example, the sensors 105 may be arranged in a hexagonal pattern, such as Fig. 8A , which shows a top view of the SMAS device 100. Fig. 8A The exemplary SMAS device 100 in FIG. 1 includes a sensor array 110 for sensing markers 102 within a fluid chamber 115. The sensor array 110 includes a plurality of sensors 105, of which sixteen sensors 105 are shown. It should be appreciated that implementations of the device 100 may include any number of sensors 105 (e.g., hundreds, thousands, millions, etc.). To avoid obscuring the drawings, the Fig. 8A Only two of the sensors 105 are labeled, namely sensors 105A and 105B. As described above, the sensors 105 may be, for example, magnetic sensors (e.g., to detect the effects of magnetism or magnetic nanoparticles). Figure 5B , 5C As described in the discussion of 5D and 5D, in general, sensor 105 can have any suitable size and shape.

[0160] like Fig. 8A As shown in FIG. 1 , each of the sensors 105 is associated with a respective binding site 116. In other words, the sensors 105 and the binding sites 116 are in a one-to-one relationship. Fig. 8A As shown in FIG. 1 , sensor 105A is associated with binding site 116A, sensor 105B is associated with binding site 116B, and each of the other unlabeled sensors 105 is also associated with a respective binding site 116. Fig. 8AIn the example embodiment of FIG. 1 , each sensor 105 is shown disposed below its respective binding site 116, but it should be appreciated that the binding site 116 may be located at other locations relative to its respective sensor 105. For example, the binding site 116 may be located to the side of its respective sensor 105. Figure 5B , 5C The discussion of binding site 116 in the description of 5D applies to Fig. 8A and other diagrams showing the binding site 116 and are not repeated here.

[0161] Fig. 8A The exemplary SMAS device 100 also includes the Figure 5B , 5C and the fluid chamber 115 in the discussion of 5D. Those descriptions also apply to Fig. 8A And will not be repeated here.

[0162] Fig. 8A The circuit 120 of the device 100 may include one or more lines 125 . Fig. 8A Each of the lines 125 in the exemplary embodiment of identifies a row or a diagonal column of the sensor array 110. For example, each of the lines 125A, 125B, 125C, and 125D identifies a different row of the sensor array 110, and each of the lines 125E, 125F, 125G, and 125H identifies a different diagonal column of the sensor array 110. Fig. 8A In the example of FIG. 1 , device 100 has eight wires 125A, 125B, 125C, 125D, 125E, 125F, 125G, and 125H, and pairs of wires 125 can be used to access individual sensors 105. For example, wires 125A and 125H can be used to access sensor 105A, and wires 125B and 125H can be used to access sensor 105B. Wires 125 can be oriented below and / or above sensors 105, such as Figure 5B , 5C As described in the discussion of 5D et al.

[0163] although Fig. 8AAn exemplary device 100 is illustrated having only sixteen sensors 105, only sixteen corresponding binding sites 116, and eight wires 125 in the sensor array 110, but it should be understood that the SMAS device 100 may have fewer or more sensors 105 in the sensor array 110, and therefore, it may have more or fewer binding sites 116. In addition, the SMAS device 100 may have more or fewer wires 125. In general, any configuration of sensors 105 and binding sites 116 may be used that allows the sensor 105 to detect a tag attached to a nucleotide incorporated into a single nucleic acid strand attached to the binding site 116. Similarly, any configuration of one or more wires 125 or some other mechanism that allows for determining whether a sensor 105 has sensed one or more tags may be used.

[0164] like Figure 8B As shown in FIG. 1 , when the sensors 105 are arranged in a hexagonal pattern, each sensor 105 has at most six nearest neighbors, all at the nearest neighbor distance 112. In other words, each sensor 105 is at a nearest neighbor distance 112 from each of the six other sensors 105 closest to it. For example, Figure 8B As shown in FIG. 1 , the unlabeled sensor 105 in the middle of the drawing has six nearest neighbor sensors 105 , labeled 105A, 105B, 105C, 105D, 105E, and 105F, all of which are a nearest neighbor distance 112 away.

[0165] The packing limit of binding sites 116 can be derived for a SMAS device 100 using an optical sensor and fluorescent labels 102 (e.g., fluorophores) and having a hexagonal pattern of binding sites 116. Assuming that the labels 102 are fluorophores, the binding sites 116 are in a hexagonal pattern, and the sensor array 110 is far from the binding sites 116, single-molecule fluorescence from the labels 102 can be projected into the far field where it can be detected by the sensor array 110 including the photosensitive sensors 105. Single-molecule super-resolution imaging techniques (such as those described in CG Galbraith and JA Galbraith, "Super-resolution microscopy at a glance", Journal of Cell Science, Vol. 124(10), 1607-11 (2011)) can be used to resolve the location of individual fluorophore labels 102 in the SMAS device 100. Because the DNA packaging size is well below the diffraction limit, the position of the fluorophore label 102 can be resolved. Although this type of detection may be somewhat complex and / or expensive, the technology has recently been introduced in commercial sequencing systems to improve the throughput of cluster-based sequencers. In addition, the technology may be implemented in the imaging of large single-molecule arrays in the near future.

[0166] A simple geometric arrangement for estimating the packing limit of binding sites 116 located in a hexagonal pattern in a SMAS device 100 using fluorophore labels 102 is shown in Fig. 9A DNA strand 101A is bound to binding site 116A, and DNA strand 101B is bound to binding site 116B. (Sensor 105 is not shown in FIG. Fig. 9A ) because the sensor array 110 is assumed to be far away from the binding sites. ) The maximum reach of the labels 102A, 102B (e.g., when a DNA strand having 150 bases is in its fully non-helical state) (when attached to an incorporated nucleotide) is represented by the dotted circle 103. To avoid crosstalk, fluorophore labels 102 attached to adjacent binding sites 116 are not allowed to occupy overlapping space during the imaging process, e.g., a fluorophore label 102A attached to a particular binding site 116A should not be allowed to reach a space accessible to a fluorophore label 102B attached to an adjacent binding site 116B when the ssDNA 101A is exploring its allowed conformational states. Such restrictions also help to avoid fluorescence quenching. Assuming that fluorophore labels 102 are used, the binding sites 116 can be densely packed in a hexagonal lattice, such as Fig. 9BAssume that the maximum length of the 150 bp DNA strand 101 is 50 nm, the size of the fluorophore label 102 is 10 nm, the minimum distance from the center of each binding site 116 to its edge is 20 nm, and each DNA strand 101 binds to the center of its respective binding site 116, and the minimum distance 112 is 140 nm. Therefore, Fig. 9B As shown in the figure, each DNA chain 101 is allowed to occupy 1.7×10 4 nm 2 The area of ​​the unit grid is 114, which yields 5.9×10 9 Chains / cm 2 , or 5.9×10 if there are about 10 instances of each DNA strand in the SMAS device 100 8 Unique chains / cm 2 The SMAS device 100 will generate about 90 Gbase of data per square centimeter of the sensor array 110. In the best case scenario, when only 3 DNA replicas are needed, the sensor array 110 maintains about 2×10 9 Unique DNA strands / cm 2 , and the SMAS device 100 is capable of generating approximately 300 Gb of data per square centimeter of the sensor array 110.

[0167] The above discussion of hexagonal arrays is in the context of fluorophore labels 102 and optical sensors 105. Hexagonal arrangements of magnetic sensors 105 may also be used. Fig. 7A and 7B The sensor packaging limit of the SMAS device 100 with a hexagonal arrangement of binding sites 116 and magnetic sensors 105 is obtained as described in the discussion of . For the magnetic sensors 105, the nearest neighbor distance 112 is about 100 nm, which means that the (hexagonal) unit grid area 114 (see Fig. 9B ) is about 8.7×10 3 nm 2 .

[0168] Fig.10 Comparison described in Fig. 7A and 7B (magnetic marker 102 and magnetic sensor 105) and Fig. 9A and 9B The density of the SMAS implementation in the context of (fluorescent markers 102 and optical sensors 105) is comparable to the density of the current state-of-the-art CLUS sequencer. For the sake of argument, assume that the pitch of the nanopore array of the patterned flow cell is about 500 nm. Fig.10As shown in the left-hand panel of FIG, the nanopores of the CLUS sequencer are arranged in a hexagonal lattice with a lattice constant of 500 nm. Each nanopore holds about 50 to about 200 identical DNA strands (generated, for example, by solid-phase bridge amplification). Fig.10 The upper right-hand side of the figure shows the hexagonal SMAS grid using fluorophore labeling and super-resolution imaging (e.g. Fig. 9A and 9B ), and Fig.10 The lower right hand side of FIG. 1 shows a square SMAS grid of a sensor array 110 using superparamagnetic nanoparticle labels and MTJs (e.g., Fig. 7A and 7B ). Fig.10 The three in the figure are scaled to show the extent to which the SMAS lattice configuration compares to the CLUS configuration. The black hexagons (left and upper right) and squares (lower right) mark the unit lattice that holds the minimum number of individual molecules required to recognize the sequence of nucleic acid strands. For the SMAS lattice, an ideal case is illustrated in which only three DNA strands are required for successful base recognition, which is discussed in further detail below. It should be noted that in the SMAS case ( Fig.10 ), the DNA instances are randomly distributed throughout the sensor array 110, and their positions can be identified during the first sequencing cycle, as discussed further below.

[0169] like Fig.10 As shown in the figure, the area of ​​the unit grid of the CLUS device is 2.2×10 5 nm 2 , which corresponds to 4.6×10 8 Clusters / cm 2 Using the assumptions made above, the CLUS sequencer generates about 70 Gbase of data per square centimeter of sensing area. Conversely, in an ideal situation, when only three instances of a chain are used, the SMAS device 100 generates about 500 Gb / cm 2 (magnetic sensor 105 (e.g., MTJ) and magnetic marker 102 (e.g., superparamagnetic nanoparticles)) and about 300 Gb / cm 2 (Optical sensor 105 (super-resolution imaging) and fluorescent label 102) data. Results for exemplary implementations of the CLUS sequencer and SMAS device 100 are summarized in the following table, which estimates sequencing throughput assuming only three instances per DNA strand and assuming ten instances per DNA strand for the SMAS implementation.

[0170]

[0171] The above table shows that when the number of DNA instances used for algorithm error correction described further below is small (e.g. <10), the SMAS device 100 outperforms the current state-of-the-art CLUS device. As the error correction process relies on more instances of each ssDNA, the SMAS device 100 begins to behave like a CLUS device, and unlike sensing clusters, there is little benefit in sensing individual molecules. Fluorescent SMAS essentially represents the limitation of reducing clusters to single molecules. One way to reduce sequencing costs is to reduce cluster size and pack DNA clusters closer to each other in order to get more information from the fixed sensing area. Although this approach reduces the amount of reagents required to run sequencing chemistry, it also significantly increases the complexity and cost of imaging hardware by continuously pushing the limits of what is currently possible with commercial optical instruments. The strategy is a difficult task because in-scaling cannot be performed without concurrent improvements in chemistry. This is because as clusters become smaller, each reaction becomes more and more important, and chemical failures that occur randomly at the single molecule level become more obvious and difficult to tolerate.

[0172] The cost of implementing super-resolution imaging in a CLUS device makes the SMAS device 100, and particularly those using magnetic sensors 105 and magnetic labels, a possible destructive sequencing alternative. The SMAS devices 100 disclosed herein, and particularly those using magnetic sensors 105, ensure excellent throughput at significantly lower instrument costs by using technology developed by the large-scale semiconductor and data storage industries and mass manufacturing.

[0173] SMAS sequencing scheme

[0174] As described above, when the SMAS device 100 is used for nucleic acid sequencing, the nucleic acid chain can be amplified before or after the nucleic acid is added to the SMAS device 100 (e.g., using bridge amplification). Regardless of how the nucleic acid is amplified, the chain can be sequenced one base at a time by SBS (e.g., by synthesizing dsDNA from ssDNA). The SMAS sequencing scheme is described assuming that the sequenced nucleic acid is DNA. It should be understood that the disclosed scheme can be modified for sequencing other nucleic acids. Such modifications will be within the capabilities of a person of ordinary skill in the art through an understanding of the disclosure herein.

[0175] To simplify the analysis and illustrate the benefits of using the disclosed SMAS device 100 instead of a CLUS sequencer, consider a DNA sequencing scenario in which a single type of label (e.g., molecular, fluorescent, magnetic, etc.) is attached to all four nucleotides (A, T, C, and G). In other words, the same label of a certain type is attached to each of the four nucleotides (e.g., if the selected label 102 is a FePt particle, each of A, T, C, and G is labeled with a FePt particle). These labeled nucleotides are then incorporated into the DNA chain one base at a time using termination chemistry, such as once the nucleotide is incorporated, the label 102 is cleaved before the polymerase moves to the next base. The sensor 105 detects the label 102 attached to the nucleotide.

[0176] An exemplary method 200 for sequencing multiple nucleotide chains (e.g., ssDNA) using the SMAS device 100 is shown in Fig.11 At 202, the method begins. At 204, one or more nucleic acid strands are optionally amplified before being added to the SMAS device 100. At 206, a plurality of S nucleic acid strands are bound to a plurality of S binding sites 116 of the SMAS device 100 (wherein the plurality includes at least two but not necessarily all binding sites 116 of the SMAS device 100). Optionally, at 208, the nucleic acid strands are amplified (e.g., via bridge amplification, which may be in addition to or performed in the amplification at 204). At 210, a sequencing procedure is performed. The sequencing procedure may be, for example, an additive method, a subtractive method, or a modified additive method as further described below. The sequencing procedure performed at 210 generates S records, each of the S records capturing M detection results of one of the plurality of S sensors (wherein, again, the plurality includes at least two but not necessarily all sensors 105 in the SMAS device 100, and the M detection results may include as few as one detection result, some subset of the total number of detection results obtained during the sequencing procedure, or all detection results obtained during the sequencing procedure). Each of the M detection results indicates whether the sensor 105 corresponding to the record detected at least one marker during a respective step of the M query steps. The M detection results may be stored in a record, which may be stored in a memory. At 212, an error correction procedure is performed, as further described below. The error correction procedure may include deterministic and / or probabilistic error correction techniques. The error correction procedure may be performed, for example, by at least one processor 130 of the SMAS device 100. Alternatively, it may be performed by a processor external to the SMAS device 100 (e.g., an off-device processor, such as in an external computer). The error correction procedure may be performed while the sequencing procedure is being performed (e.g., in real time or near real time), or it may be performed at some later time. At 214, the method 200 ends.

[0177] As described above, at 210, the SMAS device 100 can be used to implement a variety of schemes to read nucleic acid sequences (e.g., DNA sequences). In order to simplify the analysis, it is assumed that the multiple S sensors 105 of the SMAS device 100 only detect the presence or absence of the marker 102 and do not distinguish nucleotides based on the detected signal level. Therefore, in some embodiments, the record of the detection results of each sensor 105 only includes a "yes" or "no" (or 1 / 0 or any other binary indicator) indication that the sensor 105 detected the marker or did not detect the marker during a specific query step. It should be understood that other methods are feasible and within the scope of the disclosure herein. For example, different markers 102 may be attached to different nucleotides. As another example, different from a binary "yes" or "no" decision, a characteristic value (e.g., resistance, frequency, intensity, etc.) and / or recording can be detected, and a decision on whether a marker is detected is made based on the above basis. For example, instead of only using 0 and 1 (or "no" and "yes") as possible outputs of the sequencing program, using different labels for different nucleotides can result in one of the following five levels: 0 (label not detected), level 1 (label 1 detected), level 2 (label 2 detected), level 3 (label 3 detected), and level 4 (label 4 detected). In this case, the range of the detected characteristic can be limited to distinguish whether the label is fully detected and if detected, which label is detected (e.g., if the characteristic value is between 0 and the first value, it is determined that the label is not detected; if the characteristic value is between the first value and the second value, it is determined that the first label is detected; if the characteristic value is between the second value and the third value, it is determined that the second label is detected; etc.).

[0178] Below is an illustration of three examples of a DNA sequencing protocol, each of which includes repeated query cycles, each of which has four query steps. During each query cycle, four binary "yes" or "no" questions are answered for each ssDNA sequenced. In one query step, the question "Is the detected base adenine?" ("A?") is answered. In another query step, the question "Is the detected base thymine?" ("T?") is answered. In another query step, the question "Is the detected base cytosine?" ("C?") is answered. And in another query step, the question "Is the detected base guanine?" ("G?") is answered. The record of the detection results obtained during the sequencing procedure can be established as a query cycle, including repeated query cycles. Query Step. It should be understood that the order in which nucleotides are introduced and bases are detected is arbitrary (meaning that the order of the query step is arbitrary), and the order in which the bases are tested in the examples herein are This is exemplary only.

[0179] Additive method

[0180] In the additive method, the sensor 105 detects nanoscale labels 102 bound to nucleotides with cleavable linkers. All four types of nucleotides carry the same type of label 102 (e.g., molecular, fluorescent, magnetic, etc.) and use the same type of cleavable linker. According to one embodiment, a query cycle that will produce four detection results (one of which will (in the absence of errors) be a label detection for each of the plurality of S nucleic acid strands 101) involves the following steps:

[0181] 1. Obtaining baseline characteristics of each of the plurality of S sensors 105 (which may be all or less than all of the sensors 105 in the sensor array 110 ) of the SMAS device 100 (eg, by determining a baseline signal at each of the plurality of S sensors 105 ).

[0182] 2. Labeled A nucleotides are introduced and incorporated. Unbound labeled molecules are washed away.

[0183] 3. Query step 1: Get the characteristics of each of the plurality of S sensors 105 (e.g., by detecting the signal at each of the plurality of S sensors 105) and determine whether each sensor 105 detects at least one tag. Save the detection result of each sensor 105 at a location in the record corresponding to query step 1 of the current query cycle.

[0184] 4. Labeled T nucleotides are introduced and incorporated. Unbound labeled molecules are washed away.

[0185] 5. Query step 2: Get the characteristics of each of the plurality of S sensors 105 (e.g., by detecting the signal at each of the plurality of S sensors 105) and determine whether each sensor 105 detects at least one tag. Save the detection result of each sensor 105 at a location in the record of query step 2 corresponding to the current query cycle.

[0186] 6. Introduce and incorporate labeled C nucleotides. Wash away unbound labeled molecules.

[0187] 7. Query step 3: Get the characteristics of each of the plurality of S sensors 105 (e.g., by detecting the signal at each of the plurality of S sensors 105) and determine whether each sensor 105 detects at least one tag. Save the detection result of each sensor 105 at a location in the record of query step 3 corresponding to the current query cycle.

[0188] 8. Introduce and incorporate labeled G nucleotides. Wash away unbound labeled molecules.

[0189] 9. Query step 4: Get the characteristics of each of the plurality of S sensors 105 (e.g., by detecting the signal at each of the plurality of S sensors 105) and determine whether each sensor 105 detects at least one tag. Save the detection result of each sensor 105 at a location in the record of query step 4 corresponding to the current query cycle.

[0190] 10. Cut and wash away the labels of A, T, C and G nucleotides.

[0191] Then steps 1 to 10 can be repeated for the next query cycle. It should be understood that some of the ordering of steps 1 to 10 is exemplary, and further, the number and numbering of steps 1 to 10 are for convenience and can be modified. As an example, and as described above, the order in which nucleotides are introduced is arbitrary. As another example, steps 2, 4, 6 and 8 include introducing and incorporating nucleotides, and washing away unbound nucleotides in a single step, but it should be understood that each of steps 2, 4, 6 and 8 can be divided into a series of smaller steps. Similarly, steps 3, 5, 7 and 9 can be further divided into a series of smaller steps (e.g., obtaining characteristics, determining whether a tag is detected, and storing the detection results). On the contrary, steps can be combined (e.g., steps 2 and 3 can be combined, steps 4 and 5 can be combined, etc.).

[0192] It should be understood that if no errors may occur during any query cycle of the additive method, the individual bases of the individual strands can be identified (determined) once the label is detected. For example, referring to the above steps, if at query step 1 involving a labeled A nucleotide, for a particular sensor 105, the resulting characteristic indicates that the sensor 105 detects the label, then saving the detection result can be equivalent to identifying the base (T) complementary to A of the detector 105 (and the binding site 116). Similarly, if at query step 2 involving a labeled T nucleotide, for a particular sensor 105, the resulting characteristic indicates that the sensor 105 detects the label, then saving the detection result can be equivalent to identifying the base (A) complementary to T of the detector 105 (and the binding site 116). Similarly, if at query step 3 involving a labeled C nucleotide, for a particular sensor 105, the resulting characteristic indicates that the sensor 105 detects the label, then saving the detection result can be equivalent to identifying the base (G) complementary to C of the detector 105 (and the binding site 116). Finally, if at query step 4 involving a labeled G nucleotide, for a particular sensor 105, the resulting characteristic indicates that the sensor 105 detected the label, then saving the detection result can be equivalent to identifying the base (C) complementary to the G for that detector 105 (and binding site 116). However, as described in further detail below, there are several types of errors that can occur during the sequencing process (e.g., during the additive method), and therefore, in some embodiments, a record is established during the sequencing process to record the detection / non-detection of the label during each query step of each query cycle. An error correction procedure can then be applied to some or all of the records before the base is identified.

[0193] Fig.12 2 is a flow chart of a sequencing process 220 using an additive method according to some embodiments. The sequencing process 220 may be, for example, as shown and described in Fig.11The sequencing procedure performed at step 210 of the exemplary method 200 for sequencing multiple nucleic acid chains (e.g., ssDNA) using the SMAS device 100 in the discussion of . At 222, the sequencing procedure 220 begins. At 224, a baseline characteristic of each of the S sensors 105 is obtained (e.g., by at least one processor 130 of the SMAS device 100, with the aid of the circuit 120). When the query cycle begins, at 226, a first labeled nucleotide is selected (e.g., referring to steps 1 to 10 above, the first labeled nucleotide will be A). At 228, the selected labeled nucleotide is introduced into the fluid chamber 115 and the nucleotide is potentially incorporated into the nucleic acid chain bound to the binding site 116. At 230, unbound nucleotides are washed away. At 232, characteristics are obtained from each of the plurality of S sensors, and the detection results of each of the plurality of S sensors 105 are determined (e.g., a label is detected or a label is not detected). At 234, S test results are recorded in S records (e.g., with 1 indicating that a tag is detected or with 0 indicating that a tag is not detected). At 236, it is determined whether the last tested nucleotide is the last nucleotide of the query cycle. For the example ordering of the nucleotide test assumed in steps 1 to 10 above, it is determined at 236 (e.g., by at least one processor 130) whether G is the last tested nucleotide. If not, then at 238, the next labeled nucleotide to be tested in the query cycle is selected, and steps 228 to 236 are repeated until the last tested nucleotide is determined to be the last nucleotide of the query cycle at 236. At 240, the tag is cut and rinsed off. At 242, it is determined (e.g., by at least one processor 130) whether the last completed query cycle is the last query cycle of the sequencer 220. For example, the at least one processor 130 can determine whether enough test results have been recorded to enable at least one processor 130 (or some other processing entity, such as an external processor) to determine the target number of bases (e.g., 150 bases). If not, the sequencing process 220 returns to step 224. If so, the sequencing process 220 ends at 244. Again, as explained above, the order in which the nucleotides are tested is arbitrary.

[0194] The additive sequencing protocol, which in the exemplary case of DNA sequencing comprises four nucleotide incorporations and one label cleavage reaction, is summarized in Fig.13 middle. Fig.13The leftmost inset of illustrates a sensor array 110 with a total of 100 individual sensors 105, which are shown in squares. For the purpose of illustration, it is assumed that each of the 100 binding sites 116 in the sensor array 110 holds a separate DNA strand, and each DNA strand is sensed by a separate sensor 105 (in other words, the binding sites 116 and the sensors 105 are in a one-to-one relationship). Some DNA strands may be copies of other DNAs. Labeled nucleotides are added to the fluid chamber 115 one type at a time, and the labels are cut simultaneously after the nucleotides are incorporated. In the absence of errors, base recognition can be completed after five reactions (that is, four nucleotide incorporations and one base cutting reaction). If an error occurs, an error correction procedure as described below can be applied.

[0195] Subtractive Method

[0196] In the subtractive method, the sensor 105 detects nanoscale labels 102 bound to nucleotides with cleavable linkers. All four types of nucleotides carry the same type of label (e.g., molecular, fluorescent, magnetic, etc.), but each has a different type of cleavable linker. In one embodiment, a query cycle that will produce four detection results (one of which will (in the absence of errors) be a label detection for each of the plurality of three nucleic acid chains 101) in the absence of errors involves the following steps:

[0197] 1. Simultaneously introduce labeled A, T, C, and G nucleotides, incorporate, and wash out unbound labeled molecules. Obtain a baseline characteristic for each of the plurality of S sensors 105 (e.g., by detecting a signal at each of the plurality of S sensors 105). In the absence of errors, all sensors 105 will detect the label.

[0198] 2. Query step 1: Introduce a reagent (e.g., an enzyme) that cleaves the tag only from the first nucleotide (e.g., A), wash, and obtain a characteristic (e.g., a measurement signal) at each of the plurality of S sensors 105. Determine (e.g., based on a change in a baseline characteristic) which sensors 105 are no longer detecting the tag. Save the detection results of each sensor 105 at a location in the record corresponding to query step 1 of the current query cycle.

[0199] 3. Query step 2: Introduce a reagent that cleaves the label only from the second nucleotide (e.g., T), wash, and obtain a characteristic (e.g., assay signal) at each of the plurality of S sensors 105. Determine (e.g., based on a change in baseline characteristic) which sensors 105 are no longer detecting the label. Save the detection result of each sensor 105 at a location in the record corresponding to query step 2 of the current query cycle.

[0200] 4. Query step 3: Introduce a reagent that cleaves the label only from the third nucleotide (e.g., C), rinse, and obtain a characteristic (e.g., assay signal) at each of the plurality of S sensors 105. Determine (e.g., based on a change in the baseline characteristic) which sensors 105 are no longer detecting the label. Save the detection results of each sensor 105 at a location in the record corresponding to query step 3 of the current query cycle.

[0201] 5. Query step 4: Introduce a reagent that cleaves the label only from the fourth nucleotide (e.g., G), wash, and obtain a characteristic (e.g., a measurement signal) at each of the plurality of S sensors 105. Determine (e.g., based on a change in the baseline characteristic) which sensors 105 are no longer detecting the label. Save the detection results of each sensor 105 at a location in the record corresponding to query step 4 of the current query cycle.

[0202] For the next query cycle, steps 1 to 5 may be repeated. It should be appreciated that the ordering of certain of steps 1 to 5 is exemplary, and further, the number and numbering of steps 1 to 5 is for convenience and may be modified. As an example, and as previously described, the order in which the nucleotides are cleaved is arbitrary. Similarly, in step 1, nucleotides may be introduced sequentially (not necessarily simultaneously). As another example, query steps 1, 2, 3, and 4 include introducing reagents, washing, obtaining characteristics, determining which sensors are no longer (or still) detecting the marker, and saving the results in a single step, but it should be appreciated that each query step may be divided into a series of smaller steps.

[0203] It should be understood that if no errors may occur during any query cycle of the subtractive method, the individual bases of the individual strands can be identified (determined) once the removal of the label (label absence) is first detected. For example, referring to the above steps, if at query step 1 involving a labeled A nucleotide, for a particular sensor 105, the resulting characteristic indicates that the sensor 105 is no longer detecting the label, then saving the detection result can be equivalent to identifying the base (T) complementary to A of the detector 105 (and binding site 116). Similarly, if at query step 2 involving a labeled T nucleotide, for a particular sensor 105, the resulting characteristic indicates that the sensor 105 is no longer detecting the label, then saving the detection result can be equivalent to identifying the base (A) complementary to T of the detector 105 (and binding site 116). Similarly, if at query step 3 involving a labeled C nucleotide, for a particular sensor 105, the resulting characteristic indicates that the sensor 105 is no longer detecting the label, then saving the detection result can be equivalent to identifying the base (G) complementary to C for the detector 105 (and binding site 116). Finally, if at query step 4 involving a labeled G nucleotide, for a particular sensor 105, the resulting characteristic indicates that the sensor 105 is no longer detecting the label, then saving the detection result can be equivalent to identifying the base (C) complementary to G for the detector 105 (and binding site 116). However, as further detailed below, there are several types of errors that can occur during the sequencing process (e.g., during the subtractive method), and therefore, in some embodiments, a record is established during the sequencing process to record the detection / non-detection of the label during each query step of each query cycle. An error correction procedure can then be applied to some or all of the records before the base is identified.

[0204] Fig.14 2 is a flow chart of a sequencing process 250 using a subtractive method according to some embodiments. The sequencing process 250 may be, for example, as shown and described in Fig.11The sequencing procedure performed at step 210 of the exemplary method 200 for sequencing multiple nucleic acid chains (e.g., ssDNA) using the SMAS device 100 in the discussion of . The sequencing procedure 250 begins at 252. At 254, all labeled nucleotides are introduced into the fluid chamber 115 and the nucleotides are incorporated into the nucleic acid chain bound to the three binding sites 116. At 256, the unbound nucleotides are washed away. At 258, a baseline characteristic of each of the three sensors 105 is obtained (e.g., by at least one processor 130 of the SMAS device 100, with the aid of the circuit 120). Assuming that the nucleotides have been introduced into the nucleic acid chain bound to each of the three binding sites, the obtained characteristics represent the characteristics of the sensor 105 when it is detecting at least one label. At 260, one of the cleavable linkers is selected for cleavage (or, equivalently, one of the nucleotides is selected). At 262, the label attached to the selected nucleotide is cut and washed away. Assuming no errors, after step 262, the sensors 105 sensing those nucleic acid chains incorporating the tested nucleotides (e.g., nucleic acid chains to which the label is attached via the selected cleavable linker) will exhibit changes in characteristics (e.g., changes in signals associated with or generated by the sensors 105). At 264, characteristics are obtained from each of the plurality of S sensors, and the detection results of each of the plurality of S sensors 105 are determined (e.g., whether the label is detected or not detected). At 266, the S detection results are recorded in S records (e.g., with 1 indicating that the label is detected or with 0 indicating that the label is not detected). At 268, it is determined whether the last tested nucleotide is the last nucleotide of the query cycle. For the example ordering of nucleotide tests assumed in steps 1 to 5 above, it will be determined at 268 (e.g., by at least one processor 130) whether G is the last tested nucleotide. If not, then at 270 the next cleavable linker to be cleaved (or equivalently, the next nucleotide to be tested) in the query cycle is selected, and steps 262 to 268 are repeated until it is determined at 268 that the last linker cleaved (or equivalently, the last nucleotide tested) is the last linker (or nucleotide) of the query cycle. At 272, it is determined (e.g., by at least one processor 130) whether the last completed query cycle is the last query cycle of the sequencer 250. For example, the at least one processor 130 may determine whether enough detection results have been recorded to enable the at least one processor 130 (or some other processing entity, such as an external processor) to identify a target number of bases (e.g., 150 bases). If not, then the sequencer 250 returns to step 254. If so, then the sequencer 250 ends at 274. Again, as described above, the order in which the nucleotides are tested is arbitrary.

[0205] Subtractive sequencing protocols, which in the exemplary case of DNA sequencing involve one nucleotide incorporation and four base cleavage reactions, are summarized in Fig.15 middle. Fig.15 The leftmost inset of illustrates a sensor array 110 with a total of 100 individual sensors 105, which are shown in squares. For the purpose of illustration, it is assumed that each of the 100 binding sites 116 in the sensor array 110 holds a separate DNA strand, and each DNA strand is sensed by a separate sensor 105 (in other words, the binding site 116 and the sensor 105 are in a one-to-one relationship). Some DNA strands may be copies of other DNAs. All four types of labeled nucleotides are added to the fluid chamber 115 simultaneously, and the labels are removed one type of nucleotide (e.g., a cleavable linker) at a time after incorporation. In the absence of errors, base recognition can be completed after five reactions (that is, one nucleotide incorporation and four base cleavage reactions). If an error occurs, an error correction procedure as described below can be applied.

[0206] Improved additive method

[0207] In the improved additive method, the sensor 105 detects nanoscale labels 102 bound to nucleotides with cleavable linkers. All four types of nucleotides carry the same type of label 102 (e.g., molecular, fluorescent, magnetic, etc.) and use the same type of cleavable linker. The labeled nucleotides are added separately, and after each nucleotide is added, the presence of the label 102 is detected. In one embodiment, a query cycle that will produce four detection results (at least one of which will be a label detection for each of the multiple three nucleic acid chains 101) in the absence of errors involves the following steps:

[0208] 1. Obtaining baseline characteristics of each of the plurality of S sensors 105 (which may be all or less than all of the sensors 105 in the sensor array 110 ) of the SMAS device 100 (eg, by determining a baseline signal at each of the plurality of S sensors 105 ).

[0209] 2. Introduce and incorporate the first labeled nucleotide, such as labeled A nucleotide. Wash away unbound labeled molecules.

[0210] 3. Query step 1: Get the characteristics of each of the plurality of S sensors 105 (e.g., by detecting the signal at each of the plurality of S sensors 105) and determine whether each sensor 105 detects at least one tag. Save the detection result of each sensor 105 at a location in the record corresponding to query step 1 of the current query cycle.

[0211] 4. Cut and wash off the marks.

[0212] 5. Introduce and incorporate a second labeled nucleotide, such as a labeled T nucleotide. Wash away unbound labeled molecules.

[0213] 6. Query step 2: Get the characteristics of each of the plurality of S sensors 105 (e.g., by detecting the signal at each of the plurality of S sensors 105) and determine whether each sensor 105 detects at least one tag. Save the detection result of each sensor 105 at a location in the record of query step 2 corresponding to the current query cycle.

[0214] 7. Cut and wash off the marks.

[0215] 8. Introduce and incorporate a third labeled nucleotide, such as a labeled C nucleotide. Wash away unbound labeled molecules.

[0216] 9. Query step 3: Get the characteristics of each of the plurality of S sensors 105 (e.g., by detecting the signal at each of the plurality of S sensors 105) and determine whether each sensor 105 detects at least one tag. Save the detection result of each sensor 105 at a location in the record of query step 3 corresponding to the current query cycle.

[0217] 10. Cut and wash off the marks.

[0218] 11. Introduce and incorporate a fourth labeled nucleotide, such as a labeled G nucleotide. Wash away unbound labeled molecules.

[0219] 12. Query step 4: Get the characteristics of each of the plurality of S sensors 105 (e.g., by detecting the signal at each of the plurality of S sensors 105) and determine whether each sensor 105 detects at least one tag. Save the detection result of each sensor 105 at a location in the record of query step 4 corresponding to the current query cycle.

[0220] 13. Cut and wash off the marks.

[0221] Then, for the next query cycle, steps 1 to 13 can be repeated. It should be understood that some of the ordering in steps 1 to 13 is exemplary, and further, the number and numbering of steps 1 to 13 are for convenience and can be modified. As an example, and as described above, the order in which nucleotides are introduced is arbitrary. As another example, steps 2, 5, 8 and 11 include introducing and incorporating nucleotides, and washing out unbound nucleotides in a single step, but it should be understood that each of steps 2, 5, 8 and 11 can be divided into a series of smaller steps. Similarly, steps 3, 6, 9 and 12 (respectively query steps 1, 2, 3 and 4) can be further divided into a series of smaller steps (e.g., obtaining characteristics, determining whether a tag is detected, and preserving the detection results). On the contrary, steps can be combined (e.g., steps 2 and 3 can be combined, steps 3 and 4 can be combined, steps 2 to 4 can be combined, steps 5 and 6 can be combined, steps 6 and 7 can be combined, steps 5 to 7 can be combined, etc.).

[0222] It should be understood that if no errors may occur during any query cycle of the improved additive method, the individual bases of each strand can be identified (determined) once the label is detected. For example, referring to the above steps, if at query step 1 involving a labeled A nucleotide, for a particular sensor 105, the resulting characteristic indicates that the sensor 105 detects the label, then saving the detection result can be equivalent to identifying the base (T) complementary to A of the detector 105 (and the binding site 116). Similarly, if at query step 2 involving a labeled T nucleotide, for a particular sensor 105, the resulting characteristic indicates that the sensor 105 detects the label, then saving the detection result can be equivalent to identifying the base (A) complementary to T of the detector 105 (and the binding site 116). Similarly, if at query step 3 involving a labeled C nucleotide, for a particular sensor 105, the resulting characteristic indicates that the sensor 105 detects the label, then saving the detection result can be equivalent to identifying the base (G) complementary to C of the detector 105 (and the binding site 116). Finally, if at query step 4 involving a labeled G nucleotide, for a particular sensor 105, the resulting characteristic indicates that the sensor 105 detected the label, then saving the detection result can be equivalent to identifying the base (C) complementary to the G for that detector 105 (and binding site 116). However, as described in further detail below, there are several types of errors that can occur during the sequencing process (e.g., during the additive method), and therefore, in some embodiments, a record is established during the sequencing process to record the detection / non-detection of the label during each query step of each query cycle. An error correction procedure can then be applied to some or all of the records before the base is identified.

[0223] Fig.16is a flow chart of a sequencing process 350 using a modified additive method according to some embodiments. The sequencing process 350 may be, for example, as shown and described in Fig.11 The sequencing procedure performed at step 210 of the exemplary method 200 for sequencing multiple nucleic acid chains (e.g., ssDNA) using the SMAS device 100 in the discussion of . At 352, the sequencing procedure 350 begins. At 354, a baseline characteristic of each of the S sensors 105 is obtained (e.g., by at least one processor 130 of the SMAS device 100, with the aid of the circuit 120). When the query cycle begins, at 356, a first labeled nucleotide is selected (e.g., referring to steps 1 to 13 above, the first labeled nucleotide will be A). At 358, the selected labeled nucleotide is introduced into the fluid chamber 115 and the nucleotide is potentially incorporated into the nucleic acid chain bound to the binding site 116. At 360, unbound nucleotides are washed away. At 362, characteristics are obtained from each of the plurality of S sensors, and the detection results of each of the plurality of S sensors 105 are determined (e.g., a label is detected or a label is not detected). At 364, S test results are recorded in S records (e.g., with 1 indicating that a tag is detected or with 0 indicating that a tag is not detected). At 366, the tag is cut and washed away. At 368, it is determined whether the last tested nucleotide is the last nucleotide of the query cycle. For the example ordering of the nucleotide test assumed in steps 1 to 13 above, it will be determined at 368 (e.g., by at least one processor 130) whether G is the last tested nucleotide. If not, then at 370, the next labeled nucleotide to be tested in the query cycle is selected, and steps 358 to 368 are repeated until the last tested nucleotide is determined to be the last nucleotide of the query cycle at 368. At 372, it is determined (e.g., by at least one processor 130) whether the last completed query cycle is the last query cycle of the sequencer 350. For example, the at least one processor 130 can determine whether enough test results have been recorded to enable at least one processor 130 (or some other processing entity, such as an external processor) to identify a target number of bases (e.g., 150 bases). If not, the sequencing process 350 returns to step 354. If so, the sequencing process 350 ends at 374. Again, as explained above, the order of the test nucleotides is arbitrary.

[0224] An improved additive sequencing protocol (which in the exemplary case of DNA sequencing comprises four nucleotide incorporation and four base cleavage reactions) is described in Fig.17 middle. Fig.17The leftmost inset of illustrates a sensor array 110 with a total of 100 individual sensors 105, which are shown in squares. For illustrative purposes, it is assumed that each of the 100 binding sites 116 in the sensor array 110 holds a separate DNA strand, and each DNA strand is sensed by a separate sensor 105 (in other words, the binding sites 116 and sensors 105 are in a one-to-one relationship). Some DNA strands may be copies of other DNA. As shown and described, labeled nucleotides are added to the fluid chamber 115 one type at a time, and the tags are cleaved after incorporation and tag detection. In the absence of errors, base recognition can be completed after an average of 5 reactions (that is, 2.5 nucleotide incorporations and 2.5 base cleavage reactions).

[0225] Thus, in the absence of errors, for DNA sequencing, the modified additive method yields at least one base call per ssDNA after 8 reactions (4 nucleotide incorporations and 4 base cleavages) to test all bases. However, on average, base calls are made after only 5 reactions (2.5 nucleotide incorporations and 2.5 base cleavages). Because the label is removed after each nucleotide is introduced, base calls can be made in a single Multiple nucleotides are incorporated and identified during the query cycle. Specifically, in the unknown ssDNA sequence, there is a one-in-four chance that the unknown base is T. If the base is exactly T, it will be detected after one incorporation and one base cleavage reaction when the A nucleotide is introduced at the third step. There is a one-in-four chance that the unknown base is A. If the base is exactly A, it will be detected after one incorporation and one base cleavage reaction at the third step. The fifth step of the method detects the T nucleotide when it has been introduced and two introductions and two cuts have been performed. The probability that the unknown base is G is one in four. If the base is exactly G, then the query cycle The seventh step of the method detects the C nucleotide when it has been introduced and three introductions and three cuts have been performed. Finally, there is a one-fourth chance that the unknown base is C. If the base is exactly C, then the query cycle will be The eleventh step of the method detects the C nucleotide when it has been introduced and four introductions and four cuts have been performed. Therefore, an average of 2.5 queries (5 reactions) are required. Alternatively, if the unknown 4-base sequence of a particular ssDNA happens to be the best-case ATCG (for the chosen order of introduced nucleotides assumed for this example), only one query cycle is required. A total of 8 reactions (4 nucleotide incorporations and 4 base cleavages), or 2 reactions per base call. However, if the unknown sequence happens to be, for example, GCTA, GGCT, GCTT, GGGG, etc., four query cycles are required, each including all This results in a total of 32 reactions (16 nucleotide incorporations and 16 base cleavages), or 8 reactions per base call. However, on average, for a random DNA sequence, 2.5 queries or 5 reactions (2.5 nucleotide incorporations and 2.5 base cleavages) are required to make one base call.

[0226] Sources of Sequencing Errors

[0227] Ideally, the sequencing process would be error-free, whether in a CLUS device or a SMAS device 100. In other words, for example, nucleotides would always be correctly labeled, nucleotides would always be correctly incorporated into DNA, all labels would be successfully cleaved during the cleavage step, all cleaved labels would be successfully washed away, etc. However, in reality, errors can occur during any sequencing process. This section explores the sources of sequencing errors for both the CLUS device and the SMAS device 100 and describes the error mitigation strategy for the SMAS device 100. As further described below, error correction methods can be used to improve the sequencing accuracy of the SMAS device 100.

[0228] Because the modified additive method described above is a conceptually simple (and symmetrical, since each nucleotide is processed in the same way) sequencing procedure, it is a good model for illustrating how errors propagate in both the CLUS device and the SMAS device 100. Considering the four sources of error, it is assumed that the nanoscale labels are attached to the nucleotides via a cleavable linker. Each error occurs at a ratio denoted as r, which has a value from 0 to 1. The four sources of error are:

[0229] Failed nucleotide incorporation (FNI) : Failed nucleotide incorporation (FNI) occurs when a correctly labeled nucleotide molecule has not yet reached the ssDNA binding site or the polymerase fails to incorporate it. Fig.18A The FNI of the CLUS device illustrating five examples of sequencing ssDNA. After the flow of complementary nucleotides, only three of the five ssDNAs have incorporated labeled nucleotides (illustrated with magnetic labels). Thus, two out of five nucleotides (r=0.4) cannot be incorporated. Fig.18B The FNI of the SMAS device 100 is illustrated. Each of the five binding sites 116 holds an instance of ssDNA. After the flow of complementary nucleotides, only three of the five ssDNAs (those bound to binding sites 116A, 116B, and 116C) have incorporated labeled nucleotides (illustrated as having magnetic labels for example purposes only). Furthermore, two of the five ssDNA instances (r=0.4) were unable to incorporate nucleotides.

[0230] Failed Mark Removal (FLR)Failed label removal (FLR) occurs when a labeled nucleotide molecule is incorporated but the label is not removed after label detection because the cleavage reagent has not reached the linker or fails to cleave it. Fig.18C Description Fig.18A FLR of the CLUS device described in the discussion of . After incorporation of complementary nucleotides and washing to remove unincorporated nucleotides, detection of the label, and cleavage and washing of the label, one label remains attached to one of the ssDNA instances (r=0.2). Similarly, in Fig.18D In the description above Fig.18B In the FLR of the SMAS device 100 described in the discussion of , after incorporation of complementary nucleotides and washing to remove unincorporated nucleotides, detection of the label, and cleavage and washing of the label (e.g., steps 2 to 4, 5 to 7, 8 to 10, and / or 11 to 13 described above), the label remains attached to the ssDNA at binding site 116A (r = 0.2).

[0231] Failed nucleotide removal (FNR) Failed nucleotide removal (FNR) occurs when labeled nucleotides (whether complementary or non-complementary) bind non-specifically to the binding site 116 and / or the surface of the sensor 105. Fig.18E Description Fig.18A An example of a FNR of a CLUS device described in . After the flow of nucleotides and flushing to remove unbound nucleotides, the two bad nucleotides and their labels remain on the surface of the binding site. Similarly, in Fig.18F In the figure, the above Fig.18B , after nucleotide flow and flushing to remove unbound nucleotides, one bad nucleotide remains on the surface of binding site 116A and another bad nucleotide remains on the surface of binding site 116D. In this example, for both CLUS devices and SMAS device 100, r = 0.4.

[0232] Failed Label Detection (FLD) : Failed label detection (FLD) occurs when the correct complementary nucleotide is incorporated, but the label is not detected due to its absence or failure of the sensor to recognize it. Figure 18G Description Fig.18A FLD of the CLUS device described in the discussion of . After incorporation of complementary nucleotides and washing to remove unincorporated nucleotides, two of the ssDNA instances had incorporated complementary nucleotides, but the label was missing (r=0.4). Similarly, in Fig.18H In the figure, the above Fig.18BThe FLD of the SMAS device 100 described in the discussion above, after incorporating complementary nucleotides and washing to remove unbound nucleotides (e.g., steps 2, 5, 8, or 11 described above), should be attached to the labeled deletion (r = 0.4) of the nucleotides incorporated into the ssDNA at binding sites 116C and 116D.

[0233] Figures 18A to 18H The label is described as a magnet, thus indicating magnetic labels and magnetic sensors, but it should be understood that, as described above, the label can be any type of detectable label (e.g., fluorescent, magnetic, etc.) and the sensor can be any type of sensor capable of detecting the selected type of label (e.g., optical, magnetic, organometallic, charged molecules, etc.).

[0234] Assume that four error types (FNI, FLR, FNR, and FLD) occur at the same rate r, where 0 < r < 1; for example, if r = 0.01, then on average 1 in 100 cases fails. Also assume that the sensor 105 of the SMAS device 100 (e.g., the nanoscale sensor 105) can detect a single label almost every time, and the response of the large cluster sensor used in the CLUS device is linear; for example, the sensor of the CLUS device can distinguish between N and N + 1 labeled strands for all values of N.

[0235] Cluster sequencers and single-molecule array sequencers: qualitative comparison and error correction

[0236] Two types of error correction are disclosed herein, referred to as deterministic error correction and probabilistic error correction. The SMAS device 100 can use one or both types of error correction, as further described below.

[0237] As described above, the modified additive method is a good model for explaining how errors propagate and how the disclosed error correction algorithms can be implemented. It should be understood that when other sequencing methods (such as additive or subtractive methods) are used, the disclosed error mitigation algorithms can also be applied.

[0238] Consider a CLUS device and a SMAS device 100 using a modified additive method sequencing procedure, which has a large error rate of r = 0.1 (e.g., 1 failure in 10 reactions) and a small number of instances of the (ideally identical) strand; for example, N = K = 3, where the variable N represents the cluster size used in the CLUS device, and the variable K represents the number of sensors 105 of the SMAS device 100 that sense the same DNA strand instance. (As described previously, the K sensors can be close to each other, or they can be spread within the sensor array 110). To describe an embodiment of deterministic error correction, initially consider only FNI and FLR errors. Then consider FNI, FLR, and FLD errors, and describe the error mitigation strategy. Finally, consider all four types of errors, and describe the error correction procedure for resolving all four types of errors.

[0239] When using the SMAS device 100, FLR errors can be detected and removed, either during the sequencing procedure or at some subsequent time in real time. FLR errors can be detected by characterizing each of the S sensors 105 after cutting and flushing the marker. FNI errors can be detected by examining the records of each sensor 105 and identifying the query cycles in which the sensor 105 failed to detect any marker. Therefore, the modified additive method can be adjusted to add these detection steps as follows according to one embodiment:

[0240] 1. Obtaining baseline characteristics of each of the plurality of S sensors 105 (which may be all or less than all of the sensors 105 in the sensor array 110 ) of the SMAS device 100 (eg, by determining a baseline signal at each of the plurality of S sensors 105 ).

[0241] 2. Introduce and incorporate the first labeled nucleotide, such as labeled A nucleotide. Wash away unbound labeled molecules.

[0242] 3. Query step 1: Get the characteristics of each of the plurality of S sensors 105 (e.g., by detecting the signal at each of the plurality of S sensors 105) and determine whether each sensor 105 detects at least one tag. Save the detection result of each sensor 105 at a location in the record corresponding to query step 1 of the current query cycle.

[0243] 4. Cut and wash off the marks.

[0244] 5. Get characteristics for each of the plurality of S sensors 105 that detected the tag in step 3. If the characteristics obtained for any of those sensors 105 indicate that the sensor 105 is still detecting the tag, then the chemistry failed to cleave the tag (e.g., there is an FLR error for that sensor).

[0245] 6. Introduce and incorporate a second labeled nucleotide, such as a labeled T nucleotide. Wash away unbound labeled molecules.

[0246] 7. Query step 2: Get the characteristics of each of the plurality of S sensors 105 (e.g., by detecting the signal at each of the plurality of S sensors 105) and determine whether each sensor 105 detects at least one tag. Save the detection result of each sensor 105 at a location in the record of query step 2 corresponding to the current query cycle.

[0247] 8. Cut and wash off the marks.

[0248] 9. Get characteristics for each of the plurality of S sensors 105 that detected the tag in step 7. If the obtained characteristics for any of those sensors 105 indicate that the sensor 105 is still detecting the tag, then the chemistry failed to cleave the tag (e.g., there is an FLR error for that sensor).

[0249] 10. Introduce and incorporate a third labeled nucleotide, such as a labeled C nucleotide. Wash away unbound labeled molecules.

[0250] 11. Query step 3: Get the characteristics of each of the plurality of S sensors 105 (e.g., by detecting the signal at each of the plurality of S sensors 105) and determine whether each sensor 105 detects at least one tag. Save the detection result of each sensor 105 at a location in the record of query step 3 corresponding to the current query cycle.

[0251] 12. Cut and wash off the marks.

[0252] 13. Get characteristics for each of the plurality of S sensors 105 that detected the tag in step 11. If the characteristics obtained for any of those sensors 105 indicate that the sensor 105 is still detecting the tag, then the chemistry failed to cleave the tag (e.g., there is an FLR error for that sensor).

[0253] 14. Introduce and incorporate a fourth labeled nucleotide, such as a labeled G nucleotide. Wash away unbound labeled molecules.

[0254] 15. Query step 4: Get the characteristics of each of the plurality of S sensors 105 (e.g., by detecting a signal at each of the plurality of S sensors 105) and determine whether each sensor 105 detects at least one tag. Save the detection result of each sensor 105 at a location in the record of query step 4 corresponding to the current query cycle. If there are sensors 105 that are not assigned a base for the query cycle (e.g., sensors 105 that cannot detect A, T, C, or G during the query cycle), the chemistry cannot incorporate the nucleotide (e.g., for these sensors 105, FNI exists).

[0255] 16. Cut and wash off the marks.

[0256] 17. Get characteristics for each of the plurality of S sensors 105 that detected the tag in step 15. If the characteristics obtained for any of those sensors 105 indicate that the sensor 105 is still detecting the tag, then the chemistry failed to cleave the tag (e.g., there is an FLR error for that sensor).

[0257] Steps 1 to 17 can then be repeated for the next query cycle (e.g., to estimate the next base or to read the current base again if the previous query cycle cannot read the current base). It should be understood that some of the ordering of steps 1 to 17 is exemplary, and further, the number and numbering of steps 1 to 17 are for convenience and can be modified. As an example, and as described above, the order in which nucleotides are introduced is arbitrary. As another example, steps 2, 6, 10 and 14 include introducing and incorporating nucleotides, and washing away unbound nucleotides in a single step, but it should be understood that each of steps 2, 6, 10 and 14 can be divided into a series of smaller steps. Similarly, steps 3, 7, 11 and 15 (query steps 1, 2, 3 and 4, respectively) can be further divided into a series of smaller steps (e.g., obtaining characteristics, determining whether a tag is detected, and saving the detection results). Similarly, although step 15 includes identifying FNI errors, the task can be performed in separate steps. Conversely, steps may be combined (eg, some or all of steps 2 to 5, some or all of steps 6 to 9, some or all of steps 10 to 13, some or all of steps 14 to 17, etc.).

[0258] Fig.19 FIG. 4 is a flow chart of an exemplary sequencing process 400 using the improved additive method with FLR and FNI error detection according to some embodiments. The sequencing process 400 may be, for example, as shown and described in FIG. Fig.11The sequencing procedure performed at step 210 of the exemplary method 200 for sequencing multiple nucleic acid chains (e.g., ssDNA) using the SMAS device 100 in the discussion of . At 402, the sequencing procedure 400 begins. At 404, a baseline characteristic of each of the S sensors 105 is obtained (e.g., by at least one processor 130 of the SMAS device 100, with the aid of the circuit 120). When the query cycle begins, at 406, a first labeled nucleotide is selected (e.g., referring to steps 1 to 17 above, the first labeled nucleotide will be A). At 408, the selected labeled nucleotide is introduced into the fluid chamber 115 and the nucleotide is potentially incorporated into the nucleic acid chain bound to the binding site 116. At 410, unbound nucleotides are washed away. At 412, characteristics are obtained from each of the plurality of S sensors, and the detection results of each of the plurality of S sensors 105 are determined (e.g., a label is detected or a label is not detected). At 414, the S detection results are recorded in S records (e.g., with a 1 indicating that the tag was detected or a 0 indicating that the tag was not detected). At 416, the tag is cleaved and flushed away. At 418, the characteristics of those sensors 105 that detected the tag during steps 412 / 414 are obtained. At 420, it is determined whether any of the sensors 105 that detected the tag during steps 412 / 414 are still detecting the tag. If so, it is determined at 422 that an FLR error has been detected for the sensor 105 that is still detecting at least one tag, even though the tag was cleaved and flushed away at 416. The sequencing procedure 400 then continues to 424. If it is determined at 420 (e.g., by at least one processor 130) that none of the sensors 105 that detected the tag during steps 412 / 414 are still detecting the tag, the sequencing procedure also continues to 424. At 424, it is determined whether the last tested nucleotide is the last nucleotide of the query cycle. For the example ordering of nucleotide tests assumed in steps 1 to 17 above, it will be determined at 368 (e.g., by at least one processor 130) whether G is the last nucleotide tested. If not, then at 426, the next labeled nucleotide to be tested in the query cycle is selected, and steps 408 to 420 (and if applicable, to 422) are repeated until at 424, the last nucleotide tested is determined to be the last nucleotide of the query cycle. At 428, the FNI errors of those sensors in the S sensors 105 that could not detect any tags during the last completed query cycle are detected. At 430, it is determined (e.g., by at least one processor 130) whether the last completed query cycle is the last query cycle of the sequencer 400. For example, the at least one processor 130 can determine whether enough test results have been recorded to enable the at least one processor 130 (or some other processing entity, such as an external processor) to identify the target number of bases (e.g., 150 bases). If not, the sequencer 400 returns to step 404.If so, the sequencing process 400 ends at 432. Again, as described above, the order of the test nucleotides is arbitrary.

[0259] Mitigating FNI and FLR errors

[0260] To illustrate the effects of FNI and FLR errors on the CLUS device and the SMAS device 100, each type of sequencer was used to identify an exemplary DNA sequence in which FNI and FLR errors occurred randomly when reading the sequence using the modified additive method of SBS described above. Assume that the error rates of FNI and FLR errors are both An exemplary sequence is: TAG CAA GGT CCGCTA CTG GCA GAC TGG. Fig. 20 Shown throughout 18 In the query loop of the query step, There are two types of errors that can be generated. Fig. 20 As shown in Figure 1, approximately 1 in 10 reactions failed, and for the three ssDNA examples sequenced, the errors were evenly distributed between FNI errors and FLR errors. The model case represents one of many possible scenarios for collective behavior. The consequences of FNI and FLR errors on base calling accuracy were analyzed for the cases when the three DNA strands were placed on a single sensor of a CLUS device and when they were placed on three discrete nanoscale sensors 105 of a SMAS device 100.

[0261] Fig.21 Illustrate the expected signal levels detected by the CLUS device sensor, which captures the behavior of the molecular collective during the sequencing procedure. At each query step, the CLUS device sensor can detect four signal intensity levels of the molecular collective (composed of three ssDNAs): that is, 0 tags, 1 tag, 2 tags, or 3 tags are detected. The sequencing process of the CLUS device considers the combined signal of the collective and cannot distinguish when the reaction to an individual chain fails. Whenever the CLUS device sensor senses at least two tags, a base is identified at a particular query step. The threshold can be represented by a decision criterion: when the CLUS sensor signal level is greater than 1.5, a base is identified. As Fig.21 The results show that a high rate of chemical failures can lead to significant base calling errors and very low base calling accuracy. The CLUS device method only resulted in 6 of the 21 (about 29%) called bases that matched the true sequence. This level of accuracy is only slightly better than random guessing with 25% accuracy (since there are 4 bases, there is a one in four chance of correctly guessing a base). In addition, the CLUS device cannot tell the difference between successful and failed chemical reactions, nor does the CLUS device know the difference between the bases displayed in the sequence. Fig. 20) or FLR (circles filled with backslashes) errors in the CLUS apparatus. For the CLUS apparatus, collective averaging would obscure the exact location of the FLR errors. Only probabilistic error correction algorithms can be implemented to slightly improve the quality of base calls for the CLUS apparatus by essentially making educated guesses about the locations of base insertions, deletions, and substitution sites. Exemplary algorithms are described, for example, in A. Cacho et al., "A Comparison of Base-calling Algorithms for Illumina Sequencing Technology," Briefings in Bioinformatics, Vol. 17(5), pp. 786-795, 2016; W. C. Kao et al., "BayesCall: A model-based base-calling algorithm for high-throughput short-read sequencing," Genome Res., Vol. 19(10), pp. 1884-1895, 2009; and C. Ledergerber and C. Dessimoz, "Base-calling for next-generation sequencing platforms," ​​Briefings in Bioinformatics, Vol. 17(5), pp. 786-795, 2016. Bioinform.), Vol. 12, 489–97, 2011.

[0262] Fig. 22How the SMAS device 100 can provide better accuracy when using the error correction techniques described herein is described. As described above, FLR errors that occur during the sequencing process can be detected during the sequencing process. Specifically, the SMAS device 100 knows (or can find) the position of the FLR because the characteristics (e.g., signal level) of each sensor 105 are obtained and recorded after the label is cut and washed away and before the next nucleotide is introduced. FLR errors can be corrected by treating them as "undetected labels" when base calling is performed. In other words, if the record of the sequencing process contains binary (e.g., 0 / 1) entries for each query step, the FLR can be corrected by changing the values ​​at those query steps from "detected" values ​​to "undetected" values. As a specific example, if 0 represents undetected labels and 1 represents detected labels, the FLR at the mth query step will be represented by 1 in the mth position in the record before error correction. The error can be corrected by changing the value 1 at the mth position in the record to the value 0. Fig. 22 The top portion of illustrates the detection results of each of the three sensors 105 of the SMAS device 100 before error correction to remove the FLR error. Fig. 22 The lower part shows the result of correcting FLR errors before calling bases.

[0263] The improved additive sequencing procedure using the SMAS device 100 allows the query step to identify a base when more than half of the K sensors 105 (in the example where K=3 (two or three sensors 105)) detect a marker during a particular query step. However, unlike the CLUS device, the SMAS device 100 collects considerably more information because it detects the presence or absence of the marker at each of a plurality of (assumed to be 3 in the example) binding sites 116 and at each query step of the sequencing procedure. Thus, use of the SMAS device 100 may result in fewer base calls being made, but those calls result in a significantly more accurate estimated sequence than those called by the CLUS device. Specifically, for the exemplary sequence, once FLR errors (such as Fig. 22 ), using the SMAS device 100 resulted in 11 of the 16 (about 69%) bases identified matching the true sequence. Fig.21 and 22 This shows that the consequences of chemical failure on base calling accuracy are significantly different for the two types of sequencing devices, and the SMAS device 100 provides better accuracy.

[0264] When using the SMAS device 100, FNI errors can also be corrected because failed incorporation creates a characteristic signature in the SMAS sensor 105 detection results (e.g., in a record consisting of detected / not detected markers by the sensor 105 during a sequencing procedure). In particular, FNI errors in the modified additive method result in a string (continuous sequence) of zeros (or other "not detected marker" detection results) for four or more consecutive query steps. Fig.19 As explained in the discussion of , some FNI errors can be detected by identifying that a particular sensor 105 does not detect any tags during a query cycle. It should be appreciated that FNI errors can also "span" multiple query cycles. For example, assuming that in a query cycle with During the first query cycle of the query steps, a particular sensor 105 detected a tag during the A? query step, and then it did not detect any tags until the C? query step of the next query cycle. Because the C? query step is after the A? query step in the exemplary query cycle, and the modified additive method is used as a sequencing cycle, the C? query step of the first query cycle should have resulted in the detection of a tag. It should be noted that Fig.19 Step 428 of will not result in any FNI errors being detected during the first or second query cycles, since neither query cycle will result in a particular sensor 105 not detecting a tag. However, inspection of the test result record will show that an FNI error exists. FNI errors can be corrected deterministically by deleting strings (four in the case of DNA sequencing) of zeros to align the bad strand with a strand that is not affected by the FNI error. Fig.23 The FNI error is corrected by deleting several strings of four "not detected marker" entries in the record of the sequencer's test results. Fig.23 As shown in , FNI error correction results in a perfect alignment between the called sequence and the true sequence.

[0265] Qualitative analysis of a simplified model system with a finite set of errors indicates that nucleic acid sequencing using the SMAS device 100 greatly outperforms that using the CLUS device, at least when the number of instances K of the sequenced DNA strands is small and the chemical failure rate is high. To set the framework for a quantitative comparison of the two platforms, the following explores how cluster size (for the CLUS device) and the number of instances sequenced (for the SMAS device 100) affect base calling accuracy. Consider the case where N=K=11 and r=0.1 for both FNI and FLR errors. Assume that the sensor is reading the same instance sequence considered above (TAG CAA GGT CCG CTACTG GCA GAC TGG) and 18 The query cycle of the query step randomly appeared chemical errors leading to FNI and FLR. Fig.24 Description: With a high chemical failure rate ( The results of 11 exemplary SBS reactions based on DNA strands with a minimum of 1% or 10%. Fig.24 As shown in Figure 2, approximately 1 in 10 reactions failed.

[0266] Fig.25 This figure illustrates the effect of larger cluster size N on the base calling accuracy of the CLUS device. Fig.25 The expected signal level detected by the CLUS device sensor, which captures the behavior of the molecular collective during the sequencing process, is shown. At each query step, the CLUS device sensor can detect any of twelve signal intensity levels for the molecular collective (eleven ssDNAs), that is, 0 to 11 markers are detected. When the signal level detected by the CLUS sensor is greater than 5.5, the base is identified at a particular query step. Fig.25 It was shown that the failed chemistry resulted in base calling errors: only 11 of the 18 (about 61%) called bases matched the true sequence.

[0267] Fig.25 and Fig.21 Comparison indicates that the accuracy of the CLUS device is better at N=11 than when N=3. Specifically, increasing the cluster size N leads to a significant reduction in base call errors. Whereas in the case of N=3, only about 29% of the identified bases are consistent with the true sequence, increasing the cluster size to N=11 makes the consistency rate about 61% because the CLUS device benefits from the collective behavior of a larger collective. The current state-of-the-art commercial CLUS-type sequencer works with a cluster array that accommodates about 100 DNA chain instances.

[0268] Fig.26 Results are illustrated for the case of using the SMAS device 100 with K=11 (in other words, 11 instances of ssDNA, each detected by a different sensor 105) and deterministic error correction of FLR and FNI errors according to some embodiments. A base is identified at a particular query step when more than half (e.g., at least 6 for K=11) of the sensors 105 detect a marker. As detected by Fig.26 As shown, implementation of deterministic FLR error correction (middle) and FNI error correction (bottom) as described above results in a perfect alignment between the identified sequence and the true sequence. It should be noted that without error detection / correction, the identified sequence based on data from the SMAS device 100 would be identical to the identified sequence using data from the CLUS device, since the SMAS device 100 without error correction simply recreates the collective result by summing all the individual sensor results. The ability to detect and correct errors in sequencing data gives the SMAS device 100 an advantage over the CLUS device.

[0269] Therefore, if only FNI and FLR errors occur, using the SMAS device 100 together with the deterministic error correction can result in a perfect match between the true sequence and the identified sequence. In addition, if only FNI and FLR errors occur, it is actually possible to identify error-free sequences using only a single sensor 105 that reads a single ssDNA and the deterministic error correction techniques discussed above (e.g., changing the FLR to "not detected flag" and / or deleting a number of strings of a specified length (e.g., 4) of "not detected flags" from the recording of the test results).

[0270] However, when FNR and / or FDL errors are introduced, it is generally unlikely that all errors in the test result record can be eliminated using only deterministic error correction.To address FNR and / or FDL errors, probabilistic error correction may be included in addition to or in lieu of deterministic error correction.

[0271] Mitigating FNI, FLR and FNR errors

[0272] This section further includes FNR errors in the analysis. The impact of such errors on the base recognition accuracy of the CLUS device is equivalent to the impact of FNI and FLR due to the inherent averaging when the CLUS device detects the tags in the nucleic acid instance cluster. FNR errors are obviously more detrimental to the performance of the sequencing method using the SMAS device 100 because FNR errors cannot be corrected deterministically. (It should be noted that the CLUS device itself cannot correct FNR errors at all. Instead, the CLUS device relies on collective behavior to mitigate the impact of FLR and other types of errors.)

[0273] Fig. 27 To illustrate the problem introduced by the FNR error in the exemplary sequence (TAG CAA GGT CCG CTA CTG GCA GAC TGG), assume that FNI, FLR, and now FNR errors are present in 18 The query step occurs randomly during the query cycle. For example purposes, assume that K=3 (that is, each of the three binding sites 116 holds an instance of a specific ssDNA, and each of the three respective sensors 105 senses a respective one of the three ssDNA instances), that on average there are 15 failures in 100 reactions (r=0.15, which is a large chemical failure rate), and that the errors are evenly distributed between FNI errors, FLR errors, and FNR errors. Under the example conditions and assumptions made here, given only the data record created by SBS using the SMAS device 100, it is impossible to distinguish correctly detected events in the data record ( Fig. 27 ) and FNR (circle filled with a forward slash). Fig.28Illustrate the results when a base is identified under a mark detected in more than half (at least 2 out of 3) of sensors S1, S2, and S3. Although FLR errors can be corrected deterministically (as described above, by treating them as "mark not detected"), FNR errors cannot be identified because they are indistinguishable from correct mark detection events. Therefore, in this example, only 8 of the 17 (about 47%) identified bases match the true sequence. Therefore, the introduction of FNR errors makes deterministic FNI error correction more challenging because FNR errors destroy the string of four or more "mark not detected" detection results that might otherwise have been removed. If FNI error correction is implemented unprocessed by deleting several strings of four zeros in an attempt to align the bad strand with the strand not affected by the error, sequencing accuracy will not be improved. In fact, if Fig.29 As shown in , for this example, the base calling accuracy appears to have deteriorated because after removing the strings of four "no marker detected" detection results, only 9 out of 20 (45%) base calls were consistent with the true sequence.

[0274] Error correction can be improved by applying probabilistic error correction to mitigate FNR errors in addition to FLR and FNI errors. For example, note the thymine query step at position 2 (query step 2 of query cycle 1). Sensors S1 and S3 detect the marker, but S2 does not. S2 fails to detect the marker due to simultaneous FNR errors at sensors S1 and S3, or due to a FNI error at sensor S2. Assuming the probability of each error is r, the probability of simultaneous FNR errors at sensors S1 and S3 is r 2 , and the probability of an FNI error at sensor S2 is r. The error correction algorithm (e.g., performed by at least one processor 130 or another processor) assumes that the more likely event (the presence of an FNI error at sensor S2) has occurred and deletes all entries in the S2 record that displace the S2 detection results from positions 2 to 5 from the data record that captures the detection results from sensor S2. Thus, the detection results in the S2 record are compared again with the detection results generated by sensors S1 and S3, such as Fig.30 Previously (before deletion) at position 4 (in Fig.30 The detection of the G marker at position 4 (in the portion marked “A” of ) can now be attributed to FNR since sensors S1 and S3 did not detect a marker in position 4 (query step 4 of query cycle 1).

[0275] Can be in position 13 (such as Fig.30 The same error correction process is performed from left to right at 32 (labeled "C") and 46 (labeled "D") to show the gradual improvement of the alignment between the S1, S2 and S3 records of the test results, as shown in the portion labeled "B" of the figure ...C" of the figure, as shown in the portion labeled "D" of the figure, as shown in the portion labeled "B" of the figure, as shown in the portion labeled " Fig.30 As described in the section marked “E”. Fig.30 The portion marked "E" indicates that despite implementing multiple probabilistic error correction steps to align the outputs of all sensors S1, S2, and S3, it does not seem to improve the alignment between the identified sequence and the true sequence. Even after error correction, only 9 out of 20 (45%) bases were correctly identified. In other words, base identification errors still occurred. Specifically, after the error correction procedure, all three sensors S1, S2, and S3 reported that the marker was detected at the query step where the marker should have been detected, but some of the sensors also detected markers at positions 10, 22, 40, and 50 (shown in Fig.30 Marks incorrectly incorporated by FNR at ).

[0276] When the detection results of more than half of the sensors 105 are consistent (after error correction), the identification base results in a thymine insertion error at sequence position 8 (query step 22), where both sensors S1 and S3 detect a label bound to a non-complementary nucleotide during the same query step. (It should be understood that the reason why the thymine insertion error at position 8 is known is because the error data is established for illustrative purposes and is known. In one embodiment, the sensor 105 only indicates whether the label was detected during the query step, but not whether the detection (or lack of detection) is correct or incorrect. Therefore, in one embodiment, the error at query step 22 will be essentially indistinguishable from the correct detection result.) The correctly aligned true sequence and the identified sequence that clearly show the position of the single incorrect base insertion can be presented as:

[0277] Error: |Insert real sequence: TAG CAA G*G TCC GCT ACT GGC

[0278] Recognized sequence: TAG CAA GTG TCC GCT ACT GGC

[0279] * Insert position

[0280] If the base calling rule is modified to require all three sensors S1, S2, and S3 to be consistent, this insertion error can be corrected. For this rule, all three sensors S1, S2, and S3 must encounter FNR errors at the same time to cause an incorrect base call. The probability of this event is only r 3Assuming r=0.05, all three sensors S1, S2, and S3 encounter FNR events during the same query step only 125 times out of 100,000 queries on average (or a probability of 0.000125), which is extremely low even for the extremely high error rates used in the current example. However, if FLD errors also occur, implementing this rule can lead to incorrect identifications, as discussed further below.

[0281] Mitigating FNI, FLR, FNR and FLD errors

[0282] The general error correction strategy used in some embodiments addresses and mitigates all four types of chemical failures that lead to FNI, FLR, FNR, and FLD errors. Fig.31 Explain the example sequence (TAG CAAGGT CCG CTACTG GCA GACTGG), assuming that FNI, FLR, FNR and now also FLD errors are in 18 The query step occurs randomly during the query cycle. For the purpose of creating many errors in the sequencing data to provide a medium to illustrate the exemplary error correction process, a very high average error rate of 1 in 5 failed reactions ( or 20% error rate), and also assume that errors are evenly distributed among FNI errors, FLR errors, FNR errors, and FLD errors. Thus, there are approximately 20 failures in 100 reactions, and the failures are equally distributed among the four error types. It should be appreciated that this high error rate is unlikely to occur in practice, and therefore the difficulty of the examples considered here may be much higher than the difficulty that will be encountered in real-world implementations.

[0283] Under the example conditions and assumptions made here, given only the data record established by SBS using the SMAS device 100, it is impossible to distinguish between the correct nucleotide incorporation and FNR, and it is also impossible to distinguish between the correct nucleotide non-incorporation and FNI. Although FLR errors can be detected and corrected as described above (by checking the sensor 105 after cutting and washing off the mark, and treating FLR as "no mark detected"), FNR errors cannot be identified because they cannot be distinguished from correctly detecting events, and FNI and FLD errors cannot be identified because they cannot be distinguished from not incorporating the correct nucleotide. However, error mitigation can still be accomplished using probabilistic error correction techniques. For example, as described above, when less than all sensors S1, S2 and S3 detect or do not detect marks during a particular query step, the probability of two (or more) events can be calculated, and the event with the highest probability can be assumed to be a correct event, and a suitable error correction step can be adopted.

[0284] Fig.32The application of the error correction procedure to data captured during SBS under the conditions and assumptions described above is illustrated. Fig.32 The portion marked "A" of is the original data before the FLR error is removed. Assuming that the location of the FLR error is known by checking the sensor 105 signal level after cutting and washing away the mark as described above. The FLR error can be completely removed using deterministic error correction, that is, by changing the "mark detected" value (e.g., 1 or "yes") in the data record corresponding to the location of the query step where the FLR error was detected to a "mark not detected" (e.g., 0 or "no") value. It should be noted that in the display shown in Fig.31 During query cycle 15 in , the FLD error in the data of sensor S2 is followed by an FLR error. In other words, sensor S2 cannot detect the label of the incorporated nucleotide during the first query step of the 15th query cycle. The signal level of sensor S2 is checked when the label is cut after the first query step of the 15th query cycle and before the second query step of the 15th query cycle. This check shows the presence of label at sensor S2, which would be considered an FLR error because all labels should have been cut and washed away after the last query step. Therefore, even when an FLR error follows another error, it is detectable and can be removed.

[0285] Fig.32 The portion of FIG. 5 labeled "B" shows a record of detection results after FLR errors have been removed via deterministic error correction, applied as previously described. The data record shown in "B" now includes only an indication of whether a marker was detected or not detected by each of sensors S1, S2, S3 at each of the (4×18) query steps shown. (It should be appreciated that the record is comparable to Fig.32 ) As explained above, it is not known from these records which "mark detected" indications are correct and which are FNR errors, and it is not known which "mark not detected" indications are correct and which are FNI or FLD errors. Therefore, probabilistic error correction can be used to estimate the sequence.

[0286] To illustrate how probabilistic error correction can be applied, the following table shows Fig.32 The FLR error has been removed (for example from Fig.32 ) (records marked with "B" in the table). In other words, the following table shows the data records of the first five query cycles (query steps 1 to 20) of the three sensors S1, S2 and S3 after the deterministic error correction removes the FLR error. For the query steps where the sensor detects the mark, the table contains the value 1, and for the query cycle where the sensor does not detect the mark, the table contains the value 0:

[0287]

[0288]

[0289] As explained above, a simple majority vote after removing the FLR errors would result in only 8 of the 17 bases being correctly identified, as Fig.32 Probabilistic error correction can provide significant improvements as described below.

[0290] Considering query step 2 as an example, sensors S1 and S3 both detected the tag (entry in the table above is 1), but sensor S2 did not detect the tag (table entry is 0). Therefore, either sensors S1 and S3 are erroneous, or sensor S2 is erroneous. The error correction algorithm can mitigate errors in the sequenced data by considering the probabilities of various events that can lead to each of these results. Specifically, because the FLR has been removed from the data record, the only way for sensors S1 and S3 to both incorrectly detect the tag during query step 2 is if both encounter an FNR error during that query step. If the probability of an FNR error is r, then the probability that sensors S1 and S3 both encounter an FNR error during a single query step is r 2 For the purposes of this example, a high error rate of r = 0.2 is assumed, and therefore the probability that both sensors S1 and S3 incorrectly detect a marker during query step 2 is 0.04.

[0291] If sensor S2 is erroneous, it is because sensor S2 cannot detect the label due to an FLD error or an FNI error. Recall that an FLD error occurs when the correct complementary nucleotide is incorporated, but the label is missing or the sensor cannot detect its label, and an FNI error occurs when the correct complementary nucleotide is not incorporated at all during the sequencing cycle. FLD and FNI errors are mutually exclusive (that is, a sensor can only encounter one of them at a time, but never both). Therefore, assuming the probability of each type of error is r, the probability of sensor S2 encountering an FLD error or an FNI error is 2r. For the example here, a high error rate of r=0.2 has been assumed, so the probability that sensor S2 is erroneous during query step 2 is 0.4. The probability that sensor S2 is erroneous during query step 2 is compared to the probability that sensors S1 and S3 are both erroneous, because 0.4>0.04, so the probability that sensor S2 is erroneous is greater. In some embodiments, the error correction algorithm assumes that the more likely event occurs, meaning that sensor S2 is assumed to be erroneous, and the probability that sensors S1 and S3 are both erroneous is discarded and not considered further.

[0292] As explained above, sensor S2 may be erroneous due to either a FLD error or a FNI error. After a FLD error, the DNA strand sensed by sensor S2 will remain "in sync" or "aligned" with the DNA strands sensed by sensors S1 and S3. In other words, if query step m sequences the 40th base of the DNA strands sensed by each of sensors S1, S2, and S3, query step m+1 will sequence the 41st base of each strand, even if one of the sensors (e.g., sensor S2) encountered a FLD error during query step m. On the other hand, the consequence of an FNI error is that the DNA strand sensed by the sensor that encountered the FNI error becomes "out of sync" or "incorrectly aligned" with the DNA strands sensed by the sensor that did not encounter the FNI error. In the current example, if the error at query step 2 is due to FNI (e.g., it will be "behind" the DNA chain sensed by sensors S1 and S3 in four query steps, which will be the next incorporation of complementary nucleotides), then the DNA chain sensed by sensor S2 will become out of sync with the DNA chain sensed by sensors S1 and S3.

[0293] In some embodiments, the action taken by the error correction algorithm depends in part on the examination of the candidate error corrected data, which is respectively assumed that each of the two types of errors has occurred. In other words, the record of the detection result can be modified to correct the error, assuming that the error is caused by an FLD error, to produce a first candidate corrected data record, and the record of the detection result can be modified to correct the error, assuming that the error is caused by an FNI error, to produce a second candidate corrected data record. The two candidate corrected data records can then be checked and / or analyzed and / or compared to determine which is more likely to be correct. In order to correct the FLD error, the "not detected mark" indication is flipped to the "detected mark" indication. In order to correct the FNI error, the data entry is shifted four positions (e.g., to the left as a data record presented in the example herein).

[0294] To illustrate a specific example of query step 2 in the example data record, the first candidate corrected data record option A assumes that the (assumed) error affecting the output of sensor S2 is a FLD error. The assumed error is corrected by flipping the query step 2 bit in the record for sensor S2 from 0 to 1, as shown in bold, underlined value "1" in the following table option A:

[0295]

[0296] The second candidate corrected data record Option B assumes that the error affecting the output of sensor S2 is a FNI error. The assumed error is corrected by deleting the data recorded during query steps 2, 3, 4, and 5 from the sensor S2 data entry to "resynchronize" or "re-match" the data record corresponding to sensor S2 with the data records of sensors S1 and S3, which results in the following table (the values ​​originally at positions 21 to 24 are shifted into positions 17 to 20). The Option B table entries modified by the error correction algorithm are shown in bold, underlined font:

[0297]

[0298] Options A and B may then be compared and / or analyzed to determine which is more likely to be correct, and one of the options may be discarded. For example, a processor (e.g., at least one processor 130 or another processor) may determine a metric value for each candidate corrected data record and determine which of options A and B is more likely to be correct based, at least in part, on a comparison of the metric. An example of a metric is the number of query steps from the query step after the now corrected current query step and the further query step J position in the data record where the marker detection results of all three (or more generally, K) sensors are consistent. For example, using this metric, and setting the value J to 8, the metric value for option A is 3, and the metric value for option B is 6. In some embodiments, based solely on this result, it is assumed that because the metric value for option B is significantly greater than the metric value for option A, option B is more likely to be correct, and option A is discarded. In some embodiments, one of the two options is discarded only if its metric value exceeds the metric value of the other option by some threshold (e.g., a percentage, an amount (e.g., at least twice, at least 1.5 times greater, etc.), etc.). In some embodiments, option A is retained, and the options are not discarded until later.

[0299] In some embodiments, contributions to the metric value are weighted based on the distance of the data considered from the now-corrected current query step. For example, because the likelihood of additional errors having been introduced into the data record increases as more bases are sequenced (e.g., the likelihood of a certain type of error occurring in one of the K sensors between query step 3 and query step 40 is greater than the likelihood of a certain type of error occurring in one of the K sensors between query step 3 and query step 6), the metric may assume that closer data entries are more likely to be correct than more distant data entries, and thus provide more weight to data entries closer to the now-corrected data than to those more distant data entries. The weighting may be, for example, linear or nonlinear. As just one example, for a metric where data contributes up to 12 query steps away, query step contributions within four query steps of the now-corrected data may be given a weight of 1, query step contributions within five to eight query steps of the now-corrected data may be given a weight of 0.5, and query step contributions within nine to twelve query steps of the now-corrected data may be given a weight of 0.2. It should be appreciated that many possible metrics may be used, with or without weighting, and that those provided above are merely exemplary and are not intended to be limiting.

[0300] It should also be appreciated that while the metric described above uses the query step number from the query step after the now-corrected current query step and the query step J position further back in the data record where the tag detection results of all three (or more generally, K) sensors agree, it may equivalently use the query step number from the query step after the now-corrected current query step and the query step J position further back in the data record where the tag detection results of all three (or more generally, K) sensors disagree. In such a case, a large metric value will indicate more mismatches between the sensor data entries, and thus the candidate corrected data record will be more likely to be correct for a lower metric value. Any weighting to be applied may be adjusted as will be appreciated by one of ordinary skill.

[0301] It should also be appreciated that, following correction of a hypothetical error in a data record, one of the possible options need not be discarded. For example, following the (hypothetical) correction of a (hypothetical) error at query step 2 in the record of sensor S2, both options A and B may be retained, and further error detection and correction performed on both in parallel. Likewise, each time a hypothetical error is corrected, multiple options of candidate sequences may be determined and / or evaluated / compared. A running metric for each possible option / candidate sequence may be maintained at each step of the error correction process, and the most likely candidate sequence may be determined at some point (e.g., after all candidate options have been determined and evaluated (e.g., relative to each other), or after some additional number of query steps, etc.).

[0302] Furthermore, although in the above example, the probability of both sensors S1 and S3 falsely detecting a flag is immediately discarded because the probability of such an event (given the assumptions herein) is significantly lower than the probability that sensor S2 is erroneous, the same procedure may alternatively be followed as for sensor S2. In other words, option C at query step 2 may be determined, assuming that both sensors S1 and S3 experience FNR errors, and sensor S2 is correct. In such a case, the metric may be adjusted to account for the likelihood of various possible outcomes (e.g., by "penalizing" the metric for option C based on the probability that both sensors S1 and S3 simultaneously experience FNR errors (e.g., multiplying the metric by the ratio of the probability that both sensors S1 and S3 are erroneous to the probability that sensor S2 is erroneous)).

[0303] It should be appreciated that the error correction methods described herein can be used in a variety of ways to improve the accuracy of nucleic acid sequencing using the SMAS device 100. Assuming sufficient computing power, an implementation (e.g., using at least one processor 130 or another processor or processors) can determine and evaluate an exhaustive set of candidate sequences to which error correction is applied, and then select the candidate sequence that is most likely to be correct from among them. In order to reduce computational complexity, an implementation can also make decisions during the error correction process to eliminate candidate error-corrected sequences (or potential sources of error) that are considered unlikely to be correct (e.g., option C in the above example) and retain only those candidate error-corrected sequences that are more likely to be correct. It should be appreciated that the flexibility of the disclosed principles makes it suitable for error mitigation in systems with a variety of computing power.

[0304] Returning to the above example, assume that option B is the only option remaining after applying error correction to the data from query step 2, the corrected data appears as follows:

[0305]

[0306] The next query step where the three sensors S1, S2, and S3 are inconsistent is at query step 5. Once again, sensor S2 is inconsistent with sensors S1 and S3 in the same manner as in query step 2. In some embodiments, the error correction algorithm determines that (a) the probability that sensor S2 is erroneous is greater than the probability that both sensors S1 and S3 are erroneous, and (b) sensor S2 encountered an FNI error or a FLD error at query step 5. Once again, two options can be established, one option assuming that the error is an FLD error (corrected by flipping a bit), and the other option assuming that the error is an FNI (corrected by shifting the data by four positions). The corrected data record is shown below:

[0307] Option A (assuming FLD errors are corrected):

[0308]

[0309]

[0310] Option B (assuming FNI errors are corrected):

[0311]

[0312] Once again, metrics for options A and B can be calculated, and one of the options can be discarded, or both can be retained. For example, assume that option A is retained, resulting in the following error-corrected data:

[0313]

[0314] The next query step for inconsistent sensor data is query step 10. Here, sensor S1 detected the tag, but neither sensor S2 nor sensor S3 detected the tag. Because FLR errors have been removed from the data record, the only way sensor S1 could have erroneously detected the tag during query step 10 is if it encountered an FNR error during that query step. The probability of an FNR error is r. If sensors S2 and S3 are both wrong, it is because (a) both encountered an FNI error, (b) both encountered an FLD error, or (c) one of them encountered an FNI error and the other encountered an FLD error. The probability of any of the mutually exclusive events (a), (b), or (c) is 4r 2 Therefore, in some embodiments, it is assumed that the more likely event occurs, that is, the sensor S1 suffers from an FNR error (since for the assumed value of r, r>>4r 2 ). As explained above, FNR errors can be corrected by flipping the data entries from "marker detected" values ​​to "marker not detected" values, which results in the following table:

[0315]

[0316] The error correction procedure may continue as described throughout the remainder of the data record. Fig.32 The portion labeled "C" of shows the results of the example. As shown, after applying the probabilistic error correction as described above, 16 of the 20 (80%) bases were correctly identified.

[0317] Fig.33 FIG. 4 is a flow chart illustrating an error correction process 450 according to some embodiments. The error correction process 450 may be, for example, as described in Fig.11 The error correction program 212 in the embodiment of the present invention may be executed by a processor (such as described in the following discussion) Figure 5A or Fig.50At least one processor 130 in 452 is performed. At 452, the error correction program 450 starts. At 454, multiple records are identified in the sequencing data generated by the nucleic acid sequencing program using the SMAS device 100. Each of the multiple records identified includes multiple entries, each of which captures the detection result of an instance of a specific chain of nucleic acid. Therefore, if the number of records identified is K, each of the K records includes an entry / detection result / sequencing program query step. Each detection result indicates that during the query step, (a) the label was detected by the corresponding sensor 105, or (b) the label was not detected by the corresponding sensor 105. The multiple records can be identified in a variety of ways. For example, as further described below, different unique bar codes can be spliced ​​to the primer end of the nucleic acid chain so that a known sequence is read during a cycle of the sequencing program. Therefore, the multiple records can be identified by searching for sequencing data of bar codes associated with a specific chain of nucleic acid. As another example, a common sequence of entries may be identified in the sequencing data (eg, within entries recording the detection results of the first approximately 35 query steps of a sequencing process).

[0318] At 456, multiple candidate sequences of a specific strand of nucleic acid are determined based on the multiple records. Each of the multiple candidate sequences estimates at least a portion (e.g., down to one base) of the nucleic acid sequence of the specific strand of nucleic acid. In some embodiments, determining the multiple candidate sequences includes identifying a specific query step within the multiple records at which the first sensor detects a respective tag and the second sensor does not detect any tag; and establishing two candidate sequences, one of the two candidate sequences assuming that the first sensor correctly detects the respective tag and the second of the two candidate sequences assuming that the first sensor incorrectly detects the respective tag. In some embodiments, determining the multiple candidate sequences includes identifying a specific query step within the multiple records at which the first sensor detects a respective tag and the second sensor does not detect any tag; and establishing two candidate sequences, one of the two candidate sequences assuming that the second sensor incorrectly does not detect any tag and the second of the two candidate sequences assuming that the second sensor correctly does not detect any tag. In some embodiments, determining the plurality of candidate sequences comprises identifying a set of consecutive entries (e.g., four entries) in at least one of the plurality of records indicating that a tag was not detected, and deleting the set of consecutive entries indicating that a tag was not detected from at least one of the plurality of records. In some embodiments, each of the plurality of entries is a first binary value (indicating that a tag was detected) or a second binary value (indicating that a tag was not detected), and determining the plurality of candidate sequences comprises identifying a string of (e.g., four) second binary values ​​in at least one of the plurality of records, and deleting the string of second binary values ​​from at least one of the plurality of records.

[0319] At 458, a specific candidate sequence among the plurality of candidate nucleic acid sequences is identified as the sequence that is most likely to be correct from among the plurality of candidate sequences. In some embodiments, identifying the specific candidate sequence that is most likely to be correct among the plurality of candidate sequences includes determining or estimating which of the plurality of candidate sequences has the highest probability of being correct. In some embodiments, identifying the specific candidate sequence that is most likely to be correct among the plurality of candidate sequences includes determining a separate metric for each of the candidate sequences, and selecting the specific candidate sequence as the most likely to be correct based at least in part on the separate metric and criteria (e.g., minimum likelihood of occurrence, threshold likelihood of occurrence). In some embodiments, identifying the specific candidate sequence that is most likely to be correct among the plurality of candidate sequences includes identifying the majority of results of a specific query step represented by a plurality of records (e.g., more than half of the sensors 105 detected a tag or more than half of the sensors 105 did not detect a tag). In some embodiments, identifying the specific candidate sequence that is most likely to be correct among the plurality of candidate sequences includes determining a separate likelihood of occurrence for each of the plurality of candidate sequences, and selecting the specific candidate sequence based on the separate likelihood of occurrence (e.g., minimum probability) that satisfies the constraints. In some embodiments, the specific candidate sequence with the highest likelihood of occurrence among the candidate sequences is identified as the most likely to be correct. In some embodiments, one or more of the candidate sequences are eliminated based on the knowledge that a particular sequence of bases is impossible, such as a known constraint. For example, it may be known from the origin or source of the nucleic acid (e.g., human) that a particular sequence of bases is impossible, and thus candidate sequences with such impossible sequences may be eliminated from further consideration.

[0320] At 460, the error correction procedure 450 ends.

[0321] It should be understood that only when the most likely scenario is identified (e.g. Fig.33 Probabilistic error correction is successful only when the chemical failure rate is high (identification at 458 of ) is actually correct. If the chemical failure rate is high, such as in the example described herein, there may be multiple scenarios that are equally likely to occur (or whose probability of occurrence is close to each other), in which case more complex bioinformatics tools may be used. For example, candidate sequences can be eliminated based on knowledge of the source of the sequenced nucleic acid (e.g., knowledge that a specific sequence of bases is unlikely given the source / origin of a given nucleic acid). However, if implemented correctly as described herein, the error correction process results in a correct alignment of the sensor 105 output. In the example shown at Fig.32In the example, after removing FNI and FLR, all three sensors S1, S2, and S3 reported the label in the correct detection query step where the label should be detected, but the sensors were inconsistent at many query positions (5, 10, 13, 20, 22, 27, 32, 40, 41, 48, and 50), where the sensors detected labels incorrectly incorporated by FNR or were unable to detect the label due to FLD. Identifying bases when more than half of the sensors 105 in the aligned sequences were consistent resulted in an insertion of thymine at sequence position 8 (query step 22) and a deletion of guanine at position 13 (query step 32). The true sequence and the identified sequence clearly showing the correct alignment of the base insertion and deletion positions can be presented as:

[0322]

[0323] As can be appreciated from the present disclosure, coincidental FNR and FLD resulting in insertion and deletion errors cannot be corrected algorithmically and will remain undetected if the true sequence is not known. In other words, when more than half of the single-molecule sensors 105 in the aligned sequences give wrong answers, the bases are incorrectly identified. The probability of such an event depends on the rate (r value) at which chemical failures occur. As explained above, the examples presented herein use a high error rate to illustrate the application of error correction techniques. The error rate in actual implementations should be significantly reduced to reduce the likelihood that the error correction procedure is unable to correct errors. The disclosed error correction techniques can be used to correctly align the outputs of multiple sensors 105 at the query step. This can be achieved using a deep understanding of the physical origin of the possible error types (e.g., knowledge that certain sequences are impossible for the source nucleic acid), their average incidence, and their signature in the sensor sequence outputs. If the chemical error rate is high and the signature of the error is masked, the error correction algorithm can be computationally intensive and difficult to implement. The following discussion describes how the probability of incorrect base identification depends on the read length, the cluster size N (for CLUS devices), the number K of sensors sensing instances of the same nucleic acid strand (for SMAS device 100), and the chemical error rate of failure.

[0324] General quantitative results of cluster sequencers

[0325] A simple quantitative model is developed herein for estimating the probability of incorrect base identification in a cluster sequencer employing the improved additive sequencing scheme introduced above. It is assumed that various types of errors (FNI, FLR, FNR, and FLD) occur randomly at a rate r throughout the cluster, where 0 < r < 1. Initially, the cluster strands are in-phase with each other (e.g., synchronous, aligned, asynchronous), and the detected signal is proportional to the cluster size (N). A signal is detected when a complementary labeled nucleotide is introduced and successfully incorporated. When at When non-complementary nucleotides are introduced during the query cycle of the query step, no signal should be detected. Errors occur at a rate r, which results in a gradually increasing number of chains that are out of phase (out of sync) with the collective average. This reduces the intensity (or amplitude) of the collective signal when complementary nucleotides are incorporated and increases the intensity or amplitude of the background signal when non-complementary nucleotides are introduced. The average signal intensity at the query step where the label should be detected because of the introduction and successful incorporation of matching nucleotides (ON-State) is given by:

[0326]

[0327] Where C is the detection query step (or number). Similarly, the intensity at the query step where the label should not be detected due to the introduction of non-complementary nucleotides (OFF-State) is given by:

[0328]

[0329] This background signal is generated by heterogeneous nucleic acid chains that incorporate nucleotides that are not complementary to the collective average homogeneous positions. The functions of equations 1(a) and (b) are plotted on Fig.34A For N=11 and r=0.1. Fig.34B The intensity measures that illustrate how the function fits the previously described cluster model instance. As illustrated, bases are correctly identified until However, frequent errors occur at larger C values.

[0330] If through Fig.34A and 34B As shown, during early sequence query (C small), <1> and <0> The states are completely separated, but they follow the functional form expressed by Equations 1(a) and (b) and quickly approach the average value N / 2. Again, because errors are random, unrelated events, the signal measurements in the two states are centered around their collective average value. <1> and <0> discrete distribution. Specifically, when the collective average is <1> The probability that the ON-State intensity measurement value of a cluster size N is k is given by the Poisson distribution:

[0331]

[0332] Similarly, when the collective average is <0> The probability that the OFF-State intensity record value of the same cluster is k is:

[0333]

[0334] Probability function P <1> (k) and P <0> (k), N = 11, r = 0.1 and C = 0, 5, 10, 15 and 20, plotted on Fig.35 The figure shows two Poisson distributions, and the tails overlap more and more as C increases. Under the two discrete distributions, P <0或1> The sum of all possible values ​​of (k) equals 1:

[0335]

[0336] Base calling errors occur when an ON-State is mistaken for an OFF-State or vice versa. Fig.36 Explain the ON-State P at different sequence query steps C = 0, 5, 10, 15 and 20 <1> (k) and OFF-State P <0> (k) (N = 11 and r = 0.1) is a discrete probability function. The source of incorrect base calls is P <0> The tail of (k) is shown as a patterned dot when it extends above the middle value of N / 2 or as a dot at P <1> (k) Extensions below the middle value of N / 2 are shown as dashed circles. The tail of the ON-State distribution extends significantly below (exist Fig.36 Incorrect <1> ) or the tail of the OFF-State distribution (incorrect <0> ) extends above The probability of making an incorrect base call becomes very high.

[0337] Fig.37A Shown are plots of average ON-State and OFF-State intensities as a function of C (r = 0.1) and cluster size for N = 11 (top) and N = 101 (bottom). Fig.37B The OFF-State probability distribution function P is shown for cluster sizes C = 1, 10, 20, 30 and 40 (r = 0.1) and N = 11 (top) and N = 101 (bottom). <0> (k). Increasing cluster size by reducing P <0> (k) The relative width of the distribution (which increases the distance from P <1> (k)) and delay the occurrence of base call errors.

[0338] In general, the probability of incorrect base calling at the number of sequencing queries C (for cluster size N and chemical failure rate r) (denoted as P C,N,r ) is the sum of the probabilities of incorrectly identifying the OFF-State, that is, for values ​​of k exceeding k=(N+1) / 2, it is P <0> (k) values. These are Fig.36 and 37BIncreasing the cluster size N increases the initial interval between two discrete distribution peaks and delays the occurrence of base call errors. To simplify further discussion, only the case where the cluster size N is an odd number is considered to avoid the uncertainty introduced when the detected signal is N / 2 (which is neither ON-State nor OFF-State). For odd values ​​of N, P C,N,r is given by:

[0339]

[0340] Or, P C,N,r is the sum of the probabilities of incorrectly identifying the ON-State, that is, for values ​​of k below k = (N-1) / 2, it is P <1> The sum of (k) values ​​( Fig.36 ), which is given by:

[0341]

[0342] Fig.38A and 38B Equations 4(a) and 4(b) are plotted as a function of C for various combinations of N and r. Fig.38A Plotting calculation P C,N,r (C) function, r = 0.1 and N = 11, 51, 101 and 151, and Fig.38B Plotting calculation P C,N,r (C) Function, N = 101 and r = 0.1, 0.05 and 0.01. The figure shows the th The probability of incorrect base calls increases significantly. Fig.38A and 38B Indicates that as C approaches infinity, P C,N,r Close to 0.5. Fig.38A and 38B The figure in Figure 2 shows the behavior of a sequencer that analyzes a collection of molecules (e.g., a CLUS device). When C is small, the probability of incorrect base recognition (P C,n,r ) is still low, but it is above a certain threshold (C th ) increases significantly, and the threshold is determined by the magnitude of the n and r parameters. As C tends to infinity, P C,N,r Close to 0.5, at which point the intensity of the ON-State equals the intensity of the OFF-State and there is a 1 in 2 chance of making an incorrect base call. C,N,r It depends largely on these three parameters C, N, and r. The dependence on C is particularly important because C th Limit the number of consecutive bases that can be identified before the probability of an error becomes too great.

[0343] Fig.39 Describe the Nr parameter space, where the probability of an incorrect base call at position 150 (P C＝375,N,r ) is lower than 1 in 100 (Q20), 1 in 1,000 (Q30), 1 in 10,000 (Q40), and 1 in 100,000 (Q50). Increasing the cluster size N, or decreasing the chemical failure rate r, increases the threshold C th Push to a higher C value, but if Fig.39 The quantification in the medium shows that the cluster size is quite large and the allowed chemical error rate must be small to make DNA sequencers suitable for diagnostic applications.

[0344] Currently, the sequencing industry benchmark is the ability to read 150 consecutive bases with a 1 in 1,000 probability of an incorrect base call at position 150. This is generally referred to as Q30, but significantly larger sequencing quality factors of Q40 and even Q50 and longer read lengths are needed to detect rare mutations in high-precision diagnostics. C,N,r The general representation of fully explores the CNr parameter space and can be used to estimate the error tolerance and cluster size requirements of any sequencing metric. Fig.39 The region of Nr parameter space is shown, where at position 150 The probability of incorrect base calling at the target sequence is less than 1 in 100 (Q20), 1 in 1,000 (Q30), 1 in 10,000 (Q40), and 1 in 100,000 (Q50). For example, if the average cluster size N in the sequencing array is 100 molecules and the required sequencing accuracy is Q30, with a 150 bp long read segment The allowed chemical failure rate is then r≤0.002641, that is, only 26 or fewer failures are allowed in 10,000 individual single-molecule reactions on the sequencer array at any sequencing query step. If the required accuracy is Q50, only 19 or fewer errors are allowed in every 10,000 reactions. If the average cluster size N is reduced to 10 molecules, the number drops to about 6 (Q30) and about 1 (Q50) in every 10,000 reactions.

[0345] Fig.40A Shows the calculated P for various Nr combinations along the Q30 contour C,N,r (C), marked by crosses (“+” signs) in the inset, all intersections are at P C,N,r (C = 375) = 0.001. The figure shows that increasing the cluster size N not only improves the chemical failure tolerance, but also increases the chemical failure tolerance by increasing the threshold C th Pushing to a higher C value delays the occurrence of base call errors, which results in a reduction in cumulative errors. If the probability of making an incorrect base call at query cycle C is P C,N,r, then the probability of correct recognition is (1-P C,N,r ). The probability of correct identification of C continuously is:

[0346]

[0347] The probability of not making a correct base call in row C (which is the same as or less than the probability of at least one error at any query cycle C) (or the cumulative error probability ) is given by:

[0348]

[0349] Where P j,N,r It is given by Equation 4(a) or (b). Fig.40B Calculate the cumulative error probability by drawing along the same contour line And it shows that larger clusters produce lower cumulative errors.

[0350] Finally, an indication is calculated and a marker is plotted where the cumulative probability of an incorrect base call at position 150 (in some embodiments, the target read length) is less than or equal to 1 in 100 1 in 1,000 1 in 10,000 and 1 in 100,000 The Nr region of the parameter space. Fig.41 Illustrating the cumulative probability of an incorrect base call at position 150 Less than or equal to 1 / 100 1 in 1,000 1 in 10,000 and 1 in 100,000 Nr parameter space. Fig.41 The figure in quantifies that a CLUS sequencer can accommodate large DNA cluster sizes N to benefit from collective behavior, and that it may require extremely reliable chemistry (only a few dozen failures per 10,000 reactions) for high-precision diagnostic applications. More specifically, if the average cluster in the sequencing array holds, for example, 100 molecules on average, and a particular sequencing application tolerates 1 in 1,000 A cumulative base call error probability of , then only about 22 or fewer failures in 10,000 individual single-molecule reactions on the sequencer array are allowed at any sequencing query step. Fig.41 The graph in illustrates that increasing sequencing throughput by reducing cluster size N and packing more clusters into the sensing area can only be achieved with parallel improvements in sequencing chemistry. The required rate of improvement accelerates as cluster size N becomes smaller, and CLUS devices can no longer benefit from large collective behavior.

[0351] General quantitative results from single-molecule array sequencers

[0352] To compare the CLUS and SMAS platforms, a simple quantitative model was developed to estimate the probability of incorrect base recognition in the SMAS device 100. Unlike the collective case applicable to the CLUS device (described above), in which error correction is almost impossible to implement, the ability of the SMAS device 100 to sequence and record the detection results corresponding to individual nucleic acid molecules individually allows the development and implementation of powerful techniques for identifying and eliminating at least some errors in the resulting data records. One or more error correction techniques as disclosed herein can be applied to data generated from a sequencing program (such as SBS) before base recognition is performed to identify and correct errors in the detection results to improve the accuracy of the identified sequence. Specifically, the alignment of the detection results from multiple sensors 105 at some or all query steps of the sequencing program can be improved. Even if the error correction algorithm successfully correctly aligns multiple sensor detection results, incorrect base recognition can still be performed. As described above, coincidental FNR errors and FLD errors can lead to insertion and deletion errors that may not be corrected. Depending on the number of errors in the data record (which is determined in part by the chemical failure rate), the error correction process may be complex and computationally intensive, but it will be appreciated that modern processors have sufficient computational power to perform even the most computationally intensive disclosed techniques.

[0353] Below, consider the general case of K single molecule sensors 105 of the SMAS device 100, each capable of monitoring a single instance of clonal DNA. As in the analysis of the CLUS device above, it is assumed that four types of errors (FNI, FLR, FNR, and FLD) occur randomly during the sequencing process and are distributed throughout the query step.

[0354] As described above, in some embodiments, a probabilistic error correction algorithm is implemented (e.g., by at least one processor 130, which may be included in the SMAS device 100 or outside the SMAS device 100). In some embodiments, the probabilistic error correction algorithm improves the alignment of at least some sensor 105 detection results in the data record. In some embodiments, some or all of the error correction algorithms are implemented after some or all query steps have been completed and some or all data have been captured. As previously described, the error correction procedure substantially eliminates FNI and FLR, as well as some FLD. The algorithmic re-alignment of the sensor 105 detection results also makes the probability of making incorrect base calls independent of the number of query steps C. Furthermore, because the error correction algorithm re-aligns at least some of the sensor 105 detection results in the data record, thereby correcting at least some errors, the effective error rate r is less than in the CLUS case. After applying the exemplary error correction algorithm, in some embodiments, the base is incorrectly identified only when more than half of the K sensors 105 in the algorithmically aligned sequence give incorrect results.

[0355] The probability of making an incorrect base call (P K,r ) is only a function of (a) the number K of sensors 105 that sequence instances of the same nucleic acid molecule (which may be less than all sensors 105 in sensor array 110) and (b) the chemical failure rate r. Similar to the approach taken for the analysis of the CLUS device above, the value of K is constrained to odd values ​​to avoid situations where exactly half of the sensors 105 are inconsistent with the other half. The probability of making an incorrect base call is given by:

[0356]

[0357] in For example, if K = 3,

[0358]

[0359] In the example of K=3, multiplication The term explains a situation where 2 of the 3 sensors 105 simultaneously encounter an error at a particular query step (e.g., they incorrectly detect a label (FLR, FNR) or incorrectly do not detect a label (FNI, FLD)), thereby forcing an incorrect base call. Denoting the three sensors 105 as S1, S2, and S3, this scenario occurs when: (1) S1 and S2 simultaneously encounter an error, (2) S1 and S3 simultaneously encounter an error, or (3) S2 and S3 simultaneously encounter an error. The term explains the impossible situation that all three sensors S1, S2 and S3 encounter errors at the same time, which also leads to incorrect base calls. Since the largest term in the polynomial expansion is r K-1And since 0 < r < 1, the probability of making an incorrect base identification is significantly reduced by increasing the number of single-molecule sensors 105 (i.e., increasing the K value).

[0360] For example, if r = 0.1, then P K＝3,r＝0.1 = 0.029, which means that the probability of making an incorrect base identification is about three in one hundred. In other words, on average about 4.35 out of 150 base identifications will be incorrect, which is too high for some diagnostic applications. To sequence using three nanoscale sensors 105 with Q30 (P K,r = 0.001), the chemical failure rate would need to be reduced to r = 0.01837, meaning that only about 19 out of 1,000 queries would be allowed to be incorrect. However, if the number of sensors 105 (K value) is increased to 11, more than 12 failures out of one hundred reactions can be tolerated.

[0361] As done above for the CLUS device, the K-r parameter space is explored below for the SMAS device 100 to identify regions where the probability of incorrect base identification at any query position is less than one in one hundred (Q20), one in one thousand (Q30), one in ten thousand (Q40), and one in one hundred thousand (Q50). Fig.42 Illustrate the calculated results of the K-r parameter space where the probability of incorrect base identification (P K,r ) at each query step is less than one in one hundred (Q20), one in one thousand (Q30), one in ten thousand (Q40), and one in one hundred thousand (Q50). As Fig.42 shown, if the number K of single-molecule sensors 105 sensing instances of the same nucleic acid molecule is 11 and the required sequencing accuracy is Q30, the allowed chemical failure rate is which means that up to about 13 failures out of 100 individual single-molecule reactions among those 11 sensors 105 are allowed. If the required accuracy is Q50, about 6 or fewer errors out of every 100 reactions among the 11 sensors 105 are allowed.

[0362] As the comparison with Fig.39 indicates, the allowed error rate of the SMAS device 100 is significantly greater than the allowed rate for the CLUS device. However, the results alone do not fairly compare the two platforms because the probability of incorrect base identification (P C,N,r ) in the CLUS device is extremely low during early query steps and suddenly increases at the threshold query step C th . This phenomenon is discussed in conjunction with Fig.39 . On the other hand, for the SMAS device 100, the probability of incorrect base identification (P K,r) remains constant throughout the query steps and thus leads to a larger cumulative error.

[0363] A more fair way to compare the performance of the CLUS device and the SMAS device 100 is to compare the cumulative error probability of the two device types. Equation 5(b) above represents the cumulative error probability of the CLUS device. The cumulative error probability of the SMAS device 100 can also be derived. The probability of making an incorrect base call at each query step C is P K,r (Equation 6), and therefore the probability of correct recognition is (1-P K,r The probability of correctly identifying C in row form is (1-P K,r ) C , and the cumulative error probability for

[0364]

[0365] Fig.43A and 43B The cumulative probability of an incorrect base call at position 150 is shown for the CLUS device and the SMAS device 100. Equation 5(b) can be used, for example, to calculate the probability of an incorrect base call at any base position less than or equal to 150 by the CLUS device. Fig.43A The Kr parameter space of the CLUS device is shown and the cumulative probability of an incorrect base call at position 150 for the CLUS device is marked as less than or equal to 1 in 100 1 in 1,000 1 in 10,000 and 1 in 100,000 area. Fig.43B Equation (8) is evaluated and the Kr parameter space is displayed, which marks where the cumulative probability of an incorrect base call at position 150 for the SMAS device 100 is less than or equal to 1 in 100 1 in 1,000 1 in 10,000 and 1 in 100,000 area.

[0366] Fig.43A and 43B The comparison shows that the SMAS device 100 is a potentially superior sequencing platform to the CLUS device. The SMAS device 100 may have a smaller footprint (e.g., Fig. 7A , 7B, 9A, 9B, and 10) and can be more error tolerant than CLUS devices. Use of SMAS devices 100 allows for higher throughput, lower error rates, and longer read lengths than CLUS devices, which are larger and rely on macromolecular ensembles. Development of commercially viable SMAS devices 100 and / or systems can use some or all of the following: (a) high-precision nanoscale fabrication of densely packed sensors 105 capable of recognizing individual markers, (b) optimization of chemical steps that reduce error rates to acceptable levels, and / or (c) use of effective bioinformatics tools to adjust the alignment of sequencing data from at least some nanoscale sensors 105 in a data record by probabilistically eliminating errors.

[0367] Exemplary SMAS Sequencing Procedure

[0368] As explained above, improvements in sequencing throughput of a CLUS device can be achieved by reducing the cluster size N (thereby packing more clusters into the device) if the sequencing chemistry failure rate is also reduced, which can be challenging. In contrast, a feasible implementation of an error-tolerant, ultra-high throughput SMAS device 100 using a large array of single-molecule binding sites 116 according to some embodiments is presented below. For purposes of example, it is assumed that the SMAS device 100 sequences DNA, but it should be understood that, in general, any kind of nucleic acid can be sequenced.

[0369] Fig.44 and 45 An exemplary sample preparation and loading process 500 is illustrated according to some embodiments. Fig.44 is a flow chart illustrating process 500, and Fig.45 The results of the various steps of process 500 are illustrated. In some embodiments, sample preparation and loading process 500 begins at 502. At 504, DNA extraction and purification are performed, which results in several extracted DNA fragments 505, such as Fig.45 At 506, an adapter complementary to the primer is spliced ​​to one end (e.g., 3') of the extracted DNA to produce the Fig.45 At 508, PCR (or some other replication technique) is performed to produce multiple (ideally, identical) instances of the extracted strand, such as Fig.45 At 510, a molecular linker capable of establishing a strong bond (e.g., by click chemistry) on the chemically functionalized surface of the fluid chamber 115 (binding site 116) of the SMAS device 100 is attached to the other end (e.g., 5') of the ssDNA fragment, thereby generating the Fig.45 At 512, the functionalized chains are loaded into the fluid chamber 115 and randomly dispersed among the binding sites 116 and bound to the binding sites 116. Fig.45 As shown in the rightmost portion of , each of the binding sites 116 supports no more than a single DNA strand. (Although each binding site 116 can support no more than one strand, it should be understood that it is not necessary for each binding site 116 to support a DNA strand. Whether intentionally or accidentally, less than all of the binding sites 116 of the SMAS device 100 may be used.) Assuming that the extracted DNA fragments 503 are different from each other, due to the sample preparation and loading process 500, multiple instances of each of the extracted DNA fragments 505 will exist within the fluid chamber 115, but their positions are unknown. At 514, the exemplary sample preparation and loading process 500 ends.

[0370] A benefit of the exemplary sample preparation and loading process 500 is that it simplifies DNA amplification, which can be performed in bulk outside the device using, for example, conventional PCR, prior to adding DNA strands to the SMAS device 100. In contrast, when a CLUS device is used, amplification (e.g., bridge amplification) is performed only after the DNA fragments have been added to the CLUS device in order to create a continuous cluster array of amplified DNA.

[0371] After the sample preparation and loading process 500 has been performed, base calling may be performed using, for example, the additive method, the subtractive method, or the modified additive method described above. Fig.46A , 46B 46C illustrate three exemplary query cycles (for a total of 12 query steps, each being 120) performed by using an example SMAS device 100 having a sensor array 110 of 20 sensors 105 (and 20 binding sites 116) arranged in four rows and five columns. ) during the simulation detection results using the modified additive method (sensor 105 detects the label). Multiple instances of four different DNA strands are randomly distributed throughout the sensor array 110, but their specific locations in the sensor array 110 and their sequences are initially unknown.

[0372] Fig.47 How to rearrange instructions in Fig.46A , 46B and 46C to identify bases and show the positions of different DNA strands. Fig.47 Tables are provided showing the output of each sensor 105 in an exemplary array at individual query steps and the resulting base calls that led to the identified sequences. Fig.47 The right-hand side portion of is used to reorder the sensors 105 to group the detection results of the sensors 105 that sense instances of the same DNA strand. Fig.47 As shown in , four sequences were identified: GCT (chain #1), TAG (chain #2), ACG (chain #3), and TTA (chain #4).

[0373] If an error (FNI, FLR, FNR, or FLD) occurs during the query step, some of the detection results (label detected or not detected) will be incorrect, and the deterministic and / or probabilistic error detection and / or correction techniques described above can be implemented to detect and eliminate at least some errors, as long as the identity of those sensors 105 sensing instances of the same DNA strand is determined. Recall that instances of a particular DNA strand can be attached to binding sites 116 dispersed throughout the fluid chamber 115, and their locations are generally unknown at the beginning of the sequencing process. Once the process is initiated, each of the plurality of S sensors 105 detects a label at its respective binding site 116 during each query step. For error correction, a subset of the S sensors 105 that sequence instances of the same nucleic acid strand is identified.

[0374] Consider a very large sensor array 110 with 400 million different DNA strands (e.g., 4 billion binding sites 116 and 4 billion individual sensors 105), each DNA strand being about 150 bases long. This means that there are about 10 instances of each unique DNA strand randomly distributed throughout the fluid chamber 115 (and binding sites 116 and sensor array 110). For the sake of example, the sequence is also assumed to be random. Assuming a reasonably low error rate r, after the first query cycle, nearly all binding sites 116 (and sensors 105) that hold (sensed) DNA instances starting with A will be identified, those that hold (sensed) T will be identified, and those that hold (sensed) C, and those that hold (sensed) G. About 10 9 Sensor 105 will detect a marker indicating that the first base is A, about 10 9 Sensor 105 will detect a marker indicating that the first base is T, about 10 9 The sensor will detect the label indicating that the first base is C, and about 10 9 The sensor will detect a label indicating that the first base is G. After the second query cycle, nearly all binding sites 116 (and sensors 105) that hold (sens) DNA instances starting with all 16 possible combinations (AA, AT, AC, AG, TA, TT, TC, TG, CA, CT, CC, CG, GA, GT, GC, and GG) will be identified. 8 The sensor will detect the label indicating that the first and second bases are AA, about 2.5×10 8 The sensor will detect the label indicating that the first and second bases are AT, about 2.5×10 8 The sensors will detect labels indicating that the first and second bases are AC. In general, at some number D of label detections (or assuming that the modified additive method is used for sequencing), After a query step), all 4 DNA chains that keep starting with a sequence of some D-base length will be identified. D =4 2C / 5 This means that the average size of a group of sensors 105 sensing an instance of the same DNA strand in a SMAS device 100 having an array of 4 billion sensors 110 is 4×10 9 / (4 2C / 5 ). Since our examples have an average of about 10 instances per unique chain, we will perform Query cycles are performed to identify the position of the binding site 116 that keeps the instance of a specific chain. Assuming the use of the improved additive method, about 14 bases will be identified during the process. Because the human genome is not random, and not all mathematically possible sequences are displayed, significantly fewer query steps may actually be required for diagnostic applications. If a specific set of genes is targeted during DNA extraction, the identity (position) of the binding site 116 that keeps the instance of the same DNA chain can be determined with even fewer steps, which further reduces the number of possible sequences of bases and is conducive to the identification of binding sites 116.

[0375] The confidence that the correct set of binding sites 116 has been identified increases with the number of query steps, but the probability of detection errors (e.g., incorrectly detecting a tag or incorrectly not detecting a tag) also increases. Multiple errors can occur during the initial query cycle while identifying binding sites 116 that remain instances of the same chain. The results obtained with the CLUS device indicate that this may not be a problem. For example, Fig.38A It is shown that the probability of incorrect base calls made by the CLUS device during the early query step is extremely small and only occurs when the threshold C is reached. th Also recall that if no error correction is applied, the base calling accuracy of the SMAS device 100 is the same as that of the CLUS device, since the SMAS device 100 will simply report the collective result by summing the individual sensor 105 results.

[0376] Consider, for example, the 4 billion sensor array example above and consider a set of 11 sensors 105 (K=11) monitoring an instance of a particular DNA strand randomly distributed throughout the binding sites 116. Now, consider them collectively (K=N=11), as if the binding sites 116 are forming a cluster and only the combined properties (e.g., signal) of their individual sensors 105 are measured. Fig.48A and 48B Plot the calculated probability P of making an incorrect base call C,N,r , which is given by Equations 4(a) and (b) as a function of the number of query steps C and the chemical failure rate r. Fig.48AThe curve in the Cr space is marked with P C,N,r The approximate location of the threshold for the sudden increase. Fig.48B is displayed on Fig.48A , and clearly indicates the chemical failure tolerance of the SMAS device 100 containing 4 billion sensors with an average of about 10 instances of each DNA strand. The position (identity) of the about 10 binding sites 116 (and sensors 105) holding (sensing) instances of each unique DNA strand can be reliably determined as long as the error probability remains low in about 35 query steps. This limits the maximum allowed chemical failure rate to 0.013, that is, 13 out of 1,000 detection events will be tolerated. Fig.48A and 48B The calculations in indicate that if the chemical failure rate remains below about 13 incorrectly detected events per 1,000, the 4 billion sensor SMAS device 100 should be able to establish the positions of all instances of all billion different DNA strands within the fluid chamber 115 (and in the binding sites 116 and in the sensors 105). Once those positions are established, the error correction techniques described herein can be immediately implemented to eliminate errors that occur during the remaining approximately 340 query steps (assuming the use of the modified additive method).

[0377] If the expected or known chemical error rate is too high, such that errors may plague the first approximately 35 query steps, alternative methods can be used to help identify binding sites for instances carrying the same DNA strand 116. For example, different unique barcodes can be spliced ​​to the ends of primers in the extracted DNA subset so that known sequences are read during early sequencing cycles. Fig.49 The use of barcodes in sample preparation and DNA loading according to some embodiments is described. Fig.49 As shown in , unique barcodes are spliced ​​into the extracted DNA to facilitate identification of sites that retain instances of identical DNA in the presence of sequencing errors. For example, Fig.49 Four unique DNA strands are shown, each of which is assigned a unique barcode (e.g., barcode 119A is assigned to strand 1, barcode 119B is assigned to strand 2, barcode 119C is assigned to strand 3, and barcode 119D is assigned to strand 4). If the barcodes are significantly different from each other, they should be easily identifiable even if the chemical failure rate is very high. As will be appreciated, for high throughput diagnostic applications, the suitable number of unique barcodes can be very high.

[0378] The exemplary 4 billion sensor SMAS device 100 described herein is considered a fairly high throughput sequencer by current standards. Such a SMAS device 100 provides approximately 150 Giga-base (Gb) reads during a single run, which is comparable to the output of current state-of-the-art high-end sequencing systems introduced in 2020.

[0379] It should be appreciated that there are many ways to implement the devices, systems, and methods disclosed herein. For example, a system for nucleic acid sequencing may consist of a single device (e.g., SMAS device 100, which includes all hardware and software that can perform the disclosed operations), or it may include SMAS device 100 and other components that together perform the disclosed operations. For example, a system may include SMAS device 100 and at least one processor external to SMAS device 100 (e.g., in an external computer), SMAS device 100 performs a nucleic acid sequencing procedure and saves detection results from the sequencing procedure, and the at least one processor performs error detection and correction on the saved detection results and identifies bases.

[0380] Fig.50 An exemplary system 160 according to some embodiments is described. The system 160 includes (that is, includes (but is not limited to)) a fluid chamber 115, a plurality of S sensors 105, and at least one processor 130. Optionally, the system 160 includes a memory 170 for storing records containing detection results obtained during the sequencing process (e.g., one or more files with binary entries, the binary entries recording that during each of the plurality of S sensors 105, at least one marker was detected or not detected). As shown in Fig.50 As shown by the dashed line in , if the system 160 includes a memory 170 , the at least one processor 130 may be communicatively coupled to the memory 170 so that the at least one processor 130 may store data in the memory 170 and / or retrieve data from the memory 170 .

[0381] The fluid chamber 115 includes a plurality of S binding sites, each of the S binding sites being configured to bind no more than one nucleic acid strand to be sequenced. Fig.50 Four binding sites 116 are shown, but it should be appreciated that the system 160 may include more or fewer binding sites 116. Each of the three sensors 105 is configured to detect a marker present in the fluid chamber 115. Fig.50 Four sensors 105 are shown, but it should be understood that the system 160 may include more or fewer sensors 105. When the system 160 is in operation, each of the three sensors 105 detects a label attached to a nucleotide in a respective strand of a nucleic acid that is incorporated into a respective binding site 116 of the three binding sites 116. As previously described, the sensor 105 may be a magnetic sensor, an optical sensor, or any other type of sensor that can detect a label for a labeled nucleotide. The fluid chamber 115, the sensor 105, and the binding site 116 are described in detail above. Those descriptions apply to Fig.50 And will not be repeated here.

[0382] The at least one processor 130 is configured to execute one or more machine-executable instructions. When the instructions are executed, the at least one processor 130 performs a sequenced procedure including a plurality of query steps (e.g., Fig.11 , 12 , 14, 16, 44, and the like). Specifically, in operation, during the query step of the sequencing procedure, the at least one processor 130 obtains a respective characteristic of each of the S sensors 105 (represented by the dashed lines between the at least one processor 130 and the sensors 105A, 105B, 105C, and 105D). The respective characteristic indicates that the sensor 105 detected or did not detect the marker (e.g., it indicates the presence or absence of at least one marker). The at least one processor 130 may interpret the obtained characteristic to determine whether the sensor 105 detected or did not detect the presence of the marker. Based at least in part on the obtained respective characteristic, the at least one processor 130 records whether the respective sensor detected the presence or absence of the at least one marker during the query step. The at least one processor 130 is also configured to perform an error correction procedure on at least one record containing the results of the sequencing procedure. The error correction procedure may operate on some or all of the records generated by the sequencing procedure, and it may operate on the detection results from some or all of the query steps of the sequencing procedure. For example, as described above, to apply the error correction procedure, the at least one processor may identify a subset of K records and apply deterministic or probabilistic error correction thereto, wherein each of the K records in the subset corresponds to a detection result from a sensor 105 sensing an instance of the same nucleic acid strand. The sequencing procedure and the error correction procedure are described in detail above. Those descriptions are applicable to Fig.50 The system and at least one processor 130 are described above and will not be repeated here.

[0383] At least one processor 130 may be implemented via a general or special purpose processor (or processing core group) and may therefore execute a series of programmed instructions to perform various operations related to obtaining sensor 105 characteristics, performing error correction procedures, and / or interacting with a user, system operator, or other system components.

[0384] The at least one processor 130 of the system 160 may be a single processor (e.g., in the SMAS device 100), or it may include multiple processors, which may be co-located (e.g., in the SMAS device 100) or physically separated from each other. For example, a first portion of the at least one processor 130 may be included in the SMAS device 100, and a second portion of the at least one processor 130 may be external to the SMAS device 100. In embodiments where the at least one processor 130 includes a first and a second portion, the first portion may be responsible for obtaining a characteristic of the sensor 105, determining whether the sensor 105 detects a tag during an inquiry cycle based on the characteristic, and recording (e.g., in the memory 170) whether each of the S sensors 105 detects the presence or absence of at least one tag during the inquiry cycle, and the second portion is responsible for obtaining a record of the detection results and performing an error correction procedure. Alternatively, the first portion may be responsible for obtaining characteristics of the sensors 105, determining based on the characteristics whether each of the sensors 105 detected at least one marker during a query cycle, and providing an indication of whether the sensor 105 detected the marker to another entity via a communication interface (e.g., a wireless or wired interface, such as Ethernet, Wi-Fi, etc.). In such an implementation, the second portion of the at least one processor 130 may be responsible for obtaining a record of the detection results provided by the first portion of the at least one processor 130 (e.g., a file with binary entries that record whether each of the plurality of S sensors 105 detected or did not detect at least one marker during each query cycle), performing an error correction procedure, and identifying a base.

[0385] In the foregoing description and in the accompanying drawings, specific terminology has been set forth to provide a thorough understanding of the disclosed embodiments. In some instances, the terminology or the drawings may imply specific details that are not necessary to practice the invention.

[0386] To avoid unnecessarily obscuring the present invention, well-known components are shown in block diagram form and / or in some cases are not discussed in detail at all.

[0387] The section headings provided in the embodiments are for convenience or reference only and are not intended to be limiting. Section headings in no way define, limit, explain or describe the scope or extent of these sections. Furthermore, although various specific embodiments have been disclosed, it is apparent that various modifications and changes may be made to the invention without departing from the broader spirit and scope of the invention. For example, the features or aspects of any of the embodiments may be applied in combination with or in place of corresponding features or aspects of any other of the embodiments.

[0388] Certain techniques and methods disclosed herein (e.g., obtaining detection results from the sensor 105, performing error correction procedures, etc.) and / or user interfaces for constructing and managing the same may be implemented by a machine executing one or more sequences of instructions (including associated data required for proper instruction execution). Such instructions may be recorded on one or more computer-readable media for later retrieval and execution within one or more processors of a special or general-purpose computer system or consumer electronic device or appliance. Computer-readable media in which such instructions and data may be embodied include, but are not limited to, various forms of non-volatile storage media (e.g., optical, magnetic, or semiconductor storage media) and carrier waves that may be used to transmit such instructions and data via wireless, optical, or wired signal transmission media, or any combination thereof. Examples of transmission of such instructions and data via carrier waves include, but are not limited to, transmission (upload, download, electronic mail (e-mail), etc.) via one or more data transmission protocols (e.g., HTTP, FTP, SMTP, etc.) over the Internet and / or other computer networks.

[0389] Unless expressly defined otherwise herein, all terms are intended to be given their broadest possible interpretation, including the meanings encompassed by the specification and drawings and as understood by those skilled in the art and / or as defined in dictionaries, monographs, etc. As expressly stated herein, some terms may not conform to their ordinary or customary meanings.

[0390] As used in this specification and the appended claims, the singular forms "a", "an", and "the" do not exclude plural referents unless otherwise indicated. Unless otherwise indicated, the word "or" is to be interpreted as inclusive. Thus, the phrase "A or B" is to be interpreted as all of the following meanings: "A and B", "A but not B", and "B but not A". Any use of "and / or" herein does not imply that the word "or" alone is exclusive.

[0391] As used in this specification and the appended claims, phrases of the form "at least one of A, B, and C", "at least one of A, B, or C", "one or more of A, B, or C", and "one or more of A, B, and C" are interchangeable and each encompasses all of the following meanings: "only A", "only B", "only C", "A and B but not C", "A and C but not B", "B and C but not A", and "all of A, B, and C".

[0392] To the extent that the terms "include(s)," "having," "has," "with," and variations thereof are used in the embodiments or claims, such terms are intended to be inclusive in a manner similar to the term "comprising," that is, to mean "including, but not limited to,"

[0393] The terms "exemplary" and "embodiment" are used to indicate examples, not preferences or requirements.

[0394] The term "coupled" is used herein to refer to both a direct connection / attachment as well as a connection / attachment through one or more intermediate components or structures.

[0395] The terms "above," "below," "between," and "over" are used herein to refer to the relative position of one feature with respect to other features. For example, a feature disposed "above" or "below" another feature may be in direct contact with the other feature or may have intervening materials. Additionally, a feature disposed "between" two features may be in direct contact with the two features or may have one or more intervening features or materials. In contrast, a first feature that is "above" a second feature is in contact with the second feature.

[0396] The term "substantially" is used to describe a structure, construction, dimension, etc. that is largely or nearly described, but due to manufacturing tolerances and the like, may in practice result in situations where the structure, construction, dimension, etc. is not always or necessarily exactly as described. For example, describing two lengths as "substantially equal" means that describing two lengths as substantially equal means that the two lengths are the same for all practical purposes, but they may not (and need not) be exactly equal on a sufficiently small scale. As another example, a structure that is "substantially vertical" will be considered vertical for all practical purposes even if it is not exactly 90 degrees relative to horizontal.

[0397] The drawings are not necessarily drawn to scale, and dimensions, shapes, and sizes of features may vary substantially from how they are depicted in the drawings.

[0398] Although specific embodiments have been disclosed, it will be apparent that various modifications and changes may be made thereto without departing from the broader spirit and scope of the invention. For example, features or aspects of any of the described embodiments may be combined with or used in place of corresponding features or aspects of any other of the described embodiments, at least where feasible. Accordingly, the specification and drawings should be regarded in an illustrative rather than a restrictive sense.

Claims

1. A system for sequencing nucleic acids, comprising: a plurality of binding sites, each of the plurality of binding sites being configured to bind no more than one nucleic acid strand to be sequenced; a plurality of sensors configured to detect the label, each of the plurality of sensors for sensing a respective strand of nucleic acid bound to a respective binding site of the plurality of binding sites; and at least one processor configured to execute one or more machine-executable instructions that, when executed, cause the at least one processor to: (a) at each of a plurality of query steps of a sequencing procedure, and for each of the plurality of sensors: obtaining a respective characteristic of the respective sensor, wherein the respective characteristic indicates the presence or absence of at least one marker, and based at least in part on the obtained respective characteristic, recording whether the respective sensor detected the presence or absence of at least one marker during the interrogation step, and (b) performing an error correction procedure on at least one record, the at least one record comprising the results of a sequencing procedure for at least a subset of the plurality of sensors at each of the plurality of query steps, Wherein performing an error correction procedure on at least one record comprises at least one of the following: (i) subjecting at least one record to a deterministic error correction procedure, or (ii) subjecting at least one record to a probabilistic error correction procedure, Wherein performing a deterministic error correction procedure on at least one record comprises: identifying in the at least one record a set of consecutive indications that a first sensor of the plurality of sensors did not detect a marker, and deleting from the at least one record the set of consecutive indications that the first sensor of the plurality of sensors did not detect a marker, and Wherein performing a probabilistic error correction procedure on at least one record comprises: identifying a plurality of candidate sequences associated with an instance of a particular nucleic acid strand based on at least a portion of the at least one record, and A determination is made or estimated as to which of the plurality of candidate sequences has the highest probability of being correct.

2. The system of claim 1, further comprising a memory storing a plurality of records, and wherein the at least one record is one of the plurality of records.

3. The system according to claim 1, wherein: When executed, the one or more machine executable instructions further cause the at least one processor to, at each of the plurality of query steps of the sequencer and for each of the plurality of sensors: The resulting respective characteristics of the respective sensors are interpreted to determine whether the respective sensors detected the presence of the at least one marker or detected the absence of the at least one marker. The system of claim 1 , wherein each of the plurality of sensors is configured to detect a fluorophore. 5 . The system of claim 1 , wherein each of the plurality of sensors is configured to detect magnetic particles.

6. The system of claim 1, wherein each of the plurality of sensors is configured to detect charged molecules.

7. The system of claim 1, wherein each of the plurality of sensors is configured to detect an organometallic complex.

8. The system of claim 1, wherein the at least one label comprises a fluorophore.

9. The system of claim 8, wherein each of the plurality of sensors comprises an optical sensor, and wherein the respective characteristic is the wavelength, frequency, intensity, or color of light emitted by the fluorophore.

10. The system of claim 1, wherein the at least one label comprises a magnetic particle.

11. The system of claim 10, wherein each of the plurality of sensors comprises a magnetic sensor.

12. The system of claim 11, wherein the magnetic sensor comprises a magnetic oscillator, and wherein the respective characteristic is a frequency of a signal associated with or generated by the magnetic oscillator.

13. The system of claim 11, wherein the magnetic sensor comprises a magnetic tunnel junction.

14. The system of claim 11, wherein the individual characteristic is a magnetic field or resistance, a change in a magnetic field or resistance, a noise level, or a change in a noise level.

15. The system of claim 1, wherein the at least one label comprises a charged molecule.

16. The system of claim 1, wherein the at least one label comprises an organometallic complex.

17. The system of claim 1, wherein the plurality of sensors are arranged in a rectangular array.

18. The system of claim 17, wherein the at least one label is magnetic, and wherein the nearest neighbor distance between adjacent sensors in the rectangular array is at least 70 nm.

19. The system of claim 1, wherein the plurality of sensors are arranged in a hexagonal array.

20. The system of claim 19, wherein the at least one marker is fluorescent, and wherein the nearest neighbor distance between adjacent sensors in the hexagonal array is at least 140 nm.

21. The system of claim 1, wherein the plurality of binding sites are located within a fluid chamber, and wherein a surface of the fluid chamber comprises metal oxide, silicon dioxide, polypropylene, gold, glass, or silicon.

22. The system of claim 1, wherein each of the plurality of binding sites comprises a structure configured to anchor a respective strand of nucleic acid.

23. The system of claim 22, wherein the structure comprises a cavity or a ridge.

24. The system of claim 1, wherein determining or estimating which of the plurality of candidate sequences has the highest probability of being correct comprises: determining a respective metric for each of the plurality of candidate sequences; and Based at least in part on the respective metrics and criteria, a particular candidate sequence is selected as being most likely to be correct.

25. The system of claim 24, wherein the respective metric is a likelihood of occurrence, and wherein the criterion is a minimum likelihood of occurrence.

26. The system of claim 24, wherein the respective metric is a likelihood of occurrence, and wherein the criterion is a threshold likelihood of occurrence.

27. The system of claim 1, wherein determining or estimating which of the plurality of candidate sequences has a highest probability of being correct comprises eliminating at least one of the plurality of candidate sequences based on known constraints on the nucleic acid sequence of the particular nucleic acid strand.

28. The system of claim 27, wherein the known constraint is the improbability of a particular sequence of bases.

29. The system of claim 27, wherein determining or estimating which of the plurality of candidate sequences has the highest probability of being correct further comprises determining a known constraint based at least in part on a source of the particular nucleic acid strand.

30. The system of claim 1, wherein the at least one record comprises a set of binary values.

31. The system of claim 1, wherein performing the probabilistic error correction procedure on the at least one record further comprises: At least one entry of the at least one record is modified based on a majority result of the particular query step.

32. An apparatus for sequencing nucleic acids, the apparatus comprising: a fluid chamber comprising a plurality of binding sites, each of the plurality of binding sites being configured to bind no more than one nucleic acid strand to be sequenced; a plurality of magnetic sensors configured to detect labels present in the fluid chamber, each of the plurality of magnetic sensors for sensing a respective strand of nucleic acid bound to a respective binding site of the plurality of binding sites; and at least one processor configured to execute one or more machine-executable instructions that, when executed, cause the at least one processor to, at each of a plurality of query steps of a sequenced program and for each of the plurality of magnetic sensors: obtaining a respective characteristic of the respective magnetic sensor, wherein the respective characteristic is indicative of the presence or absence of at least one marker, determining, based at least in part on the obtained respective characteristic, whether the respective magnetic sensor detected the presence or absence of at least one marker during the interrogation step, and performing an error correction procedure on at least one record, the at least one record comprising the results of a sequencing procedure for at least a subset of the plurality of magnetic sensors at each of the plurality of query steps, Wherein performing an error correction procedure on at least one record comprises at least one of the following: (i) subjecting at least one record to a deterministic error correction procedure, or (ii) subjecting at least one record to a probabilistic error correction procedure, Wherein performing a deterministic error correction procedure on at least one record comprises: identifying in the at least one record a set of consecutive indications that a first sensor of the plurality of sensors did not detect a marker, and deleting from the at least one record the set of consecutive indications that the first sensor of the plurality of sensors did not detect a marker, and Wherein performing a probabilistic error correction procedure on at least one record comprises: identifying a plurality of candidate sequences associated with an instance of a particular nucleic acid strand based on at least a portion of the at least one record, and A determination is made or estimated as to which of the plurality of candidate sequences has the highest probability of being correct.

33. The device according to claim 32, wherein: When executed, the one or more machine-executable instructions further cause the at least one processor, at each of the plurality of query steps of the sequencer and for each of the plurality of magnetic sensors: Whether the respective magnetic sensor detected the presence or absence of at least one marker during the interrogation step is recorded in a respective record associated with the respective magnetic sensor.

34. The device of claim 33, further comprising: A memory for storing multiple records, And wherein the respective record associated with the respective magnetic sensor is one of the plurality of records.

35. The apparatus of claim 32, wherein determining whether the respective magnetic sensor detects the presence or absence of the at least one marker during the interrogation step comprises: A determination is made as to whether the resulting respective characteristic of the respective magnetic sensor meets or exceeds a threshold value.

36. The apparatus of claim 32, wherein determining whether the respective magnetic sensor detects the presence or absence of the at least one marker during the interrogation step comprises: The resulting respective characteristics of the respective magnetic sensors are compared to previously detected values.

37. The apparatus of claim 36, wherein the previously detected value is a baseline value.

38. The apparatus of claim 36, wherein the previously detected value is a frequency, a magnetic field, or a noise level.

39. The device of claim 32, wherein each of the plurality of magnetic sensors is configured to detect magnetic particles.

40. The device of claim 32, wherein each of the plurality of magnetic sensors is configured to detect charged molecules.

41. The device of claim 32, wherein each of the plurality of magnetic sensors is configured to detect an organometallic complex.

42. The device of claim 32, wherein the at least one label comprises a magnetic particle.

43. The device of claim 32, wherein the at least one label comprises a charged molecule.

44. The device of claim 32, wherein the at least one label comprises an organometallic complex.

45. The device of claim 32, wherein each of the plurality of magnetic sensors comprises a magnetic oscillator, and wherein the respective characteristic is a frequency of a signal associated with or generated by the magnetic oscillator.

46. ​​The device of claim 32, wherein each of the plurality of magnetic sensors comprises a magnetic tunnel junction.

47. The device of claim 32, wherein the individual characteristic is a magnetic field or resistance, a change in a magnetic field or resistance, a noise level, or a change in noise level.

48. The device of claim 32, wherein the plurality of magnetic sensors are arranged in a rectangular array.

49. The device of claim 48, wherein the at least one label is magnetic, and wherein the nearest neighbor distance between adjacent magnetic sensors in the rectangular array is at least 70 nm.

50. The device of claim 32, wherein a surface of the fluid chamber comprises metal oxide, silicon dioxide, polypropylene, gold, glass, or silicon.

51. The device of claim 32, wherein each of the plurality of binding sites comprises a structure configured to anchor a respective strand of nucleic acid.

52. The device of claim 51, wherein the structure comprises a cavity or a ridge.

53. The apparatus of claim 32, wherein determining or estimating which of the plurality of candidate sequences is most likely to be correct comprises: determining a respective metric for each of the plurality of candidate sequences; and Based at least in part on the respective metrics and criteria, a particular candidate sequence is selected as being most likely to be correct.

54. The device of claim 53, wherein the respective metric is a likelihood of occurrence, and wherein the criterion is a minimum likelihood of occurrence.

55. The device of claim 53, wherein the respective metric is a likelihood of occurrence, and wherein the criterion is a threshold likelihood of occurrence.

56. The apparatus of claim 32, wherein determining or estimating which of the plurality of candidate sequences is most likely to be correct comprises eliminating at least one of the plurality of candidate sequences based on known constraints on the nucleic acid sequence of the particular nucleic acid strand.

57. An apparatus according to claim 56, wherein the known constraint is the improbability of a specific sequence of bases.

58. The apparatus of claim 56, wherein determining or estimating which of the plurality of candidate sequences is most likely to be correct further comprises determining a known constraint based at least in part on a source of the particular nucleic acid strand.

59. The device of claim 32, wherein the at least one record comprises a set of binary values, wherein a first binary value indicates that the at least one marker was detected and a second binary value indicates that a marker was not detected, and wherein performing the error correction procedure comprises: identifying a sequence of second binary values ​​in the at least one record, and The sequence of second binary values ​​is deleted from the at least one record.

60. The device of claim 59, wherein the string of second binary values ​​has a length of four.

61. The apparatus of claim 32, wherein performing a probabilistic error correction procedure on the at least one record further comprises: At least one entry of the at least one record is modified based on a majority result of the particular query step.

62. A method for sequencing a plurality of nucleic acid chains using a sequencing device, the sequencing device comprising a fluid chamber and three sensors configured to detect a label present in the fluid chamber, each of the three sensors being used to sense a respective nucleic acid chain bound to a respective one of three binding sites within the fluid chamber, each of the three binding sites being configured to bind no more than one nucleic acid chain for sequencing, the method comprising: Binding the plurality of nucleic acid chains to the three binding sites; performing a sequencing procedure including M query steps to generate S records, each of the S records capturing M detection results of a respective one of the S sensors, each of the M detection results indicating whether a respective one of the S sensors detected at least one marker in the fluid chamber during a respective one of the M query steps; and applying an error correction procedure to at least a subset of the S records to estimate the nucleic acid sequence of at least one of the plurality of nucleic acid chains, Wherein applying an error correction procedure to at least a subset of the S records comprises at least one of: (i) applying a deterministic error correction procedure to at least a subset of the S records, or (ii) applying a probabilistic error correction procedure to at least a subset of the S records, Wherein applying a deterministic error correction procedure to at least a subset of the S records comprises: identifying, in at least one record of said at least one subset of said S records, a set of consecutive indications that a marker was not detected, and deleting from said at least one subset of said S records said set of consecutive indications for which no marker was detected, and wherein said at least one subset of said S records comprises an odd number of at least three records representing sequencing results of instances of the first nucleic acid strand, and Wherein applying a probabilistic error correction procedure to at least a subset of the S records comprises: identifying in each of the at least one subset of the S records a majority of detection results for a particular query step; and The bases of the first nucleic acid strand are identified or not identified based at least in part on the majority of detection results.

63. A method according to claim 62, wherein the subset of the S records captures the results of a sequencing procedure for an instance of a particular nucleic acid chain.

64. The method of claim 63, further comprising amplifying or replicating the specific nucleic acid chain to establish an instance of the specific nucleic acid chain before binding the multiple nucleic acid chains to the three binding sites.

65. The method of claim 64, wherein amplifying or replicating comprises performing at least one procedure that promotes polymerase chain reaction (PCR).

66. A method according to claim 62, wherein each record of at least a subset of the S records corresponds to a respective instance of a particular nucleic acid strand.

67. The method of claim 66, further comprising identifying a subset of the S records prior to applying the error correction procedure.

68. The method of claim 67, wherein identification of the subset of the S records is based on knowledge of a specific barcode associated with the specific nucleic acid strand.

69. The method of claim 67, wherein identifying the subset of the S records comprises identifying a specific barcode associated with the specific nucleic acid strand in each record of the subset of the S records.

70. The method of claim 67, wherein identifying the subset of the S records comprises identifying a shared sequence of entries in each record of the subset of the S records.

71. The method of claim 62, wherein the sequencing procedure comprises: (a) introducing labeled nucleotides into the fluid chamber; (b) washing away unbound molecules; (c) obtaining a first characteristic from a first sensor of the S sensors; (d) obtaining a second characteristic from a second sensor of the S sensors; (e) determining whether the first sensor detects at least one marker in the fluid chamber based on the first characteristic; (f) determining whether the second sensor detects at least one marker in the fluid chamber based on the second characteristic; (g) recording in a first record of the S records a first indication indicating whether the first sensor detected at least one marker in the fluid chamber; (h) recording a second indication in a second record of the S records, the second indication indicating whether the second sensor detected at least one marker in the fluid chamber; Repeating (a) to (h) for at least one other labeled nucleotide; and After repeating (a) to (h) for the at least one other labeled nucleotide, the label is cleaved and washed away.

72. The method of claim 62, wherein the sequencing procedure comprises: (a) introducing a plurality of labeled nucleotides into the fluid chamber, each of the plurality of labeled nucleotides using a respective linker; (b) washing away unbound nucleotides; (c) cleaving the first linker; (d) obtaining a first characteristic from a first sensor; (e) obtaining a second characteristic from a second sensor; (f) determining whether the first sensor detects at least one marker in the fluid chamber based on the first characteristic; (g) determining whether the second sensor detects at least one marker in the fluid chamber based on the second characteristic; (h) recording in a first record of the S records a first indication indicating whether the first sensor detected at least one marker in the fluid chamber; (i) recording a second indication in a second record of the S records, the second indication indicating whether the second sensor detected at least one marker in the fluid chamber; cleaving the second linker; and After cleavage of the second linker, (d) to (i) are repeated.

73. The method of claim 62, wherein the sequencing procedure comprises: (a) introducing labeled nucleotides into the fluid chamber; (b) washing away unbound molecules; (c) obtaining a first characteristic from a first sensor; (d) obtaining a second characteristic from a second sensor; (e) determining whether the first sensor detects at least one marker in the fluid chamber based on the first characteristic; (f) determining whether the second sensor detects at least one marker in the fluid chamber based on the second characteristic; (g) recording in a first record of the S records a first indication indicating whether the first sensor detected at least one marker in the fluid chamber; (h) recording a second indication in a second record of the S records, the second indication indicating whether the second sensor detected at least one marker in the fluid chamber; (i) cutting and washing away the markings; and After cleavage and washing away of the label, (a) to (i) are repeated for at least one other labeled nucleotide.

74. The method of claim 62, wherein the number of records in at least one subset of the S records is an odd number.

75. The method of claim 62, wherein each of the M test results in each of the S records is represented by a binary value, and wherein performing the sequencing procedure comprises: in response to respective ones of the S sensors detecting the at least one marker, recording a first binary value in respective ones of the S records, and In response to a respective one of the S sensors not detecting the at least one marker, a second binary value is recorded in the respective one of the S records.

76. The method of claim 75, wherein the set of consecutive indications is a series of second binary values.

77. The method of claim 76, wherein the string of second binary values ​​has a length of four.

78. The method of claim 75, wherein the sequencing procedure comprises (a) a first query step, (b) a mark removal step of removing marks present in the fluid chamber after the first query step, (c) a sensing step of detecting residual marks present in the fluid chamber after the mark removal step, and (d) a second query step after the sensing step, and wherein applying a deterministic error correction procedure to at least a subset of the S records further comprises: In response to determining through the sensing step that a specific sensor among the S sensors detects a residual mark in the fluid chamber, the second binary value is recorded in a specific position of a specific record among the S records, wherein the specific record captures the detection result of the specific sensor, wherein the specific position captures the result of the second query step.

79. The method of claim 62, wherein applying a deterministic error correction procedure to at least a subset of the S records further comprises modifying one or more of the at least a subset of the S records.

80. The method of claim 79, wherein the subset of the S records captures the results of a sequencing procedure for an instance of a particular nucleic acid strand.

81. The method of claim 80, further comprising amplifying or replicating the specific nucleic acid chain to establish an instance of the specific nucleic acid chain before binding the multiple nucleic acid chains to the three binding sites.

82. The method of claim 81, wherein amplifying or replicating comprises performing at least one procedure that promotes polymerase chain reaction (PCR).

83. The method of claim 79, wherein each record of at least a subset of the S records corresponds to a respective instance of a particular nucleic acid strand.

84. The method of claim 83, further comprising identifying a subset of the S records prior to applying the error correction procedure.

85. A method according to claim 84, wherein identification of the subset of S records is based on knowledge of a specific barcode associated with the specific nucleic acid strand.

86. The method of claim 84, wherein identifying the subset of the S records comprises identifying a specific barcode associated with the specific nucleic acid strand in each record of the subset of the S records.

87. The method of claim 84, wherein identifying the subset of the S records comprises identifying a shared sequence of entries in each record of the subset of the S records.

88. The method of claim 79, wherein the number of records in at least one subset of the S records is an odd number.

89. The method of claim 79, wherein the sequencing procedure comprises (a) a first query step, (b) a mark removal step of removing marks present in the fluid chamber after the first query step, (c) a sensing step of detecting residual marks present in the fluid chamber after the mark removal step, and (d) a second query step after the sensing step, and wherein applying a deterministic error correction procedure to at least a subset of the S records further comprises: In response to determining through the sensing step that a specific sensor among the S sensors detects a residual mark in the fluid chamber, a second binary value is recorded in a specific position of a specific record of the S records, wherein the specific record captures the detection result of the specific sensor, wherein the specific position captures the result of the second query step, wherein the second binary value indicates that the respective sensor did not detect the mark.

90. The method of claim 79, wherein modifying one or more of the at least one subset of the S records comprises: identifying, in at least one record of said at least one subset of said S records, a set of consecutive indications that a marker was not detected, and The set of consecutive indications in which no marker was detected is deleted from the at least one record.

91. The method of claim 79, wherein the at least one subset of the S records consists of first, second, and third records, and wherein for a selected test result of the M test results, modifying one or more of the at least one subset of the S records comprises: In response to the selected detection results in at least two of the first, second, and third records being the same, recording bases of the first nucleic acid strand based at least in part on the same selected detection results.

92. The method of claim 79, wherein the at least one label is magnetic or fluorescent.

93. The method of claim 79, wherein the at least one label comprises a charged molecule or an organometallic complex.

94. The method of claim 62, wherein the at least one subset of the S records consists of first, second, and third records, and wherein for a selected test result of the M test results, applying a deterministic error correction procedure to at least one subset of the S records further comprises: In response to the selected detection results in at least two of the first, second, and third records being the same, recording bases of the first nucleic acid strand based at least in part on the same selected detection results.

95. The method of claim 62, wherein for selected ones of the M test results, applying a deterministic error correction procedure to at least a subset of the S records further comprises: In response to selected detection results in more than half of at least one subset of the S records indicating detection of the at least one marker in the fluid chamber, a base of at least one of the plurality of nucleic acid strands is identified.

96. The method of claim 62, wherein the at least one label is magnetic or fluorescent.

97. The method of claim 62, wherein the at least one label comprises a charged molecule or an organometallic complex.

98. A method of mitigating errors in sequencing data generated by a nucleic acid sequencing procedure using a single molecule sensor array, the single molecule sensor array having a plurality of sensors, each of the plurality of sensors being associated with a respective binding site of a plurality of binding sites, each of the plurality of binding sites being configured to bind no more than one nucleic acid strand to be sequenced, the method comprising: identifying a plurality of records in the sequencing data, each of the plurality of records capturing a respective sequencing result for a respective instance of a first strand of nucleic acid, each of the plurality of records having a plurality of entries, each of the plurality of entries indicating, for a respective query step in a plurality of query steps of the nucleic acid sequencing procedure, (a) detection of a marker by a respective sensor associated with the respective instance of the first strand of nucleic acid, or (b) non-detection of a marker by the respective sensor associated with the respective instance of the first strand of nucleic acid; determining a plurality of candidate sequences of the first strand of nucleic acid based on the plurality of records, each of the plurality of candidate sequences estimating at least a portion of a nucleic acid sequence of the first strand of nucleic acid; and A particular candidate sequence of the plurality of candidate sequences is identified as at least a portion of the nucleic acid sequence of the first strand of nucleic acid, the particular candidate sequence being most likely to be correct among the plurality of candidate sequences.

99. The method of claim 98, wherein identifying the plurality of records comprises: The sequencing data of the barcode associated with the first strand of nucleic acid is searched.

100. The method of claim 98, wherein identifying the plurality of records comprises: A common sequence of entries in each of the plurality of records is identified.

101. The method of claim 98, wherein said at least a portion of said nucleic acid sequence of said first strand of nucleic acid is a single base.

102. The method of claim 98, wherein determining the plurality of candidate sequences of the first strand of nucleic acid comprises: identifying a particular query step in the plurality of records at which the first sensor detected a respective marker and the second sensor did not detect any marker; establishing a first candidate sequence, the first candidate sequence assuming that the first sensor correctly detects the respective markers; and A second candidate sequence is established, the second candidate sequence assuming that the first sensor incorrectly detected the respective marker.

103. The method of claim 98, wherein determining the plurality of candidate sequences of the first strand of nucleic acid comprises: identifying a particular query step in the plurality of records at which the first sensor detected a respective marker and the second sensor did not detect any marker; establishing a first candidate sequence, the first candidate sequence assuming that the second sensor incorrectly detects no markers; and A second candidate sequence is established that assumes that the second sensor correctly detects no markers.

104. The method of claim 98, wherein each of the plurality of entries is a first binary value or a second binary value, wherein the first binary value indicates that the marker was detected by the respective sensor, and The second binary value indicates that no label was detected by the respective sensor, and wherein determining the plurality of candidate sequences of the first strand of nucleic acid comprises: identifying a sequence of second binary values ​​in at least one of the plurality of records, and The string of second binary values ​​is deleted from the at least one of the plurality of records.

105. The method of claim 104, wherein the string of second binary values ​​has a length of four.

106. The method of claim 98, wherein determining the plurality of candidate sequences of the first strand of nucleic acid comprises: A set of consecutive entries indicating that a marker was not detected is identified in at least one of the plurality of records, and the set of consecutive entries indicating that a marker was not detected is deleted from the at least one of the plurality of records.

107. The method of claim 98, wherein identifying a particular candidate sequence among the plurality of candidate sequences that is most likely to be correct comprises determining or estimating which of the plurality of candidate sequences has a highest probability of being correct.

108. A method according to claim 98, wherein at least a portion of the nucleic acid sequence of the first strand of nucleic acid is a single base, and wherein identifying the particular candidate sequence that is most likely to be correct among the multiple candidate sequences comprises identifying a majority of results for the particular query step represented by the multiple records.

109. The method of claim 98, wherein identifying the particular candidate sequence among the plurality of candidate sequences that is most likely to be correct comprises: Determining the respective occurrence likelihood of each of the plurality of candidate sequences; and The specific candidate sequence is selected based on the respective likelihood of occurrence of the specific candidate sequence satisfying the constraints.

110. The method of claim 109, wherein the constraint is a minimum probability.

111. The method of claim 109, wherein the constraint is that the individual likelihood of occurrence of the particular candidate sequence is higher than the individual likelihood of occurrence of all other candidate sequences in the plurality of candidate sequences.

112. The method of claim 98, wherein identifying the particular candidate sequence among the plurality of candidate sequences that is most likely to be correct comprises eliminating at least one of the plurality of candidate sequences based on a known constraint of the nucleic acid sequence of the first strand of nucleic acid.

113. The method of claim 112, wherein the known constraint is the improbability of a particular sequence of bases.

114. The method of claim 112, further comprising determining the known constraint based at least in part on a source of the first strand of nucleic acid.

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