Multiscale DNA microscopy

Abstract

Lymphatic, nervous, and tumoral tissues, among others, exhibit physiology that emerges from three-dimensional interactions between genetically unique cells. A technology capable of volumetrically imaging genotypes and morphologies in a single de novo measurement would therefore provide a critical view into the biological complexity of living systems. The present disclosure achieves this by extending DNA microscopy, an imaging modality that encodes a spatio-genetic map of a specimen via a massive distributed network of DNA molecules inside it, to three dimensions and multiple length scales in developing zebrafish embryos.

Description

UCT-01725 MULTISCALE DNA MICROSCOPY RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Patent Application serial number 63 / 531,156, filed on August 7, 2023, which is hereby incorporated by reference herein in its entirety. STATEMENT REGA RDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with government support under GM143017 awarded by the National Institutes of Health. The government has certain rights in the invention. BACKGROUND

[0003] Genomic mosaicism, the property whereby nucleotide-level differences present across the genomes of cells within tissues, are critical to organism biology and human health1. Data sets that have highlighted this intra-organismal and intra-tissue genomic diversity from the immune system2to the nervous system3have showcased the magnitude of missing detail in coarse gene-counts when they are not read out with DNA and RNA sequences from the same specimens.

[0004] These observations have therefore drawn a line between tissue genomic biology that is amenable to probe hybridization measurements4, where a gene’s status may be reduced to presence-versus-absence, and “de novo” sequencing-based assays which access a different level of information entirely. Concerted efforts to mend this blind spot include 2D biological pixelation5to assign positional markers to DNA and RNA sequences, and sequencers built around individual samples6. In each of these cases, trade-offs between depth of focus, depth of capture, signal density, and resolution have placed hard bounds on the detail accessible. The genetic landscape of cell microenvironments – fundamentally phenomena that involve genetically unique three-dimensional neighborhoods – remains something we can only extrapolate, not image.

[0005] DNA microscopy has previously been demonstrated in dense 2D multicellular specimens7and has more recently been applied to the study of cell-surface protein polarity8. Other theoretical variants have also been proposed9;10. Broadly, DNA microscopy uses a stand- alone chemical reaction to randomly tag a sample’s biomolecules with unique DNA molecular 1 FoleyHoagUS12404641.3UCT-01725 identifiers, or UMIs. It then converts these DNA tags into an intercommunicating molecular network, where molecular copies of the original products are allowed to migrate, either by constrained or unconstrained diffusion, and link up. The resulting linking frequencies encode spatial proximities of the original UMI tags, in the form of a UEI (unique linking-event identifier) matrix – whose rows and columns are individual UMI-tagged molecules. A statistical inverse problem is then solved on this matrix to in- fer the relative coordinates of the original UMIs. Any DNA or RNA sequence that these UMIs tagged may then be mapped to their corresponding locations, thereby assembling a complete spatio-genetic image of the original specimen.

[0006] Because it captures images from within a specimen and provides nucleotide-level readouts, DNA microscopy potentiates fully volumetric “de novo” / zero-knowledge spatio- genetic imaging. Two key barriers to broad application of DNA microscopy in three- dimensional tissues have been (1) high temperature thermal cycling for in situ PCR, that complicates uniform diffusion loci within the specimen, and (2) the multiplicity of length scales – from gross morphology down to single cells – over which a tissue with non-uniform molecular density would need to be reconstructed.

[0007] A need exists for improved DNA microscopy that is suitable for broad application in three-dimensional tissues. SUMMARY OF THE INVENTION

[0008] Embodiments of the present disclosure relate to multiscale DNA microscopy, and more specifically, to volumetric imaging of an intact organism by a distributed molecular network.

[0009] In one embodiment, the present invention is a method for identifying spatial distribution of target nucleic acids in a sample, the method comprising: (a) adding to each of a plurality of the target nucleic acids in the sample a unique molecular identifier (UMI) and either a first type adapter comprising a first universal sequence or a second type adapter comprising a second universal sequence, thereby generating a plurality of UMI-labeled target nucleic acids; (b) contacting a pair of UMI-labeled target nucleic acids with a unique event identifier (UEI) DNA probe, a first UMI-labeled target nucleic acid in the pair comprising a first universal sequence, a second UMI-labeled target nucleic acid comprising the second universal sequence, and wherein the UEI DNA probe comprises sequences complimentary to the first and the second universal sequences; (c) based on the pair of UMI-labeled target nucleic acids as a template, extending the UEI DNA probe, thereby generating a plurality of 2 FoleyHoagUS12404641.3UCT-01725 UEI DNA fragments, each UEI DNA fragment comprising a unique pair of the UMIs corresponding the pair of UMI-labeled target nucleic acids; and (d) determining a count of each of the plurality of UEI DNA fragments, wherein the count corresponds to spatial proximity of the pair of UMI-labeled template nucleic acids. BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0010] Figs.1A-L illustrate volumetric DNA microscopy chemistry according to embodiments of the present disclosure. Volumetric DNA microscopy chemistry begins by in situ synthesis of cDNA amplicons in fixed and permeabilized tissue (A). Pre-circularized UMIs are then added (B) to undergo rolling circle amplification (C), or RCA, which generates tandem copies of UMIs that undergo constrained diffusion about their points of origin. Oligos bridge adjacent UMIs to a new “UEI” amplicon. cDNA and UEI amplicons together undergo in situ amplification via in vitro transcription (D), with a complementary ligation reaction simultaneously fusing UMI-containing byproducts into a different set of UEI-links. These data collectively encode proximity and cDNA sequence data (E). Using fluorescent nucleotides during RCA shows a lack of signal when linear UMIs are used (F) compared to circularized UMIs (G-H) in zebrafish embryos (scale bars100μm). Sequencing rarefaction of UEIs (I), UMIs from UEI amplicons (J), UMIs from cDNA amplicons (K), and contiguous UEI-matrix sizes (L) are shown.

[0011] Figs.2A-L illustrate geodesic spectral embeddings (GSE) applied to DNA microscopy simulation and experiment according to embodiments of the present disclosure. Ground truth positions (A,E) are used to simulate UEI-count matrices that sample the distribution of pairwise proximities of points across the data set (1 × 104UMIs / 1 × 105UEIs in 2D; 5 × 104UMIs / 2.5 × 106UEIs in 3D). Projected gradient descent on eigenvectors of the “raw” count matrix, as in the sMLE algorithm, gives useful but blurred solutions (B,F). This artifact is corrected by GSE (C,G). Corresponding applications of UMAP produces distortions while obscuring geometry (D,H). Applying GSE to previous (6.5 × 104UMIs / 7.9 × 105UEIs) DNA microscopy samples (I, scale bar 100μm) whereby UMI-barcoded transcripts (J) undergo unconstrained diffusion (K) allows a sharpening of resulting inferred images (L).

[0012] Figs.3A-G illustrate large-scale 3D inference for whole-organism DNA microscopy according to embodiments of the present disclosure. Sub-sampling data-sets to 104 UMIs allows reconstruction of granular “sub-solutions” (A). A putative full reconstruction of all 106 UMIs for each sub-solution is then performed by solving a linear interpolation (B). These 3 FoleyHoagUS12404641.3UCT-01725 linear interpolations are then collated by PCA into a fully integrated solution (C). UEI data from the original two embryos (D,F; scale bars 200µm) are subjected to this image inference to give final GSE embeddings for the full 106-UMI data sets (E and G, respectively). Axes in GSE plots indicate scales at different locations, with arrows having length of 3 GSE-units (1 / e-association fall-offs).

[0013] Figs.4A-K illustrate spatio-genetic maps of embryos at multiple length scales according to embodiments of the present disclosure. Spectral clustering allows embryos to be divided between cephalic / head and caudal / tail domains (A, B). Performing Fisher’s Exact Test on each mapped gene using this separation allows for the identification of gene enrichment (C). Performing UMAP-embedding on gene-counts in 105 GSE-neighborhoods (D) provides a joint spatial-genetic embedding (E) of embryos 1 (top) and 2 (bottom). Plotting a heat map on top of this embedding shows differences between summed expression of genes commonly expressed outside of the head region (F) and those predominantly expressed in the head region (G). Gene-gene physical connectivity can similarly be plotted in each of the two embryos (H, I) and the relative proximity of mRNA to other categories of molecular species (rRNA, MT-rRNA, and gDNA) can be visualized (J, K).

[0014] Figs.5A-F illustrate an experimental flow of volumetric DNA microscopy according to embodiments of the present disclosure. “XXXXXX” corresponds to sample barcodes (arbitrary 6nt identifiers).

[0015] Figs.6A-F illustrate assigning global and local subspace coordinates to count matrix observables according to embodiments of the present disclosure. GSE begins by taking an arbitrary count matrix and transforming it into a block-symmetric matrix describing a bipartite graph (A). It asserts that the counts in this matrix describe the overlaps between diffusion “fields” of the rows and columns of this matrix in an embedding space (B). The GSE procedure begins by forming several random tessellations of the top eigenvectors of the count matrix (C), with each tessellation consisting of multiple sectors (illustrated as sizes m1+m2 +m3 = m). The top eigenvectors of each sector are calculated by collapsing the other sectors into single rows / columns of “local” count matrices (D). These eigenvector subspaces, combined with eigenvectors from the “global” count matrix, are used to calculate nearest neighbors on a per-sector / per-tessellation basis (E). The coordinates of any pair of points across the data set can then be compared by analyzing the eigenvector subspace dimensions they share (F). 4 FoleyHoagUS12404641.3UCT-01725

[0016] Figs.7A-F illustrate GSE’s numerical procedure to estimate the geodesic distance between any two points according to embodiments of the present disclosure. GSE’s numerical procedure to estimate the geodesic distance between any two points begins by constructing local tangent spaces within the eigenvector subspaces in Fig 1 to construct local tangent spaces (A). Projecting each point’s counts onto its own local tangent space then allows the calculation of count covariance matrices, labeled as “count-diffusion metrics” (B). Then, taking any two points in the data set, a shortest piecewise-linear path is constructed using knowledge of tangent spaces alone (C). This path is then inputted into a rescaled distance that applies the count-diffusion metrics from earlier (D). This geodesic estimate can then be applied both to a point’s already established 2E nearest neighbors (from Fig 1) and to a random selection of 2dK′other points – where here we set K′ ← 10d – across the data set. Both sets of distances are sorted independently, and the lowest K′ distances from each set are retained and placed in a Gaussian kernel matrix (E). This kernel matrix is then used to generate a “geodesic kernel matrix”,whose eigenvectors are then used to construct the solution to the embedding problem (F).

[0017] Fig.8 illustrates volumetric DNA microscopy image inference according to embodiments of the present disclosure. The original sMLE algorithm (Weinstein et al 2019) employed eigenvectors derived directly from the UEI-connectivity matrix to perform projected gradient descent on a statistical objective that optimized the UMI (point) coordinates relative to the observations. GSE, introduced in the published preprint Qian and Weinstein 2023, constructs these same eigenvectors but then uses the subspace they form to generate modified eigenvectors, belonging to a “GSE matrix” consisting of the matrix- product WN, where W is a row-normalized Gaussian kernel matrix and N is a row- normalized UEI matrix. In order to accommodate noise in large, deeply sampled data sets, sub-sampled GSE is adopted, that iteratively samples sub-sets of UMIs / points from the full- dataset and then performs a linear interpolation, using the raw UEI matrix, to all other points. The interpolated full solutions generated from each sub-solution can then be used to generate a consensus. In parallel, filtered GSE may be performed by generating putative solutions (for example, using the interpolated full solutions from aforementioned sub-samplings) and removing the uppermost quantile of UMIs with a large UEI spread in these putative solution coordinates. In the bottom right-hand side, “registration decoherence” is showing, displaying relative performance of reconstructed coordinates of positions in a 2D simulation between GSE and UMAP. 5 FoleyHoagUS12404641.3UCT-01725

[0018] Fig.9 illustrates updated volumetric DNA microscopy workflow according to embodiments of the present disclosure. During the initial extension (with a non-strand displacing DNA polymerase) of the RCA product from cDNA’s 3’-end along the pre- circularized UMI backbone, dNTP is used (with A,C,G, and T). During RCA, dNTP is replaced by A,U,G,C. Finally, during IVT, USER enzyme mix (UDG and Endonuclease VIII) is used to actively digest all dU-containing substrate, therefore eliminating the RCA product and mitigating the effects of large amounts of DNA template that, during the generation of RNA copies during IVT, are otherwise capable of recombining to produce long-range linking events between non-adjacent UMIs.

[0019] Fig.10 illustrates a 24hpf zebrafish embryo (left, scale bar 200um) according to embodiments of the present disclosure. GSE reconstruction of 7e7 UMIs, in 3D from an intact zebrafish embryo using the protocol (middle and right) using sub-sampled GSE, involving 50 sub-sampled data sets of 20,000 UMIs / points each.

[0020] Fig.11 is a schematic diagram of an exemplary computing node according to embodiments of the present disclosure. DETAILED DESCRIPTION

[0021] As used herein, the term “adding” refers to covalently linking one molecule to another molecule, either directly or indirectly.

[0022] DNA microscopy encodes the spatial organization and molecular identity of biomolecules simultaneously from a single biological specimen (cells, tissue, etc.) into a DNA sequencing library. The current disclosure builds on this by performing spatial encoding at multiple scales (from < 1 micron up to 10s of microns) simultaneously. It does so by introducing 2 new chemistries that, in an orthogonal fashion, encode proximity between adjacent molecules and those that are simply nearby one another.

[0023] A fixed specimen has its biomolecules tagged with a DNA oligonucleotide that has, attached to it, either a copy (if these biomolecules are DNA or RNA) or a label (if the biomolecules are proteins targeted by DNA / RNA-conjugated antibodies). These oligonucleotides are then used to grab hold of pre-prepared circular DNA molecules that are deposited on the sample. These circular DNA molecules are made to contain a string of randomized DNA bases (A,C,G, or T), called a UMI (or unique molecular identifier) such that the potential diversity is enormous — a randomized string of length 20, for example, has 4^20 or a trillion possibilities. Even though a real mixture of these will not contain that full diversity, one can be pretty certain because of this that when one oligonucleotide grabs hold 6 FoleyHoagUS12404641.3UCT-01725 of one UMI, no other oligonucleotide in the rest of the specimen has grabbed hold of that same UMI.

[0024] The circular UMI-containing DNA molecules are now "primed" with DNA oligonucleotides that can extend along and copy them. A strand-displacing DNA polymerase (e.g., phi29 DNA polymerase) is then used to perform rolling circle amplification, or RCA. The RCA products are effectively DNA "hairballs", contains 10s-100s of copies of the since UMI that belonged to the original circular DNA molecule that spawned them. These hairballs, as they grow, run up into one another.

[0025] A flanking DNA molecule is then deposited that anneals (i.e., forms a double strand) with 2 of these hairballs. The UMIs from both of DNA hairballs it anneals are then copied onto this flanking molecule. Now 2 distinct UMIs exist on a single DNA molecule (which was not the case before). At this point < 1um length scales are encoded into DNA sequences, because the hairball sizes are themselves < =1um.

[0026] To encode larger length scales into the same output, the UMIs from each DNA hairball are copied via in vitro transcription (IVT) into artificial RNA molecules. These RNA molecules diffuse and collide with one another. By including (along with the RNA polymerase responsible for IVT) two additional enzymes -- a pyrophosphatase that converts the 5' triphosphate on each RNA molecule to monophosphates and an RNA ligase -- these colliding RNA molecules can themselves be linked up. From this, the in situ reaction produces an entirely distinct molecular population of RNA molecules containing distinct UMIs, with these associations having occurred due to proximity over diffusion length scales (10s of microns).

[0027] The resulting library of RNA and DNA molecules are amplified and sequenced on a DNA sequencer. As with the original DNA microscopy technology, these sequences encode a massive proximity matrix, whose rows and columns are individual UMIs and whose elements are their relative linking frequencies (i.e., the number of times that these were observed). The image of the original specimen is then probabilistically inferred on the basis of a model of the reaction physics, and the molecular identities are assigned for a full spatio- genetic image.

[0028] In various embodiments, one may include additional randomized DNA bases, called UEIs (or unique event identifiers) that uniquely label each linking event.

[0029] Additional background information is available in Weinstein, et al, DNA Microscopy: Optics-free Spatio-genetic Imaging by a Stand-Alone Chemical Reaction, Cell Volume 178, Issue 1, 27 June 2019, Pages 229-241.e16 (https: / / doi.org / 10.1016 / j.cell.2019.05.019), and in 7 FoleyHoagUS12404641.3UCT-01725 Zhang, et al, U.S. Pat. No.11,339,390, each of which is hereby incorporated by reference in its entirety.

[0030] The present disclosure improves on the length scales accessible to DNA microscopy as compared to alternative approaches. It also allows the entire reaction to occur under constant temperature, making it more compatible with clinical pathology and whole mount (3D) imaging.

[0031] As discussed in the background, there were two key barriers to broad application of DNA microscopy in three-dimensional tissues, and the present disclosure provides methods that overcome these barriers first experimentally, by introducing layered in situ chemistries that encode – at low and constant temperature – multiple length scales simultaneously into the output of DNA microscopy reactions. Second, the disclosed methods introduce an inference methodology uniquely tailored to handle DNA microscopy measurement noise that reconstructs encoded molecular positions over multiple length scales. The present disclosure demonstrates the effectiveness of the disclosed methods on both earlier and newer data sets.

[0032] All publications cited therein are hereby incorporated by reference.

[0033] The present disclosure may be embodied as a system, a method, and / or a computer program product. The computer program product may include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present disclosure.

[0034] The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of the computer readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD- ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating 8 FoleyHoagUS12404641.3UCT-01725 through a waveguide or other transmission media (e.g., light pulses passing through a fiber- optic cable), or electrical signals transmitted through a wire.

[0035] Computer readable program instructions described herein can be downloaded to respective computing / processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and / or a wireless network. The network may comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and / or edge servers. A network adapter card or network interface in each computing / processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing / processing device.

[0036] Computer readable program instructions for carrying out operations of the present disclosure may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++ or the like, and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The computer readable program instructions may execute entirely on the user’s computer, partly on the user’s computer, as a stand-alone software package, partly on the user’s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user’s computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present disclosure.

[0037] Aspects of the present disclosure are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart 9 FoleyHoagUS12404641.3UCT-01725 illustrations and / or block diagrams, can be implemented by computer readable program instructions.

[0038] These computer readable program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and / or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function / act specified in the flowchart and / or block diagram block or blocks.

[0039] The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0040] The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and / or flowchart illustration, and combinations of blocks in the block diagrams and / or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions.

[0041] In a first example embodiment, the present invention is a method for identifying spatial distribution of target nucleic acids in a sample. In a 1staspect of the 1stexample 10 FoleyHoagUS12404641.3UCT-01725 embodiment, the method comprises adding to each of a plurality of the target nucleic acids in the sample a unique molecular identifier (UMI) and either a first type adapter comprising a first universal sequence or a second type adapter comprising a second universal sequence, thereby generating a plurality of UMI-labeled target nucleic acids.

[0042] In a 2ndaspect of the 1stexample embodiment, the method comprises contacting a pair of UMI-labeled target nucleic acids with a unique event identifier (UEI) DNA probe, a first UMI-labeled target nucleic acid in the pair comprising a first universal sequence, a second UMI-labeled target nucleic acid comprising the second universal sequence, and wherein the UEI DNA probe comprises sequences complimentary to the first and the second universal sequences. The remainder of features and example features are as defined above with respect to the 1staspect of the 1stexample embodiment.

[0043] In a 3rdaspect of the 1stexample embodiment, the method comprises based on the pair of UMI-labeled target nucleic acids as a template, extending the UEI DNA probe, thereby generating a plurality of UEI DNA fragments, each UEI DNA fragment comprising a unique pair of the UMIs corresponding the pair of UMI-labeled target nucleic acids. The remainder of features and example features are as defined above with respect to the 1stand 2ndaspects of the 1stexample embodiment.

[0044] In a 4thaspect of the 1stexample embodiment, the method comprises determining a count of each of the plurality of UEI DNA fragments, wherein the count corresponds to spatial proximity of the pair of UMI-labeled template nucleic acids. The remainder of features and example features are as defined above with respect to the 1stto 3rdaspects of the 1stexample embodiment.

[0045] In a 5haspect of the 1stexample embodiment, the method further comprises determining the correspondence between each UMI and each of the plurality of the UMI- labeled target nucleic acids. The remainder of features and example features are as defined above with respect to the 1stto 4thaspects of the 1stexample embodiment.

[0046] In a 6thaspect of the 1stexample embodiment, step (a) comprises: (1) adding to each of the plurality of the target nucleic acids either the first type adapter or the second type adapter; (2) annealing the plurality of the target nucleic acids linked to either the first type adapter or the second type adaptor with a plurality of circular DNAs, wherein each circular DNA comprises a unique UMI; and (3) conducting a rolling cycle amplification (RCA) to add a unique UMI to each of the plurality of target nucleic acids, thereby generating a plurality of UMI-labeled target nucleic acids, each of which comprises tandem repeats of a 11 FoleyHoagUS12404641.3UCT-01725 UMI. The remainder of features and example features are as defined above with respect to the 1stto 5thaspects of the 1stexample embodiment.

[0047] In a 7thaspect of the 1stexample embodiment, the RCA is conducted in the presence of dATPs, dCTPs, dGTPs, and dTTPs. The remainder of features and example features are as defined above with respect to the 1stto 6thaspects of the 1stexample embodiment.

[0048] In an 8thaspect of the 1stexample embodiment, the RCA comprises: (i) extending each of the plurality of target nucleic acids along a circular DNA backbone using a non- strand displacing DNA polymerase to add one copy of a unique UMI to each of the plurality of target nucleic acids; and (ii) generating a plurality of UMI-labeled target nucleic acids with a strand-displacing DNA polymerase, wherein each of the plurality of UMI-labeled target nucleic acids comprises tandem repeats of a UMI. The remainder of features and example features are as defined above with respect to the 1stto 7thaspects of the 1stexample embodiment.

[0049] In a 9thaspect of the 1stexample embodiment, step (i) is conducted in the presence of dATPs, dCTPs, dGTPs, and dTTPs. The remainder of features and example features are as defined above with respect to the 1stto 8thaspects of the 1stexample embodiment.

[0050] In a 10thaspect of the 1stexample embodiment, the non-strand displacing DNA polymerase is a T4 DNA polymerase. The remainder of features and example features are as defined above with respect to the 1stto 9thaspects of the 1stexample embodiment.

[0051] In a 11thaspect of the 1stexample embodiment, generating a plurality of UMI-labeled target nucleic acids with the strand-displacing DNA polymerase is conducted in the presence of dATPs, dCTPs, dGTPs, and dUTPs, thereby generating dUTP-containing UMI-labeled target nucleic acids. The remainder of features and example features are as defined above with respect to the 1stto 10thaspects of the 1stexample embodiment.

[0052] In a 12thaspect of the 1stexample embodiment, the UEI DNA probe comprises a random sequence, and further wherein determining the count of each of the plurality of UEI DNA fragments comprises determining a count of the random sequences of each of the plurality of UEI DNA fragments. The remainder of features and example features are as defined above with respect to the 1stto 11thaspects of the 1stexample embodiment.

[0053] In a 13thaspect of the 1stexample embodiment, extending the UEI DNA probe based on the pair of UMI-labeled target nucleic acids as the template comprises gap-fill extension and ligation. The remainder of features and example features are as defined above with respect to the 1stto 12thaspects of the 1stexample embodiment. 12 FoleyHoagUS12404641.3UCT-01725

[0054] In a 14thaspect of the 1stexample embodiment, determining the count of each of the plurality of UEI DNA fragments further comprises amplifying and sequencing the UEI DNA fragments. The remainder of features and example features are as defined above with respect to the 1stto 13thaspects of the 1stexample embodiment.

[0055] In a 15thaspect of the 1stexample embodiment, the amplification comprises: (1) conducting an in situ in vitro transcription (IVT) of the plurality of UEI DNA fragments to generate RNA transcripts of the plurality of UEI DNA fragments; (2) isolating the RNA transcripts from the sample; (3) conducting a reverse transcription of the isolated RNA transcripts to generate amplicons of the plurality of UEI DNA fragments; and (4) amplifying the amplicons of the plurality of UEI-containing DNA fragments. The remainder of features and example features are as defined above with respect to the 1stto 14thaspects of the 1stexample embodiment.

[0056] In a 16thaspect of the 1stexample embodiment, the method comprises amplifying and sequencing the plurality of UMI-labeled target nucleic acids. The remainder of features and example features are as defined above with respect to the 1stto 15thaspects of the 1stexample embodiment.

[0057] In a 17thaspect of the 1stexample embodiment, the amplifying the plurality of UMI- labeled target nucleic acids comprises: (1) conducting in situ in vitro transcription (IVT) of the plurality of UMI-labeled target nucleic acids to generate RNA transcripts of the UMI- labeled target nucleic acids; (2) isolating the RNA transcripts from the sample; (3) conducting a reverse transcription of the RNA transcripts to generate amplicons of the UMI- labeled target nucleic acids; and (4) amplifying the amplicons of the plurality of UMI-labeled target nucleic acids. The remainder of features and example features are as defined above with respect to the 1stto 16thaspects of the 1stexample embodiment.

[0058] In a 18thaspect of the 1stexample embodiment, the IVT further comprises digesting dUTP-containing UMI-labeled target nucleic acids. The remainder of features and example features are as defined above with respect to the 1stto 17thaspects of the 1stexample embodiment.

[0059] In a 19thaspect of the 1stexample embodiment, the sample is a fixed tissue. The remainder of features and example features are as defined above with respect to the 1stto 18thaspects of the 1stexample embodiment.

[0060] In a 20thaspect of the 1stexample embodiment, the sample is permeabilized. The remainder of features and example features are as defined above with respect to the 1stto 19thaspects of the 1stexample embodiment. 13 FoleyHoagUS12404641.3UCT-01725

[0061] In a 21staspect of the 1stexample embodiment, the target nucleic acids are endogenous to the sample. The remainder of features and example features are as defined above with respect to the 1stto 20thaspects of the 1stexample embodiment.

[0062] In a 22ndaspect of the 1stexample embodiment, the target nucleic acids are exogenously added to the sample. The remainder of features and example features are as defined above with respect to the 1stto 21staspects of the 1stexample embodiment.

[0063] In a 23rdaspect of the 1stexample embodiment, the plurality of the target nucleic acids comprises target nucleic acids covalently or noncovalently linked to a biomolecule. The remainder of features and example features are as defined above with respect to the 1stto 22ndaspects of the 1stexample embodiment.

[0064] In a 24thaspect of the 1stexample embodiment, the plurality of target nucleic acids comprises an RNA molecule. The remainder of features and example features are as defined above with respect to the 1stto 23rdaspects of the 1stexample embodiment.

[0065] In a 25thaspect of the 1stexample embodiment, the plurality of target nucleic acids comprises an mRNA molecule. The remainder of features and example features are as defined above with respect to the 1stto 24thaspects of the 1stexample embodiment.

[0066] In a 26thaspect of the 1stexample embodiment, the plurality of target nucleic acid comprises a DNA molecule. The remainder of features and example features are as defined above with respect to the 1stto 25thaspects of the 1stexample embodiment.

[0067] In a 27thaspect of the 1stexample embodiment, the plurality of target nucleic acids comprises a cDNA molecule. The remainder of features and example features are as defined above with respect to the 1stto 26thaspects of the 1stexample embodiment.

[0068] In a 28thaspect of the 1stexample embodiment, the method further comprises conducting an in situ reverse transcription of an RNA molecule in the sample to generate the cDNA molecule. The remainder of features and example features are as defined above with respect to the 1stto 27thaspects of the 1stexample embodiment.

[0069] In a 29thaspect of the 1stexample embodiment, each UMI is a random sequence. The remainder of features and example features are as defined above with respect to the 1stto 28thaspects of the 1stexample embodiment.

[0070] In a 30thaspect of the 1stexample embodiment, each unique event identifier (UEI) DNA probe comprises a sample barcode. The remainder of features and example features are as defined above with respect to the 1stto 29thaspects of the 1stexample embodiment. 14 FoleyHoagUS12404641.3UCT-01725

[0071] In a 31staspect of the 1stexample embodiment, the sample barcode is an arbitrary six- nucleotide identifier. The remainder of features and example features are as defined above with respect to the 1stto 30thaspects of the 1stexample embodiment.

[0072] In a 32ndaspect of the 1stexample embodiment, the method further comprises mapping the plurality of UMI-labeled target nucleic acids to a coordinate space based on the count of each of the plurality of UEI DNA fragments. The remainder of features and example features are as defined above with respect to the 1stto 31staspects of the 1stexample embodiment.

[0073] In a 33rdaspect of the 1stexample embodiment, mapping the plurality of UMI-labeled target nucleic acids to the coordinate space comprises minimizing an objective function comprising a proximity term based on the count of each of the plurality of UEI DNA fragments. The remainder of features and example features are as defined above with respect to the 1stto 32ndaspects of the 1stexample embodiment.

[0074] In a 34thaspect of the 1stexample embodiment, minimizing the objective function comprises gradient descent. The remainder of features and example features are as defined above with respect to the 1stto 33rdaspects of the 1stexample embodiment.

[0075] In a 35thaspect of the 1stexample embodiment, mapping the plurality of UMI-labeled target nucleic acids to the coordinate space comprises constructing a global proximity matrix based on the count of each of the plurality of UEI DNA fragments. The remainder of features and example features are as defined above with respect to the 1stto 34thaspects of the 1stexample embodiment.

[0076] In a 36thaspect of the 1stexample embodiment, constructing the global proximity matrix comprises determining a plurality of geodesic distances, each corresponding to one of the pairs of UMI-labeled template nucleic acids. The remainder of features and example features are as defined above with respect to the 1stto 35thaspects of the 1stexample embodiment.

[0077] In a 37thaspect of the 1stexample embodiment, determining the plurality of geodesic distances comprises defining a local tangent space for each of the plurality of UEI DNA fragments. The remainder of features and example features are as defined above with respect to the 1stto 36thaspects of the 1stexample embodiment.

[0078] In a 38thaspect of the 1stexample embodiment, defining the local tangent space comprises clustering. The remainder of features and example features are as defined above with respect to the 1stto 37thaspects of the 1stexample embodiment. 15 FoleyHoagUS12404641.3UCT-01725

[0079] In a 39thaspect of the 1stexample embodiment, the invention provides a computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processor to cause the processor to perform a method according to any one of the 32thto 38thaspects of the 1stexample embodiment. The remainder of features and example features are as defined above with respect to the 1stto 38thaspects of the 1stexample embodiment.

[0080] The descriptions of the various embodiments of the present disclosure have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application or technical improvement over technologies found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein. EXEMPLIFICATION

[0081] Example 1 – Experimental Methods for Examples 2-5

[0082] Zebrafish embryos preparation

[0083] AB-wildtype zebrafish were kept and crossed in accordance with the approved protocols and ethical guidelines of the University of Chicago Institutional Animal Care and Use Committee. Embryos were collected at 24 hours post fertilization (hpf), dechorionated with 1mg / ml pronase 5min at 28°C. Dechorionated embryos were fixed in 4% paraformaldehyde in 1xPBS at 4°C overnight. After dehydration in 100% methanol for 15- 30min at room temperature, the embryos were stored at -80°C for at least 2hrs before use. Embryos were successively rehydrated with 75%, 50% and 25% methanol in 1xPBS for 5min each and washed four times with 1xPBST (1xPBS + 0.01%Tween-20), 5min per wash at room temperature. The embryos were then permeabilized with 0.5-1 x 10-4U / ul Thermolabile proteinase K for 12min at room temperature. The Proteinase K was then inactivated at 55°C for 15min.

[0084] Reverse transcription (RT)

[0085] After permeabilization, embryos were incubated at 4°C for 1hr under slow rotation (10rpm) followed by 10min of 65°C incubation in a pre-RT buffer comprising 20% formamide, 0.5U / ul Superase-In, 4.4mM DTT, 0.5 ug / ul rBSA, in 1xPBS and then cooled 16 FoleyHoagUS12404641.3UCT-01725 down to 4°C immediately. After one water rinse, reverse transcription mix (1x FS buffer, 4.4mM DTT, 400uM dNTP, 32uM aminoallyl-dUTP, 0.5ug / ul rBSA, 1U / ul Superase-In, 10U / ul Super- script III, and 1uM 21.068C-8N RT-primer) was added and underwent 4°C incubation for 1hr, 60°C 3min, and 37°C overnight under slow horizontal orbital rotation, followed by 1hr of 50°C incubation. After RT, embryos were washed 3x in PBST and 1x with water, incubated in ExoI mix (1x ExoI buffer, 1.43U / ul Exo-I) at 4°C 1hr under slow rotation, followed by 37°C 1hr to remove the RT primer and displaced cDNA. Embryos were again washed 3x in PBST and 1x with water.

[0086] Tagmentation

[0087] Transposomes were assembled according to manufacturer protocol. Oligos 22tn5.003A and 22tn5.MOS-3p were resuspended to 100uM individually in annealing buffer (40mM Tris-HCl pH8, 50mM NaCl). These annealed at 95°C 2min, followed by 1 degree-C decrements per minute for 70min. Transposome assembly mix (25uM of the annealed oligo- duplex, 1ug / ul tagmentase) was then mixed and incubated at 23°C for 30min. Glycerol was then added to 50% and stored until use at -20°C. Following reverse-transcription of samples transposome-glycerol stock was diluted 3:10 in tagmentase dilution buffer. This diluted solution was then added at a further 1:50 dilution to transposome reaction mix containing 5mM MgCl2, 10mM Tris-HCl (pH7.5), 10% N,N-Dimethylformamide, 9% PEG8000, and 850uM ATP. This mix was added to samples, and incubated at 4°C 1hr under slow rotation followed by 55°C 1hr. Samples were then washed 2x in PBST and 1x in PBS.

[0088] Cross-linking and transposome denaturation

[0089] BS(PEG)5 mix was prepared in 1xPBS to 5mM concentration and added to samples for incubation at room temperature for 1hr under slow (6rpm) rotation. Samples were then rinsed with 1M Tris pH 8, and quenched in this buffer 30min at room temperature.4xSSC was then added, samples were incubated 10min under slow rotation, and then at 70°C for 15min. 10% formamide / 2xSSC was then added, the samples were incubated at 4°C under slow rotation for 10min, and then incubated at 50°C for 10min.

[0090] 3’ adapter ligation and circDNA annealing

[0091] 3’ adapter ligation mix (500nM 22tn5.005, 500nM 22tn5.006, 1.25U / ul SplintR ligase, 1x SplintR Reaction buffer containing ATP) was added to samples, which were incubated at 4°C 1hr followed by 23°C overnight. After ligation, samples were washed 3x in PBST, and 3’ phosphates on the ligated oligos were removed with 0.5U / ul Quick CIP in 1x CutSmart buffer by incubation at 4°C 1hr under slow rotation followed by 37°C 1hr. Samples 17 FoleyHoagUS12404641.3UCT-01725 were then again washed 3x in 2xSSCT. Circ6G1 and Circ7G1 were prepared using T4 DNA ligase and a short splint oligo (An, Ran, et al. Nucleic Acids Research 45.15 (2017): e139-e139) and purified using a Zymo Research oligo spin column. Products were checked for size and purity via TBE-urea gel. CircDNA annealing mix (100nM Circ6G1, 100nM Circ7G1, in 1x Hyb buffer, containing 2x SSC, 10% formamide, 0.1% Tween-20) was added to samples and incubated overnight at 40°C under slow rotation. Samples were then washed in Hyb buffer at 40°C for 30min under slow rotation, and then washed in 2xSSCT, 1xSSCT, and finally 1xPBST.

[0092] Circular DNA annealing and rolling circle amplification (RCA)

[0093] Samples were rinsed with water and RCA mix (25ng / ul T4g32, 1x phi29 reaction buffer, 0.5ug / ul rBSA, 250uM dNTP, 0.2U / ul phi29 polymerase) was added, incubated at 4°C 1hr under slow rotation, and then 30°C overnight (no rotation). In cases where fluorescence was to be observed, RCA mix was supplemented with 20uM fluorescein-12- dUTP. Samples were washed 3x in 2xSSCT.

[0094] UEI oligos annealing and T4 DNA extension / ligation

[0095] UEI annealing mix (100nM 21.004G1 / 2-BC oligo mix, 100nM 21.073pt, 100nM 21.074B, 2xSSC, 5% formamide, 0.1% Tween-20) was added to samples, incubated at 4°C 1hr under slow rotation, and then 50°C 2hrs. After bringing to room temperature, samples were washed in hybridization buffer (2xSSC, 5% formamide, 0.1% Tween-20) 1hr at 50°C, followed by washes in 2xSSCT, 1xSSCT, and then 1xPBST. After water rinse, ligation / extension mix (1x T4 ligase buffer including ATP, 1mM dNTP, 0.15U / ul T4 DNA polymerase, 20U / ul T4 DNA ligase) was added and incubated 1hr under slow ration at 4C, followed by room temperature (23°C) incubation 40min. Samples were then washed 3x in PBST, followed by a water rinse.

[0096] In vitro transcription (IVT)

[0097] IVT-ligation mix was prepared by adding to final concentrations together, in order, oligo

[0098] 21.075 (100nM), 21.066C3 (1uM), 1x IVT reaction buffer, 7.5mM rNTP mix, 100ng / ul T4g32, 0.5U / ul T4 RNA ligase 2, 0.25U / ul RppH, 10% T7 Enzyme Mix, 73.6ug / ul 4arm- PEG20K-Vinylsulfone, and 6.4ug / ul 3-arm Thiocure-333 (PEG reagents being thawed from -80°C immediately prior to reaction). Mixes were added to individual zebrafish embryos at a total volume of 30ul. Hydrogel was allowed to form around samples for 2hrs at room temp. Reaction was then incubated at 37°C 20hrs. Afterward, hydrogels were denatured 18 FoleyHoagUS12404641.3UCT-01725 via addition of 12ul denaturation solution (457.5mM KOH, 100mM EDTA, 42.5mM DTT) for 2hrs at 4°C. Denaturation was stopped by addition of 12ul stop solution (600 mM Tris- HCl pH7.5, 0.4N HCl). After mixing, 30ul proteinase K mix (0.28% Tween-20, 0.09U / ul proteinase K, 8.6 mM Tris-HCl pH7.5) was added to the 54ul samples for a total of 54ul. This was incubated at 50°C 1hr.

[0099] RNA isolation and cDNA synthesis

[0100] RNA was purified by addition of 1.2x RNAClean XP beads, following manufacturer protocols, and eluted into water. DNAse I digestion was performed (final concentration of 0.8U / ul Superase-In, 0.1U / ul DNAse I, 1x DNAse I reaction buffer) at 37°C for 30min. RNA was again purified via 1.2x RNAclean XP, and eluted into water. Reverse transcription was carried out in a final concentration of 500nM each of RT primers (21.077 and 21.085), 500uM dNTP, 1x FS buffer, 5mM DTT, 1U / ul Superase-In, and 10U / ul Super- script III. Primers were added first to RNA / water-eluent and incubated at 65°C 5min, after which the mixture was placed promptly on ice. Samples were then incubated 1hr at 50°C, followed by inactivation at 70°C, and kept at 4°C. ExoI enzyme was then added directly to the product to final concentration of 3.3U / ul. After mixing, this was incubated at 37°C for 30min, followed by heat-inactivation at 80°C for 20min.

[0101] Library preparation

[0102] cDNA products (from IVT products) were then amplified in two separate PCR reactions. “cDNA-amplicons” were amplified by adding ExoI-digested product at a final 1:80 dilution into 4 separate reactions (per embryo) containing final concentrations of 300nM 21.046G1-BC primer, 300nM 21.081b primer, 1x HiFi PCR buffer, 200uM dNTP, 2mM MgSO4, and 0.02U / ul Platinum Taq HiFi. This reaction was thermocycled 95°C 2min, 5x(95°C 30s, 56°C 30s, 68°C 2min), 20x(95°C 30s, 68°C 2min), 68°C 5min, 4°C. “UEI- amplicons” were amplified by adding ExoI-digested product at a final 1:40 dilution into 2 separate reactions (per embryo) containing final concentrations of 300nM 21.077-G1 primer, 300nM 21.076BB primer, 3.3uM each of 4E4.interf1 and 4E.interf2 (3’P-capped oligos to interfere with PCR recombination7(Turchaninova, Maria A., et al. European journal of immunology 43.9 (2013): 2507-2515)), 5% DMSO, 1x HiFi PCR buffer, 200uM dNTP, 2mM MgSO4, and 0.02U / ul Platinum Taq HiFi. This was thermocycled 95°C 2min, 1x(95°C 30s, 66°C 30s, 68°C 2min), 18x(95°C 30s, 68°C 2min), 68°C 5min, 4°C. PCR products were then purified using a 0.75x volume of Ampure XP beads, following manufacturer protocol. Products were quantified and sequenced on an Illumina NextSeq 500 instrument, including 19 FoleyHoagUS12404641.3UCT-01725 the sequencing primer sbs3b as a custom spike-in according to manufacturer protocol.

[0103] Sequence Analysis

[0104] Sequence analysis was performed using the pipeline previously described7, with code updated for the larger scale of data available at github.com / wlab-bio / vdnamic.

[0105] Briefly, sequencing reads were demultiplexed via the barcodes depicted in Figure 5. Subsequently, for each amplicon type, sequence elements (UMI type I, UMI type II, UEIs, and cDNA inserts) were separately clustered using a 1bp difference-criterion using the EASL algorithm7.

[0106] For UEI data sets, each UEI was assigned a UMI-pair by plurality (relevant only if a specific UEI appeared to show two different pairings of UMIs – a signature of PCR recombination). The resulting “consensus pairings” were then pruned, with each UMI required to be associated with 2 UEIs, and each association (unique UMI-UMI pair) required to be associated by at least 2 reads. The largest contiguous matrix (found via single-linkage clustering, with rarefaction depicted in Figure 1J) was retained for image inference.

[0107] For cDNA insert sequence data, reads grouped by the same UMI had a sequence- consensus generated by majority-vote. These sequences were then trimmed to eliminate sequence adapters. Those inserts retaining at least 25bp of non-artificial sequences (at least among known artificial sequences) were then counted toward the cDNA-insert UMIs (depicted as rarefaction in Figure 1I). These consensus inserts were then inputted into STAR alignment (https: / / github.com / alexdobin / STAR) using the Danio Rerio genome assembly GRCz11. Gene-assignments were performed using GTF annotations, with priority assignment to rRNA in case of an ambiguous match.

[0108] The UMIs from genome-mapped cDNA amplicons were then matched back to the UMIs in the UEI amplicons of the corresponding specimen. The gene-calls were then applied to label UMIs in the UEI-inferred image.

[0109] Simulations

[0110] All simulations were performed by taking the raw coordinates depicted in Figs 2A,E and calculating Gaussian “point-spread functions”. For UMI i and UMI j at ground truth positions xiand xj, respectively, and with N being the sum-total of all counts in the simulated data set, we assigned a raw count nij ← NegativeBinomial(mean = µij, p) where and p ← 0.8.20 FoleyHoagUS12404641.3UCT-01725

[0111] Clustering

[0112] The preliminary segmentation analysis of GSE inferences (Fig 3E-G) was performed by taking UEI-associations collectively – and an equivalent total number of nearest neighbors (such that for k nearest neighbors, k ← NUEIs / mUMIs) – and calculating diffusion kernels within the GSE embedding coordinatesGraph Laplacian matrix formed by the “pseudo-linkages” then underwent spectral clustering as previously described7down to a conductance threshold of 0.2, requiring a minimum segment size of 50 UMIs.

[0113] Inter-segment UEI counts then defined a new UEI-count matrix that was row- normalized.

[0114] The top eigenvector – specifically, its median – provided the boundary for memberships visualized in Fig 4A-B of cephalic vs caudal.

[0115] For gene-gene UEI matrices (Figs 4J-K), a similar summation of categories was performed as with segments above. The symmetric normalized Graph Laplacian was used to generate 100 eigenvectors from which proximities to each of the molecular species, rRNA, MT-rRNA, and gDNA. For a gene i relative to any one of these molecular species, heredesignated c, this proximity was estimated through the Gaussian kernel e−||yi−yc||2 / s2with. A linear transform was then applied to afix the locations of each rRNA, MT-rRNA, and gDNA to the vertices of each ternary plot.

[0116] Table S1: Cephalic and caudal genes used in Fig 4F-G. Cephalic genes were 21 FoleyHoagUS12404641.3UCT-01725 generated by performing a database search20(“The Zebrafish Information Network (ZFIN).” The Zebrafish Information Network, https: / / zfin.org). The first 20 cephalic genes were collected by filtering for “telencephelon” and selecting those genes with clear evidence of predominant expression in the head in 24hpf embryos in ISH images. The final 8 (cdh2- trpm2) were taken from those known to be expressed in the optic nerve head during early development. Cau- dal genes were collected by filtering for “caudal fin” and “tail bud” and selecting those genes with clear evidence of predominant expression in the caudal region in 24hpf embryos in ISH images.

[0117] GSE (Geodesic Spectral Embeddings)

[0118] GSE begins by “de-identifying” type I and type II UMIs in our data set (Fig 6A): taking the rectangular mIx mIIUEI-count matrix of mItype I UMIs and mIItype II UMIs and converting it into a square m x m symmetric matrix, consisting of m = mI+ mIIUMIs. UMI-UMI interactions are modeled statistically as illustrated in Fig 6B. There, the observed UEI matrix counts nij– associating UMI i with UMI j – are generated stochastically according to probabilities, wij, that go up the closer UMI i is to UMI j in the embedding space and go down the further apart they are in the embedding space. The set of all UMI / point positions which collectively best comports with this model is what we will call the optimal GSE embedding.

[0119] Evaluating embedding positions in this way, however, most of all requires a way to estimate the distance between them, given the original count data. Most commonly, this is done by taking the subspace formed by the top E eigenvectors of the data matrix and finding a straight-line Euclidean distance between two points (Coifman, Ronald R., and Ste´phane Lafon. App and comp harmonic analysis 21.1 (2006): 5-30; Van der Maaten, Laurens, and Geoffrey Hinton. Journal of machine learning research 9.11 (2008); McInnes, Leland, John Healy, and James Melville. arXiv preprint arXiv:1802.03426 (2018)) with the goal of identifying and focusing on nearest-neighbor relations. GSE does this as an initial processing step, but uses the resulting putative nearest neighbors only to form local tangent spaces about each point. These tangent spaces will allow us to estimate the geodesic distances along the d- dimensional surface (sitting in the full m-dimensional data space) we wish to represent in the final embedding.

[0120] These tangent spaces may involve the E “global” eigenvectors of the full symmetric count matrix in Fig 6A. However, global eigenvectors that describe the dominant axes of variance for the full data set may – on their own – be insufficient to differentiate the tangent 22 FoleyHoagUS12404641.3UCT-01725 spaces of neighboring points. To avoid this problem, GSE augments the global eigenvector subspace by performing several random, distinct tessellations of this subspace (Fig 6C). Each tessellation partitions the original points into ∼ sectors of ∼points each.

[0121] The choicehere is motivated by the fact that the total computational complexity of analyzing all sectors together will ultimately scale as the product of the number of tessellations and the number of points per tessellation, ie the total number of points in the data set. Each of these sectors now possesses smaller “local” count matrices generated by collapsing and summing the matrix elements belonging to all other sectors, as illustrated in Fig 6D. Each of these smaller matrices, because they include ∼ points and ∼ sections, will be of size.

[0122] GSE then appends the E eigenvectors generated from these local matrices to the original E-dimensional global eigenvector subspace, forming a fuller subspace spanned by 2E eigenvectors describing each point’s local neighborhood. These local neighborhoods are then used to find putative 2E nearest neighbors (the minimum to span the full eigenvector subspace) for each point in the data set (Fig 6E) using a standard kNN algorithm. The 2E nearest-neighbors for each point are then shuffled between tessellations, in order to allow each point – within each tessellation – to have a local neighborhood that extends beyond the boundaries of the sector into which it was assigned.

[0123] Although each sector now has a locally defined eigenvector subspace, this eigenvector subspace contains coordinates for the collapsed counts of all other sectors. These collapsed- sector coordinates can then be used to bridge the coordinates of points that have been assigned to different sectors (Fig 6F).

[0124] GSE then uses each point’s 2E nearest neighbors from before to perform a local PCA analysis, giving each point its own d basis vectors – where d is the low-dimensionality of the intended embedding – that constitute the local tangent spaces for the high-dimensional surface (Fig 7A). For point i, we use these basis vectors to construct a tangent space projection matrix Mi. Projecting the original counts associating different data points onto these tangent spaces then allows calculation of d x d count covariance matrices Σi(Fig 7B). For any vector z, we can then write the re-scaled square-distance zTΣi−1z with a diffusion-distance metric Σi−1in the neighborhood of point i.

[0125] For any given pair of points i and j at positions ziand zj, respectively, GSE uses the 23 FoleyHoagUS12404641.3UCT-01725 procedure described so far to estimate a geodesic distance between them in two steps.First, the shortest connecting path between ziand zjis estimated by adding difference-vectorsprojected onto their respective tangent spaces to give the intermediate points zi+ αMi(zj–zi) and zj+βMj(zi– zj). The scalar values α and β are then adjusted to minimize theEuclidean distance between the resulting vector sums (Fig 7C), which uniquely specifies apiecewise linear path from zito zj. Second, the geodesic distance is estimated as thediffusion-distance traversed by this path, calculated using distance metrics Σi−1and Σj−1(Fig 7D).

[0126] GSE then collates these distances across all random tessellations (from Fig 6) and incorporates them together into a single geodesic similarity matrix that determines – for every point – the half of data points that are closer to it than the other half along the d- dimensional surface swept out by the tangent spaces calculated earlier (Fig 7E). GSE approximates this geodesic similarity matrix in a sparse matrix by, for every point i, randomly and uniformly selecting a set of other points across the data set, estimating their geodesic distances to point i, and retaining the lowest 1 / 2dfraction of these distances. These retained points, along with the nearest-neighbors found in the original eigenvector subspace, are inserted into the corresponding row in the form of a sparse set of Gaussian proximities.

[0127] GSE uses the geodesic similarity matrix as part of what we call the “GSE matrix” : a mathematical description of how the original count matrix ought to be embedded across the d-dimensional tangent spaces used to construct . The top eigenvectors of this matrix are considered to be putative solutions to the d-dimensional embedding problem. In serving this purpose will be a projection of the count data into the geodesic similarity matrix so that.

[0128] Because we consider the top eigenvectors of to fit the data to the global curvature of the data set, we now apply an incremental projected gradient descent on a global objective function (Fig 7F). The objective function we use here is the Kullback-Leibler divergence, measured between the data counts nijand the proximities in the embedding space, wherexi is the d-dimensional embedding coordinate of point i and where the amplitude. Here and elsewhere in this paper, subscript “·” denotes index summation, such that. 24 FoleyHoagUS12404641.3UCT-01725

[0129] Example 2 - Volumetric DNA microscopy

[0130] Encoding multiple length scales into DNA microscopy data set requires engineering how UEIs either localize or de-localize from their UMIs of origin. We reasoned that a separation of UEI length scales could be achieved by initially dispersing UMI copies over short (<1µm) lengths via constrained diffusion and later dispersing UMI copies over long(>10µm) lengths via unconstrained diffusion. DNA microscopy7had previously achievedthe larger of the two length scales, using biocompatible PEG hydrogels formed around the sample to eliminate convection and limit the range of DNA molecule migration during the reaction to ~ 50µm diameters11. We sought to execute this in parallel with ~1µm diameter DNA dispersion12;6achieved by rolling circle amplification, or RCA, in which the leading end of a DNA molecule, polymerizing along a circular template, diffuses while anchored to its point of origin.

[0131] The multiscale-encoding reaction is depicted in Figs 1 and S1. Briefly, an RNA molecule in a fixed cell would first be copied to a cDNA molecule having a protruding 3’ end that contained one of two universal DNA sequences (Fig 1A). Pre-circularized DNA molecules, containing 25nt randomized UMI sequences, would then be deposited on the sample, the protruding ends would anneal (Fig 1B) and a strand-displacing DNA polymerase would extend the cDNA and copy the UMI to this elongating DNA polymer by RCA. Like in the first demonstration of DNA microscopy7, two distinct “UMI types”, so that hetero-links would form, but homo-links would not (Fig 5).

[0132] The resulting DNA nanoballs would physically press up against one another (Fig 1C), and a flanking oligonucleotide containing a randomized UEI sequence would then both copy and label each UMI-UMI pairing uniquely. An in vitro transcription reaction (IVT), driven by synthetic T7 phage promoters would then be used to generate RNA-copies of both these RCA-UEIs and the original cDNA.

[0133] These RNA-copies could then be made to undergo a process mirroring the original DNA microscopy reaction: diffusing and linking together, to form distinct IVT-UEIs (Fig 1D). The latter process was achieved using an enzyme cocktail of T7 RNA polymerase to generate RNA copies, a pyrophosphatase to convert triphosphate RNA ends to monophosphates, and an RNA ligase to catalyze RNA copy-linking. All of these products – abbreviated RCA-UEIs, IVT-UEIs, and cDNA – would then be amplified by RT-PCR and sequenced (Fig 1E) for image inference and genome alignment.

[0134] We first sought to determine whether RCA polonies in the whole mount setting could be generated the way depicted in Fig 1A. Zebrafish embryos at 24 hpf were fixed in 4% 25 FoleyHoagUS12404641.3UCT-01725 formaldehyde overnight at 4°C and permeabilized with methanol (SI: Experimental method). In situ reverse transcription was performed with random primers (SI: Experi- mental method). Tn5 transposase was then used to first open RNA:cDNA duplexes and then incorporate 3’ ssDNA adapters13;14, in order to create a template to which circular oligos could anneal .

[0135] We compared RCA reactions that included dUTP-fluorescein by annealing either lin- ear (Fig 1F) or pre-circularized (Fig 1G) UMIs and found, as expected, DNA products generated in the latter but not the former. This signal was increased further by additional permeabilization of embryos with proteinase K (Fig 1H). This demonstrated the permeability of the embryo under fixation conditions to circularized UMIs, enzymes, and other reagents.

[0136] Next, we performed “end-to-end” situ reactions on 24 hpf embryos. The resulting number of distinct UEIs (Fig 1I), accompanying UMIs (Fig 1J), and separately amplified UMIs on cDNA-amplicons (Fig 1K) could be found increasing with read-counts, with only the latter two beginning to saturate. The sizes of contiguous UEI-matrices (Fig 1L), describing the number of UMIs that – through some set of UEI-links – were mutually connected, also increased with read-depth. Consensus cDNA amplicons were then mapped to the zebrafish genome (SI: Sequence analysis).

[0137] Example 3 – Image Inference

[0138] Inferring a DNA microscopy image from sequencing data is, at its greatest level of generality, a problem of calculating which putative molecular positions maximize a function that describes the probability of the data given these positions (Figs S2, S3). Absent constraints, this solution is prone to both measurement noise and non-uniqueness.

[0139] A spectral maximum likelihood estimate, or sMLE, confines the position-solution to a linear combination of the top principal components, or eigenvectors, of the UEI matrix7. The optimal linear combination is determined by first adding the top d eigenvectors (for a d- dimensional inference) of the UEI matrix so that these maximize the original probability, then expanding this to the top 2d eigenvectors, the top 3d, and so on until the solution converges.

[0140] Eigenvectors of the “raw” UEI matrix are, however, ill-suited as a basis to construct a solution that would be correct at multiple length scales. The reason for this is that the least- squares problem that the top eigenvectors of the UEI matrix provide penalizes all discrepancies between the solution and the observations equally.

[0141] To solve this, we implemented a dimensionality reduction approach, called Geodesic Spectral Embeddings, or GSE, to replace the eigenvector matrix derived from the raw UEI 26 FoleyHoagUS12404641.3UCT-01725 matrix. GSE eigenvectors are derived from a kernel proximity matrix describing the distances traversed along the low-dimensional manifold swept out by the data points in the large m- dimensional space of the full UEI matrix (SI: GSE). GSE eigenvectors are then used as a basis to maximize the original probability function to complete the image inference.

[0142] Deriving these new eigenvectors includes two parameter choices. One is the degree to which the data is tessellated in order to analyze local “neighborhoods” of the UEI matrix. The second is the number of eigenvectors generated from the raw count matrix to analyze the curvature of the data manifold. Unless otherwise indicated, in the data shown we use 10 tessellations and 50 eigenvectors in each data set.

[0143] Applying GSE to simulations (SI: Simulations), in which a diffusion kernel operating over a single length-scale (uniformly indicated by each grid in Fig 2) generated UEI-counts using with a negative binomial probability, significantly outperformed sMLE and UMAP (Figs 2A-D) in 2D. GSE can, in this context, be regarded as simply a distinct dimensionality reduction method anchored by a DNA microscopy reaction-diffusion probability model. Further applying GSE to 3D simulations (Figs 2E-H) demonstrated the algorithm’s generality in addressing non-uniform point distributions in higher dimensions.

[0144] We next applied GSE to single length-scale DNA microscopy data7. In this experiment, similar to that described in Fig 1A-E, an ensemble of cells in culture are plated(Fig 2I), and specified gene amplicons are tagged with UMIs (Fig 2J) that then undergo in situ amplification-reaction, unconstrained diffusion, UEI-linking (Fig 2K). The resulting UEIs are sequenced and the image inferred.

[0145] Applying GSE to this data over a single iteration yielded resolution comparable to that found using sMLE previously7. Iterating GSE three times, each time treating newly gen- erated GSE eigenvectors as updated “raw” count matrix eigenvectors (SI: GSE), as well as increasing the number of data-tessellations from 10 to 20, improved cell boundaries substantially (Fig 2L). Example 4 – Whole organism DNA microscopy inference

[0146] Inference of simulations and older data sets, such as those in Fig 2, involved 104to105UMIs. Expanding this inference to 106UMIs, such as the sequenced whole organisms(Figs 1G-J) posed a unique problem, owing to the fact that GSE detects local curvature via linear approximations, meaning that its ability to do so begins to fail as increasing numbers of points create local “jaggedness” in the data manifold that does not exist in smaller data sets.

[0147] To solve this, for each data set, we sub-sampled data to several small 104UMI data sets27 FoleyHoagUS12404641.3UCT-01725 (Fig 3A). For each of these “sub-solutions” (here numbering 25), a linear interpolation was then performed to estimate the locations of all UMIs not included in that specific sub-solution (Fig 3B). Performing PCA on the UMI covariances then gave a new set of eigenvectors / components to construct the global solution by an incremental projected gradient descent, on the original probability function that modeled the DNA microscopy reaction, as before (Fig 3C).

[0148] Taking the original embryos (Figs 3D,F), whole organism inferences were generated (Fig 3E,G). Spectral clustering (SI: Clustering) similar to that previously used for segmentingcells in DNA microscopy7was applied to identify segments within the data, where a segmentwas defined as including UMIs that communicated discernibly more frequently with one another with others that were otherwise nearby. The resulting images, with colors introduced to visualize distinct clusters, recapitulated gross embryo morphology, highlighting a “lobe” structure to the head and a well-defined tail / caudal region. We next sought to examine the differential representations of gene transcripts across the inferred 3D images. Example 5 – Genomic sequence distribution analysis

[0149] We began by establishing a means to identify embryonic regions, by first aggregating UEIs between distinct segments colorized in Fig 3, then taking the first eigenvector of the resulting UEI graph and bisecting points at its median. The resulting division of UMIs is depicted by distinct colors for embryos 1 and 2 in Fig 4A and B, respectively. Next, we aggregated all genome-mapped UMIs together, and constructed contingency tables (one per gene) to perform Fisher’s Exact Test on each, providing an effective upper-bound on the p- values for null hypotheses (spatial distributions independent from 3D location).

[0150] Although a large number of statistical differences were detected across the genome, we narrowed our focus to those 14 head-enriched genes with p < 0.001 and fold-differences of ≥ 2 (Fig 4C). Of these 14 at 24hpf, 6 (fam168a15, arnt216, tcf417, sdc218, tjp2a19, polr1a20) were known predominantly or exclusively expressed in the brain, 5 (usp2421, rarga22, copa20, map1sa20, rnf1420) were predominantly expressed more generally in the cephalic region, and 3 (itpr2, spata13, eef1da) were involved in general cellular process across the organism and otherwise known to be ubiquitously expressed. Taken collectively, these were consistent with matching gene expression characteristics to the anatomical structures in the head and brain.

[0151] We next sought to highlight the spatio-genetic image’s recapitulation of known expression patterns still further by examining a distinct set of 28 genes commonly expressedin the head-region at 24hpf and 14 genes commonly expressed in the tail-region at 24hpf2028 FoleyHoagUS12404641.3UCT-01725 (Table 1). To do this, we implemented a joint spatial-genetic embedding scheme similar to a joint-embedding scheme previously used for immunoglobulins2. Specifically, for each embryo, 1×105UMI “neighborhoods” were assigned by randomly choosing genome-mapped UMIs throughout the data set, and finding the 1000 nearest-neighbors of each (within the GSE embedding) that also mapped to the genome. These neighbor- hoods, sometimes overlapping (Fig 4D) formed a new high-dimensional data set (this time in gene expression space). The resulting vectors then underwent dimensionality reduction with UMAP (generated here using 30 PCs and 30 nearest-neighbors).

[0152] The cephalic and caudal clusters of both embryos (Fig 4E) partitioned in a manner consistent with GSE alone (Fig 4A-B: same colorscale, with neighborhoods including UMIs from both cephalic and caudal clusters assigned an average color). Summing the expression of all 14 caudal (Fig 4F, Table 1) and all 28 cephalic (Fig 4G) genes drawn from previously measured ISH patterns yielded distinctive patterns consistent with the inferred locations along the caudal-cephalic axis.

[0153] Having established the recapitulation of gross morphology with DNA microscopy, we next sought to examine the application of such whole organism images to sub-cellular localization of molecular species. To do this, we summed UEI-counts between distinct genes / biotypes, rather than distinct UMIs. The resulting graphs for embryos 1 and 2, depicted in Figs 4H and 4I, respectively, with the top 20 connected nodes labeled in each case. These graphs showed large amounts of connectivity around rRNA, MT-rRNA, and genomic DNA.

[0154] We reasoned that despite this high degree of connectivity between all three molecular species, a central expectation in cellular trafficking would be that mRNA would localize – on average – to non-mitochondrial rRNA specifically. We therefore used the top 100 eigenvectors of row- and column-normalized gene-gene UEI matrices (SI: Clustering) from each embryo separately to estimate each gene’s proximity to rRNA, MT-rRNA, and gDNA, and used ternary plots (Figs 4J,K) to visualize these. As expected, mRNA differentially but preferentially localized to rRNA exclusively in both embryos. This high- lighted that although the data set encoded whole-organism morphology, it nevertheless retained sub- cellular spatial information.

[0155] We have demonstrated here the capability for a massive (>106) distributed molecular network to volumetrically image a biological specimen from the “inside-out”. The implications of this work are threefold.

[0156] First, we have shown that DNA is capable of encoding massive images and that these images are capable of being decoded without the use of any specialized instrumentation 29 FoleyHoagUS12404641.3UCT-01725 beyond a DNA sequencer. This lays a critical foundation for the economy of scale this technology provides, and a broader democratization of 3D spatio-genetic imaging. This provides a clear path toward use in clinical settings, in which the impact of somatic mutationand genomic “idiosyncracy” in tumors1, lymphocytes2, the brain3and the gut microbiome,play a critical role. Still further, the fact that all readouts are “zero-knowledge” opens up unexplored spatio-genetic complexity in non-model organisms.

[0157] Second, the inferred images here exhibit an inherent tension between being both connectivity maps and representations of Cartesian coordinates. We have shown that in simulation and practice, the implementation of a distinct methodology for dimensionality reduction – Geodesic Spectral Embeddings, or GSE – provides a scalable and reliable solution to reconciling these two disparate properties that is complementary to other common dimensionality-reduction methods. GSE may have broader application to other large data sets requiring similar reconciliation the connectivities of nodes and their low-dimensional representations.

[0158] Third and finally, continued improvements to volumetric DNA microscopy chemistry and inference will provide a platform – distinct from and potentially complementary to conventional light and electron microscopy – for the analysis of biological circuits. The effective resolution of DNA microscopy follows a dependence on UEI-counts similar to stochastic super-resolution light microscopy’s dependence on photon-counts7, with the diffusion length scale (whether unconstrained, or constrained in the case of RCA) divided by the square root of the number of UEIs belonging to the resolved UMI. A 1µm size of RCA polonies with the 3 to 4 UEIs per UMI highlighted in Figure 1 therefore avails us of roughly the same length in resolution. Sequencing deeper, and increasing reaction yield would, however, push us well below the sub-micron regime.

[0159] In this work, we have demonstrated the ability for volumetric DNA microscopy to capture both RNA and DNA, and looking forward we anticipate acquiring proteomic details via oligo-antibody conjugates. As efforts accelerate to perform system-wide maps of neuronal circuitry in particular, the need to supplement these insights with those from molecular genetics, from gene expression, to genomic mosaicism, to spatio-proteomic measurement will take on increasing importance. We view volumetric DNA microscopy as poised to form a critical foundation to this broader undertaking.

[0160] Example 6 - Updated Image Inference Process 30 FoleyHoagUS12404641.3UCT-01725

[0161] The image inference process, which is the core computational method of volumetric DNA microscopy, has been refined to improve spatial reconstruction accuracy and robustness, especially for larger datasets. As shown in Fig.8, key updates include: 1. Enhanced Sub-sampling and Interpolation Building on the computational approach described in the original preprint, the updated method uses sub-sampling and interpolation as a crucial pre-processing step: a) Random Iterative Sampling: The full dataset is randomly subsampled multiple times to generate contiguous UMI-UMI networks. b) Linear Interpolation: For each subsampled network, linear interpolation is performed to estimate positions for all UMIs in the full dataset. c) Rank Transformation: A key innovation is applied to the interpolated coordinates. For each dimension in each sub-sample interpolation, a rank transformation is performed. This transformation replaces raw coordinate values with their rank (order), effectively introducing uniform spacing between points.

[0162] The rank transformation proves to be more robust to noise in larger datasets, particularly those with ~7x10^6 or more data points. This approach helps mitigate the impact of outliers and provides a more consistent basis for subsequent steps in the inference process. 2. Refined Basis Generation for Projected Gradient Descent in sub-sampled GSE a) SVD on Rank-Transformed Data: Instead of using the raw interpolated coordinates, the rank-transformed coordinates from multiple sub-samples are used as input for Singular Value Decomposition (SVD). b) Orthogonalization: The resulting singular vectors are orthogonalized to generate a basis set. c) Projected Gradient Descent: This orthogonalized basis is then used to perform projected gradient descent on the probability objective function, as in the original method.

[0163] The uniform spacing introduced by rank transformation helps in creating a more stable and representative basis for the gradient descent, particularly beneficial for large, complex datasets.

[0164] Example 7 - Updated Experimental Protocol

[0165] The experimental protocol has been modified to reduce artifacts and improve the specificity of UEI formation. As shown in Fig.9, key updates include: 1. Incorporation of Uracil and USER Enzyme Treatment 31 FoleyHoagUS12404641.3UCT-01725 a) During the rolling circle amplification (RCA) step, dUTP is used in place of dTTP. This substitution introduces uracil bases into the amplified DNA "nanoballs". b) In the subsequent in situ in vitro transcription (IVT) reaction, a mixture of Uracil DNA glycosylase (UDG) and Endonuclease VIII (equivalent to the USER enzyme from New England Biolabs) is included. c) The USER enzyme treatment during IVT removes the uracil-containing DNA nanoballs generated by RCA. This step significantly reduces UEI formation as a consequence of long-range recombination, improving the spatial specificity of the technique.

[0166] The removal of RCA products during IVT helps confine UEI formation to more localized regions, enhancing the accuracy of spatial reconstruction. This modification addresses a potential source of noise in the original protocol, where persistent RCA products could lead to spurious long-range connections. 2. Initial Non-Strand Displacing Extension immediately before RCA a) Prior to the RCA step, an initial extension reaction is performed using a non-strand displacing DNA polymerase (e.g., T4 DNA polymerase) in combination with standard dNTPs (no dUTP). b) This extension step copies the first UMI, creating an intact UMI-cDNA template that survives the subsequent USER enzyme digestion.

[0167] This modification ensures that at least one copy of each UMI-cDNA pair remains intact throughout the protocol, even after the removal of uracil-containing RCA products. This preservation of original molecular information enhances the robustness and accuracy of the final spatial reconstruction.

[0168] Fig.10 shows image produced using updated protocol and image inference process.

[0169] Computer Implemented Methods

[0170] Referring now to Fig.11, a schematic of an example of a computing node is shown. Computing node 10 is only one example of a suitable computing node and is not intended to suggest any limitation as to the scope of use or functionality of embodiments described herein. Regardless, computing node 10 is capable of being implemented and / or performing any of the functionality set forth hereinabove.

[0171] In computing node 10 there is a computer system / server 12, which is operational with numerous other general purpose or special purpose computing system environments or configurations. Examples of well-known computing systems, environments, and / or configurations that may be suitable for use with computer system / server 12 include, but are 32 FoleyHoagUS12404641.3UCT-01725 not limited to, personal computer systems, server computer systems, thin clients, thick clients, handheld or laptop devices, multiprocessor systems, microprocessor-based systems, set top boxes, programmable consumer electronics, network PCs, minicomputer systems, mainframe computer systems, and distributed computing environments that include any of the above systems or devices, and the like.

[0172] Computer system / server 12 may be described in the general context of computer system-executable instructions, such as program modules, being executed by a computer system. Generally, program modules may include routines, programs, objects, components, logic, data structures, and so on that perform particular tasks or implement particular abstract data types. Computer system / server 12 may be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote computer system storage media including memory storage devices.

[0173] As shown in Fig.11, computer system / server 12 in computing node 10 is shown in the form of a general-purpose computing device. The components of computer system / server 12 may include, but are not limited to, one or more processors or processing units 16, a system memory 28, and a bus 18 that couples various system components including system memory 28 to processor 16.

[0174] Bus 18 represents one or more of any of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, and a processor or local bus using any of a variety of bus architectures. By way of example, and not limitation, such architectures include Industry Standard Architecture (ISA) bus, Micro Channel Architecture (MCA) bus, Enhanced ISA (EISA) bus, Video Electronics Standards Association (VESA) local bus, Peripheral Component Interconnect (PCI) bus, Peripheral Component Interconnect Express (PCIe), and Advanced Microcontroller Bus Architecture (AMBA).

[0175] Computer system / server 12 typically includes a variety of computer system readable media. Such media may be any available media that is accessible by computer system / server 12, and it includes both volatile and non-volatile media, removable and non-removable media.

[0176] System memory 28 can include computer system readable media in the form of volatile memory, such as random access memory (RAM) 30 and / or cache memory 32. Computer system / server 12 may further include other removable / non-removable, 33 FoleyHoagUS12404641.3UCT-01725 volatile / non-volatile computer system storage media. By way of example only, storage system 34 can be provided for reading from and writing to a non-removable, non-volatile magnetic media (not shown and typically called a "hard drive"). Although not shown, a magnetic disk drive for reading from and writing to a removable, non-volatile magnetic disk (e.g., a "floppy disk"), and an optical disk drive for reading from or writing to a removable, non-volatile optical disk such as a CD-ROM, DVD-ROM or other optical media can be provided. In such instances, each can be connected to bus 18 by one or more data media interfaces. As will be further depicted and described below, memory 28 may include at least one program product having a set (e.g., at least one) of program modules that are configured to carry out the functions of embodiments of the disclosure.

[0177] Program / utility 40, having a set (at least one) of program modules 42, may be stored in memory 28 by way of example, and not limitation, as well as an operating system, one or more application programs, other program modules, and program data. Each of the operating system, one or more application programs, other program modules, and program data or some combination thereof, may include an implementation of a networking environment. Program modules 42 generally carry out the functions and / or methodologies of embodiments as described herein.

[0178] Computer system / server 12 may also communicate with one or more external devices 14 such as a keyboard, a pointing device, a display 24, etc.; one or more devices that enable a user to interact with computer system / server 12; and / or any devices (e.g., network card, modem, etc.) that enable computer system / server 12 to communicate with one or more other computing devices. Such communication can occur via Input / Output (I / O) interfaces 22. Still yet, computer system / server 12 can communicate with one or more networks such as a local area network (LAN), a general wide area network (WAN), and / or a public network (e.g., the Internet) via network adapter 20. As depicted, network adapter 20 communicates with the other components of computer system / server 12 via bus 18. It should be understood that although not shown, other hardware and / or software components could be used in conjunction with computer system / server 12. Examples, include, but are not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data archival storage systems, etc.

[0179] In various embodiments, a learning system is provided. In some embodiments, a feature vector is provided to a learning system. Based on the input features, the learning system generates one or more outputs. In some embodiments, the output of the learning system is a feature vector. In some embodiments, the learning system comprises a SVM. In 34 FoleyHoagUS12404641.3UCT-01725 other embodiments, the learning system comprises an artificial neural network. In some embodiments, the learning system is pre-trained using training data. In some embodiments training data is retrospective data. In some embodiments, the retrospective data is stored in a data store. In some embodiments, the learning system may be additionally trained through manual curation of previously generated outputs.

[0180] In some embodiments, the learning system, is a trained classifier. In some embodiments, the trained classifier is a random decision forest. However, it will be appreciated that a variety of other classifiers are suitable for use according to the present disclosure, including linear classifiers, support vector machines (SVM), or neural networks such as recurrent neural networks (RNN).

[0181] Suitable artificial neural networks include but are not limited to a feedforward neural network, a radial basis function network, a self-organizing map, learning vector quantization, a recurrent neural network, a Hopfield network, a Boltzmann machine, an echo state network, long short term memory, a bi-directional recurrent neural network, a hierarchical recurrent neural network, a stochastic neural network, a modular neural network, an associative neural network, a deep neural network, a deep belief network, a convolutional neural networks, a convolutional deep belief network, a large memory storage and retrieval neural network, a deep Boltzmann machine, a deep stacking network, a tensor deep stacking network, a spike and slab restricted Boltzmann machine, a compound hierarchical-deep model, a deep coding network, a multilayer kernel machine, or a deep Q-network.

[0182] The present disclosure may be embodied as a system, a method, and / or a computer program product. The computer program product may include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present disclosure.

[0183] The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of the computer readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD- ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded 35 FoleyHoagUS12404641.3UCT-01725 device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber- optic cable), or electrical signals transmitted through a wire.

[0184] Computer readable program instructions described herein can be downloaded to respective computing / processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and / or a wireless network. The network may comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and / or edge servers. A network adapter card or network interface in each computing / processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing / processing device.

[0185] Computer readable program instructions for carrying out operations of the present disclosure may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++ or the like, and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The computer readable program instructions may execute entirely on the user’s computer, partly on the user’s computer, as a stand-alone software package, partly on the user’s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user’s computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present disclosure. 36 FoleyHoagUS12404641.3UCT-01725

[0186] Aspects of the present disclosure are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer readable program instructions.

[0187] These computer readable program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and / or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function / act specified in the flowchart and / or block diagram block or blocks.

[0188] The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0189] The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and / or flowchart illustration, and combinations of blocks in the block diagrams and / or flowchart illustration, can be implemented by special 37 FoleyHoagUS12404641.3UCT-01725 purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions. References [1] Jeremy Thorpe, Ikeoluwa A Osei-Owusu, Bracha Erlanger Avigdor, Rossella Tupler, and Jonathan Pevsner. Mosaicism in human health and disease. Annual review of genetics, 54:487–510, 2020. [2] Chenqu Suo, Krzysztof Polanski, Emma Dann, Rik GH Lindeboom, Roser Vilarrasa-Blasi, Roser Vento-Tormo, Muzlifah Haniffa, Kerstin B Meyer, Lisa M Dratva, Zewen Kelvin Tuong, et al. Dandelion uses the single-cell adaptive immune receptor repertoire to explore lymphocyte developmental origins. Nature Biotech- nology, pages 1–12, 2023. [3] Sara Bizzotto and Christopher A Walsh. Genetic mosaicism in the human brain: from lineage tracing to neuropsychiatric disorders. Nature Reviews Neuroscience, 23(5):275–286, 2022. [4] Lisa N Waylen, Hieu T Nim, Luciano G Martelotto, and Mirana Ramialison. From whole-mount to single-cell spatial assessment of gene expression in 3d. Communi- cations biology, 3(1):602, 2020. [5] Anjali Rao, Dalia Barkley, Gustavo S Franc¸a, and Itai Yanai. Exploring tissue archi- tecture using spatial transcriptomics. Nature, 596(7871):211–220, 2021. [6] Shahar Alon, Daniel R Goodwin, Anubhav Sinha, Asmamaw T Wassie, Fei Chen, Evan R Daugharthy, Yosuke Bando, Atsushi Kajita, Andrew G Xue, Karl Marrett, et al. Expansion sequencing: Spatially precise in situ transcriptomics in intact bio- logical systems. Science, 371(6528):eaax2656, 2021. [7] Joshua A Weinstein, Aviv Regev, and Feng Zhang. Dna microscopy: optics-free spatio-genetic imaging by a stand-alone chemical reaction. Cell, 178(1):229–241, 2019. [8] Filip Karlsson, Tomasz Kallas, Divya Thiagarajan, Max Karlsson, Maud Schweitzer, Jose Fernandez Navarro, Louise Leijonancker, Sylvain Geny, Erik Pettersson, Jan Rhomberg-Kauert, et al. Molecular pixelation: Single cell spatial proteomics by sequencing. bioRxiv, June 2023. [9] Ian T Hoffecker, Yunshi Yang, Giulio Bernardinelli, Pekka Orponen, and Bjo¨rn Ho¨gberg. A computational framework for dna sequencing microscopy. Proceed- ings of the National Academy of Sciences, 116(39):19282–19287, 2019. 38 FoleyHoagUS12404641.3UCT-01725

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Claims

UCT-01725 What is claimed is:

1. A method for identifying spatial distribution of target nucleic acids in a sample, the method comprising: (a) adding to each of a plurality of the target nucleic acids in the sample a unique molecular identifier (UMI) and either a first type adapter comprising a first universal sequence or a second type adapter comprising a second universal sequence, thereby generating a plurality of UMI-labeled target nucleic acids; (b) contacting a pair of UMI-labeled target nucleic acids with a unique event identifier (UEI) DNA probe, a first UMI-labeled target nucleic acid in the pair comprising a first universal sequence, a second UMI-labeled target nucleic acid comprising the second universal sequence, and wherein the UEI DNA probe comprises sequences complimentary to the first and the second universal sequences; (c) based on the pair of UMI-labeled target nucleic acids as a template, extending the UEI DNA probe, thereby generating a plurality of UEI DNA fragments, each UEI DNA fragment comprising a unique pair of the UMIs corresponding the pair of UMI-labeled target nucleic acids; and (d) determining a count of each of the plurality of UEI DNA fragments, wherein the count corresponds to spatial proximity of the pair of UMI-labeled template nucleic acids.

2. The method of claim 1, further comprising determining the correspondence between each UMI and each of the plurality of the UMI-labeled target nucleic acids.

3. The method of claim 1 or 2, wherein step (a) comprises: (1) adding to each of the plurality of the target nucleic acids either the first type adapter or the second type adapter; (2) annealing the plurality of the target nucleic acids linked to either the first type adapter or the second type adapter with a plurality of circular DNAs, wherein each circular DNA comprises a unique UMI; and (3) conducting a rolling cycle amplification (RCA) to add a unique UMI to each of the plurality of target nucleic acids, thereby generating a plurality of UMI-labeled target nucleic acids, each of which comprises tandem repeats of a UMI.

4. The method of claim 3, wherein the RCA is conducted in the presence of dATPs, dCTPs, dGTPs, and dTTPs. 41 FoleyHoagUS12404641.3UCT-01725 5. The method of claim 3, wherein the RCA comprises: (i) extending each of the plurality of target nucleic acids along a circular DNA backbone using a non-strand displacing DNA polymerase to add one copy of a unique UMI to each of the plurality of target nucleic acids; and (ii) generating a plurality of UMI-labeled target nucleic acids with a strand- displacing DNA polymerase, wherein each of the plurality of UMI-labeled target nucleic acids comprises tandem repeats of a UMI.

6. The method of claim 5, wherein step (i) is conducted in the presence of dATPs, dCTPs, dGTPs, and dTTPs.

7. The method of claim 5 or 6, wherein the non-strand displacing DNA polymerase is a T4 DNA polymerase.

8. The method of any one of claims 5-7, wherein generating a plurality of UMI-labeled target nucleic acids with the strand-displacing DNA polymerase is conducted in the presence of dATPs, dCTPs, dGTPs, and dUTPs, thereby generating dUTP-containing UMI-labeled target nucleic acids.

9. The method of any one of claims 1-8, wherein the UEI DNA probe comprises a random sequence, and further wherein determining the count of each of the plurality of UEI DNA fragments comprises determining a count of the random sequences of each of the plurality of UEI DNA fragments.

10. The method of any one of claims 1-9, wherein extending the UEI DNA probe based on the pair of UMI-labeled target nucleic acids as the template comprises gap-fill extension and ligation.

11. The method of any one of claims 1-10, wherein determining the count of each of the plurality of UEI DNA fragments further comprises amplifying and sequencing the UEI DNA fragments.

12. The method of any one of claims 1-11, wherein the amplification comprises: 42 FoleyHoagUS12404641.3UCT-01725 (1) conducting an in situ in vitro transcription (IVT) of the plurality of UEI DNA fragments to generate RNA transcripts of the plurality of UEI DNA fragments; (2) isolating the RNA transcripts from the sample; (3) conducting a reverse transcription of the isolated RNA transcripts to generate amplicons of the plurality of UEI DNA fragments; and (4) amplifying the amplicons of the plurality of UEI-containing DNA fragments.

13. The method of claim 2, comprising amplifying and sequencing the plurality of UMI- labeled target nucleic acids.

14. The method of claim 13, wherein the amplifying the plurality of UMI-labeled target nucleic acids comprises: (1) conducting in situ in vitro transcription (IVT) of the plurality of UMI-labeled target nucleic acids to generate RNA transcripts of the UMI-labeled target nucleic acids; (2) isolating the RNA transcripts from the sample; (3) conducting a reverse transcription of the RNA transcripts to generate amplicons of the UMI-labeled target nucleic acids; and (4) amplifying the amplicons of the plurality of UMI-labeled target nucleic acids.

15. The method of claim 12 or 14, wherein the IVT further comprises digesting dUTP- containing UMI-labeled target nucleic acids.

16. The method of any one of claims 1-15, wherein the sample is a fixed tissue.

17. The method of any one of claims 1-16, wherein the sample is permeabilized.

18. The method of any one of claims 1-17, wherein the target nucleic acids are endogenous to the sample.

19. The method of any one of claims 1-17, wherein the target nucleic acids are exogenously added to the sample. 43 FoleyHoagUS12404641.3UCT-01725 20. The method of any one of claims 1-19, wherein the plurality of the target nucleic acids comprises target nucleic acids covalently or noncovalently linked to a biomolecule.

21. The method of any one of claims 1-20, wherein the plurality of target nucleic acids comprises an RNA molecule.

22. The method of claim 21, wherein the plurality of target nucleic acids comprises an mRNA molecule.

23. The method of any one of claims 1-22, wherein the plurality of target nucleic acid comprises a DNA molecule.

24. The method of claim 23, wherein the plurality of target nucleic acids comprises a cDNA molecule.

25. The method of claim 24, wherein the method further comprises conducting an in situ reverse transcription of a RNA molecule in the sample to generate the cDNA molecule.

26. The method of any one of claims 1-25, wherein each UMI is a random sequence.

27. The method of any one of claims 1-26, wherein each unique event identifier (UEI) DNA probe comprises a sample barcode.

28. The method of claim 27, wherein the sample barcode is an arbitrary six-nucleotide identifier.

29. The method of any one of claims 1-28, further comprising mapping the plurality of UMI-labeled target nucleic acids to a coordinate space based on the count of each of the plurality of UEI DNA fragments. 44 FoleyHoagUS12404641.3UCT-01725 30. The method of claim 29, wherein mapping the plurality of UMI-labeled target nucleic acids to the coordinate space comprises minimizing an objective function comprising a proximity term based on the count of each of the plurality of UEI DNA fragments.

31. The method of claim 30, wherein minimizing the objective function comprises gradient descent.

32. The method of any one of claims 29-31, wherein mapping the plurality of UMI- labeled target nucleic acids to the coordinate space comprises constructing a global proximity matrix based on the count of each of the plurality of UEI DNA fragments.

33. The method of claim 32, where constructing the global proximity matrix comprises determining a plurality of geodesic distances, each corresponding to one of the pairs of UMI- labeled template nucleic acids.

34. The method of claim 33, wherein determining the plurality of geodesic distances comprises defining a local tangent space for each of the plurality of UEI DNA fragments.

35. The method of claim 34, wherein defining the local tangent space comprises clustering.

36. A computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processor to cause the processor to perform a method according to any one of claims 29-35. 45 FoleyHoagUS12404641.3

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