Adjusting oligonucleotide-cluster location in images in real time using band-edge spectral regions

Abstract

The present disclosure describes systems, non-transitory computer-readable media, and methods for determining adjusted locations of clusters of oligonucleotides based on a phase difference between band-edge spectral regions of a nucleotide-sample-slide region image. For example, the disclosed systems (i) identify a pair of band-edge spectral regions from a spatial frequency band in an oligonucleotide-cluster image and (ii) determine a phase difference between the pair of band-edge spectral regions. Based on the phase difference, the disclosed systems generate a location error in at least one direction for predicted locations of the oligonucleotide clusters. Based on the location error, the disclosed systems determine adjusted locations of the oligonucleotide-clusters within the nucleotide-sample-slide region.

Description

ADJUSTING OLIGONUCLEOTIDE-CLUSTER LOCATION IN IMAGES IN REAL TIME USING BAND-EDGE SPECTRAL REGIONSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to and the benefit of U.S. Provisional Patent Application No. 63 / 699,012, filed on September 25, 2024, entitled “ADJUSTING OLIGONUCLEOTIDE- CEUSTER LOCATION IN IMAGES IN REAL TIME USING BAND-EDGE SPECTRAL REGIONS,” (IP-2805-PRV), which is incorporated herein by reference in its entirety.BACKGROUND

[0002] In recent years, biotechnology firms and research institutions have improved hardware and software for sequencing nucleotides and determining nucleobase calls for genomic samples. For instance, some existing sequencing machines and sequencing-data-analysis software (together “existing sequencing systems”) predict individual nucleobases within sequences, such samples by using conventional Sanger sequencing or sequencing-by-synthesis (SBS) methods. When using SBS, existing sequencing systems can monitor millions to billions of oligonucleotides being synthesized in parallel and in clusters from templates for one or more samples to predict nucleobase calls for growing nucleotide reads. A camera in many existing sequencing systems captures images of irradiated fluorescent tags incorporated into oligonucleotides or images of other signals indicating incorporated nucleobases.

[0003] To effectively identify which signals come from which clusters of oligonucleotides in a sequencing cycle — and determine accurate nucleobase calls for such clusters — existing sequencing systems must accurately locate the clusters of oligonucleotides on a flow cell or other nucleotide- sample slide. After capturing such images, some existing sequencing systems determine nucleobase calls for nucleotide reads corresponding to individual oligonucleotide clusters. By iteratively incorporating nucleobases into the oligonucleotides of such clusters and capturing images of emitted light signals (or other signals) in various sequencing cycles, existing sequencing systems can determine nucleotide reads and, after further and secondary analysis of such reads, determine the nucleobase sequence and genotype present in genomic samples.

[0004] Despite recent advances to cluster-location estimates, existing sequencing systems often inaccurately estimate the locations of clusters of oligonucleotides on flow cells or other nucleotide- sample slides, rely on incorrect estimated locations of clusters, and, consequently, can sometimes determine incorrect nucleobase calls. While fiducials and other physical markers that may be present on a nucleotide-sample slide can help as reference points for cluster location within an image, images with insufficient resolution and such physical markers on a nucleotide-sample slide sometimes do not support accurately accounting for image jitter, which is caused by high frequency motion of a stage on the line scanning system. Additionally, existing sequencing systems that relyAttorney Docket No. IP-2805-PCT 1 Patent Applicationexclusively on fiducials or other physical reference points exhibit limitations when adjusting for image distortions, such as distortions resulting from the optics or geometry of a lens — whether that be linear distortion (e.g., magnification, skew, translation) or nonlinear distortion (e.g., barrel or pincushion). For example, existing sequencing systems often correct for distortion in real time utilizing polynomial fitting by maximizing a chastity value for nucleotide reads to “pass filter” and, upon passing, analyzing such reads for variant calls. This chastity-based approach, however, relies on subsampled chastity values for a subset of oligonucleotide clusters and, therefore, is susceptible to relatively low base-call diversity, jitter, or flow-cell defects. Additionally, past research has proven it difficult for a sequencing device to efficiently identify a global, optimal solution in an image’s higher-order parameter space while escaping local optima.

[0005] Because existing sequencing systems that rely exclusively on fiducials or other physical markers often cannot account for jitter and / or optical distortion without sufficient image resolution, such existing systems can improve in accurately identifying signals emitted from the cluster of oligonucleotides and captured by an image. Without a better model to compensate for such location-tracking issues, existing sequencing systems will sometimes exhibit a reduced signal-to- noise ratio (SNR) for a signal emitted by oligonucleotide clusters. Not only can incorrect clusterlocation estimates sometimes cause incorrect base calls from poorly SNR-adjusted signals, but existing sequencing systems exhibiting such cluster-location-estimate inaccuracies tend to (i) produce fewer oligonucleotide clusters that pass quality filters (e.g., chastity filters) and / or (ii) produce fewer oligonucleotide clusters with high quality nucleotide reads (or subsequences of such reads) that can be used for mapping and aligning (e.g., because of hard or soft clipping of nucleotide reads).

[0006] To compensate for cluster-location-estimate inaccuracies, some existing sequencing systems have used (or attempted to use) nucleotide-sample slides with a denser distribution of fiducials (or other physical markers) and a corresponding increase in image resolution from more granular camera lenses. For instance, some existing sequencing systems have added and relied on fiducials on flow cells to improve cluster-location estimation in sequencing devices that use two- channel or three-channel implementations to detect signals from oligonucleotide clusters. But adding fiducials introduces both space and computing constraints in a technical environment in which the sequencing speed of a sequencing device is critical. Additional fiducials or other physical markers not only consume space on the substrate of a nucleotide-sample slide and leave less space for nanowells and / or clusters of oligonucleotides, but also pose challenges in flow cell manufacturing. Further, the amount of optical distortion and jitter affecting predicted locations of clusters of oligonucleotides can be specific to each type of sequencing platform, flow cell and the physical layout of nanowells. Consequently, existing sequencing systems with increased fiducialAttorney Docket No. IP-2805-PCT 2 Patent Applicationdensities reduce the number of oligonucleotide clusters that can be sequenced in a sequencing run and reduce throughput in a nanometric space that supports millions to billions of clusters. Exasperating the space constraints, additional computational processing during a sequencing device’s registration process is required to process and calibrate as the number of fiducials or other physical markers increase in density on a nucleotide-sample slide.

[0007] These along with additional problems and issues exist with regard to existing sequencing systems.SUMMARY

[0008] This disclosure describes one or more embodiments of systems, non-transitory computer-readable media, and methods that solve one or more of the foregoing problems in the art or provide other advantages in the art. For example, the disclosed systems more accurately estimate the location of oligonucleotide clusters on a flow cell (or other nucleotide-sample slide) by (i) identifying a pair of band-edge spectral regions from a spatial frequency band in an oligonucleotide-cluster image and (ii) determining a phase difference between the pair of bandedge spectral regions. To more accurately estimate oligonucleotide-cluster locations, the disclosed systems can identify one or more pairs of band-edge spectral regions for an image (e.g., image patch) depicting signals from oligonucleotide clusters at predicted locations within a region of a nucleotide-sample slide. The disclosed systems further determine respective phase differences between pairs of band-edge spectral regions. Based on the respective phase difference between one or more pairs of band-edge spectral regions, the disclosed systems generate a location error in at least one direction (e.g., a horizontal direction and / or a vertical direction) for the predicted locations of the oligonucleotide clusters within the region of the image.

[0009] By accounting for such location errors, the disclosed systems can determine adjusted locations of oligonucleotide clusters during a sequencing cycle and determine more accurate base calls for such clusters using signals from the adjusted cluster locations. As explained further below, in some embodiments, the disclosed systems can adjust oligonucleotide-cluster locations to compensate for optical distortion in one direction and compensate for jitter in another direction.

[0010] Additional features and advantages of one or more embodiments of the present disclosure are outlined in the description that follows, and in part can be determined from the description, or may be learned by the practice of such example embodiments.BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The detailed description provides one or more embodiments with additional specificity and detail through the use of the accompanying drawings, as briefly described below.

[0012] FIG. 1 illustrates a diagram of an environment in which a location-error-prediction system can operate in accordance with one or more implementations.Attorney Docket No. IP-2805-PCT 3 Patent Application

[0013] FIG. 2 illustrates a diagram showing the effects of jitter and optical distortion on locations of clusters of oligonucleotides in accordance with one or more embodiments.

[0014] FIG. 3 illustrates an overview of the location-error-prediction system determining a phase difference between a pair of band-edge spectral regions, adjusting a predicted location of a cluster of oligonucleotides based on the phase difference, and determining a base call for the cluster of oligonucleotides based on the adjusted location in accordance with one or more embodiments.

[0015] FIG. 4A illustrates the location-error-prediction system identifying pairs of band-edge spectral regions according to a hexagon layout in accordance with one or more embodiments.

[0016] FIG. 4B illustrates the location-error-prediction system identifying pairs of shape- simplified band-edge spectral regions with simplified orientations adjusted from a hexagon layout to accelerate computation in accordance with one or more embodiments.

[0017] FIG. 5 A illustrates the location-error-prediction system identifying pairs of band-edge spectral regions according to a diamond layout in accordance with one or more embodiments.

[0018] FIG. 5B illustrates the location-error-prediction system identifying pairs of shape- simplified band-edge spectral regions with simplified geometric layouts and orientations adjusted from a diamond layout to accelerate computation in accordance with one or more embodiments.

[0019] FIG. 6 illustrates the location-error-prediction system identifying pairs of band-edge spectral regions according to a square layout in accordance with one or more embodiments.

[0020] FIG. 7 illustrates exemplary nucleotide-sample slide heat maps showing x and y errors and summed location errors in accordance with one or more embodiments.

[0021] FIGS. 8A-8B illustrate the location-error-prediction system extracting and transforming an image patch of a nucleotide-sample-slide region and identifying pairs of band-edge spectral regions from a spatial frequency band, determining phase differences between band-edge spectral regions, and generating location errors for one or more oligonucleotide clusters depicted within the image patch based on the phase differences in accordance with one or more embodiments.

[0022] FIG. 9A illustrates the location-error-prediction system applying an image-patch grid to an image patch of nucleotide-sample-slide-region image in accordance with one or more embodiments.

[0023] FIG. 9B illustrates the location-error-prediction system determining adjusted locations of clusters of oligonucleotides in the image patch using the image-patch grid in accordance with one or more embodiments.

[0024] FIG. 10A illustrates an exemplary heat map of cell-specific x location errors determined by the location-error-prediction system for predicted locations of clusters of oligonucleotides depicted by image patches mapped to grid cells of an image-patch grid in accordance with one or more embodiments.Attorney Docket No. IP-2805-PCT 4 Patent Application

[0025] FIG. 10B illustrates an exemplary heat map of cell-specific y location errors determined by the location-error-prediction system for predicted locations of clusters of oligonucleotides depicted by image patches mapped to grid cells of the image-patch grid in accordance with one or more embodiments.

[0026] FIG. 11 illustrates a uniform subsampled image-patch grid and a staggered subsampled image-patch grid in accordance with one or more embodiments.

[0027] FIG. 12A illustrates decomposing exemplary fully-sampled and subsampled imagepatch grids (e.g., PHI matrices) into two matrices — an A matrix associated with jitter and a B matrix associated with optical distortion — for determining location errors of a fully-sampled image-patch grid based on subsampled location errors by the least squares algorithm in accordance with one or more embodiments.

[0028] FIG. 12B illustrates decomposing an exemplary subsampled image-patch grid (e.g., PHI matrix) into two matrices — an A matrix associated with jitter and a B matrix associated with optical distortion — for determining location errors of a fully-sampled image-patch grid based on subsampled location errors by the least squares algorithm in accordance with one or more embodiments.

[0029] FIG. 13 A illustrates a shifted staggered subsampled image-patch grid to improve the rank of matrix in accordance with one or more embodiments.

[0030] FIG. 13B illustrates an Eigenvalue graph of the staggered subsampled image-patch grid matrix and the shifted staggered subsampled image-patch grid matrix.

[0031] FIG. 14 illustrates mean square errors of the grid cells of a subsampled image-patch grid in accordance with one or more embodiments.

[0032] FIG. 15A illustrates summary tables of sequencing run statistics in accordance with one or more embodiments.

[0033] FIG. 15B illustrates a quality score graph in accordance with one or more embodiments.

[0034] FIG. 16 illustrates oligonucleotide-cluster locations and colored contour rings of equalizer coefficients trained based on distorted oligonucleotide-cluster locations in existing sequencing systems and adjusted oligonucleotide-cluster locations in location error prediction system in accordance with one or more embodiments.

[0035] FIG. 17 illustrates a flowchart of a series of acts for determining an adjusted location of at least one cluster of oligonucleotides based on at least one location error in accordance with one or more embodiments of the present disclosure.

[0036] FIG. 18 illustrates a flowchart of a series of acts for determining adjusted locations of clusters of oligonucleotides based on location errors determined from phase differences betweenAttorney Docket No. IP-2805-PCT 5 Patent Applicationpairs of band-edge spectral regions in accordance with one or more embodiments of the present disclosure

[0037] FIG. 19 illustrates a block diagram of an example computing device in accordance with one or more embodiments of the present disclosure.DETAILED DESCRIPTION

[0038] This disclosure describes one or more embodiments of a location-error-prediction system that more accurately estimates, in a given sequencing cycle, a location of oligonucleotide clusters on a flow cell or other nucleotide-sample slide by (i) identifying a pair of band-edge spectral regions from a spatial frequency band in a nucleotide-sample-slide-region image and (ii) determining a phase difference between the pair of band-edge spectral regions. For example, in some cases, the location-error-prediction system identifies multiple pairs of band-edge spectral regions for an image patch depicting signals from oligonucleotide clusters at predicted locations within a region of a nucleotide-sample slide. The location-error-prediction system further determines respective phase differences between one or more pairs of band-edge spectral regions. Based on the respective phase difference between the pairs of band-edge spectral regions, the location-error-prediction system generates a location error in a single direction or in multiple directions (e.g., an x direction and / or ay direction) for the predicted locations of the oligonucleotide clusters within the nucleotide-sample-slide region. Based on the location error, the location-error- prediction system can determine adjusted locations of the oligonucleotide clusters and determine base calls for the oligonucleotide clusters at such adjusted locations — in the same sequencing cycle and in real time relative to capturing the image comprising the pair of band-edge spectral regions.

[0039] As indicated above, in some cases, the location-error-prediction system identifies and utilizes pairs of band-edge spectral regions based on a geometric layout outlining an arrangement of oligonucleotide-cluster locations. The particular number of band-edge spectral region pairs depends on the geometric layout (e.g., hexagon, diamond, square) based on which oligonucleotide clusters are arranged within a region of a particular nucleotide-sample slide. The geometric layout of oligonucleotide clusters arrangement within such a nucleotide-sample-slide region (e.g., subtile) affects the phase difference (e.g., phase angle) used for a particular pair of band-edge spectral regions. For instance, the location-error-prediction system can identify a phase difference between a pair of band-edge spectral regions based on a hexagonal, diamond, or square layout of oligonucleotide-cluster locations within a nucleotide-sample-slide region (e.g., a flow-cell region). Indeed, the location-error-prediction system determines a location error in a direction corresponding to the pair of band-edge spectral regions. Specifically, the location-error-prediction system determines a phase angle between pairs of band-edge spectral regions and a fixed distance between oligonucleotide clusters within a particular nucleotide-sample-slide region.Attorney Docket No. IP-2805-PCT 6 Patent Application

[0040] By determining phase differences between pairs of band-edge spectral regions, the location-error-prediction system can determine an oligonucleotide cluster’s location error that is not only specific to an image channel and specific to a sequencing cycle but also applicable to other oligonucleotide clusters in the same nucleotide-sample-slide region. As just indicated, the location- error-prediction system can determine channel-specific location errors for predicted locations of oligonucleotide clusters based on one or more phase differences between one or more pairs of bandedge spectral regions from an image captured in the specific channel (e.g., blue channel, green channel) and in a specific sequencing cycle. Such channel-specific and / or cycle-specific location errors can accordingly result in an adjusted location of an oligonucleotide cluster for one channel in a sequencing cycle and another adjusted location of the same oligonucleotide cluster for another channel in the same sequencing cycle. As described further below, the location-error-prediction system can also determine such channel-specific and / or cycle-specific location errors applicable to all oligonucleotide clusters in a given region of a nucleotide-sample slide by subsampling pairs of band-edge spectral regions in the given region of the nucleotide-sample slide.

[0041] In some cases, the location-error-prediction system determines both location errors and adjusted locations of oligonucleotide clusters according to an image-patch grid corresponding to an image patch. Such an image-patch grid comprises grid cells corresponding to image patches for subregions of a flow cell or other nucleotide-sample slide. For instance, the location-error- prediction system can access a predetermined image-patch grid and, for each grid cell within the image-patch grid, determine a pair of location errors (e.g., in an x direction and a y direction) for predicted locations of oligonucleotide clusters. Based on the pair of location errors, the location- error-prediction system adjusts the predicted locations of oligonucleotide clusters in each grid cell of the image-patch grid.

[0042] When using an image-patch grid, in some cases, the location-error-prediction system further generates or utilizes a subsampled version of an image-patch grid. Such a subsampled image-patch grid comprises subsampled grid cells corresponding to a subset of image patches. For instance, the subsampled image-patch grid can include subsampled grid cells that have been staggered in locations. When utilizing such a subsampled image-patch grid, the location-error- prediction system can determine location errors for the clusters of oligonucleotides, for example, in the form of an optical distortion vector in one direction (e.g., x direction) and a jitter vector in another direction (e.g., y direction). Further, the location-error-prediction system can identify a corresponding pair of location errors for each grid cell of the larger, non-subsampled image-patch grid by utilizing the optical distortion and jitter vectors. By using a subsampled image-patch grid, the location-error-prediction system can significantly decrease compute for location errors applicable to millions or billions of oligonucleotide clusters in a flow cell rather than computeAttorney Docket No. IP-2805-PCT 7 Patent Applicationlocation errors for each grid cell of a larger, non-subsampled image-patch grid. For example, the location-error-prediction system can reduce compute of location errors for the number of grid cells from 3,456 of a non-subsampled image-patch grid to a 216 subsampled grid cells, thereby producing a 16-fold reduction in computational resources.

[0043] The location-error-prediction system provides several advantages over existing sequencing systems. For instance, the location-error-prediction system improves the accuracy of estimating a physical location of a cluster of oligonucleotides within a region of a nucleotide- sample slide — but without relying on fiducials or other physical markers for orientation purposes within a nucleotide-sample slide. As indicated above, some existing sequencing systems lack sufficient image resolution to accurately determine oligonucleotide-cluster locations based on distances from fiducials (or other physical markers) and can likewise exhibit instrument-to- instrument variation in flow cells that challenge estimating oligonucleotide-cluster locations. Rather than relying on such fiducials and the varying distance among physical markings in a flow cell, the location-error-prediction system can determine a phase difference between one or more pairs of band-edge spectral regions — which include the nanometric physical locations of clusters emitting signals — to estimate the adjusted locations of oligonucleotide clusters or wells. Because the location-error-prediction system identifies the pairs of band-edge spectral regions within images specific to each sequencing device, the location-error-prediction system inherently adjusts for the instrument-specific variations in optical distortion and jitter when determining the phase difference between a pair of band-edge spectral regions. Indeed, the location-error-prediction system can accurately determine adjusted oligonucleotide-cluster locations in flow cells (or other nucleotide-sample slides) configured for two, three, four, or any number of channels, in addition to several other differences in instrument-to-instrument biochemistries, image resolutions, etc. Accordingly, the location-error-prediction system introduces a new model of determining oligonucleotide-cluster locations in real time during a sequencing cycle relative to existing sequencing systems that must rely on fiducials as reference points that can themselves be distorted and subject to the unreliable effects of camera-image resolution and physical variations on an instrument.

[0044] In addition to improved accuracy in adjusting cluster locations, the location-error- prediction system improves the space and computing efficiency relative to alternative approaches to cluster-location prediction. As indicated above, some existing sequencing systems attempt to use nucleotide-sample slides with a denser distribution of fiducials (or other physical markers) to better estimate cluster location using the fiducials as references. But such a denser fiducial distribution consumes space that could be used for additional clusters and requires further computation based on additional fiducials to estimate cluster locations during registration cycles.Attorney Docket No. IP-2805-PCT 8 Patent ApplicationIn contrast to a problematic increase in fiducial density, the location-error-prediction system improves cluster-location prediction by (i) identifying a pair of band-edge spectral regions from a spatial frequency band in a nucleotide-sample-slide-region image and (ii) determining phase differences between the pair of band-edge spectral regions. By doing so in a given sequencing cycle, the location-error-prediction system can accurately and dynamically predict the location of clusters of oligonucleotides while maintaining, eliminating, or reducing the number of fiducials on the nucleotide-sample slide, resulting in higher sequencing throughput and lower computation costs. Because the location-error-prediction system leverages phase differences among band-edge- region pairs and need not rely on physical markings on a nucleotide-sample slide, the location- error-prediction system facilitates tighter pitches (i.e., smaller distances between clusters) but without tightening the tolerances for jitter and optical distortion. Because the location-error- prediction system can determine location errors at an image level or image-patch level and adjust cluster location within the image or image patch based on such location errors, the location-error- prediction system need not rely on physical markings in a nucleotide-sample slide that would consume space necessary for tighter pitches.

[0045] In addition to improved location accuracy and efficient space consumption, the location- error-prediction system also improves the real-time operation of a special-purpose computer or machine — that is, the operation of a sequencing device with specialized cameras during a sequencing cycle or run. A sequencing cycle of a sequencing run can last mere seconds to minutes. By determining location errors and adjusted locations of oligonucleotide clusters, the location- error-prediction system enhances the robustness against stage jitter or unexpected optical distortion, which are commonly faced in field operation with aging equipment. The location-error-prediction system adjusts for such jitter and optical distortion by leveraging band-edge spectral regions. By identifying, for a particular sequencing cycle, a pair of band-edge spectral regions from a spatial frequency band within an image depicting oligonucleotide clusters at predicted locations and determining, for the same particular sequencing cycle, a phase difference between the pair of bandedge spectral regions, the location-error-prediction system can determine a location error and adjusted location of an oligonucleotide cluster during that same particular sequencing cycle. In determining a more accurate adjusted location for the oligonucleotide cluster, the location-error- prediction system also increases the accuracy with which it separates and determines the values for signals emitted by individual oligonucleotide clusters incorporating fluorescently tagged nucleotides in a given sequencing cycle.

[0046] As part of improving the operation of a sequencing device, the location-error-prediction system can simplify the functioning of an equalizer that converts received dispersed-over-pixels intensity energy (e.g., in a signal) into an intensity value representing light emitted from anAttorney Docket No. IP-2805-PCT 9 Patent Applicationoligonucleotide cluster and intensity values for adjacent oligonucleotide clusters. By determining more accurate oligonucleotide-cluster locations, the location-error-prediction system improves signal calibration and signal normalization of the signals emitted by such oligonucleotide clusters. For example, by estimating more accurate, adjusted locations of oligonucleotide clusters, the location-error-prediction system reduces signal overlap between adjacent oligonucleotide clusters and, in turn, improves signal discrimination among oligonucleotide clusters, thereby improving signal calibration. Such improved signal discrimination facilitates better isolating signals to be normalized by minimizing initial variations in signal intensity across oligonucleotide clusters.

[0047] Beyond improving the operation of a sequencing device, the location-error-prediction system can accurately determine locations of clusters of oligonucleotides without requiring the computational resources to compute location error for each oligonucleotide cluster. Specifically, in some embodiments, the location-error-prediction system utilizes grid cell-specific location errors (also referred to herein simply as “cell-specific location errors”) from a subsampled image-patch grid to more accurately determine location errors of all image patches of a nucleotide-sample-slide image. For example, in some cases, the location-error-prediction system can accurately determine the location errors of the subsampled grid cells corresponding to merely a subset of image patches of a nucleotide-sample-slide region image. By limiting its more accurate phase-difference-based method of estimating cluster location to a subset of image patches, the location-error-prediction system can preserve computer processing and other computational resources that would have been required to determine phase differences and corresponding location errors for each oligonucleotide cluster on a nucleotide-sample slide. As explained further below, in some embodiments, the location-error-prediction system can further determine a jitter vector and an optical distortion vector based on the location errors of the subset of image patches and uses these vectors to determine location errors for all the image patches with minimal additional computational resources (e.g., by reducing compute operations for location errors from 3,456 image patches of a nonsubsampled image-patch grid to a subset of 216 image patches, thereby producing a 16-fold reduction in computational resources). Thus, by minimizing the number of initial location-error determinations to a subset of image patches followed by applying the location-error determinations to corresponding image patches in a grid, the location-error-prediction system conserves computational resources when determining more accurate locations of clusters of oligonucleotides within the image patches relative to existing sequencing systems.

[0048] In addition to the computer processing preserved by such a subsampled approach, in some implementations, the location-error-prediction system preserves computational resources by sharing Fast Fourier Transform (FFT) matrices between (i) focus estimation in a diagnostic for a sequencing device and (ii) determining adjusted oligonucleotide-cluster locations. In someAttorney Docket No. IP-2805-PCT 10 Patent Applicationembodiments of focus estimation, the location-error-prediction system determines full-width half max (FWHM) values based on FFT in which the location-error-prediction system generates the FFT matrices. In these or other embodiments, the grid of FWHM values (e.g., a 12 by 18 matrix) covers a whole tile image (e.g., an image depicting a tile of a flow cell). The location-error- prediction system can determine such FWHM values based on a subsampled image-patch grid used for determining location errors for oligonucleotide clusters via band-edge spectral regions. Indeed, because the location-error-prediction system utilizes the same subsampled image-patch grid and reuses the FFT matrices from focus estimation determination when determining the location errors of the clusters of oligonucleotides, location-error-prediction system can decrease the computational cost that would have been required to re-determine FFT matrices, thereby resulting in a negligible increase in computational cost. By avoiding the need to generate two sets of FFT matrices, the location-error-prediction system preserves significant computational resources.

[0049] As illustrated by the foregoing discussion, the present disclosure utilizes a variety of terms to describe features and advantages of the location-error-prediction system. Additional detail is now provided regarding the meaning of such terms. For example, as used herein, the term “sample” refers to a specimen, culture, or the like that is suspected of including a target nucleic acid. In some embodiments, the sample comprises DNA, ribonucleic acid (RNA), peptide nucleic acid (PNA), locked nucleic acid (LNA), chimeric or hybrid forms of nucleic acids as targets. The sample can likewise include any biological, clinical, surgical, agricultural-atmospheric, or aquaticbased specimen containing one or more nucleic acids. A sample also includes any isolated or extracted nucleic acid sample from an organism, such a genomic DNA, fresh-frozen, or formalin- fixed paraffin-embedded nucleic acid specimen. In some cases, accordingly, a sample can include a full genome or partial genome that is isolated or extracted (e.g., in whole or in part by a kit) from an organism and that is prepared to undergo sequencing or an assay in a sequencing device. A sample can be from a single individual, a collection of nucleic acid samples from genetically related members, nucleic acid samples from genetically unrelated members, nucleic acid samples (matched) from a single individual such as a tumor sample and normal tissue sample, or sample from a single source that contains two distinct forms of genetic material, such as maternal and fetal DNA obtained from a maternal subject, or the presence of contaminating bacterial DNA in a sample that contains plant or animal DNA. In some embodiments, the source of nucleic acid material can include nucleic acids obtained from a newborn, for example as typically used for newborn screening.

[0050] The sample can include high molecular weight material, such as genomic DNA (gDNA). The sample can include low molecular weight material such as nucleic acid molecules obtained from FFPE or archived DNA samples. In another implementation, low molecular weight materialAttorney Docket No. IP-2805-PCT 11 Patent Applicationincludes enzymatically or mechanically fragmented DNA. The sample can include cell-free circulating DNA. In some implementations, the sample can include nucleic acid molecules obtained from biopsies, tumors, scrapings, swabs, blood, mucus, urine, plasma, semen, hair, laser capture micro-dissections, surgical resections, and other clinical or laboratory obtained samples. In some implementations, the sample can be an epidemiological, agricultural, forensic, or pathogenic sample. In some implementations, the sample can include nucleic acid molecules obtained from an animal such as a human or mammalian source. In another implementation, the sample can include nucleic acid molecules obtained from a non-mammalian source such as a plant, bacteria, virus, or fungus. In some implementations, the source of the nucleic acid molecules may be an archived or extinct sample or species.

[0051] As further used herein, the term “sequencing run” refers to an iterative process on a sequencing device to determine a primary structure of nucleotide sequences from a sample (e.g., genomic sample). In particular, a sequencing run includes cycles of sequencing chemistry and imaging performed by a sequencing device (including an imaging device, such as a CCD or CMOS) that incorporate nucleobases into growing oligonucleotides to determine nucleotide reads from nucleotide sequences extracted from a sample (or other sequences within a library fragment) and seeded throughout a flow cell or other nucleotide-sample slide. In some cases, a sequencing run includes replicating oligonucleotides derived or extracted from one or more genomic samples seeded in clusters throughout a flow cell. Upon completing a sequencing run, a sequencing device can generate base-call data in a file, such as a binary base call (BCL) sequence file or a fast-all quality (FASTQ) file.

[0052] Relatedly, the term “sequencing cycle” (or “cycle”) refers to an iteration of adding or incorporating one or more nucleobases to one or more oligonucleotides representing or corresponding to a sample’s sequence (e.g., a genomic or transcriptomic sequence from a sample) or a corresponding adapter sequence. In some cases, a sequencing cycle includes an iteration of both incorporating nucleobases into clusters of oligonucleotides using sequencing chemistry and capturing images of such clusters attached to a nucleotide-sample slide (e.g., a flow cell). Accordingly, cycles can be repeated as part of sequencing a nucleic-acid polymer (e.g., a sample genomic sequence). For example, in one or more embodiments, each sequencing cycle involves incorporating nucleobases into either a single nucleotide read in which DNA or RNA strands are read in only a single direction or paired-end reads in which DNA or RNA strands are read from both ends but in different cycles. Further, in certain cases, each sequencing cycle involves a camera taking an image of the nucleotide-sample slide or multiple sections of the nucleotide-sample slide to generate image data for determining a particular nucleobase added or incorporated into particular oligonucleotides. Following the image capture stage, a sequencing system can remove certainAttorney Docket No. IP-2805-PCT 12 Patent Applicationfluorescent labels from incorporated nucleobases and perform another sequencing cycle until the nucleic-acid polymer has been completely sequenced. In one or more embodiments, a sequencing cycle includes a cycle within an SBS run. A sequencing cycle can include one or both of an indexing cycle and a genomic sequencing cycle. For instance, one cluster of oligonucleotides or a set of clusters of oligonucleotides may be undergoing a genomic sequencing cycle in which nucleobases corresponding to a sample genomic sequence are incorporated and another cluster of oligonucleotides or another set of clusters of oligonucleotides may be concurrently undergoing an indexing cycle in which nucleobases corresponding to an indexing sequence for a nucleotide read are incorporated.

[0053] Further, as used herein, the term “nucleotide-sample slide” (or “nucleotide-sample substrate”) refers to a plate or substrate, such as a flow cell, comprising oligonucleotides for sequencing nucleotide sequences from genomic samples or other sample nucleic-acid polymers. In particular, a nucleotide-sample slide can refer to a substrate containing fluidic channels through which reagents and buffers can travel as part of sequencing. For example, in one or more embodiments, a flow cell (e.g., a patterned flow cell or non-pattemed flow cell) may comprise small fluidic channels and oligonucleotide samples that can be bound to adapter sequences on the substrate. In other implementations, a nucleotide-sample slide can be an open substrate with one or more regions for oligonucleotide samples to be analyzed and the oligonucleotide samples may be positioned using charged pads or other means. In yet another implementation, the nucleotide- sample slide can be a membrane having a nanopore through which one or more oligonucleotide samples may pass.

[0054] Relatedly, as used herein, the term “region of a nucleotide-sample slide” (or “nucleotide- sample slide region”) refers to an area that is part of a nucleotide-sample slide. In particular, a region of a nucleotide-sample slide can refer to a discrete portion of a nucleotide-sample slide that differs from other portions of the nucleotide-sample slide. For instance, a region of a nucleotide- sample slide can include a subsection of patterned flow cell comprising one or more wells (e.g., a nano-wells) or a discrete subsection of a non-pattered flow cell (e.g., a subsection corresponding to one or more clusters). In some cases, a region (e.g., section) of a nucleotide-sample slide includes a tile or a sub-tile of a flow cell having clusters of oligonucleotides growing in parallel.

[0055] Moreover, as used herein, the term “cluster of oligonucleotides” (or “cluster” or “oligonucleotide cluster”) refers to a localized group or collection of DNA or RNA molecules on a nucleotide-sample slide, such as a flow cell, or other solid surface. In particular, a cluster includes tens, hundreds, thousands, or more copies of a cloned or the same DNA or RNA segment. For example, in one or more embodiments, a cluster includes a grouping of oligonucleotides immobilized in a section of a flow cell or other nucleotide-sample slide. In some embodiments,Attorney Docket No. IP-2805-PCT 13 Patent Applicationclusters are evenly spaced or organized in a systematic structure within a patterned flow cell. By contrast, in some cases, clusters are randomly organized within a non-pattemed flow cell. A cluster of oligonucleotides can be imaged utilizing one or more light signals. For instance, an oligonucleotide-cluster image may be captured by a camera during a sequencing cycle of light emitted by irradiated fluorescent tags incorporated into oligonucleotides from one or more clusters on a flow cell.

[0056] As further used herein, the term “base call” (or “nucleobase call”) refers to a determination or prediction of a particular nucleobase (or nucleobase pair) for an oligonucleotide (e.g., nucleotide read) during a sequencing cycle or for a genomic coordinate of a genomic sample. In particular, a base call can indicate a determination or prediction of the type of nucleobase that has been incorporated within an oligonucleotide on a nucleotide-sample slide (e.g., read-based nucleobase calls). In some cases, for a nucleotide read, a base call includes a determination or a prediction of a nucleobase based on intensity values resulting from fluorescent-tagged nucleotides added to an oligonucleotide of a nucleotide-sample slide (e.g., in a cluster of a flow cell). As suggested above, a single base call can be an adenine (A) call, a cytosine (C) call, a guanine (G) call, a thymine (T) call, or an uracil (U) call. Note that the terms nucleobase and nucleotide base are interchangeable.

[0057] Furthermore, as used herein the term “signal” refers to a signal emitted, reflected, or otherwise communicated from a labeled nucleotide base or a group of labeled nucleotide bases (e.g., labeled nucleotide bases added to a cluster of oligonucleotides). In particular, a signal can refer to a signal indicating the type of base. For example, a signal can include a light signal emitted or reflected from a fluorescent tag of a nucleotide base or fluorescent tags of multiple nucleotide bases incorporated into oligonucleotides. In some implementations, the location-error-prediction system triggers the signal through an external stimulus, such as a laser or other light source. In some cases, the location-error-prediction system triggers the signal through some internal stimuli. Further, in some embodiments, location-error-prediction system observes the signal using a filter applied when capturing an image of the nucleotide-sample slide (e.g., region or section of the nucleotide-sample slide). As suggested above, in certain instances, a signal includes an aggregate of the signals provided by each labeled nucleotide base added to individual oligonucleotides in a cluster of oligonucleotides.

[0058] Additionally, as used herein, the term “intensity value” refers to a value indicating a characteristic or attribute of a signal emitted, reflected, or otherwise communicated from a labeled nucleobase or a group of labeled nucleobases from a cluster of oligonucleotides. In particular, an intensity value can refer to a value associated with a color intensity (e.g., wavelength) or a light intensity (e.g., brightness). In some cases, the location-error-prediction system captures severalAttorney Docket No. IP-2805-PCT 14 Patent Applicationimages of a cluster of oligonucleotides with labeled nucleobases using different channels. Thus, an intensity value of a signal can correspond to the intensity of the signal as observed through a particular channel. In one or more embodiments, the intensity value is a measured degree of intensity for a cluster of oligonucleotides at the predicted location, and the location-error-prediction system can accordingly be applied to 16 quadrature amplitude modulation (QAM) modulation or pulse amplitude modulation (PAM) 4 modulation (e.g., using amplitude to encode base-call information).

[0059] Further, as used herein, the term “channel” refers to a range or fdter of light, intensity, or color used to detect and / or measure a signal from a cluster of oligonucleotides. For example, a channel can include a particular range of light, intensity, or color of a laser used to illicit a fluorescent signal from fluorescent tags on nucleobases incorporated into oligonucleotides within a cluster. In some embodiments, the location-error-prediction system utilizes a two-channel implementation by, for instance, using two different ranges of light, intensities, or colors to illicit signals from clusters per sequencing cycle and capturing two corresponding images of a region of a nucleotide-sample slide per sequencing cycle. The first and second images can capture the intensity values of the emitted signal from the clusters that correspond to first and second light ranges. In some embodiments, the location-error-prediction system can utilize a single channel implementation, three-channel implementation, or four-channel implementation.

[0060] As further used herein, the term “spatial frequency band” refers to a range of frequencies in a frequency domain across space of an image. For example, the spatial frequency band can include a range of frequencies in the frequency domain across a space (e.g., x and / or y directions) of an image transformed from the spatial domain to the frequency domain via a transformation operation, such as a Fourier Transform operation. To illustrate, a transformed digital image of signals emitted from clusters of oligonucleotides represents the frequency component of the signals and the spatial frequency band includes the range of frequencies that can be captured by the cameras of the sequencing device. Because the terms frequency domain and spectral domain can be used interchangeably, the term “spatial frequency band” can alternatively be expressed as “spatial spectral band” and, as explained below, is the relevant band comprising a band-edge spectral region.

[0061] Relatedly, as used herein, the term “band-edge spectral region” refers to an edge portion or outer section of a spatial frequency band. For example, a band-edge spectral region can include the portion or outer section of the spatial frequency band that contains repeated frequency information due to excess bandwidth capability of cameras used to capture the image. To illustrate, an image transformed from a spatial domain to a frequency domain can include frequency information at an edge of the transformed image that is repeated at an opposite edge of the image.Attorney Docket No. IP-2805-PCT 15 Patent ApplicationThus, a band-edge spectral region can include an edge portion of the transformed image that has frequency information repeated in a second and opposite edge portion of the transformed image.

[0062] As used herein, the term “phase” refers to an angular component for a feature in a transformed image. For example, a phase can include an angular component of a waveform (e.g., sinusoidal wave) representing a feature, such as a point, pattern or texture, relative to an origin. When a digital image has undergone a Fourier Transform, the phase can represent an angular component of a specific feature within the Fourier-transformed image. In some cases, the phase of a complex number a + bj can be represented as an angle, measured in radians, from a point 1 + 0j to a + bj, with counterclockwise denoting positive angle. In such cases, the phase can also be referred to as an angle or argument in mathematical terms. In the foregoing example, the phase is the angle between the positive real axis and the line joining the origin and the complex number a + bj. As depicted herein in FIGS. 4A - 6 and according to some embodiments, a color represents a relevant feature for the phase of a nucleotide-sample-slide region image.

[0063] Relatedly, as used herein, the term “phase difference” refers to a variation in phase between corresponding frequency components of a transformed image. For instance, in some cases, a phase difference indicates a disparity in the phases of frequencies in a pair of band-edge spectral regions. To illustrate, the location-error-prediction system can utilize a complex number to represent a phase of frequency components of each band-edge spectral region in a pair to determine a phase angle representing the phase difference between the pair of band-edge spectral regions. Accordingly, a phase angle is an example of and can be synonymous with a phase difference. Accordingly, a phase angle includes an angular component of a complex number representing a frequency in a transformed domain. For example, a phase angle indicates the position of a waveform relative to a reference point or the zero crossing in time or space, typically measured in degrees or radians. To illustrate, the phase angle of a particular band-edge spectral region (or combination of band-edge spectral regions) reveals information about the spatial alignment and periodic features of the image, with changes in phase angle corresponding to shifts or translations in the spatial domain. As explained further below with respect to FIGS. 8A-8B and other embodiments, the location-error-prediction system can determine a phase angle measuring a phase difference between a pair of band-edge spectral regions using a complex number representing one of the band-edge spectral regions and a conjugate of the complex number representing the other band-edge spectral region in the pair.

[0064] Additionally, as used herein, the term “location” refers to a specific position on a nucleotide-sample slide. In particular, a location can include coordinates on a nucleotide-sample slide where clusters of oligonucleotides are attached to the nucleotide-sample slide. In some embodiments, the location-error-prediction system can determine an error for a location (i.e.,Attorney Docket No. IP-2805-PCT 16 Patent Applicationlocation error) that estimates a distance by which a predicted location of a cluster of oligonucleotides deviates from a true or expected location of a cluster of oligonucleotides, e.g., a nano well location in the flow cell where a cluster of oligonucleotides grow. For example, the location-error-prediction system can determine or measure location error in terms of pixels (e.g., x error = 0.246 pixels or y error = 0.154 pixels). In some implementations, the location-error- prediction system can determine or measure the location error in terms of other metrics, such as angstroms, nanometers, micrometers, etc. Because a patterned or non-pattemed nucleotide-sample slide can include wells or nano wells comprising oligonucleotide clusters, this disclosure sometimes refers to a well location as an example of an oligonucleotide-cluster location.

[0065] Further, the term “predicted location,” as used herein, refers to an approximated position of a cluster of oligonucleotides on a nucleotide-sample slide. For instance, the location-error- prediction system can receive an image of a signal of a cluster of oligonucleotides and, based on pixels of the image showing a signal of incorporated nucleobases, determine a predicted location of the cluster. For example, in some embodiments, the location-error-prediction system can determine the predicted location of the cluster by processing the image of the signal and utilizing location models on the processed image. Relatedly, as used herein, the term “adjusted location” refers to a predicted location of a cluster of oligonucleotides adjusted by a location error. For example, the location-error-prediction system can determine a location error in at least one direction of a predicted location of a cluster of oligonucleotides and modify the predicted location using the location error to determine an adjusted location of the cluster of oligonucleotides. As indicated above, the location error can account or reflect a single direction (e.g., an x direction or ay direction) or multiple directions (e.g., an x direction and ay direction).

[0066] Moreover, as used herein, the term “jitter” (or “location jitter”) refers to positional variations, deviations, and / or drift from the actual location of a cluster on the nucleotide-sample slide during sequencing. For example, movement of the nucleotide-sample slide, parts of the sequencer, and / or imaging path can cause location jitter. Location jitter is further described and addressed in U.S. Application No. 18 / 405,320, entitled, “Jitter Correction Image Analysis,” (IP- 2499-US), fded Jan. 5, 2024, and U.S. Provisional Application No. 63 / 587,001, entitled “Tracking and Modifying Cluster Location on Nucleotide-Sample Slides in Real Time,” (IP-2619-PRV), fded Sept. 29, 2023, which are hereby incorporated by reference in their entirety.

[0067] Furthermore, as used herein, the term “optical distortion” refers to a deviation in a captured image resulting from the optics of a sensor. For example, optical distortion includes deviations from the true or original spatial arrangement of clusters of oligonucleotides on a nucleotide-sample slide caused by optics of a camera associated with a sequencing device. ToAttorney Docket No. IP-2805-PCT 17 Patent Applicationillustrate, optical distortion includes the discrepancies in the locations of clusters of oligonucleotides introduced during the imaging process.

[0068] As used herein, the term “smoothing model” refers to a model designed to reduce noise. In particular, a smoothing model mitigates fluctuations or outliers in location errors or in signal and / or image data. For instance, a smoothing model may employ various methods to filter values across signal or image data, such as a median filter, a Gaussian filter, a mean filter, a bilateral filter, etc. As described further below, a smoothing model can mitigate fluctuations or outliers in location errors determined across different subsections of an image (e.g., location errors across image patches).

[0069] Additionally, as used herein, the term “image-patch grid” refers to a grid for segmenting an image of a nucleotide-sample slide. For example, an image-patch grid includes grid cells that can align with and contain portions of an image of a nucleotide-sample slide. As described below, the location-error-prediction system can overlay a grid on an image of a nucleotide-sample slide and segment portions of the image, such as image patches, to assign and demarcate a portion of the image in each grid cell. Further, an image-patch grid can include a full-resolution image-patch grid or a subsampled image-patch grid. For example, a full-resolution image-patch grid can include an image-patch grid for which the location-error-prediction system samples every grid cell (e.g., to determine a location error for each grid cell). Relatedly, the term “subsampled image-patch grid” refers to an image-patch grid for which a subset of the grid cells has been sampled from a larger or more granular image-patch grid. Such a subset of grid cells can be referred to as subsampled grid cells. As illustrated below, a subsampled image-patch grid can include various numbers of subsampled grid cells in various configurations.

[0070] Moreover, as used herein, the term “image patch” refers to a portion of a digital image of a nucleotide-sample slide. For example, an image patch can include a subsection of an image of a nucleotide-sample slide from multiple subsections of the nucleotide-sample slide, such as a tile or a sub-tile. To illustrate, an image patch can include or be demarcated by a matrix of pixels that, in some cases, can be chosen by apower of 2 (e.g., 128 pixels by 128 pixels; 64 pixels by 64 pixels; 32 pixels by 32 pixels) to facilitate FFT. Accordingly, an image patch can include signals of up to hundreds or thousands of clusters of oligonucleotides; and an image can include tens, hundreds, or thousands of image patches.

[0071] Furthermore, as used herein, the term “jitter vector” refers to a series of numbers that estimates jitter or compensates for jitter in an image. For example, ajitter vector includes a series of numbers that quantifies the effects of jitter on oligonucleotide clusters in a particular direction (e.g., a y direction) with respect to a nucleotide-sample slide. Ajitter vector can be determined with or without reference to grid cells of an image-patch grid. When such a grid is used, however, ajitterAttorney Docket No. IP-2805-PCT 18 Patent Applicationvector can be determined based on location errors of subsampled grid cells of a subsampled imagepatch grid applied to an image of the nucleotide-sample slide. For example, in some cases, the location-error-prediction system determines grid cell-specific location errors of the subsampled grid cells based on a phase difference between pairs of band-edge spectral regions for an image patch within each subsampled grid cell. The location-error-prediction system can further utilize the jitter vector when determining location errors for the grid cells of a full-resolution grid applied to the image of the nucleotide-sample slide.

[0072] Additionally, as used herein, the term “optical distortion vector” refers to a series of numbers that estimates optical distortion or compensates for optical distortion in an image. For example, an optical distortion vector includes a series of numbers that quantifies the effects of optical distortion on oligonucleotide clusters in a particular direction (e.g., an x direction) with respect to a nucleotide-sample slide. An optical distortion vector can be determined with or without reference to grid cells of an image-patch grid. When such a grid is used, however, an optical distortion vector can be determined based on location errors of subsampled grid cells of a subsampled image-patch grid applied to an image of the nucleotide-sample slide. For example, in some cases, the location-error-prediction system determines grid cell-specific location errors of the subsampled grid cells based on a phase difference between pairs of band-edge spectral regions for an image patch within each subsampled grid cell. The location-error-prediction system can further utilize the optical distortion vector when determining location errors for the grid cells of a fullresolution grid applied to the image of the nucleotide-sample slide.

[0073] Further, as used herein, the term “equalizer” refers to a model or system that can use a function to convert dispersed energy of a response signal into values representing one or more estimated response signals from one or more clusters of oligonucleotides and / or reduce noise that is part of such a response signal. In particular, an equalizer includes a model that converts received dispersed-over-pixels intensity energy (e.g., signal values) into an intensity value representing light emitted from an oligonucleotide cluster and intensity values for adjacent oligonucleotide clusters by linearly weighting pixel intensities and / or energy. For example, in some cases, the equalizer receives an input image and gathers signal values (e.g., light energy) across pixels in the image and converts the energy to an intensity value for one or more oligonucleotide clusters during a sequencing cycle in a channel. In some embodiments, the equalizer utilizes equalizer coefficients (e.g., an image matrix comprising equalizer coefficients) to increase or maximize the signal-to- noise ratio of the intensity data by weighting signal values depicted in the image to determine a weighted sum of the signal values of the pixels. Accordingly, in one or more embodiments, the equalizer can combine the signal values from one or more oligonucleotide clusters to increase or maximize one or more signal values of a target oligonucleotide cluster and minimize the signalAttorney Docket No. IP-2805-PCT 19 Patent Applicationvalues (e.g., crosstalk) from adjacent oligonucleotide clusters while accounting for the amplified noise in a sequencing device. In some embodiments, the equalizer is a linear equalizer that utilizes a linear filter that can be designed or optimized to filter out noise. In some embodiments, the linear filter can be applied to each cluster individually or across an entire image. In one or more embodiments, the equalizer can utilize different equalizer coefficients for different channels.

[0074] Relatedly, as used herein, the term “equalizer coefficients” refers to weights or values applied to an image of oligonucleotide clusters that adjust for (or reduce) noise from adjacent oligonucleotide clusters and / or the optical distortion and / or dispersion effects of a transmission medium. Accordingly, an equalizer coefficient can include a weighted value that, when applied to an image of oligonucleotide clusters, adjusts for inter-symbol interference (e.g., crosstalk) of one cluster of oligonucleotides on a target oligonucleotide cluster. For example, in one or more embodiments, the equalizer coefficients apply weighted values to the image to measure one or more signal values of the target oligonucleotide cluster while minimizing the signal values of the neighboring oligonucleotide clusters. As a further example, the equalizer coefficients can represent an equalizer response that, when applied to one or more signal values, generates an estimated response signal (e.g., output) that mimics the estimated response signal (input) by mitigating or reversing the effects of an imaging device on the expected response signal while capturing an image of the expected response signal. In one or more embodiments, the location-error-prediction system utilizes an equalizer to apply equalizer coefficients to an image with pixels that represent one or more signal values from one or more clusters of oligonucleotides.

[0075] The following paragraphs describe a location-error-prediction system with respect to illustrative figures that portray example embodiments and implementations. For example, FIG. 1 illustrates a schematic diagram of a computing system 100 in which a location-error-prediction system 106 operates in accordance with one or more embodiments. As illustrated, the computing system 100 includes a sequencing device 102 connected to a local device 108 (e.g., a local server device), one or more server device(s) 110, and a client device 114. As shown in FIG. 1, the sequencing device 102, the local device 108, the server device(s) 110, and the client device 114 can communicate with each other via a network 118. The network 118 comprises any suitable network over which computing devices can communicate. Example networks are discussed in additional detail below with respect to FIG. 19. While FIG. 1 shows an embodiment of the location- error-prediction system 106, this disclosure describes alternative embodiments and configurations below.

[0076] As indicated by FIG. 1, the sequencing device 102 comprises a computing device and a sequencing device system 104 for sequencing a genomic sample or other nucleic-acid polymer. In some embodiments, by executing the sequencing device system 104 using a processor, theAttorney Docket No. IP-2805-PCT 20 Patent Applicationsequencing device 102 analyzes nucleotide fragments or oligonucleotides extracted from genomic samples to generate nucleotide reads or other data utilizing computer implemented methods and systems either directly or indirectly on the sequencing device 102. More particularly, the sequencing device 102 receives nucleotide-sample slides (e.g., flow cells) comprising nucleotide fragments (e.g., genomic DNA fragments) extracted from samples and further copies and determines the nucleobase sequence of such extracted nucleotide fragments.

[0077] In one or more embodiments, the sequencing device 102 utilizes SBS to sequence nucleotide fragments into nucleotide reads and determine nucleobase calls for the nucleotide reads. In addition or in the alternative to communicating across the network 118, in some embodiments, the sequencing device 102 bypasses the network 118 and communicates directly with the local device 108 or the client device 114. By executing the sequencing device system 104, the sequencing device 102 can further store the nucleobase calls as part of base-call data that is formatted as a binary base call (BCL) file or a fast-all quality (FASTQ) file and send the BCL file or FASTQ file to the local device 108 and / or the server device(s) 110.

[0078] As further indicated by FIG. 1, the local device 108 is located at or near a same physical location of the sequencing device 102. Indeed, in some embodiments, the local device 108 and the sequencing device 102 are integrated into a same computing device. The local device 108 may run the location-error-prediction system 106 to generate, receive, analyze, store, and transmit digital data, such as by receiving signals of cluster of oligonucleotides and / or base-call data or determining base calls based on analyzing such signals and / or base call data. The location-error-prediction system 106 operates / exists on the sequencing device 102. As indicated by the dashed lines encompassing the location-error-prediction system 106, the location-error-prediction system 106 can alternatively operate / exist on the local device 108, the server device(s) 110, and / or the client device 114. As shown in FIG. 1, the sequencing device 102 may send (and the local device 108 may receive) base-call data generated during a sequencing run of the sequencing device 102. By executing software in the form of the location-error-prediction system 106, the local device 108 may identify pairs of band-edge spectral regions from a spatial frequency band in an oligonucleotide-cl uster image, determine a phase difference between respective pairs of band-edge spectral regions, determine adjusted locations of clusters of oligonucleotides, and generate base calls for the clusters of oligonucleotides based on the adjusted locations.

[0079] As further indicated by FIG. 1, the server device(s) 110 are located remotely from the local device 108 and the sequencing device 102. Similar to the local device 108, in some embodiments, the server device(s) 110 include a version of the location-error-prediction system 106 as part of a sequencing system 112. Accordingly, the server device(s) 110 may generate, receive, analyze, store, and transmit digital data, such as by receiving base-call data, quality data,Attorney Docket No. IP-2805-PCT 21 Patent Applicationand other data relevant to sequencing nucleic-acid polymers. As indicated above, the sequencing device 102 may send (and the server device(s) 110 may receive) base-call data from the sequencing device 102. The server device(s) 110 may also communicate with the client device 114. In particular, the server device(s) 110 can send data to the client device 114, including read data, nucleic-acid polymer sequences, error data, and other sequencing related information.

[0080] In some embodiments, the server device(s) 110 comprise a distributed collection of servers where the server device(s) 110 include a number of server devices distributed across the network 118 and located in the same or different physical locations. Further, the server device(s) 110 can comprise a content server, an application server, a communication server, a web-hosting server, or another type of server.

[0081] As further illustrated and indicated in FIG. 1, by executing a sequencing application 116, the client device 114 can generate, store, receive, and / or send digital data. In particular, the client device 114 can receive sequencing data from the local device 108 or receive call fdes (e.g., BCL, FASTQ) and sequencing metrics from the sequencing device 102. Furthermore, the client device 114 may communicate with the local device 108 or the server device(s) 110 to receive nucleobase calls and / or other metrics, such as a base-call-quality metrics or pass-filter metrics. The client device 114 can accordingly present or display information pertaining to nucleobase calls within a graphical user interface of the sequencing application 116 to a user associated with the client device 114. For example, the client device 114 can present nucleic acid sequences, structural variant calls, and / or sequencing metrics for a sequenced genomic sample within a graphical user interface of the sequencing application 116.

[0082] Although FIG. 1 depicts the client device 114 as a desktop or laptop computer, the client device 114 may comprise various types of client devices. For example, in some embodiments, the client device 114 includes non-mobile devices, such as desktop computers or servers, or other types of client devices. In yet other embodiments, the client device 114 includes mobile devices, such as laptops, tablets, mobile telephones, or smartphones. Additional details regarding the client device 114 are discussed below with respect to FIG. 19.

[0083] As further illustrated in FIG. 1, the client device 114 includes the sequencing application 116. The sequencing application 116 may be a web application or a native application stored and executed on the client device 114 (e.g., a mobile application, desktop application). The sequencing application 116 can include instructions that (when executed) cause the client device 114 to receive data from the location-error-prediction system 106 and present, for display at the client device 114, base-call data from, for instance, a BCL or FASTQ file.

[0084] As further illustrated in FIG. 1, a version of the location-error-prediction system 106 may be located and implemented (e.g., entirely or in part) on the client device 114 or the sequencingAttorney Docket No. IP-2805-PCT 22 Patent Applicationdevice 102. In yet other embodiments, the location-error-prediction system 106 is implemented by one or more other components of the computing system 100, such as the local device 108. In particular, the location-error-prediction system 106 can be implemented in a variety of different ways across the sequencing device 102, the local device 108, the server device(s) 110, and the client device 114. For example, the location-error-prediction system 106 can be downloaded from the server device(s) 110 to the sequencing device system 104 and / or the local device 108 where all or part of the functionality of the location-error-prediction system 106 is performed at each respective device within the computing system 100.

[0085] As mentioned above, the location-error-prediction system 106 can adjust predicted locations of clusters of oligonucleotides by correcting for jitter and optical distortion. FIG. 2 illustrates a diagram showing the effects of jitter and optical distortion on locations of clusters of oligonucleotides in accordance with one or more embodiments. As indicated above, such jitter can represent local linear drift or linear positional changes of oligonucleotide clusters. Further, such optical distortion can include non-linear deviations in an image resulting from an optical lens.

[0086] As illustrated in FIG. 2, a total error (e.g., a total location error) can include a jitter error and an optical distortion error. Specifically, in some implementations, the location-error-prediction system 106 can determine a total error by summing the jitter error and the optical distortion error. Such jitter and optical distortion can be caused by different aspects of a sequencing device. As a sequencing device progresses through sequencing cycles of a sequencing run and a stage on the sequencing device moves, for instance, a sequencing device can cause jitter error. Indeed, by running sequencing cycles, a sequencing device inherently includes movement / vibration of the stage, which cannot be completely eliminated, resulting in location errors when predicting locations of the clusters of oligonucleotides. In addition to such jitter, optics of the cameras of a sequencing device cause optical distortion error. For example, optical distortions in sequencing-cycle images of a region of a nucleotide-sample slide result from the geometry of the lens used to acquire the images. As described further below, the location-error-prediction system demonstrates, and researchers determined, that jitter error can vary as a function of y along a y-axis and optical distortion error can vary as a function of x along an x-axis, as described in greater detail in FIG. 7.

[0087] As further illustrated in FIG. 2, a location-jitter diagram 202 illustrates the effects of jitter on clusters of oligonucleotides in a portion of an image of a nucleotide-sample slide. Specifically, the location-jitter diagram 202 illustrates vectors representing location errors of clusters of oligonucleotides resulting from jitter. For example, each arrow of location-jitter diagram 202 portrays a vector representing the location error of the corresponding cluster of oligonucleotides at a corresponding location on the nucleotide-sample slide. As mentioned, while jitter error varies as a function of y, location errors for the predicted locations of the clusters ofAttorney Docket No. IP-2805-PCT 23 Patent Applicationoligonucleotides resulting from jitter can include both an x component and a y component, as shown in the location-jitter diagram 202.

[0088] As additionally shown in FIG. 2, an optical distortion diagram 204 illustrates the effects of optical distortion on the clusters of oligonucleotides in the portion of the image of a nucleotide- sample slide. Specifically, the optical distortion diagram 204 illustrates vectors representing location errors of the clusters of oligonucleotides resulting from optical distortion. For example, each arrow of the optical distortion diagram 204 portrays a vector representing the location error of the corresponding cluster of oligonucleotides at that location on the nucleotide-sample slide. As mentioned, while optical distortion varies as a function of x, location errors for the predicted locations of the clusters of oligonucleotides resulting from optical distortion can include both an x component and a y component, as shown in the optical distortion diagram 204.

[0089] As further illustrated in FIG. 2, a total location-error diagram 206 represents the total error of predicted locations of the clusters of oligonucleotides due to both jitter error and optical distortion error. In particular, the total location-error diagram 206 illustrates vectors representing the total location errors of the clusters of oligonucleotides based on the sum of the jitter error and the optical distortion error. For example, each arrow of the total location-error diagram 206 portrays a vector representing the location error of the corresponding cluster of oligonucleotides at that location on the nucleotide-sample slide. As shown, the total location error of the clusters of oligonucleotides on the nucleotide-sample slide can vary widely in both direction and magnitude.

[0090] As also indicated by FIG. 2, various problems arise because of the total location error in the predicted locations of the clusters of oligonucleotides. For instance, the location errors in the predicted locations result in a reduced number of oligonucleotide clusters or nucleotide reads that pass filter (PF). For example, location errors can cause existing sequencing systems to measure a reduced intensity of the signal of a cluster of oligonucleotides, which can result in the cluster of oligonucleotides failing to pass filter, as described in more detail below with respect to FIG. 15 A. Moreover, the predicted location errors result in a reduced percentage of base calls or nucleotide reads that satisfy a threshold quality score (e.g., as measured by % Q30 or percentage that satisfy a Q-score of 30), as discussed in more detail with respect to FIG. 15B.

[0091] In addition to reduced clusters or reads passing filter or satisfying quality-score thresholds, in one or more embodiments, the errors in the predicted locations of the clusters of oligonucleotides vary across sequencing instruments or sequencing devices. This variation across instruments reduces the effectiveness of location-error correction models employed in existing sequencing systems. In contrast, as described in further detail below, the location-error-prediction system 106 can determine adjusted locations of the clusters of oligonucleotides to correct forAttorney Docket No. IP-2805-PCT 24 Patent Applicationlocation errors resulting from jitter and optical distortion — independent of the type of sequencing instrument or sequencing device being used.

[0092] As just mentioned, in one or more implementations, the location-error-prediction system 106 determines adjusted locations of the clusters of oligonucleotides to correct for location errors, such as those resulting from jitter and optical distortion. For example, in accordance with one or more embodiments, FIG. 3 illustrates an overview of the location-error-prediction system 106 determining a phase difference between a pair of band-edge spectral regions, adjusting a predicted location of a cluster of oligonucleotides based on the phase difference, and determining a base call for the cluster of oligonucleotides based on the adjusted location.

[0093] As shown in FIG. 3, in some embodiments, the location-error-prediction system 106 performs an act 302 of identifying a pair of band-edge spectral regions within an image. Specifically, for a given sequencing cycle, the location-error-prediction system 106 can identify one or more pairs of band-edge spectral regions from a spatial frequency band within an image depicting signals of clusters of oligonucleotides at predicted locations within a nucleotide-sample slide. For example, the location-error-prediction system 106 can identify the pair of band-edge spectral regions from an image of a subdivision of a nucleotide-sample slide, such as an image patch depicting a tile or sub-tile of the nucleotide-sample slide. As shown in FIG. 3, in some implementations, the location-error-prediction system 106 can identify a pair of band-edge spectral regions Al and Bl from a spatial frequency band of an image patch and / or a pair of band-edge spectral regions A2 and B2 from a spatial frequency band of an image patch.

[0094] As further illustrated in FIG. 3, in one or more embodiments, the location-error- prediction system 106 performs an act 304 of determining a phase difference between the pair of band-edge spectral regions. In particular, the location-error-prediction system 106 can determine a phase difference in the frequencies of repetitive signals in the pair of band-edge spectral regions. Because the pair of band-edge spectral regions Al and Bl include the same signal information at different phases, for example, the location-error-prediction system 106 can determine a phase difference between this repetitive signal information. To illustrate, the location-error-prediction system 106 can utilize the first band-edge spectral region Al and a conjugate of the second bandedge spectral region Bl to determine a phase angle, as described in more detail with respect to FIG. 8B. The location-error-prediction system 106 can similarly determine a phase angle based on a first band-edge spectral region A2 and a conjugate of a second band-edge spectral region B2.

[0095] After determining a phase difference and as further shown in FIG. 3, in one or more implementations, the location-error-prediction system 106 performs an act 306 of generating at least one location error based on the phase difference. As indicated above, the location-error- prediction system 106 can generate a location error in one or more directions. For example, theAttorney Docket No. IP-2805-PCT 25 Patent Applicationlocation-error-prediction system 106 can determine the location error based on the phase difference between the pair of band-edge spectral regions Al and Bl and / or the phase difference between pair of band-edge spectral regions A2 and B2. Based on the phase difference(s), the location-error- prediction system 106 generates the location error. As shown in FIG. 3, for example, a vector 307 represents a distance (or magnitude) and a direction of such a location error for one or more clusters depicted by an image of a nucleotide-sample-slide region. As illustrated, the vector 307 can represent an optical distortion error in an x direction; but additional and alternative location errors are described below.

[0096] As further indicated by FIG. 3, in some embodiments, the location-error-prediction system 106 can determine the location error based on phase differences between multiple pairs of band-edge spectral regions. For example, the location-error-prediction system 106 can determine the location error from pairs of band-edge spectral regions according to a geometric layout of the clusters of oligonucleotides on a nucleotide-sample slide. Examples of different pairs of band-edge spectral regions and geometric layouts (e.g., hexagon, diamond, square) are described in further detail below with respect to FIGS. 4A-6.

[0097] After determining a location error and as further illustrated in FIG. 3, in some implementations, the location-error-prediction system 106 performs an act 308 of determining an adjusted location of at least one cluster of oligonucleotides. In particular, the location-error- prediction system 106 utilizes the at least one location error to determine the adjusted location of the clusters of oligonucleotides in the image. To illustrate, the location-error-prediction system 106 utilizes the location error (e.g., as illustrated by the vector 307) to determine an adjusted location 312 of the cluster of oligonucleotides from a predicted location 310 of the cluster of oligonucleotides as described in further detail with respect to FIG. 9B.

[0098] As also depicted in FIG. 3, in one or more embodiments, the location-error-prediction system 106 performs an act 314 of determining base call(s) for the at least one cluster of oligonucleotides. For instance, the location-error-prediction system 106 determines a base call for a cluster of oligonucleotides based on the adjusted location 312 of the cluster of oligonucleotides and intensity values for signals of the cluster of oligonucleotides. To illustrate, in some cases, the location-error-prediction system 106 (i) determines respective nucleobase probabilities for the cluster of oligonucleotides based on comparing corresponding intensity values of the cluster of oligonucleotides at the adjusted location 312 to intensity-value base-decision boundaries (e.g., a Gaussian distribution with a centroid) and (ii) generates a base call for the cluster of oligonucleotides based on determining a highest nucleobase probability. Indeed, by utilizing the adjusted location 312, the location-error-prediction system 106 can more accurately determine base calls for the various clusters of oligonucleotides within the image as demonstrated in FIGS. 15 A-Attorney Docket No. IP-2805-PCT 26 Patent Application16, because intensity values of higher signal to noise ratios (SNRs) at the adjusted locations are obtained.

[0099] As noted above, in one or more implementations, the location-error-prediction system 106 identifies pairs of band-edge spectral regions according to a geometric layout for cluster locations of clusters of oligonucleotides on a nucleotide-sample slide. Indeed, in some embodiments, the location-error-prediction system 106 can identify pairs of band-edge spectral regions according to a hexagon shape, a diamond shape, a square shape, etc. in accordance with one or more embodiments, FIGS. 4A-4B, 5A-5B, and 6 illustrate the location-error-prediction system 106 identifying pairs of band-edge spectral regions according to a hexagon shape, a diamond shape, and a square shape, respectively.

[0100] As portrayed in FIG. 4A, for example, the location-error-prediction system 106 identifies band-edge spectral regions from a spatial frequency band within a transformed image 400 depicting signals of clusters of oligonucleotides at predicted locations within the nucleotide- sample slide. Specifically, the location-error-prediction system 106 utilizes a transformation model (e.g., 2D fast Fourier Transform) to transform a raw image from a spatial domain to a frequency domain in the transformed image 400 including a spatial frequency band. In these or other embodiments, the transformation model utilizes a transformation operation, such as a 2D Fourier Transform, to perform the transformation. As depicted in FIG. 4A, the transformed image 400 illustrates frequencies of signals emitted by the clusters of oligonucleotides as colored squares. For example, each colored square of the transformed image 400 can include one or more clusters of oligonucleotides. To illustrate, colored square 407 exhibits a darker shade of a color (e.g., dark blue) indicating that the corresponding area of the transformed image 400 (e.g., an image patch for a nucleotide-sample-slide subregion) exhibits a phase with a normalized frequency of 0.6, as indicated by a key 402.

[0101] As just referenced, FIG. 4 A includes the key 402 that serves as a visual guide for interpreting the signal frequencies of the clusters of oligonucleotides in the transformed image 400. Specifically, the key 402 uses a gradient of colors. This gradient visually represents the phase of the frequencies of the transformed image 400 normalized to within a range of [0, 1], where one gradient end color (e.g., cool shade of red) of the gradient represents a phase with a normalized frequency of 1, another gradient end color (e.g., warm shade of red) of the gradient represents a phase with a normalized frequency of 0, and intermediate colors of the gradient represent phases with normalized frequencies between 1 and 0. For example, intermediate colors include a first color (e.g., light red) for a normalized frequency of 0.9 on the key 402, a second color (e.g., violet) for a normalized frequency of 0.8, a third color (e.g., indigo) for a normalized frequency of 0.7, a fourth color (e.g., dark blue) for a normalized frequency of 0.6, a fifth color (e.g., light blue) for aAttorney Docket No. IP-2805-PCT 27 Patent Applicationnormalized frequency of 0.5, a sixth color (e.g., blue-green) for a normalized frequency of 0.4, a seventh color (e.g., green) for a normalized frequency of 0.3, an eighth color (e.g., yellow) for a normalized frequency of 0.2, and a ninth color (e.g., orange) for a normalized frequency of 0.1. Additionally, the transformed image 400 also represents the magnitude of the signal frequencies (e.g., the strength of each frequency in the signal) of the clusters of oligonucleotides with varying color intensities. For example, in the transformed image 400, lighter shaded colors exhibit weaker frequencies than darker shaded colors exhibiting stronger frequencies.

[0102] As further illustrated in FIG. 4A and as mentioned above, in one or more embodiments, the location-error-prediction system 106 identifies pairs of band-edge spectral regions (e.g., a set of pairs of band-edge spectral regions) within the spatial frequency band within the transformed image 400. In particular, the location-error-prediction system 106 identifies the pairs of band-edge spectral regions according to a geometric layout for the cluster locations of the clusters of oligonucleotides on the nucleotide-sample slide. In these or other embodiments, the location-error- prediction system 106 determines a layout of the clusters of oligonucleotides on the nucleotide- sample slide based on the type of nucleotide-sample slide used for a sequencing device.

[0103] For instance, in one or more implementations, the location-error-prediction system 106 determines that the layout of clusters of oligonucleotides within the imaged region of the nucleotide-sample slide follow a hexagon layout and, therefore, identifies the pairs of band-edge spectral regions according to a hexagon layout. To illustrate, the location-error-prediction system 106 identifies a set of pairs of band-edge spectral regions within the spatial frequency band according to a hexagon layout. In these or other embodiments, the location-error-prediction system 106 identifies a set of three pairs of band-edge spectral regions including a first pair 404 of bandedge spectral regions Al and Bl, a second pair 406 of band-edge spectral regions A2 and B2, and a third pair 408 of band-edge spectral regions A3 and B3.

[0104] As additionally shown in FIG. 4A, in some embodiments, the location-error-prediction system 106 identifies pairs 404, 406, and 408 of band-edge spectral regions within the edge (e.g., the outer edge) of the spatial frequency band. Because of excess bandwidth in the sequencingdevice cameras, the edge of the spatial frequency band includes redundant information that the location-error-prediction system 106 utilizes to identify the pairs 404, 406, and 408 of band-edge spectral regions. Specifically, the location-error-prediction system 106 identifies the pairs 404, 406, and 408 of band-edge spectral regions such that a second band-edge spectral region within a pair of band-edge spectral regions (e.g., Bl, B2, or B3) includes redundant frequency information relative to a first band-edge spectral region (e.g., Al, A2, or A3). Thus, in some implementations, the location-error-prediction system 106 can utilize the redundant frequency information toAttorney Docket No. IP-2805-PCT 28 Patent Applicationdetermine a phase difference between the pairs 404, 406, and 408 of band-edge spectral regions, as discussed in further detail below with respect to FIG. 8B.

[0105] In one or more embodiments, the location-error-prediction system 106 identifies pairs of band-edge spectral regions in a particular configuration relative to a hexagon shape and various axes. For example, the location-error-prediction system 106 can identify the pair of band-edge spectral regions such that the first pair 404 of band-edge spectral regions aligns on a vertical axis or y axis. In these or other embodiments, the location-error-prediction system 106 can identify the second pair 406 of band-edge spectral regions to align on an axis set at a 60-degree angle (or rc / 3 radians) relative to the first pair 404 of band-edge spectral regions; and identify the third pair 408 of band-edge spectral regions to align on an axis set at a 120-degree angle (or 2jr / 3 radians) relative to the first pair 404 of band-edge spectral regions.

[0106] By identifying pairs of band-edge spectral regions in a particular configuration relative to various axes, the location-error-prediction system 106 facilitates determining location errors in multiple directions along corresponding axes. In some embodiments, for instance, the location- error-prediction system 106 can determine a y direction component of a location error (or a y location error) using the first pair 404 of band-edge spectral regions, as described in further detail below. Similarly, in these or other embodiments, the location-error-prediction system 106 can determine x and y direction components of a location error using the second pair 406 of band-edge spectral regions and the third pair 408 of band-edge spectral regions. Further, in one or more implementations, the location-error-prediction system 106 can utilize the sum of the x and y direction components of the location error to determine a total location error with a specific direction and magnitude as discussed in further detail below. Moreover, in some embodiments, the location-error-prediction system 106 can identify the pairs of band-edge spectral regions according to a hexagon shape using different configurations by identifying pairs of band-edge spectral regions that align on different axes.

[0107] In addition to leveraging different axes and directions for location-error determinations, in some implementations, the location-error-prediction system 106 identifies pairs of band-edge spectral regions for images taken at each sequencing cycle and for each channel. For example, the location-error-prediction system 106 takes images at each sequencing cycle throughout a sequencing run. Additionally, in these or other embodiments, the location-error-prediction system 106 can identify the pairs of band-edge spectral regions for an image taken for each channel at each sequencing cycle to correct for location error caused by jitter and / or optical distortion as further described below.

[0108] In one or more embodiments, the location-error-prediction system 106 can also identify shape-simplified band-edge spectral regions to accelerate the processing time for determiningAttorney Docket No. IP-2805-PCT 29 Patent Applicationphase differences. In accordance with one or more embodiments, FIG. 4B illustrates the location- error-prediction system 106 identifying pairs of shape-simplified band-edge spectral regions with simplified orientations that have been adjusted from a hexagon shape or layout.

[0109] As depicted in FIG. 4B, in one or more implementations, the location-error-prediction system 106 identifies pairs of shape-simplified band-edge spectral regions (e.g., a set of pairs of band-edge spectral regions) within the spatial frequency band within a transformed image 410. In these or other embodiments, the location-error-prediction system 106 generates the transformed image 410 using similar methods to those for generating the transformed image 400. Accordingly, FIG. 4B includes a key 412 for the transformed image 410 that, like the key 402 in FIG. 4 A, uses a gradient of colors to indicate the magnitude of the location error as measured in pixels, wherein the first color (e.g., red) represents a phase of 1 or 0 and intermediate colors represent phase values between 1 and 0. Additionally, similar to the identification of band-edge spectral regions as described above with respect to FIG. 4A, the location-error-prediction system 106 identifies the simplified pairs of band-edge spectral regions according to a geometric layout of the cluster locations on the nucleotide-sample slide based on the type of nucleotide-sample slide. Rather than determining pairs of band-edge spectral regions according to a hexagonal shape as in FIG. 4A, however, the location-error-prediction system 106 can determine pairs of shape-simplified bandedge spectral regions.

[0110] To illustrate, the location-error-prediction system 106 identifies a set of pairs of shape- simplified band-edge spectral regions within the spatial frequency band such that the shape- simplified band-edge spectral regions have simpler geometric shapes and / or orientations relative to those in FIG. 4A. For example, rather than identifying rectangular shaped band-edge spectral regions with a diagonal orientation relative to the x andy directions of the transformed image 410 — such as band-edge spectral regions A2, B2, A3 and B3 within the transformed image 400 of FIG. 4A — the location-error-prediction system 106 identifies a rectangular (or square) shaped band-edge spectral regions with sides aligned with the x and y directions of the transformed image 410, such as band-edge spectral regions A2, B2, A3 and B3 of FIG. 4B. In other words, as depicted in FIG. 4B, the location-error-prediction system 106 identifies shape-simplified band-edge spectral regions by identifying non-diagonally oriented (e.g., rectangular) band-edge spectral regions. In these or other embodiments, the location-error-prediction system 106 identifies a set of three pairs of bandedge spectral regions, including (i) a first pair 414 of band-edge spectral regions Al and Bl on the top and bottom of the transformed image 410, respectively, (ii) a second pair 416 of shape- simplified band-edge spectral regions A2 and B2, and (iii) a third pair 418 of shape-simplified band-edge spectral regions A3 and B3 on the sides of the transformed image 410.Attorney Docket No. IP-2805-PCT 30 Patent Application[OHl] In some implementations, the location-error-prediction system 106 employs a mask function with the shape-simplified band-edge spectral regions to determine a phase difference. For example, the location-error-prediction system 106 uses the pairs of band-edge spectral regions to determine a phase difference as discussed in further detail below with respect to FIGS. 8 A and 8B. When doing so, the location-error-prediction system 106 multiplies the shape-simplified band-edge spectral regions by a mask function. By utilizing the shape-simplified band-edge spectral regions and the masking function, the location-error-prediction system 106 can decrease the time and computational resources used for determining a phase difference.

[0112] As just mentioned, in some embodiments, the location-error-prediction system 106 employs a mask function with the shape-simplified band-edge spectral regions. Specifically, the location-error-prediction system 106 uses a mask function to accelerate identifying regions of interest, such as band-edge spectral regions arranged in a hexagon shape or layout — from simplified-and-rectangular regions of an image patch. In particular, the location-error-prediction system 106 uses a binary mask function comprising 0 values and 1 values (e.g., mask function 010) to (i) multiply complex values after FFT within a band-edge region by a 1 value and (ii) multiply complex values outside of a band-edge region by a 0 value. For example, when identifying pairs of band-edge spectral regions for a hexagon layout, the mask function can include 1 values within 6 rotated matrix regions that cover 6 corresponding band-edge spectral regions in a hexagon layout. By contrast, the mask function for such a hexagon layout can include 0 values within 6 simplified-and-rectangular matrix regions — but such 0 values are placed only in the portions of the simplified-and-rectangular matrix regions that do not overlap with the corresponding rotated matrix regions. By multiplying by 1 the complex values within the rotated matrix regions by 1 values — and multiplying by 0 the complex values within the simplified-and-rectangular matrix regions that do not overlap with the rotated matrix regions — the location-error-prediction system 106 generates matrices comprising 1 values identifying the band-edge regions and 0 values identifying non-bandedge regions.

[0113] As mentioned previously, in one or more implementations, the location-error-prediction system 106 identifies pairs of band-edge spectral regions according to a variety of geometric layouts, including a diamond layout, for cluster locations of clusters of oligonucleotides on the nucleotide-sample slide. In accordance with one or more embodiments, FIG. 5A illustrates the location-error-prediction system 106 identifying pairs of band-edge spectral regions according to a diamond layout or shape.

[0114] As illustrated in FIG. 5A, in some implementations, the location-error-prediction system 106 identifies band-edge spectral regions from a spatial frequency band within an image with characteristics similar to the image shown in FIG. 4A. For example, the location-error-predictionAttorney Docket No. IP-2805-PCT 31 Patent Applicationsystem 106 transforms a raw image to generate a transformed image 500 including a spatial frequency band. As shown in FIG. 5A, the transformed image 500 illustrates the frequencies of signals emitted by the clusters of oligonucleotides as colored squares, where each colored square of the transformed image 500 can include one or more clusters of oligonucleotides. To illustrate, a colored square 507 has a darker shade of color (e.g., dark blue) indicating that the corresponding area of the transformed image 500 (e.g., an image patch for a nucleotide-sample-slide subregion) exhibits a phase with a normalized frequency of 0.6, as indicated by a key 502. Just like the key 402 in FIG. 4A, the key 502 in FIG. 5A uses a gradient of colors to indicate the magnitude of the location error as measured in pixels. For example, the key 502 includes a gradient of colors where one gradient end color (e.g., cool shade of red) of the gradient represents a phase with a normalized frequency of 1, another gradient end color (e.g., warm shade of red) of the gradient represents a phase with a normalized frequency of 0, and intermediate colors of the gradient represent phases with normalized frequencies between 1 and 0, as described above for the key 402.

[0115] As also depicted in FIG. 5A and as mentioned above, in one or more embodiments, the location-error-prediction system 106 identifies pairs of band-edge spectral regions (e.g., a set of pairs of band-edge spectral regions) within the spatial frequency band within the transformed image 500 according to a diamond layout or shape. For example, the location-error-prediction system 106 identifies each of the band-edge spectral regions Al, Bl, A2, and B2 for the transformed image 500 with sides at a diagonal orientation relative to the x andy directions to form an overall diamond shape. As with the pairs of band-edge spectral regions of FIG. 4A, the location-error-prediction system 106 determines the diamond layout or shape in FIG. 5 A based on the layout of the clusters of oligonucleotides on the nucleotide-sample slide and based on the type of nucleotide-sample slide used for a sequencing device. In these or other embodiments, rather than determining three pairs of band-edge spectral regions as in FIG. 4A, the location-error-prediction system 106 identifies a set of two pairs of band-edge spectral regions including a first pair 504 of band-edge spectral regions Al and Bl and a second pair 506 of band-edge spectral regions A2 and B2.

[0116] In one or more embodiments, the location-error-prediction system 106 identifies the pairs of band-edge spectral regions according to a diamond layout or shape using a particular configuration. For example, the location-error-prediction system 106 can identify the pair of bandedge spectral regions such that the first pair 504 of band-edge spectral regions aligns on an axis 45 degrees left of a vertical or y axis. In these or other embodiments, the location-error-prediction system 106 can identify the second pair 506 of band-edge spectral regions to align on an axis set at a 90-degree angle relative to the first pair 504 of band-edge spectral regions. In these or other embodiments, as with the pairs of band-edge spectral regions discussed relative to FIG. 4A, the location-error-prediction system 106 can determine x and y direction components of a locationAttorney Docket No. IP-2805-PCT 32 Patent Applicationerror using the first pair 504 of band-edge spectral regions and the second pair 506 of band-edge spectral regions in FIG. 5A and a total error by summing the x and y direction components of the location error. Further, in some embodiments, the location-error-prediction system 106 can identify the pairs of band-edge spectral regions according to a diamond shape using different configurations by identifying pairs of band-edge spectral regions that align on different axes.

[0117] As noted above with respect to FIG. 4B, the location-error-prediction system 106 can identify shape-simplified band-edge spectral regions to accelerate the processing time for determining phase differences. For example, the location-error-prediction system 106 can identify simplified geometric layouts or shapes and orientations of the band-edge spectral regions. In accordance with one or more embodiments, FIG. 5B illustrates the location-error-prediction system 106 identifying pairs of shape-simplified band-edge spectral regions with simplified geometric shapes and orientations that have been adjusted from a diamond shape.

[0118] As shown in FIG. 5B, in one or more implementations, the location-error-prediction system 106 identifies pairs of shape-simplified band-edge spectral regions (e.g., a set of pairs of band-edge spectral regions) within the spatial frequency band within a transformed image 508. In one or more embodiments, the location-error-prediction system 106 generates the transformed image 508 using similar methods to those for generating the transformed image 500 and, therefore, the transformed image 508 shares the same phase and other characteristics as the transformed image 500. Accordingly, FIG. 5B includes the key 502 next to the transformed image 508, which is the same key for the transformed image 500 described above.

[0119] When performing the accelerated version of the phased-difference-based method of estimating cluster location depicted in FIG. 5B, in some embodiments, the location-error-prediction system 106 identifies the pairs of shape-simplified band-edge spectral regions with simplified orientations similar to the shape-simplified band-edge spectral regions described above with respect to FIG. 4B. Accordingly, in one or more implementations, the location-error-prediction system 106 can also identify simplified geometric shapes or layouts of the shape-simplified bandedge spectral regions. For instance, the location-error-prediction system 106 identifies squareshaped band-edge spectral regions Al, Bl, A2, and B2, including (i) a first pair 510 of band-edge spectral regions Al and Bl and (ii) a second pair 512 of band-edge spectral regions A2 and B2. Further, the location-error-prediction system 106 can utilize a mask function with the shape- simplified band-edge spectral regions to determine phase difference, as described further below with respect to FIGS. 8 A and 8B.

[0120] As just mentioned, in some implementations, the location-error-prediction system 106 uses a mask function with the shape-simplified band-edge spectral regions. Specifically, the location-error-prediction system 106 uses a mask function to accelerate identifying regions ofAttorney Docket No. IP-2805-PCT 33 Patent Applicationinterest, such as band-edge spectral regions arranged in a diamond shape or layout — from simplified-and-rectangular regions of an image patch. In particular, the location-error-prediction system 106 uses a binary mask function comprising 0 values and 1 values (e.g., mask function 010) to (i) multiply complex values after FFT within a band-edge region by a 1 value and (ii) multiply complex values outside of a band-edge region by a 0 value. For example, when identifying pairs of band-edge regions for a diamond layout, the mask function can include 1 values within 4 rotated matrix regions that cover 4 corresponding band-edge regions in a diamond layout. By contrast, the mask function for such a diamond layout can include 0 values within 4 simplified-and-rectangular matrix regions — but again such 0 values are placed only in the portions of the simplified-and- rectangular matrix regions that do not overlap with the corresponding rotated matrix regions. Again, in these or other embodiments, the location-error-prediction system 106 multiplies by 1 the complex values within the rotated matrix regions by 1 values — and multiplies by 0 the complex values within the simplified-and-rectangular matrix regions that do not overlap with the rotated matrix regions — to generate matrices comprising 1 values identifying the band-edge regions and 0 values identifying non-band-edge regions.

[0121] As noted previously, in one or more implementations, the location-error-prediction system 106 identifies pairs of band-edge spectral regions according to a geometric layout for cluster locations of clusters of oligonucleotides on the nucleotide-sample slide. As also mentioned above, in some embodiments, the location-error-prediction system 106 can identify pairs of band-edge spectral regions according to a variety of geometric layouts including a square shape. FIG. 6 illustrates the location-error-prediction system 106 identifying pairs of band-edge spectral regions according to a square shape in accordance with one or more embodiments.

[0122] As portrayed in FIG. 6, in some implementations, the location-error-prediction system 106 identifies band-edge spectral regions from a spatial frequency band within an image with characteristics similar to the image shown in FIG. 4A. For example, the location-error-prediction system 106 transforms a raw image to generate a transformed image 600 including a spatial frequency band. As shown in FIG. 6, the transformed image 600 illustrates the frequencies of signals emitted by the clusters of oligonucleotides as colored squares where each colored square of the transformed image 600 can include one or more clusters of oligonucleotides. To illustrate, a colored square 607 has a lighter shade of color (e.g., yellow) indicating that the corresponding area of the transformed image 600 (e.g., an image patch for a nucleotide-sample-slide subregion) exhibits a phase with a normalized frequency of 0.2, as indicated by a key 602. Just like the key 402 in FIG. 4A, the key 602 in FIG. 6 uses a gradient of colors to indicate the magnitude of the location error as measured in pixels. For example, the key 602 includes a gradient of colors where one gradient end color (e.g., cool shade of red) of the gradient represents a phase with a normalizedAttorney Docket No. IP-2805-PCT 34 Patent Applicationfrequency of 1, another gradient end color (e.g., warm shade of red) of the gradient represents a phase with a normalized frequency of 0, and intermediate colors of the gradient represent phases with normalized frequencies between 1 and 0, as described above for the key 402.

[0123] As further illustrated in FIG. 6 and as mentioned above, in one or more embodiments, the location-error-prediction system 106 identifies pairs of band-edge spectral regions (e.g., a set of pairs of band-edge spectral regions) within the spatial frequency band within the transformed image 600 according to a square shape. As described with respect to the pairs of band-edge spectral regions of FIGS. 4A and 5A, the location-error-prediction system 106 determines the square layout or shape based on the layout of the clusters of oligonucleotides on the nucleotide-sample slide and based on the type of nucleotide-sample slide used for a sequencing device. Similar to the two pairs of band-edge spectral regions in FIG. 5 A, the location-error-prediction system 106 identifies a set of two pairs of band-edge spectral regions including a first pair 604 of band-edge spectral regions Al and Bl and a second pair 606 of band-edge spectral regions A2 and B2.

[0124] In one or more embodiments, the location-error-prediction system 106 identifies the pairs of band-edge spectral regions according to a square layout or shape using a particular configuration. For example, the location-error-prediction system 106 can identify the pair of bandedge spectral regions, such that the first pair 604 of band-edge spectral regions aligns on a vertical or y axis. In these or other embodiments, the location-error-prediction system 106 can identify the second pair 606 of band-edge spectral regions to align on an x axis. Moreover, in these or other embodiments, the location-error-prediction system 106 can determine a y direction component of a location error (or a y location error) using the first pair 604 of band-edge spectral regions as described in further detail below. Similarly, in these or other embodiments, the location-error- prediction system 106 can determine an x direction component of a location error using the first pair 604 of band-edge spectral regions and the second pair 606 of band-edge spectral regions. Similarly to previously described embodiments, the location-error-prediction system 106 can utilize the sum of the x and y direction components of the location error to determine a total location error with a specific direction and magnitude.

[0125] As previously mentioned, in one or more embodiments, the location-error-prediction system 106 generates location errors for clusters of oligonucleotides on a nucleotide-sample slide in various directions. Indeed, in one or more implementations, the location-error-prediction system 106 can determine a location error in an x direction (also referred to herein as an “x error”), a location error in ay direction (also referred to herein as a “y error”), or a location error in a direction with both x and y direction components (e.g., a total error, a summed location error, or a “z error”). FIG. 7 illustrates exemplary nucleotide-sample slide heat maps showing x andy errors and summed location errors in accordance with one or more embodiments.Attorney Docket No. IP-2805-PCT 35 Patent Application

[0126] As depicted in FIG. 7, each of heat maps 702, 704, 706, 708, 710, and 712 represent a region of a nucleotide-sample slide (e.g., a tile of a flow cell). Specifically, each of the heat maps 702, 704, 706, 708, 710, and 712 includes many image patches (e.g., 3600 image patches), where each image patch includes a number of pixels in the x and y directions (e.g., 64 by 64 pixels). As shown in FIG. 7, the intensity of the colors in the heat maps 702 and 704 indicate the magnitude of x errors and y errors, respectively, that represent location errors caused by optical distortion. By contrast, the intensity of the colors in the heat maps 706 and 708 indicate the magnitude of x errors and y errors, respectively, that represent location errors caused by jitter. In further contrast, the intensity of the colors in the heat maps 710 and 712 indicate the magnitude of summed x errors and y errors, respectively, caused by a combination of optical distortion and jitter. In these and other embodiments, the location-error-prediction system 106 determines such x and y errors based on phase differences between pairs of band-edge spectral regions as discussed throughout this specification (e.g., FIGS. 3-6, 8A-9B).

[0127] As further illustrated in FIG. 7, each of the heat maps 702, 704, 706, 708, 710, and 712 includes a key to the right that serves as a visual guide for interpreting errors of the heat map. Specifically, the keys use a gradient of colors to indicate the magnitude of the location error in pixels. For example, the keys include a gradient of colors representing a number of pixels of the location error as follows: a first color (e.g., dark red) represents 0.3 pixels, a second color (e.g., light red) represents 0.2 pixels, a third color (e.g., orange) represents 0.1 pixels, a fourth color (e.g., yellow) represents 0.5 pixels, a fifth color (e.g., green) represents 0 pixels (i.e., no error), a sixth color (e.g., light blue) represents -0.1 pixels, a seventh color (e.g., intermediate blue) represents - 0.2 pixels, and an eighth color (e.g., dark blue) represents -0.3 pixels. In these or other embodiments, because the origin of the coordinates is at the top left of the image, a positive value represents an error in the positive direction (e.g., to the right in the x direction or down in the y direction) and a negative value represents an error in the negative direction (e.g., to the left in the x direction or up in the y direction).

[0128] In some embodiments, as shown in FIG. 7, the heat maps 702, 704, 706, 708, 710, and 712 also include numerical image-patch indicators on the x and y axes indicating row data for image patches along the y axis and column data for image patches along the x axis. For example, for heat maps 702 and 704, the numerical image-patch indicators along the x axis indicate each row includes 72 image patches. By contrast, the numerical image-patch indicators along the y axis indicate each column includes 48 image patches.

[0129] As additionally indicated by FIG. 7, optical distortion varies as a function of x. In particular, both the x and y errors caused by optical distortion vary as a function of x. For example, the heat map 702 illustrates the x error caused by optical distortion; and the heat map 704 illustratesAttorney Docket No. IP-2805-PCT 36 Patent Applicationthe y error caused by optical distortion. Further, in each of the heat maps 702 and 704, color bands illustrating location errors of the clusters of oligonucleotides in the individual image patches vary in the x direction. For instance, the heat maps 702 and 704 each include color bands running from top to bottom in the y direction indicating that the location errors of the clusters of oligonucleotides within each color band are the same.

[0130] To illustrate the significance of such color bands for optical distortion, in the heat map 702 illustrating the x error of optical distortion, the color bands on the left side of the image are generally a first color (e.g., yellow) and a second color (e.g., orange), such as color band 714 in the second color (e.g., orange) and color band 716 in the first color (e.g., yellow); color bands in the middle are generally a third color (e.g., blue) and fourth color (e.g., green), such as color bands 718 in the fourth color (e.g., green) and a color band 720 in the third color (e.g., blue); and color bands on the left side are generally a fifth color (e.g., red), such as color band 722 in the fifth color (e.g., red). Similarly, in the heat map 704 illustrating the y error of optical distortion, the color bands on the left side and in the middle of the image are largely a first color (e.g., blue) and a second color (e.g., green), such as color bands 724 in the second color (e.g., green) and color band 726 in a shade of the first color (e.g., light blue); while color bands on the right side are generally a third color (e.g., yellow, such as the color from color band 728) and a fourth color (e.g., orange, such as the color from color band 730). The fact that the color bands of the heat maps 702 and 704 run from top to bottom and change colors from left to right indicates that optical distortion varies as a function of x.

[0131] As further indicated by FIG. 7, jitter varies as a function of y. In particular, both the x and y errors of jitter vary as a function of y. For example, the heat map 706 illustrates the x error of jitter; and the heat map 708 illustrates the y error of jitter. Further, in each of the heat maps 706 and 708, color bands illustrating location errors in the individual error patches vary in the y direction. For instance, in each of the heat maps 706 and 708, color bands illustrating location errors in the clusters of oligonucleotides of the individual image patches vary in the y direction. For example, the heat maps 706 and 708 each include color bands running from left to right in the x direction indicating that the location errors of the clusters of oligonucleotides within each band are the same.

[0132] To illustrate the significance of such color bands for jitter, in the heat map 706 illustrating the x error of jitter, the color bands at the top of the image are generally a first color (e.g., lighter shade of blue or teal, such as the color from color bands 732); color bands in the middle are generally a second color (e.g., red, such as the color from color bands 734); and color bands at the bottom are generally a third color (e.g., green, such as the color from color band 736) and a fourth color (e.g., blue, such as the color from color band 738). Similarly, in the heat map 708Attorney Docket No. IP-2805-PCT 37 Patent Applicationillustrating the y error of jitter, the color bands at the top are generally a first color (e.g., lighter shade of blue or teal, such as the color from color band 740) and a second color (e.g., orange, such as the color from color band 742); color bands in the middle are generally a third color (e.g., yellow, such as the color from color bands 744) and a fourth color (e.g., green, such the color from as color bands 746); and color bands at the bottom of the image are generally the first color (e.g., another shade of blue or darker teal, such the color from as color band 748) and the fourth color (e.g., green, such the color from as color band 750). The fact that the color bands of the heat maps 706 and 708 run from left to right and change colors from top to bottom indicates that optical distortion varies as a function of y.

[0133] As also depicted in FIG. 7, the heat maps 710 and 712 illustrate the sum of the location errors caused by optical distortion and jitter and together represent the total location error. Specifically, the heat map 710 illustrates the sum of the x error for optical distortion and the x error for jitter by summing the x errors and y errors from the heat maps 702 and 706, respectively. Similarly, the heat map 712 illustrates the sum of the y error for optical distortion and the y error for jitter by summing the heat maps 704 and 708. Thus, the color of each image patch within the heat map 710 represents the total x error for the clusters of oligonucleotides within each image patch and the color of each image patch within the heat map 712 represents the total y error for the clusters of oligonucleotides within each image patch.

[0134] To illustrate such summed location errors in x and y directions, the clusters of oligonucleotides depicted by the image patches within the first area 752 that is a first color (e.g., intermediate blue) of heat map 710 exhibit location errors around -0.2 pixels representing the sum of the corresponding areas of the color bands 720 and 732 of heat maps 702 and 706, respectively. Furthermore, the clusters of oligonucleotides depicted by the image patches within the second area 754 that is a second color (e.g., dark red) exhibit location errors around +0.3 pixels representing the sum of the corresponding areas of the color bands 714 and 734 of heat maps 702 and 706, respectively. Additionally, the sum of the total x error and the total y error for each image patch represents the total location error for the clusters of oligonucleotides depicted by each image patch.

[0135] Because optical distortion can vary as a function of x and jitter can vary as a function of y, in some implementations, the location-error-prediction system 106 can subsample an image patch to reduce the computing power required to base call clusters of oligonucleotides. Specifically, the location-error-prediction system 106 can minimize the computing power of base calling clusters of oligonucleotides by subsampling an image patch when determining adjusted locations of clusters of oligonucleotides across an image patch of a nucleotide-sample slide. For example, the location- error-prediction system 106 can utilize a subsampled image-patch grid when determining adjusted locations of clusters of oligonucleotides as described with respect to FIGS. 11-14.Attorney Docket No. IP-2805-PCT 38 Patent Application

[0136] As previously noted, in one or more embodiments, the location-error-prediction system 106 determines location errors of oligonucleotide clusters based on phase differences between pairs of band-edge spectral regions. In accordance with one or more embodiments, FIGS. 8A and 8B illustrate the location-error-prediction system 106 determining phase differences between bandedge spectral regions identified from an image patch and generating location errors based on the phase differences. As an overview, FIG. 8 A illustrates the location-error-prediction system 106 extracting and transforming an image patch from an image of a nucleotide-sample-slide region and identifying pairs of band-edge spectral regions from a spatial frequency band in accordance with one or more embodiments. Further, FIG. 8B illustrates the location-error-prediction system 106 determining phase differences between such pairs of band-edge spectral regions and generating location errors for one or more oligonucleotide clusters depicted within the image patch based on the phase differences in accordance with one or more embodiments.

[0137] As illustrated in FIG. 8A, in one or more implementations, the location-error-prediction system 106 performs an act 800 of extracting an image patch 802 from an image of a region of a nucleotide-sample slide. Specifically, the location-error-prediction system 106 extracts the image patch 802 from a nucleotide-sample-slide image taken during a sequencing cycle by a sequencing device. In some embodiments, the location-error-prediction system 106 captures the image in a channel of the sequencing device (e.g., a multi-channel sequencing device). Indeed, in some implementations, the image patch 802 includes signals emitted by many clusters of oligonucleotides (e.g., hundreds or thousands of clusters of oligonucleotides) during the sequencing cycle. Moreover, in one or more embodiments, the location-error-prediction system 106 extracts the image patch 802 according to a predetermined size (e.g., 64 pixels by 64 pixels). In these or other embodiments, the size of the image patch 802 corresponds to a region or subregion of a nucleotide-sample slide, such as a tile or sub-tile.

[0138] After extracting the image patch 802 and as further illustrated in FIG. 8A, in one or more implementations, the location-error-prediction system 106 performs an act 804 of transforming the image patch 802. In particular, the location-error-prediction system 106 transforms the image patch 802 from a spatial domain to a frequency domain into a transformed image patch 806. For instance, the location-error-prediction system 106 utilizes a transformation model with a transformation operation (e.g., 2D Fourier Transform) to generate the transformed image patch 806. Furthermore, in some embodiments, the transformed image patch 806 includes a spatial frequency band in which a frequency component of the signals from clusters of oligonucleotides are represented using color to show phase and intensity of such color to show magnitude.

[0139] To illustrate an example of the color’s frequency representing phase and the color’s intensity representing magnitude, FIG. 8A includes a key 808 for the transformed image patch 806Attorney Docket No. IP-2805-PCT 39 Patent Applicationthat serves as a visual guide for interpreting the signal frequencies of the clusters of oligonucleotides in the transformed image patch 806. Specifically, just like the key 402 in FIG. 4A, the key 808 uses a gradient of colors wherein one gradient end color (e.g., cool shade of red) of the gradient represents a phase with a normalized frequency of 1, another gradient end color (e.g., warm shade of red) of the gradient represents a phase with a normalized frequency of 0, and intermediate colors of the gradient represent phases with normalized frequencies between 1 and 0.

[0140] After extracting and transforming the image patch 802, as additionally shown in FIG. 8 A, in some implementations, the location-error-prediction system 106 performs an act 810 of identifying pairs of band-edge spectral regions (e.g., a set of pairs of band-edge spectral regions) within the spatial frequency band of the transformed image patch 806. Specifically, the location- error-prediction system 106 identifies the pairs of band-edge spectral regions according to a geometric layout, such as a hexagon layout, for the cluster locations of the clusters of oligonucleotides on the nucleotide-sample slide, as discussed above with respect to FIGS. 4A-6. As shown in FIG. 8 A, in this example, the location-error-prediction system 106 identifies a set of three pairs of band-edge spectral regions including a first pair of band-edge spectral regions Al and Bl, a second pair of band-edge spectral regions A2 and B2, and a third pair of band-edge spectral regions A3 and B3.

[0141] After identifying the relevant pairs and as shown now in FIG. 8B, in one or more embodiments, the location-error-prediction system 106 can perform an act 812 of determining phase differences between the pairs of band-edge spectral regions. In some cases, the location- error-prediction system 106 determines a respective phase difference between each pair of the set of pairs of band-edge spectral regions. For example, the location-error-prediction system 106 can determine a phase difference 814 between the pair of band-edge spectral regions Al and Bl, a phase difference 816 between the pair of band-edge spectral regions A2 and B2, and a phase difference 818 between the pair of band-edge spectral regions A3 and B3.

[0142] To illustrate the basis for the phase difference 814, the band-edge spectral regions Al and Bl include the same signals emitted by the clusters of oligonucleotides (e.g., the signals of Al are repeated in Bl). Indeed, each of band-edge spectral region Al and Bl include the same general pattern of the colored squares representing the signals emitted by the clusters of oligonucleotides, but with variation in color between the band-edge spectral region Al and the band-edge spectral region Bl. This color variation across the band-edge spectral regions Al and Bl results from a variation in the phase of frequency of signals represented in the band-edge spectral regions Al and Bl. From this phase variation from the band-edge spectral regions Al and Bl, the location-error- prediction system 106 determines the phase difference 814. The location-error-prediction system 106 can likewise determine the phase difference 816 from the band-edge spectral regions A2 andAttorney Docket No. IP-2805-PCT 40 Patent ApplicationB2 and the phase difference 818 from the band-edge spectral regions A3 and B3 based on similar comparisons of phase.

[0143] In addition or in the alternative, in one or more implementations, the location-error- prediction system 106 determines a phase difference for the transformed image patch 806 using each of the pairs of the band-edge spectral regions 814-818. For example, the location-error- prediction system 106 can determine the phase difference by determining a given phase angle ( for the transformed image patch 806 according to the following Equation (1):In Equation (1), the * symbol indicates a conjugate of the complex number(s), 4 represents the mathematical operation for measuring any angle, ° represents the Hadamard product (i.e., element- wise product), Bfrepresents a number (e.g., complex number) for a given band-edge spectral region of a pair, and Afrepresents another number (e.g., complex number) for another given band-edge spectral region of the pair. For example, the location-error-prediction system 106 can determine a complex number representing each of the band-edge spectral regions Al -A3 and B1-B3. In these or other embodiments, the complex number Al can represent the band-edge spectral region Al, the complex number B 1 can represent the band-edge spectral region B 1 , etc. Accordingly, the location- error-prediction system 106 can determine a product of a band-edge spectral region (e.g., Bl) and the conjugate of the band-edge spectral region pair (Al*) as part of determining the phase difference for the transformed image patch 806. As shown above, in some embodiments, the location-error-prediction system 106 determines such a product for every pair of band-edge spectral regions (e.g., Al and Bl, A2 and B2, and A3 and B3) and performs the summation to determine the phase angle, wherein the phase angle represents the phase difference for the transformed image patch 806.

[0144] To further illustrate, in some implementations, the location-error-prediction system 106 determines a given phase angle (< >[) according to the following Equation (2):In Equation (2), the complex number ztrepresents a sum of complex numbers within the ith pair of band-edge spectral regions, and 4 represents an angle between a positive real axis and a line that connects the origin and the complex number. To determine zt, in these or other embodiments, the location-error-prediction system 106 uses the following Equation (3):Attorney Docket No. IP-2805-PCT 41 Patent ApplicationIn Equation (3), 0 represents a rotation angle associated with a pair of band-edge regions. In the case of a hexagon layout, 0 = radians; in the case of a diamond layout, 0 = radians;in the case of a square layout, 0 = 0,^. radians, and the term df represents the distance (e.g., pixel distance) in spatial domain between the band-edge spectral regions in a pair of band-edge spectral regions. Ax0, Ay0are the initial offsets between the well coordinates and its nearest integral pixel in the x- and y-direction.

[0145] Additionally, in one or more embodiments, the location-error-prediction system 106 can perform the act 812 of determining the phase difference when the location-error-prediction system 106 determines the band-edge spectral regions according to a diamond shape or a square shape (e.g., as discussed above with respect to FIG. 5A-6). As described above with respect to determining the phase difference for band-edge spectral regions in a hexagon shape, the location- error-prediction system 106 can determine the phase difference for band-edge spectral regions in a hexagon shape by determining a phase angle ( for the transformed image patch 806 using Equations (1), (2), and (3), as described above.

[0146] After determining phase differences and as further shown in FIG. 8B, in some implementations in which band-edge spectral regions come from a hexagon shape, the location- error-prediction system 106 performs an act 820 of translating the phase difference into x and y location errors. Specifically, the location-error-prediction system 106 can utilize the phase difference to determine x and y location errors from band-edge spectral regions in a hexagon shape according to the following Equations (4) and (5):(4)Ax = Sx ■ pitch(5)Ny = Sy ■ pitchIn Equations (4) and (5), pitch represents the distance between nearest clusters of oligonucleotides (or between nano wells comprising oligonucleotide clusters) on the nucleotide-sample slide, 8x represents an angle along an x-axis, and Sy represents an angle along the y-axis. Moreover, in one or more embodiments, the location-error-prediction system 106 determines Sx and Sy according to the following Equation (6):such that:Attorney Docket No. IP-2805-PCT 42 Patent ApplicationIn Equation (6), the symbol Vi = 1,2,3 refers to the three pairs of band-edge spectral regions (e.g., Al and Bl, A2 and B2, and A3 and B3). Thus, Equation (6) solves a least square optimization problem based on the phase differences of the three pairs of band-edge spectral regions to optimize angles 8x and 8y to determine the most accurate location errors (e.g., x and y location errors).

[0147] Furthermore, in one or more implementations in which band-edge spectral regions come from a diamond shape, the location-error-prediction system 106 likewise performs the act 820 of translating the phase difference into x and y location errors. Specifically, the location-error- prediction system 106 can utilize the phase difference to determine x and y location errors from band-edge spectral regions in a diamond shape according to the following Equations (7) and (8):y = ( i + 02) ’ pitch / 2 2n (8)

[0148] In Equations (7) and (8), the symbols ( ^and (f>2 represent a first phase angle and a second phase angle, respectively; the symbol pitch represents a distance between nearest clusters of oligonucleotides (or between nano wells comprising oligonucleotide clusters) on the nucleotide- sample slide; and the symbol ti represents radians. Because 2 radians equal 360 degrees and phase angles are represented here in radians, the number 2 can be used to normalize a given phase angle.

[0149] Additionally, in some embodiments in which band-edge spectral regions come from a square shape, the location-error-prediction system 106 performs an act 820 of translating the phase difference into x and y location errors. Specifically, the location-error-prediction system 106 can utilize the phase difference to determine x and y errors from band-edge spectral regions in a square shape according to the following Equations (9) and (10):Ax = —<p'2■ pitch / 2 (9)Ay = 0i ■ pitch / 2n (10)

[0150] In Equations (9) and (10), the symbols(p2' , pitch, and it represent the same variables as described above with respect to Equations (7) and (8).

[0151] As indicated above, in certain implementations, the location-error-prediction system 106 is implemented on a sequencing device that utilizes two or more different channels. In such cases, the location-error-prediction system 106 can identify, for each channel, a pair of band-edge spectral regions from a channel-specific spatial frequency band within a channel-specific image depicting signals of an oligonucleotide cluster at a predicted location specific to the channel-specific image. The location-error-prediction system 106 can likewise determine a phase difference between the pair of band-edge spectral regions within the channel-specific image. The location-error-predictionAttorney Docket No. IP-2805-PCT 43 Patent Applicationsystem 106 can further determine a channel-specific or image-specific location error in at least one direction for the predicted location of the oligonucleotide cluster and subsequently determine, based on the channel-specific or image-specific location error, a channel-specific or image-specific adjusted location of the oligonucleotide cluster. The location-error-prediction system 106 can accordingly perform operations according to Equations (1) - (10) with respect to a specific image in a given channel at a given sequencing cycle.

[0152] In a two-channel implementation, for example, the location-error-prediction system 106 can perform the foregoing actions with respect to a specific image and specific channel. To illustrate, in some embodiments, the location-error-prediction system 106 (i) identifies, for a given sequencing cycle in a first channel, a first pair of band-edge spectral regions from a first spatial frequency band within a first image depicting signals of the cluster of oligonucleotides at a first predicted location within a nucleotide-sample slide and (ii) identifies, for the sequencing cycle in a second channel, a second pair of band-edge spectral regions from a second spatial frequency band within a second image depicting signals of the cluster of oligonucleotides at a second predicted location within the nucleotide-sample slide. The location-error-prediction system 106 subsequently (i) determines a first phase difference between the first pair of band-edge spectral regions and (ii) determines a second phase difference between the second pair of band-edge spectral regions.

[0153] The first and second phase differences can likewise result in channel-specific or imagespecific location errors and adjusted locations. Based on the first phase difference, for example, the location-error-prediction system 106 generates a first location error in at least one direction for the first predicted location of the cluster of oligonucleotides. Based on the first location error and for the sequencing cycle, the location-error-prediction system 106 determines a first adjusted location of the cluster of oligonucleotides within the nucleotide-sample slide. Similarly, based on the second phase difference, the location-error-prediction system 106 generates a second location error in at least one direction for the second predicted location of the cluster of oligonucleotides. Based on the second location error and for the sequencing cycle, the location-error-prediction system 106 determines a second adjusted location of the cluster of oligonucleotides within the nucleotide- sample slide. The location-error-prediction system 106 can likewise generate a base call for the cluster of oligonucleotides based on (i) the first adjusted location of the cluster of oligonucleotides within the first image and corresponding intensity values and (ii) the second adjusted location of the cluster of oligonucleotides within the second image and corresponding intensity values.

[0154] In some implementations, the location-error-prediction system 106 aggregates the location errors determined from multiple pairs of band-edge spectral regions to generate a summed or total location error for determining an adjusted cluster location. For example, in these or otherAttorney Docket No. IP-2805-PCT 44 Patent Applicationembodiments, the location-error-prediction system 106 can combine the x location error and the y location error to determine a total location error. Further, in one or more embodiments, the location-error-prediction system 106 can apply the total location error, or the individual x and y errors, of an image patch to the predicted oligonucleotide-cluster locations to determine an adjusted location, as discussed in further detail below with respect to FIG. 9B.

[0155] As mentioned above, in one or more implementations, the location-error-prediction system 106 can determine adjusted locations of clusters of oligonucleotides within an image patch. Indeed, in some embodiments, the location-error-prediction system 106 determines the adjusted locations of the clusters of oligonucleotides by utilizing an image-patch grid when determining location errors for the predicted locations of the clusters of oligonucleotides. In accordance with one or more embodiments, FIGS. 9A and 9B illustrate the location-error-prediction system 106 applying an image-patch grid to a nucleotide-sample-slide-region image and determining adjusted locations of clusters of oligonucleotides in the image patch within each cell of the image-patch grid.

[0156] As portrayed in FIG. 9A, for example, the location-error-prediction system 106 performs an act 902 of utilizing an image-patch grid to segment image patches of a nucleotide-sample-slide region image. In some such embodiments, the location-error-prediction system 106 optionally determines a nucleotide-sample-slide configuration 904 of a corresponding nucleotide-sample slide (e.g., a flow-cell configuration of a flow cell). For example, the location-error-prediction system 106 determines aspects of the nucleotide-sample-slide configuration 904, such as the geometric layout of the cluster locations of the clusters of oligonucleotides (e.g., hexagon, diamond, rhombus, square), the pitch of oligonucleotide clusters or nano wells within the nucleotide-sample slide (e.g., 300 nm, 400 nm, 600 nm), a corresponding number and layout of image subregions (e.g., image patches) of the nucleotide-sample slide, and predicted locations of clusters of oligonucleotides (e.g., predicted locations of nano wells comprising oligonucleotide clusters).

[0157] As further indicated by FIG. 9A, in one or more embodiments, based on the nucleotide- sample-slide configuration 904, the location-error-prediction system 106 accesses an image-patch grid 906 comprising grid cells that correspond to the subregions of the nucleotide-sample slide, where the image-patch grid 906 can also include the predicted locations of clusters of oligonucleotides. In addition to determining the nucleotide-sample-slide configuration 904, as further shown in FIG. 9A, the location-error-prediction system 106 can also optionally perform an act 908 of generating indices of expected locations closest to image patch centers, where expected locations represent theoretical locations (e.g., cluster or nano well locations) and not affine transformed locations that could account for optical distortion. The location-error-prediction system 106 can subsequently utilize these indices of the expected locations (e.g., cluster orAttorney Docket No. IP-2805-PCT 45 Patent Applicationnano well locations) to find corresponding affine transformed cluster coordinates (e.g., x and y coordinates in the pixel space) and locate nearest image patch centers of integral pixels when mapping image pixels for a grid cell to the predicted locations of the clusters of oligonucleotides. In one or more embodiments, the location-error-prediction system 106 determines the initial offsets (Ax0, Ay0) of Equation (3) above.

[0158] After determining the nucleotide-sample-slide configuration 904 and indices of expected locations from the act 908, as further illustrated in FIG. 9A, the location-error-prediction system 106 performs an act 910 of mapping image pixels for a grid cell of the image-patch grid 906 to predicted locations of clusters of oligonucleotides within the grid cell. In particular, the location-error-prediction system 106 maps the image pixels of an image 912 of a nucleotide- sample-slide region to the predicted locations of the clusters of oligonucleotides for each grid cell of the image-patch grid 906. By performing pixel -to-cluster-location mapping from the act 910, in some embodiments, the location-error-prediction system 106 can generate a look-up table of pairs of band-edge estimated location errors (x error, y error), and use each pair of errors to correct all the locations mapped to their associated grid cell.

[0159] Asjust suggested and depictednowinFIG. 9B, after mapping image pixels, the location- error-prediction system 106 performs an act 914 of placing an image patch of the image 912 of the nucleotide-sample-slide region within the grid cell of the image-patch grid 906. As suggested by the overlap between the image-patch grid 906 and a region of the image 912 shown in FIG. 9B, the location-error-prediction system 106 can place multiple image patches of the image 912 within corresponding grid cells of the image-patch grid 906. For example, the location-error-prediction system 106 can utilize the indices of cluster locations closest to the image patch centers of the image 912 to find corresponding affine transformed cluster coordinates (e.g., x and y coordinates in the pixel space), locate the nearest image patch centers of integral pixels (e.g., a center grid cell), and place the image patches within corresponding grid cells.

[0160] As suggested above, in one or more embodiments, the location-error-prediction system 106 places the image patches within the grid cells. For example, the location-error-prediction system can place one image patch of the image 912 within a grid cell of the image-patch grid 906. To illustrate, for a full resolution image-patch grid, the location-error-prediction system 106 places each image patch of the image 912 within a grid cell of the image-patch grid 906 such that each grid cell of the image-patch grid 906 includes at least one corresponding image patch of the image 912. In some cases, the location-error-prediction system 106 places multiple image patches from the image 912 within a single grid cell of the image-patch grid 906 such that each grid cell includes multiple corresponding image patches. Additionally, in one or more implementations, the location-Attorney Docket No. IP-2805-PCT 46 Patent Applicationerror-prediction system 106 places a subset of the image patches within the grid cells to generate a subsampled image-patch grid, as described further below with respect to FIGS. 11-12B.

[0161] After placing image patches, as further depicted in FIG. 9B, the location-error-prediction system 106 performs an act 916 of determining a pair of location errors for the grid cell. In particular, the location-error-prediction system 106 generates the pair of location errors in one or more directions for the predicted locations of the clusters of oligonucleotides. For instance, the location-error-prediction system 106 can determine a location error in the x direction and a location error in the y direction, as described above with respect to FIGS. 8 A and 8B.

[0162] Indeed, in some implementations, the location-error-prediction system 106 can determine grid cell-specific location errors for the predicted locations of the clusters of oligonucleotides. For example, for a given grid cell, the location-error-prediction system 106 can determine a first phase angle between a first pair of band-edge spectral regions to determine a location error in one direction (e.g., an x direction) using the first phase angle and the distance between the clusters of oligonucleotides (e.g., the pitch). Further, in these or other embodiments, the location-error-prediction system 106 can determine a second phase angle between a second pair of band-edge spectral regions to determine a second location error in another direction (e.g., a y direction) using the second phase angle and the distance between the clusters of oligonucleotides. Moreover, in one or more embodiments, the location-error-prediction system 106 utilizes the location errors to determine adjusted locations of the clusters of oligonucleotides within the grid cell.

[0163] After determining a pair of location errors, as further illustrated in FIG. 9B, the location- error-prediction system 106 optionally applies a smoothing model 918 to the cell-specific location errors in the grid cells of the image-patch grid 906. In particular, in some embodiments, the location-error-prediction system 106 determines location errors for a subset of image patches of the image 912 within the subsampled grid cells of a subsampled image-patch grid. In these or other embodiments, the location-error-prediction system 106 utilizes the location errors of the subset of image patches corresponding to the subsampled grid cells to determine location errors for the image patches within the grid cells of the image 912. In some implementations, the location-error- prediction system 106 applies the smoothing model 918 to the location errors of the image patches of the image 912.

[0164] As just mentioned, in one or more embodiments, the location-error-prediction system 106 applies the smoothing model 918 to the location errors of the image patches of the image 912 (e.g., non-subsampled image patches). Specifically, the location-error-prediction system 106 can include smoothing variables of the smoothing model 918 when determining the location errors for across image patches of the image 912 (e.g., across non-subsampled image patches). For instance,Attorney Docket No. IP-2805-PCT 47 Patent Applicationthe location-error-prediction system 106 can utilize an error determination model to determine the location errors for the image patches, as described in further detail below. Indeed, in these or other embodiments, the location-error-prediction system 106 can incorporate the smoothing variables of the smoothing model 918 into the error determination model when determining — and adjusting — the location errors for the image patches to simultaneously determine the location errors for the image patches and apply the smoothing model 918 to the location errors of the image patches of the image 912 — such that the fluctuation of location error between adjacent image patches does not vary above a threshold. Thus, the location-error-prediction system 106 uses the smoothing model to generate smoothed location errors for the predicted locations of the clusters of oligonucleotides across the image patches of the image 912 to avoid abrupt or inconsistent changes in location errors from image patch to image patch. Additional detail regarding the smoothing model 918 and incorporation of the smoothing variables in the error determination model is provided with respect to FIG. 11.

[0165] As mentioned above and as additionally shown in FIG. 9B, in some embodiments, the location-error-prediction system 106 performs an act 920 of determining adjusted locations of the clusters of oligonucleotides within the grid cell based on the location errors. Specifically, for a given grid cell of the image-patch grid 906, the location-error-prediction system 106 utilizes the location errors (or the smoothed location errors) to determine adjusted locations of the clusters of oligonucleotides of the image patch within the grid cell. For example, the location-error-prediction system 106 utilizes the predicted locations of the clusters of oligonucleotides and the location errors to determine the adjusted locations of the cluster of oligonucleotides.

[0166] To illustrate the difference between predicted and adjusted oligonucleotide-cluster locations, as shown in FIG. 9B, images 922 and 924 depict an expected location of a target cluster of oligonucleotides (e.g., location of a nano well comprising an oligonucleotide cluster) as a center black dot in each of the images 922 and 924. The images 922 and 924 further illustrate colored contour rings representing the trained equalizer coefficients based on distorted predicted cluster locations in existing sequencing system radiating outward from the true location of the target cluster of oligonucleotides. Indeed, in some implementations, as predicted cluster locations suffer from a x-direction optical distortion and an equalizer is trained to correct for such an optical distortion, as shown in the image 922, the expected cluster location (shown as the center black dot) of the target cluster of oligonucleotides is positioned left (e.g., in a negative x direction) of the center of the colored contour rings of equalizer coefficients.

[0167] As further shown in FIG. 9B, in one or more embodiments, the location-error-prediction system 106 can determine an adjusted location of the target cluster of oligonucleotides at (or near) the expected location of the target cluster, as illustrated in the image 924. As the adjusted wellAttorney Docket No. IP-2805-PCT 48 Patent Applicationlocations are not distorted and the resulting trained equalizer will not correct optical distortion, the expected location (shown as the center black dot) of the target cluster of oligonucleotides is perfectly positioned at the center of the colored contour rings of equalizer coefficients. For example, the location-error-prediction system 106 determines the adjusted location of the target cluster of oligonucleotides at (or near) the center of the signal emitted from the target cluster by applying (e.g., adjusting in an x and / or y direction) the location errors to the predicted location. Specifically, the location-error-prediction system 106 can add the location error to the predicted location of a target cluster of oligonucleotides. To illustrate, if the location-error-prediction system 106 determines a location error of -0.2 pixels in the x direction, the location-error-prediction system 106 can determine the adjusted location of the target cluster by adjusting the predicted location +0.2 pixels in the x direction. Similarly, if the location-error-prediction system 106 determines a location error of -0.3 pixels in the y direction, the location-error-prediction system 106 can additionally or alternatively determine the adjusted location of the target cluster by adjusting the predicted location +0.3 pixels in the x direction.

[0168] Additionally, in one or more implementations, the location-error-prediction system 106 determines adjusted locations for neighboring clusters of oligonucleotides of the center cluster of oligonucleotides. For example, the location-error-prediction system 106 can determine adjusted locations for the predicted locations of the neighboring clusters of oligonucleotides that are represented by the non-centered black dots in the image 922 and positioned or seeded within a same region or subregion (e.g., tile or sub-tile) of a nucleotide-sample slide. Indeed, the location-error- prediction system 106 can determine the adjusted locations for the neighboring clusters of oligonucleotides by applying a cell-specific location error of the grid cell in which the target and neighboring clusters of oligonucleotides are positioned. Further, in some embodiments, the location-error-prediction system 106 can more accurately base call the target and neighboring clusters of oligonucleotides using the adjusted locations thereof and corresponding intensity values from the target and neighboring clusters of oligonucleotides.

[0169] Moreover, in some implementations, the location-error-prediction system 106 can determine adjusted locations of the clusters of oligonucleotides by utilizing a single-direction location error. For example, in one or more embodiments, the location-error-prediction system 106 can determine the adjusted locations of the oligonucleotide clusters in only an x direction (e.g., using an x error) or in only a y direction (e.g., using a y error). In these or other embodiments, the location-error-prediction system 106 can correct for location errors caused by a single factor, such as optical distortion, jitter, etc.

[0170] As noted above, in some embodiments, the location-error-prediction system 106 generates base calls for clusters of oligonucleotides based on adjusted locations of the clusters ofAttorney Docket No. IP-2805-PCT 49 Patent Applicationoligonucleotides. Specifically, the location-error-prediction system 106 can utilize the adjusted locations of the clusters of oligonucleotides and the intensity values for the signals of the clusters of oligonucleotides in a single channel to determine the base calls for the clusters of oligonucleotides. Furthermore, in one or more implementations, the location-error-prediction system 106 can determine adjusted locations for clusters of oligonucleotides within images captured for each channel from multiple channels of a sequencing device and generate base calls for the clusters of oligonucleotides.

[0171] To illustrate one such multi-channel approach, in some embodiments, the location-error- prediction system 106 can repeat each of the acts described in FIGS. 9A and 9B for each image captured for each of multiple channels of the sequencing device in real time during a sequencing cycle. Under such a multi-channel approach, the location-error-prediction system 106 can identify an adjusted location of a target cluster of oligonucleotides in a first channel shown in the image 924 and an intensity value of the signal of the target cluster in the first channel. Similarly, the location-error-prediction system 106 can identify an additional adjusted location of the target cluster of oligonucleotides in a second channel (not shown) and an intensity value of an additional signal of the target cluster in the second channel. The location-error-prediction system 106 further (i) determines respective nucleobase probabilities for the target cluster of oligonucleotides based on comparing corresponding intensity values of the target cluster of oligonucleotides in each channel and at each adjusted location to intensity-value base-decision boundaries (e.g., a Gaussian distribution with a centroid) and (ii) generates a base call for the target cluster of oligonucleotides based on determining a highest nucleobase probability.

[0172] As mentioned previously, in some embodiments, the location-error-prediction system 106 determines cell-specific location errors for predicted locations of clusters of oligonucleotides. Indeed, in some implementations, the location-error-prediction system 106 can utilize an imagepatch grid to determine the cell-specific location errors for the predicted locations of the clusters of oligonucleotides. In accordance with one or more embodiments, FIGS. 10A and 10B illustrate exemplary heat maps of cell-specific location errors for predicted locations of clusters of oligonucleotides. As an overview, FIG. 10A illustrates an exemplary heat map of cell-specific x location errors determined by the location-error-prediction system 106 for predicted locations of clusters of oligonucleotides depicted by image patches mapped to grid cells of an image-patch grid. Similarly, FIG. 10B illustrates an exemplary heat map of cell-specific y location errors determined by the location-error-prediction system 106 for predicted locations of clusters of oligonucleotides depicted by image patches mapped to grid cells of the image-patch grid.

[0173] As just indicated, in one or more embodiments, the location-error-prediction system 106 can utilize an image-patch grid to determine cell-specific x errors for each grid cell of the image-Attorney Docket No. IP-2805-PCT 50 Patent Applicationpatch grid. As shown in FIG. 10A, a heat map 1002 represents (or depicts a same area as) an image of a region of a nucleotide-sample slide (e.g., an image of a tile of a flow cell). In one or more implementations, the heat map 1002 includes 3,600 image patches, where (i) each image patch includes 64 by 64 pixels and (ii) each image patch depicts a subregion of a nucleotide-sample slide that includes many individual clusters of oligonucleotides (e.g., each subregion includes hundreds or thousands of clusters of oligonucleotides). As further shown in FIG. 10A, each colored dot of the heat map 1002 can represent a single image patch. In these or other embodiments, the colors and corresponding shade of the dots in the heat map 1002 indicate the magnitude of the location error in the x direction.

[0174] As just mentioned, in some embodiments, the colors and corresponding shades of the dots in the heat map 1002 indicate the corresponding magnitude as measured in pixels (e.g., 0.1, 0.3 pixels) of the location error in the x direction. To illustrate, FIG. 10A includes key 1004 that serves as a visual guide for interpreting the x errors of the heat map 1002. Specifically, the key 1004 uses a gradient of colors to indicate the magnitude of the location error in pixels. For example, the key 1004 includes a gradient of colors representing a number of pixels of the location error in an x direction as follows: a first color (e.g., dark red) represents 0.3 pixels, a second color (e.g., light red) represents 0.2 pixels, a third color (e.g., orange) represents 0.1 pixels, a fourth color (e.g., yellow) represents 0.5 pixels, a fifth color (e.g., green represents) 0 pixels (i.e., no error), a sixth color (e.g., light blue) represents -0.1 pixels, a seventh color (e.g., intermediate blue) represents - 0.2 pixels, and an eighth color (e.g., dark blue) represents -0.3 pixels. In these or other embodiments, a positive value represents an error in the positive direction (e.g., to the right) and a negative value represents an error in the negative direction (e.g., to the left). In some implementations, as shown in FIG. 10A, the heat map 1002 also includes scale indicators on the bottom and left axes indicating the size of the heat map 1002 measured in pixels (e.g., approximately 2,800 pixels on the y axis by 5,000 pixels on the x axis).

[0175] As noted previously, in one or more embodiments, the location-error-prediction system 106 can utilize an image-patch grid to determine cell-specific x errors for each grid cell of the image-patch grid. In particular, the location-error-prediction system 106 can determine the cellspecific x errors for each individual grid cell of the image-patch grid. For a single image patch that corresponds to a single grid cell and that has been subject to a Fast Fourier Transform operation, for example, the location-error-prediction system 106 identifies one or more pairs of band-edge spectral regions within a spatial frequency band of a transformed image patch, determines a phase difference between each band-edge spectral region of the one or more pairs of band-edge spectral regions, and generates the x location error based on the phase difference, as described above with respect to FIGS. 3-9B. Such an x location error determined for an individual transformed imageAttorney Docket No. IP-2805-PCT 51 Patent Applicationpatch can accordingly be used as a cell-specific x error for all predicted cluster locations within a grid cell.

[0176] As further illustrated in FIG. 10A, in one or more implementations, the heat map 1002 illustrates general patterns of x location errors as determined by the location-error-prediction system 106. Specifically, FIG. 10A illustrates a first color band 1006 of varying shades of a first color (e.g., red) running from top to bottom on the left side of the heat map 1002, a second color band 1008 of varying shades of the first color (e.g., red) running from top to bottom on the right side of the heat map 1002, and a third color band 1010 of varying shades of a second color (e.g., blue) running from top to bottom in the middle of the heat map 1002. As indicated above, the first color band 1006, the second color band 1008, and the third color band 1010 each indicate a pattern of location error in an x direction caused by optical distortion. The relationship between such general patterns of x errors and optical distortion is discussed above with respect to FIG. 7.

[0177] In addition to determining cell-specific y errors, in some embodiments, the location- error-prediction system 106 utilizes an image-patch grid to determine cell-specific y errors for each grid cell of the image-patch grid. As shown in FIG. 10B, a heat map 1012 represents (or depicts a same area as) an image of a region of a nucleotide-sample slide (e.g., an image of a tile of a flow cell). Similar to the heat map 1002 depicted in FIG. 10A, the heat map 1012 depicted in FIG. 10B includes 3,600 image patches, where (i) each image patch includes 64 by 64 pixels, (ii) each image patch depicts a subregion of a nucleotide-sample slide that includes many individual clusters of oligonucleotides (e.g., each subregion includes hundreds or thousands of clusters of oligonucleotides), and (iii) each colored dot of the heat map 1012 can represent a single image patch. Similarly, the colors and corresponding shade of the dots in the heat map 1012 indicate the magnitude of the location error in the y direction.

[0178] As indicated by a key 1014 in FIG. 10B, in one or more embodiments, the colors and corresponding shades of the dots indicate the magnitude as measured in pixels of the location error in the y direction. Just like the key 1004 in FIG. 10 A, the key 1014 in FIG. 10B uses a gradient of colors to indicate the magnitude of the location error as measured in pixels. For example, the key 1014 includes a gradient of colors representing a number of pixels for the location error in a y direction using the same pixel measurements (e.g., 0.1, -0.1) and up-and-down directions (e.g., positive = down, negative = up) as described above for the key 1004.

[0179] As previously mentioned, in some embodiments, the location-error-prediction system 106 can utilize an image-patch grid to determine cell-specific y errors for each grid cell of the image-patch grid. For a single image patch that corresponds to a single grid cell and that has been subject to a Fast Fourier Transform (FFT) operation, for example, the location-error-prediction system 106 identifies one or more pairs of band-edge spectral regions in a transformed image patch,Attorney Docket No. IP-2805-PCT 52 Patent Applicationdetermines a phase difference between each band-edge spectral region, and generates the y location error based on the phase difference, as described above with respect to FIGS. 3-9B. Such a y location error determined for an individual transformed image patch can accordingly be used as a cell-specific y error for all predicted cluster locations within a grid cell.

[0180] As also depicted in FIG. 10B, in some implementations, the heat map 1012 illustrates general patterns of y location errors as determined by the location-error-prediction system 106. Specifically, FIG. 10B illustrates a first color band 1016 of varying shades of a first color (e.g., blue) at the top of the heat map 1012, a second color band 1018 of varying shades of a second color (e.g., yellow) located beneath the first color band 1016, and a third color band 1020 of varying shades of the first color (e.g., blue) near the bottom of the heat map 1012. As indicated above, the first color band 1016, the second color band 1018, and the third color band 1020 each indicate a pattern of location error in a y direction caused by jitter. The relationship between such general patterns of y errors and jitter are discussed above with respect to FIG. 7.

[0181] In one or more embodiments, as previously noted with respect to FIG. 7, the location- error-prediction system 106 can reduce the computing power required for base calling clusters of oligonucleotides by utilizing a subsampled image-patch grid when determining adjusted locations of clusters of oligonucleotides. For example, the location-error-prediction system 106 can utilize subsampled image-patch grids as described with respect to FIGS. 11, 12A-12B, 13A-13B, and 14. The following paragraphs describe FIGS. 11 - 14 and corresponding image-patch grids.

[0182] As mentioned above, in one or more implementations, the location-error-prediction system 106 can utilize a subsampled image-patch grid when determining adjusted locations of clusters of oligonucleotides. Indeed, in some embodiments, the location-error-prediction system 106 can utilize a uniform subsampled image-patch grid or a staggered subsampled image-patch grid for determining adjusted locations of clusters of oligonucleotides on a nucleotide-sample slide. FIG. 11 illustrates a uniform subsampled image-patch grid and a staggered subsampled imagepatch grid in accordance with one or more embodiments.

[0183] As illustrated in FIG. 11, in some implementations, the location-error-prediction system 106 can access a subsampled image-patch grid to segment image patches of a nucleotide-sample- slide region image and determine location errors for the grid cells as described above with respect to FIGS. 9A and 9B. As depicted in FIG. 11, for example, the location-error-prediction system 106 can access a uniform subsampled image-patch grid 1100 or a staggered subsampled image-patch grid 1102. In these or other embodiments, the uniform subsampled image-patch grid 1100 and the staggered subsampled image-patch grid 1102 each include subsampled grid cells, as illustrated in FIG. 11 by the solid squares.Attorney Docket No. IP-2805-PCT 53 Patent Application

[0184] In one or more embodiments, each of the uniform subsampled image-patch grid 1100 and the staggered subsampled image-patch grid 1102 can include varying numbers of grid cells in varying layouts. For instance, each of the uniform subsampled image-patch grid 1100 and the staggered subsampled image-patch grid 1102 include a set of 216 subsampled grid cells in a layout comprising 48 grid cells in the y direction by 72 grid cells in the x direction. To further illustrate, the uniform subsampled image-patch grid 1100 includes one of every four grid cells as a subsampled grid cell resulting in a 12 by 18 subsampled grid with 216 subsampled grid cells in total. The number and layout of the subsampled grid cells of a subsampled image-patch grid can vary according to the particular embodiments (e.g., 24 by 36 grid cells for a subsampled imagepatch grid, 40 by 60 grid cells for a subsampled image-patch grid) or can vary within a single application. Indeed, additional examples of subsampled image-patch grids are included in FIGS. 12A and 12B.

[0185] In one or more implementations, uniform subsampled image-patch grids include the subsampled grid cells at a uniform y coordinate in the x direction and a uniform x coordinate in the y direction. In other words, the subsampled grid cells are arranged or intersect at a uniform y coordinate across the rows and at a uniform x coordinate down the columns as shown in the uniform subsampled image-patch grid 1100.

[0186] In contrast to such uniform subsampled image-patch grids, in some embodiments, the location-error-prediction system 106 can access or use staggered subsampled image-patch grids that include the subsampled grid cells at different offsets. As shown in FIG. 11, for example, the staggered subsampled image-patch grid 1102 includes four offsets such that the subsampled grid cells are staggered relative to one another in an x direction and a y direction. Indeed, staggered subsampled image-patch grid 1102 includes the first four subsampled grid cells in the top row such that each successive subsampled grid cell is at a different y coordinate than the others. Further, the staggered subsampled image-patch grid 1102 includes this four-offset staggering (in the y direction) of subsampled grid cells repeated in the next four subsampled grid cells of the top row. Furthermore, the staggered subsampled image-patch grid 1102 continues to repeat this pattern across the first row and in each subsequent row.

[0187] As further shown in FIG. 11, the staggered subsampled image-patch grid 1102 includes an additional four offset staggering of the subsampled grid cells in each column. For example and as shown in FIG. 11, the staggered subsampled image-patch grid 1102 includes the first four subsampled grid cells in the left-most column such that each successive subsampled grid cell is at a different x coordinate than the others. Moreover, the staggered subsampled image-patch grid 1102 includes this four-offset staggering (in the x direction) of subsampled grid cells repeated in the next four subsampled grid cells of the left column. Additionally, the staggered subsampledAttorney Docket No. IP-2805-PCT 54 Patent Applicationimage-patch grid 1102 continues to repeat this pattern across the left-most column and in each subsequent column.

[0188] The location-error-prediction system 106 can use such a subsampled image-patch grid to selectively and more efficiently determine location errors of predicted oligonucleotide-cluster locations for oligonucleotide clusters positioned within different sections of an image of a nucleotide-sample-slide region (e.g., a tile of a flow cell) — rather than determine location errors independently for oligonucleotide clusters positioned within each and every section of such a nucleotide-sample-slide-region image. To do so, in one or more embodiments, the location-error- prediction system 106 can determine cell-specific location errors for grid cells of a non-subsampled image-patch grid, where the grid cells correspond to image patches, based on corresponding location errors of subsampled grid cells of a subsampled image-patch grid, where the subsampled grid cells correspond to subsampled image patches of a nucleotide-sample-slide-region image.

[0189] To leverage location errors determined for a subsampled grid cell for location errors in other, surrounding subsampled grid cells, however, the location-error-prediction system 106 initially determines location errors for such a subsampled grid cell. For example, the location-error- prediction system 106 can determine a total cell-specific location error for a grid cell of the imagepatch grid by summing an optical distortion vector and a jitter vector. Specifically, the location- error-prediction system 106 can determine an optical distortion vector for a grid cell of the imagepatch grid that estimates the optical distortion in a first direction and represents the cell-specific location error in the first direction (e.g., a x direction). Similarly, the location-error-prediction system 106 can determine a jitter vector for the grid cell of the image-patch grid that estimates the jitter in a second direction and represents the cell-specific location error in the second direction (e.g., an y direction). Rather than determine location errors and / or both an optical distortion vector and a jitter vector for each individual grid cell in an image-patch grid, however, the location-error- prediction system 106 can determine cell-specific location errors for subsampled grid cells and subsequently utilize an error determination model, such as a least-squares model, to (i) determine optical distortion and jitter vectors for oligonucleotide clusters located in subsampled grid cells based on corresponding cell-specific location errors and (ii) map the location errors based on optical distortion and jitter vectors to corresponding grid cells of a larger, non-subsampled image-patch grid.

[0190] As just mentioned, in some embodiments, the location-error-prediction system 106 can utilize a least-squares model to efficiently determine optical distortion and jitter vectors for subsampled grid cells of a subsampled image-patch grid. For example, the location-error- prediction system 106 can utilize a least-squares model to determine the optical distortion and jitter vectors by (i) determining observed band-edge-region errors (v) representing a pair of band-edgeAttorney Docket No. IP-2805-PCT 55 Patent Applicationspectral regions within an image of a subregion of a nucleotide-sample slide based on Equations (1) - (10) above and (ii) determining estimated band-edge-region errors representing the pair of band-edge spectral regions based on an optical distortion vector and a jitter vector (e.g., v = Aj + Bd). As described below, the location-error-prediction system 106 determines the relevant optical distortion vector and jitter vector resulting from minimizing a least squared error between the observed band-edge-region errors (v) and the estimated / predicted band-edge-region errors (v).

[0191] To illustrate, the location-error-prediction system 106 can determine the optical distortion and jitter vectors utilizing a least-squares model according to the following Equation (H):In Equation (11 ), j represents the jitter vector (e.g., estimated jitter vector), d represents the optical distortion vector (e.g., estimated optical distortion vector), and v represents the observed band- edge-region errors, as noted above. Further, A and B represent matrices as described below and the location-error-prediction system 106 defines p.M JVaccording to Equation (15) as described below. In these or other embodiments, the matrix representing the subsampled image-patch grid (also referred to herein as the “C matrix”) includes the following term from the least-squares model:As mentioned above and in Equation (12), in these or other embodiments, the location-error- prediction system 106 determines the jitter vector O') and the optical distortion vector (d) by determining observed band-edge-region errors (v) from Equations (1) - (10) above utilizing a subsampled image-patch grid. In particular, the location-error-prediction system 106 determines a length-M column vector representing jitter (j) and a length- column vector representing optical distortion (d). In this example, the location-error-prediction system 106 determines matrices A and B by initializing A and B to be all-zero matrices of L x M and / . x N, respectively. Then for every unique mapped index I 6 1<-> (m,ri), set Ai m= 1 and Bt n= 1. In these or other embodiments, A represents the number ofnon-zero elements in an MxN matrix PHlE{0,l}, where 0 indicates that no estimate of a total location error is present (e.g., because the image-patch grid is a subsampled image-patch grid). Furthermore, in some embodiments, the location-error-prediction system 106 defines n as a vector of random noise that has assumed zero-mean with variance o^.

[0192] As mentioned above when applying a least-squares model, the location-error-prediction system 106 determines the relevant optical distortion vector and jitter vector resulting from a least squared error between the observed band-edge-region errors and the estimated band-edge-regionAttorney Docket No. IP-2805-PCT 56 Patent Applicationerrors. Accordingly, the location-error-prediction system 106 can further determine estimated band-edge-region errors. Specifically, the location-error-prediction system 106 can determine the estimated band-edge-region errors according to the following Equation (13): v = Aj + Bd + n (13)In Equation (13), A and B represent the same matrices as described above, j represents the jitter vector, and d represents the optical distortion vector. Additionally, in some implementations, the location-error-prediction system 106 minimizes the squared error between the observed band-edge- region errors v and the estimated band-edge-region errors v according to the following Equation (14):Further, in the least-squares model shown above, the location-error-prediction system 106 defines pm,n according to the following Equation (15):In these or other embodiments, IRK denotes a length- ^ row vector of ones. Moreover, in one or more embodiments, the C matrix (and therefore the subsampled image-patch grid) may not be full rank. In these or other embodiments, the location-error-prediction system 106 can access a full rank subsampled image-patch grid as described below with respect to FIGS. 13 A and 13B.

[0193] As indicated above, a location error determined from image patch to image patch — and corresponding grid cell to grid cell — may differ or abruptly change outside an expected deviation. To avoid such inconsistencies and abrupt location-error deviations between neighboring image patches, the location-error-prediction system 106 can use a smoothing model. Accordingly, in one or more implementations, the location-error-prediction system 106 can incorporate smoothing variables of a smoothing model into the least-squares model when determining the jitter and optical distortion vectors. Specifically, the location-error-prediction system 106 can incorporate smoothness terms into the least-squares model in a variety of ways including according to the following Equation (16):Attorney Docket No. IP-2805-PCT 57 Patent ApplicationIn Equation (16), the symbols kj and kd represent smoothing variables form a smoothing model and the location-error-prediction system 106 defines H according to the Equation (19) as shown below. Further 0NxMand 0MxJVrepresent all-zero matrices of size N x M and M x N, respectively. In these or other embodiments, the C matrix representing the subsampled image-patch grid includes the following term from the least-squares model:

[0194] Additionally, in some embodiments, the location-error-prediction system 106 minimizes the squared error between the observed band-edge-region errors and the estimated band-edge- region errors according to the following Equation (18):

[0195] According to Equation (18), by adding two smoothing terms including kj and kdthe location-error-prediction system 106 reduces the abrupt changes or differences in cell-specific location errors determined between adjacent grid cells or between corresponding image patches. In these or other embodiments, the location-error-prediction system defines Hk according to the following Equation (19):In Equation 19, HKhas a size as follows: (K-2) x K. Thus, the location-error-prediction system can penalize j and d for being non-smooth. In these or other embodiments, the magnitude of the penalty depends on smoothing variables kj and kd.

[0196] In the alternative to a least-square model, the location-error-prediction system 106 can use a generalized mean-square model to (i) determine optical distortion and jitter vectors for oligonucleotide clusters located in subsampled grid cells based on corresponding cell-specific location errors and (ii) map the determined optical distortion and jitter vectors to corresponding grid cells of a larger, non-subsampled image-patch grid. In some implementations, the location- error-prediction system 106 utilizes such a mean-square model to determine the optical distortion and jitter vectors according to the following Equation (20):Attorney Docket No. IP-2805-PCT 58 Patent Application

[0197] In Equation (20), the symbol o'2represents the variance. Further, W represents the combined jitter vector (j) and optical distortion vector (d). Moreover, Equation (20) incorporates smoothing terms Rj, Rjd, and R that the location-error-prediction system 106 defines according to the following respective Equations (21), (22), and (23):

[0198] As mentioned above, j represents a jitter vector (e.g., an observed jitter vector) and d represents an optical distortion vector (e.g., an observed optical distortion vector). Further, 0NxMand 0MxJVrepresent all-zero matrices of size N x M and M x N respectively as described above with respect to Equation (16). In these or other embodiments, the location-error-prediction system 106 determines W to minimize the following Equation (24):

[0199] As noted previously, in one or more implementations, the location-error-prediction system 106 determines a total cell-specific location error for each grid cell of the image-patch grid by summing an optical distortion vector and a jitter vector. In particular, the location-error- prediction system 106 sums the optical distortion vector and the jitter vector to determine a total cell-specific location error for each grid cell that the location-error-prediction system 106 can apply to the predicted locations of the clusters of oligonucleotides mapped to the image patches within the grid cells. To illustrate, the location-error-prediction system 106 can generate a full-resolution image-patch grid with cell-specific location errors for each grid cell based on the optical distortion vector and the jitter vector. Furthermore, the location-error-prediction system 106 utilizes the cellspecific location errors for each grid cell to determine adjusted locations of the clusters of oligonucleotides of each image patch within each grid cell. By generating the full-resolution image patch grid using the optical distortion vector and the jitter vector obtained from a subsampledAttorney Docket No. IP-2805-PCT 59 Patent Applicationimage-patch grid, the location-error-prediction system 106 preserves computing efficiency relative to alternative approaches to cluster-location prediction.

[0200] As previously mentioned, in some implementations, the location-error-prediction system 106 can utilize a subsampled image-patch grid when determining adjusted locations of clusters of oligonucleotides. As further mentioned above, the number and layout of the subsampled grid cells of a subsampled image-patch grid can vary. In accordance with one or more embodiments, FIGS. 12A and 12B illustrate exemplary subsampled image-patch grids.

[0201] As shown in FIGS. 12A and 12B, in one or more embodiments, the location-error- prediction system 106 can access a wide variety of subsampled image-patch grids. Specifically, the location-error-prediction system 106 can access subsampled image-patch grids with a wide variety of subsampled grid cell layouts when determining adjusted locations for the clusters of oligonucleotides within image patches as described above with respect to FIGS. 9A, 9B, and 11. For example, the location-error-prediction system 106 can access subsampled image-patch grids, such as subsampled image-patch grids 1206 and 1212.

[0202] Additionally, in one or more implementations, the location-error-prediction system 106 can also access full-resolution image-patch grids, such as full -resolution image-patch grid 1200. In some embodiments, the solid-filled grid cells of the image-patch grids 1200-1216 represent sampled grid cells. A sampled grid cell, for example, includes a grid cell for which the location- error-prediction system 106 determines location errors by determining a phase difference between one or more pairs of band-edge spectral regions of the image patch within the grid cell as described in FIGS. 8A and 8B. For example, the location-error-prediction system 106 can sample every grid cell in a full -resolution image-patch grid as exemplified by the full-resolution image-patch grid 1200. In contrast, for a subsampled image-patch grid, the location-error-prediction system 106 may only sample a portion of the grid cells as exemplified by the solid squares of the subsampled image-patch grids 1206 and 1212. As used herein, the term “subsampled grid cell” refers to the sampled grid cells of a subsampled image-patch grid.

[0203] As further illustrated in FIG. 12 A, in some implementations, the location-error- prediction system 106 can access subsampled image-patch grids with many different layouts of the sampled grid cells. In one or more implementations, the full-resolution image-patch grid 1200 (e.g., PHI matrix) is alternatively represented as shown in A matrix 1202 and B matrix 1204. Further, in one or more implementations, the location-error-prediction system 106 can access a subsampled image-patch grid with subsampled grid cell columns wherein one or more subsampled grid cells in a column are offset from other subsampled grid cells in the column as illustrated by the subsampled image-patch grid 1206. In some embodiments, the subsampled image-patch grid 1206 (e.g., PHI matrix) is alternatively represented as shown in A matrix 1208 and B matrix 1210.Attorney Docket No. IP-2805-PCT 60 Patent ApplicationSimilarly, as shown in FIG. 12B, the subsampled image-patch grid 1212 (e.g., PHI matrix) is alternatively represented as shown in A matrix 1214 and B matrix 1216.

[0204] As additionally shown in FIGS. 12A and 12B, in some implementations, the location- error-prediction system 106 access subsampled image-patch grids with varying numbers of rows and columns. Specifically, a subsampled image-patch grid can include various numbers of rows and / or columns. For example, the location-error-prediction system 106 can access a subsampled image-patch grid with various numbers of rows, such as 4, 12, 24, 32, 48, 216, and others. Moreover, the location-error-prediction system 106 can access a subsampled image-patch grid with various numbers of columns such as 4, 8, 12, 24, 72, and others. Furthermore, in one or more embodiments, the location-error-prediction system 106 access subsampled image-patch grids with various numbers of subsampled grid cells such as 24, 32, 216, and others.

[0205] As previously noted, in one or more implementations, the location-error-prediction system 106 can access a subsampled image patch-grid to determine the location errors for the image patches of a nucleotide-sample-slide region image. Indeed, in some embodiments, the location- error-prediction system 106 can access a staggered subsampled image-patch grid for determining the location errors of the image patches. In these or other embodiments, the location-error- prediction system 106 accesses a shifted staggered subsampled image-patch grid to determine the location errors of the image patches. FIG. 13 A illustrates a shifted staggered subsampled imagepatch grid in accordance with one or more embodiments.

[0206] As portrayed in FIG. 13 A, in some implementations, the location-error-prediction system 106 can access a staggered subsampled image-patch grid 1300 to determine the location errors of the image patches corresponding to the grid cells of these image-patch grids. Specifically, in some instances, the C matrix defined in Equation (12) corresponding to the staggered subsampled image-patch grid 1300 can be rank deficient. For example, the staggered subsampled image-patch grid 1300 represents a matrix of 48 rows and 72 columns of subsampled grid cells as illustrated by the solid squares of the staggered subsampled image-patch grid 1300. For example, in one or more embodiments, the staggered subsampled image-patch grid 1300 can represent a C matrix as described above with respect to the least-squares model for determining jitter and optical distortion vectors of FIG. 11. The staggered subsampled image-patch grid 1300 further includes 12 identical 16 by 16 blocks as outlined by the grid lines of the staggered subsampled image-patch grid 1300. The C matrix defined in Equation (12) corresponding to the staggered subsampled image-patch grid 1300 is rank deficient by 15 as illustrated in FIG. 13B.

[0207] As further illustrated in FIG. 13 A, in one or more implementations, the location-error- prediction system 106 can access a shifted staggered subsampled image-patch grid 1302. In particular, the location-error-prediction system 106 can access the shifted staggered subsampledAttorney Docket No. IP-2805-PCT 61 Patent Applicationimage-patch grid 1302, which represents the staggered subsampled image-patch grid 1300 with various 16 by 16 blocks shifted (e.g., by a circular shift) as illustrated by the shifted blocks 1304. In some embodiments, the location-error-prediction system 106 can access the shifted staggered subsampled image-patch grid 1302 with various of the 16 by 16 blocks shifted in either a horizontal or vertical direction. For instance, the shifted blocks 1304 (i.e., blocks 1-4, 6, and 8) show the amount of each shift of the various 16 by 16 blocks. In these or other embodiments, the C matrix defined in Equation (12) corresponding to the shifted staggered subsampled image-patch grid 1302 is a full-rank matrix as shown in FIG. 13B and described further below. Additionally, in these or other embodiments, the shifted staggered subsampled image-patch grid 1302 preserves the rowheights and the column- weights of the staggered subsampled image-patch grid 1300.

[0208] As mentioned above, the C matrix defined in Equation (12) corresponding to the staggered subsampled image-patch grid 1300 is rank deficient while the shifted staggered subsampled image-patch grid 1302 is full-rank. FIG. 13B illustrates an Eigenvalue graph of the staggered subsampled image-patch grid 1300 matrix and the shifted staggered subsampled imagepatch grid 1302 matrix.

[0209] As depicted in FIG. 13B, the staggered subsampled image-patch grid 1300 is rank deficient. Specifically, the staggered subsampled image-patch grid 1300 is rank deficient by 15 as illustrated in the Eigenvalue graph 1306. In particular, the Eigenvalue graph 1306 illustrates the square root of the Eigenvalues of the C matrix defined in Equation (12) on the y axis against the rank on the x axis for the matrices of the staggered subsampled image-patch grid 1300 and the shifted staggered subsampled image-patch grid 1302. For example, the Eigenvalue graph 1306 shows the square roots of the Eigenvalues of the C matrix of the staggered subsampled image-patch grid 1300 plotted with a dashed line 1308. As illustrated, the plotted square roots of the Eigenvalues of the matrix of the staggered subsampled image-patch grid 1300 have a maximum rank of 105 which is 15 short of the required 120 for a full-rank matrix. In contrast, the Eigenvalue graph 1306 shows the square roots of the Eigenvalues of the matrix of the shifted staggered subsampled imagepatch grid 1302 plotted with a solid line 1310. As illustrated in FIG. 13B, the plotted square roots of the Eigenvalues of the shifted staggered subsampled image-patch grid 1302 reach a rank of 120. Thus, the matrix of the shifted staggered subsampled image-patch grid 1302 is a full-rank matrix.

[0210] As noted above, in some implementations, the location-error-prediction system 106 can incorporate smoothing variables of a smoothing model into the error determination model when determining location errors for the predicted locations of the clusters of oligonucleotides of a nucleotide-sample slide. Indeed, in one or more embodiments, the location-error-prediction system 106 can incorporate smoothing variables of the smoothing model into the error determination model to minimize an error (e.g., a least squares error or a mean square error) of the grid cells.Attorney Docket No. IP-2805-PCT 62 Patent ApplicationFIG. 14 illustrates mean square errors of the grid cells of a subsampled image-patch grid in accordance with one or more embodiments.

[0211] As illustrated in FIG. 14, in one or more implementations, the location-error-prediction system 106 accesses a subsampled image-patch grid 1400 to determine the location errors for a full-resolution image-patch grid based on an optical distortion vector and a jitter vector as described above with respect to FIG. 11. Specifically, the location-error-prediction system 106 determines cell-specific location errors for each of the subsampled grid cells (shown as solid boxes in the subsampled image-patch grid 1400) from phase differences between pairs of band-edge spectral regions of the image patches within the subsampled grid cells as described with respect to FIGS. 9A-9B. Further, in some embodiments, the location-error-prediction system 106 determines the location errors for each of the grid cells of a full-resolution image-patch grid based on an optical distortion vector and a jitter vector. In these or other embodiments, when determining the optical distortion vector and the jitter vector the location-error-prediction system 106 can minimize an error (e.g., a least squares error or a mean square error) between an observed band-edge-region errors and the estimated band-edge-region errors.

[0212] As mentioned previously, in some implementations, the location-error-prediction system 106 can minimize an error (e.g., a mean square error) between observed band-edge-region errors and estimated band-edge-region errors. For example, as shown in FIG. 14, an analytical heat map 1402 illustrates mean square errors for the grid cells of the full-resolution image-patch grid that the location-error-prediction system 106 generated from the subsampled image-patch grid 1400 without incorporating smoothing variables into the mean-square model. Moreover, the analytical heat map 1402 includes key 1404 that serves as a visual guide for interpreting the mean square errors of the analytical heat map 1402. Specifically, the key 1404 uses a gradient of colors ranging from one color to another color (e.g., dark red to purple) representing mean square errors from 0.9 to 0.01. For example, the colors of the key 1404 represent mean square errors as follows: a first color (e.g., dark red) represents a mean square error of 0.09, a second color (e.g., red) represents a mean square error of 0.08, a third color (e.g., orange) represents a mean square error of 0.07, a fourth color (e.g., yellow) represents a mean square error of 0.055, a fifth color (e.g., green) represents a mean square error of 0.045, a sixth color (e.g., blue) represents a mean square error of 0.03, a seventh color (e.g., dark blue) represents a mean square error of 0.02, and an eighth color (e.g., purple) represents a mean square error of 0.01.

[0213] As also depicted in FIG. 14, the analytical heat map 1402 includes sharp transitions between the mean square errors of the image patches. For instance, the analytical heat map 1402 includes image patches of a first color (e.g., yellow), such as image patch 1406 indicating relatively low mean square errors of about 0.055. These image patches of a first color in the analytical heatAttorney Docket No. IP-2805-PCT 63 Patent Applicationmap 1402 correspond to the subsampled grid cells of the subsampled image-patch grid 1400. Further, the remaining grid cells of the analytical heat map 1402 are generally image patches of a second color (e.g., red), such as grid cell 1408, or image patches of a third color (e.g., dark red), such as grid cell 1410, indicating relatively high mean square errors of about 0.08 and 0.09, respectively. Thus, the analytical heat map 1402 illustrates sharp transitions of mean square errors between the first-color (e.g., yellow) image patches corresponding to the subsampled grid cells of the subsampled image-patch grid 1400 and the second-color (e.g., red) and third-color (e.g., dark red) image patches corresponding to the image patches of the subsampled image-patch grid 1400. Accordingly, the analytical heat map 1402 illustrates that without the smoothing variables incorporated into the mean-square model, the location-error-prediction system 106 generates a fullresolution image-patch grid with high variation of mean square errors between image patches.

[0214] As further illustrated in FIG. 14, a smoothed analytical heat map 1412 illustrates mean square errors for the grid cells of the full-resolution image-patch grid that the location-error- prediction system 106 generated from the same subsampled image-patch grid 1400 with smoothing variables incorporated into the mean-square model. Furthermore, the smoothed analytical heat map 1412 includes key 1414 which, just like the key 1404, uses a gradient of colors ranging from one color to another color (e.g., dark red to purple) representing mean square errors. However, unlike the key 1404 which represents mean square errors from 0.9 to 0.01, the key 1414 represents mean square errors from 0.5 to 0.005. For example, the colors of the key 1414 represent mean square errors as follows: a first color (e.g., dark red) represents a mean square error of 0.05, a second color (e.g., red) represents a mean square error of 0.045, a third color (e.g., orange) represents a mean square error of 0.035, a fourth color (e.g., yellow) represents a mean square error of 0.03, a fifth color (e.g., green) represents a mean square error of 0.02, a sixth color (e.g., blue) represents a mean square error of 0.015, a seventh color (e.g., dark blue) represents a mean square error of 0.01, and an eighth color (e.g., purple) represents a mean square error of 0.005.

[0215] As additionally shown in FIG. 14, the smoothed analytical heat map 1412 includes smoothed transitions between the mean square errors of the image patches and generally lower mean square errors. For instance, the smoothed analytical heat map 1412 includes image patches of a first color (e.g., yellow), such as image patch 1416, and image patches of a second color (e.g., green), such as image patch 1418, indicating relatively low mean square errors of about 0.030 and 0.02, respectively. These image patches of a first and second color include the bulk of the image patches of the smoothed analytical heat map 1412 and do not strongly correspond to the subsampled grid cells of the subsampled image-patch grid 1400. Further, the remaining grid cells of the smoothed analytical heat map 1412 are generally image patches of a third color (e.g., light red), such as grid cell 1420 indicating slightly higher, but still relatively low mean square errors of aboutAttorney Docket No. IP-2805-PCT 64 Patent Application0.035 to 0.04. Thus, the smoothed analytical heat map 1412 illustrates smoothed transitions of mean square errors and generally lower mean square errors for all the image patches. Accordingly, the smoothed analytical heat map 1412 illustrates that by incorporating the smoothing variables, the location-error-prediction system 106 generates a full -resolution image-patch grid with low variation of mean square errors and generally low mean square errors. By including the smoothing variables of a smoothing model into the error determination model, in one or more embodiments, the location-error-prediction system 106 more accurately identifies the location errors of the grid cells of a full-resolution image-patch grid generated from a subsampled image-patch grid.

[0216] As noted previously, in one or more implementations, the location-error-prediction system 106 generates base calls for the clusters of oligonucleotides based on the adjusted locations of the clusters of oligonucleotides and intensity values for signals of the cluster of oligonucleotides, as described above with respect to FIGS. 9A and 9B. Indeed, in some embodiments, the location- error-prediction system 106 improves the accuracy of base calling relative to existing sequencing systems as illustrated by various metrics including a Percent Passing Filter (% Pf) metric and a Percent Quality Score 30 (% Q30) metric. FIG. 15A illustrates summary tables of sequencing run statistics in accordance with one or more embodiments. FIG. 15B illustrates a quality score graph in accordance with one or more embodiments.

[0217] As portrayed in FIG. 15 A, in some implementations, the location-error-prediction system 106 improves % Pf relative to existing sequencing systems using existing location-error- prediction techniques. Specifically, the % Pf metric indicates the percentage of clusters of oligonucleotides on a nucleotide-sample slide that pass quality filtering criteria of a sequencing device, such as satisfying a chastity value for an oligonucleotide cluster or corresponding nucleotide read. In one or more embodiments, the quality filtering criteria of sequencing devices include signal intensity and SNR, among others, which in turn depend on accurate determinations of locations of the clusters of oligonucleotides. In one or more implementations, the location-error- prediction system 106 more accurately determines locations of clusters of oligonucleotides by determining adjusted locations of the clusters of oligonucleotides as described above. Accordingly, in some embodiments, by determining the adjusted locations and generating base calls based on the adjusted locations, as previously described, the location-error-prediction system 106 improves the % Pf, as illustrated by summary tables 1500 and 1502. Specifically, in these or other embodiments, by accurately determining locations of clusters of oligonucleotides, the location- error-prediction system 106 extracts higher quality intensity signals with a higher SNR relative to existing sequencing systems.

[0218] As just mentioned, the location-error-prediction system 106 improves the % Pf as illustrated by summary tables 1500 and 1502. Specifically, in some implementations, the location-Attorney Docket No. IP-2805-PCT 65 Patent Applicationerror-prediction system 106 improves the % Pf by several percentage points. For example, summary table 1500 illustrates statistics of two mates from paired-end reads, R1 and R2, using existing location-error-prediction techniques. In particular, the % Pf for each of the read mates R1 and R2 of summary table 1500 is 74.12%. In contrast, summary table 1502 illustrates statistics of two mates from paired-end reads, R1 and R2, using the location-error-prediction system 106 to determine adjusted locations of the clusters of oligonucleotides, as described above, and generating base calls from the adjusted locations. Additionally, the location-error-prediction system 106 incorporated a smoothing model as described above for the read mates R1 and R2 of paired-end reads of the summary table 1502. The % Pf for each of the read mates R1 and R2 of paired-end reads of the summary table 1502 is 76.44%. Thus, in this example, the location-error-prediction system 106 improved the % Pf by 2.32% relative to conventional location-error-prediction techniques. For certain nucleotide-sample slides comprising 25 billion nano wells for oligonucleotide clusters, for example, a one percent increase in % Pf corresponds to a yield increase of 250 million nucleotide reads.

[0219] As previously mentioned, FIG. 15B illustrates a quality score graph 1504 in accordance with one or more embodiments. Specifically, the quality score graph 1504 illustrates that the location-error-prediction system 106 improves the percentage of clusters of oligonucleotides with a PhRED-scaled quality score (also referred to as a Q-score) meeting a threshold quality criterion (e.g., a Q-score of 30 or higher) in each sequencing run of a sequencing device relative to existing sequencing systems using existing location-error-prediction techniques. In one or more embodiments, Q-score measures the accuracy of base calls on a nucleotide read or, more generally, a sequencing run. A Q-score of 30 indicates that there is a 1 in 1,000 chance of an incorrect base call. Thus, a Q-score of 30 or higher represents an accurate base call with a very low chance of error. The percent Q30 (% Q30) assesses the percentage of base calls with a Q-score of 30 or higher for a sequencing cycle. In one or more implementations, one factor required for accurate base calls that can reach a Q-score of 30 or higher is the accuracy of the location of the clusters of oligonucleotides. Accordingly, in some embodiments, by determining more accurate adjusted locations of the clusters of oligonucleotides, the location-error-prediction system 106 improves the % Q30 as illustrated in the quality score graph 1504.

[0220] As just mentioned, the location-error-prediction system 106 improves the % Q30 as illustrated in the quality score graph 1504. Specifically, in some implementations, the location- error-prediction system 106 improves the % Q30 by several percentage points at any given cycle. For example, the quality score graph 1504 includes the % Q30 on the x axis and the cycle number on the y axis. Additionally, the quality score graph 1504 illustrates the % Q30 for each sequencing cycle of a sequencing run employing existing location-error-prediction techniques with a plot lineAttorney Docket No. IP-2805-PCT 66 Patent Application1506. Further, the quality score graph 1504 illustrates the % Q30 for each sequencing cycle of a sequencing run employing the location-error-prediction system 106 with a plot line 1508. In this example, the location-error-prediction system 106 determines adjusted locations of the clusters of oligonucleotides, as described above, and generates base calls from the adjusted locations. Additionally in this example, the location-error-prediction system 106 incorporates a smoothing model (e.g., a median 3x3 smoothing). As the quality score graph 1504 shows, the location-error- prediction system 106 consistently improves the % Q30 for each sequencing cycle by several percentage points.

[0221] As previously noted, in one or more embodiments, the location-error-prediction system 106 can determine more accurate locations of clusters of oligonucleotides on a nucleotide-sample slide relative to existing sequencing systems. FIG. 16 illustrates cluster locations and equalizer coefficients trained based on distorted cluster locations in existing sequencing system (left) and the adjusted well locations in location-error-prediction system 106 (right) in accordance with one or more embodiments.

[0222] As depicted in FIG. 16, in one or more implementations, the location-error-prediction system 106 determines a more accurate location of a cluster of oligonucleotides relative to existing sequencing systems. For example, an image 1600 illustrates an expected location 1602 of a cluster of oligonucleotides relative to the colored contour rings of equalizer coefficients trained based on distorted predicted locations in existing sequencing system. Similarly, an image 1614 illustrates an expected location 1616 of a cluster of oligonucleotides relative to the colored contour rings of equalizer coefficients trained based on adjusted well locations in the location-error-prediction system 106 in accordance with one or more embodiments. Specifically, each of the image 1600 and the image 1614 illustrate the expected locations of clusters of oligonucleotides as black dots and the equalizer coefficients of the respective images as contour rings. Note that the expected location 1602 and the expected location 1616 are the same expected location of the cluster of oligonucleotides, but utilize different reference numbers for ease of reference.

[0223] As further shown in FIG. 16, for instance, the image 1600 includes contour rings 1604- 1612 of the equalizer coefficients from high values to low values respectively. Specifically, contour ring 1604 is a first color (e.g., dark red), contour ring 1606 is a second color (e.g., red), contour ring 1608 is a third color (e.g., orange), contour ring 1610 is a fourth color (e.g., yellow), and contour ring 1612 is a fifth color (e.g., green). Similarly, the image 1614 includes colored contour rings 1618-1626 of the equalizer coefficients from high values to low values respectively. In particular, contour ring 1618 is a first color (e.g., dark red), contour ring 1620 is a second color (e.g., red), contour ring 1622 is a third color (e.g., orange), contour ring 1624 is a fourth color (e.g., yellow), and contour ring 1626 is a fifth color (e.g., green).Attorney Docket No. IP-2805-PCT 67 Patent Application

[0224] As further illustrated in FIG. 16, in some embodiments, the location-error-prediction system 106 includes key 1628 which serves as a visual guide for interpreting the values of equalizer coefficients of each of image 1600 and image 1614. Specifically, the key 1628 uses a gradient of colors ranging from one color to another color (e.g., dark red to dark blue).

[0225] As also depicted in FIG. 16, in some implementations, as predicted cluster locations in the existing sequencing system suffer from a x-direction optical distortion, the equalizer is trained to correct for such an optical distortion. Specifically, the image 1600 shows the equalizer coefficients determined by the existing sequencing system use less accurate cluster locations. For example, the image 1600 includes distances (e.g., in nanometers) of the nucleotide-sample slide on both the x axis and y axis with the expected location 1602 of the center cluster of oligonucleotides at a coordinate of 0 by 0 nanometers. It is observed that there is a gap between expected location 1602 and the center of contour rings of equalizer coefficients, indicating that the predicted cluster locations suffer from an x-direction optical distortion and the equalizer trained in the location-error- prediction system 106 corrects for such an optical distortion. Moreover, in one or more embodiments, the fact that the center of the contour rings 1604-1612 overlaps with the expected cluster location illustrates that the equalizer trained on adjusted cluster locations in the location- error-prediction system 106 does not need to compensate for any optical distortion in locations, suggesting a better estimation of cluster locations.

[0226] FIGS. 1-16, the corresponding text, and the examples provide a number of different methods, systems, devices, and non-transitory computer-readable media of the location-error- prediction system 106. In addition to the foregoing, one or more implementations can also be described in terms of flowcharts comprising acts for accomplishing a particular result, as shown in FIGS. 17 and 18. FIG. 17 illustrates a flowchart of a series of acts for determining an adjusted location of at least one cluster of oligonucleotides based on at least one location error in accordance with one or more embodiments of the present disclosure. FIG. 18 illustrates a flowchart of a series of acts for determining adjusted locations of clusters of oligonucleotides based on location errors determined from phase differences between pairs of band-edge spectral regions in accordance with one or more embodiments of the present disclosure. While FIGS. 17-18 illustrate acts according to one embodiment, alternative embodiments may omit, add to, reorder, and / or modify any of the acts shown in FIGS. 17-18. The acts of FIGS. 17-18 can be performed as part of a method. Alternatively, a non-transitory computer readable storage medium can comprise instructions that, when executed by one or more processors, cause a computing device or a system to perform the acts depicted in FIGS. 17-18. In still further embodiments, a system comprising an imaging system, a fluidic system, and a computer comprising: at least one processor; and a non-transitory computer readableAttorney Docket No. IP-2805-PCT 68 Patent Applicationmedium comprising instructions that, when executed by one or more processors, cause the system to perform the acts of FIGS. 17-18.

[0227] As shown in FIG. 17, the series of acts 1700 includes an act 1702 of identifying a pair of band-edge spectral regions from a spatial frequency band within an image depicting signals of clusters of oligonucleotides at a predicted location within a nucleotide-sample slide, an act 1704 of determining a phase difference between the pair of band-edge spectral regions, an act 1706 of generating at least one location error in at least one direction for the predicted location of the at least one cluster of oligonucleotides based on the phase difference, and an act 1708 of determining an adjusted location of the at least one cluster of oligonucleotides within the nucleotide-sample slide based on the at least one location error. For example, the series of acts 1700 can include acts to perform any of the operations described in the following clauses:CLAUSE 1. A computer-implemented method comprising: identifying, for a sequencing cycle, a pair of band-edge spectral regions from a spatial frequency band within an image depicting signals of at least one cluster of oligonucleotides at a predicted location within a nucleotide-sample slide; determining a phase difference between the pair of band-edge spectral regions; generating at least one location error in at least one direction for the predicted location of the at least one cluster of oligonucleotides based on the phase difference; and determining, based on the at least one location error and for the sequencing cycle, an adjusted location of the at least one cluster of oligonucleotides within the nucleotide-sample slide.CLAUSE 2. The computer-implemented method of clause 1, further comprising determining, for the sequencing cycle, the adjusted location of the at least one cluster of oligonucleotides by: identifying an additional pair of band-edge spectral regions from an additional portion of the spatial frequency band within the image; determining an additional phase difference between the additional pair of band-edge spectral regions; generating a first location error in a first direction and a second location error in a second direction for the predicted location of the at least one cluster of oligonucleotides based on the additional phase difference; and determining, for the sequencing cycle, the adjusted location of the at least one cluster of oligonucleotides based on the first location error in the first direction and second location error the second direction.CLAUSE 3. The computer-implemented method of clause 1 or 2, further comprising:Attorney Docket No. IP-2805-PCT 69 Patent Applicationdetermining, for a first channel of the image depicting signals of the at least one cluster of oligonucleotides, the at least one location error in the at least one direction for the predicted location of the at least one cluster of oligonucleotides based on the phase difference; determining, based on the at least one location error for the first channel, the adjusted location of the at least one cluster of oligonucleotides; determining, for a second channel of an additional image depicting additional signals of the at least one cluster of oligonucleotides, at least one additional location error in the at least one direction for the predicted location of the at least one cluster of oligonucleotides based on the phase difference; and determining, based on the at least one additional location error for the second channel, an additional adjusted location of the at least one cluster of oligonucleotides.CLAUSE 4. The computer-implemented method of any of clauses 1-3, further comprising generating a base call for the at least one cluster of oligonucleotides based on the adjusted location within the image, the additional adjusted location within the additional image, and intensity values for the signals of the at least one cluster of oligonucleotides.CLAUSE 5. The computer-implemented method of any of clauses 1-4, further comprising: identifying the pair of band-edge spectral regions from the spatial frequency band within the image depicting signals of a target cluster of oligonucleotides and neighboring clusters of oligonucleotides adjacent to the target cluster of oligonucleotides; and determining, based on the at least one location error, the adjusted location for the target cluster of oligonucleotides and the neighboring clusters of oligonucleotides.CLAUSE 6. The computer-implemented method of clauses 1-5, further comprising identifying the pair of band-edge spectral regions according to a geometric layout for cluster locations of clusters of oligonucleotides within a region of the nucleotide-sample slide.CLAUSE 7. The computer-implemented method of clause 6, further comprising identifying the pair of band-edge spectral regions according to a hexagon layout, a square layout, or a diamond layout for the cluster locations within the region of the nucleotide-sample slide.CLAUSE 8. The computer-implemented method of clause 6, further comprising: identifying a set of pairs of band-edge spectral regions based on the geometric layout for cluster locations within the region of the nucleotide-sample slide; and determining a respective phase difference between each pair of the set of pairs of bandedge spectral regions.CLAUSE 9. The computer-implemented method of any of clauses 1-9, further comprising generating the at least one location error in at least one direction by:Attorney Docket No. IP-2805-PCT 70 Patent Applicationdetermining a phase angle between the pair of band-edge spectral regions; and determining the at least one location error in at least one direction based on the phase angle and a distance between clusters of oligonucleotides within the nucleotide-sample slide.CLAUSE 10. The computer-implemented method of clause 9, further comprising determining the phase angle between the pair of band-edge spectral regions by: extracting, from the image, a first band-edge spectral region of the pair of band-edge spectral regions and a second band-edge spectral region of the pair of band-edge spectral regions; and determining a product of the first band-edge spectral region and a conjugate of the second band-edge spectral region.CLAUSE 11. The computer-implemented method of any of clauses 1-10, further comprising generating the at least one location error in at least one direction by: determining a first phase angle between the pair of band-edge spectral regions; determining a first location error in a first direction based on the first phase angle and a distance between clusters of oligonucleotides within the nucleotide-sample slide; determining a second phase angle between an additional pair of band-edge spectral regions from the spatial frequency band within the image; and determining a second location error in a second direction based on the second phase angle and the distance between clusters of oligonucleotides within the nucleotide-sample slide.CLAUSE 12. The computer-implemented method of clauses 1-11, further comprising: accessing an image-patch grid comprising grid cells corresponding to image patches depicting subregions of a nucleotide-sample slide; determining, for each grid cell of the image-patch grid, at least one cell-specific location error for predicted locations of clusters of oligonucleotides; and determining, based on the at least one cell-specific location error, adjusted locations of the clusters of oligonucleotides within each grid cell of the image-patch grid.CLAUSE 13. The computer-implemented method of clause 12, further comprising: mapping image pixels for a grid cell of the image-patch grid to the predicted locations of clusters of oligonucleotides of a subset of clusters within the grid cell; placing a patch of the image within the grid cell of the image-patch grid; and determining, for each grid cell of the image-patch grid, the at least one cell-specific location error for the predicted locations of clusters of oligonucleotides.CLAUSE 14. The computer-implemented method of any of clauses 1-13, further comprising instructions:Attorney Docket No. IP-2805-PCT 71 Patent Applicationapplying a smoothing model to cell-specific location errors in grid cells of an image-patch grid; generating, utilizing the smoothing model and a cell-specific location error in a grid cell for the at least one cluster of oligonucleotides, at least one smoothed location error for the predicted location of the at least one cluster of oligonucleotides; and determining, based on the at least one smoothed location error, the adjusted location of the at least one cluster of oligonucleotides.CLAUSE 15. The computer-implemented method of clause 13, further comprising determining, for each grid cell of the image-patch grid, the at least one cell-specific location error for the predicted locations of clusters of oligonucleotides by: identifying a subsampled image-patch grid comprising subsampled grid cells corresponding to a subset of image patches; determining, for each subsampled grid cell of the subsampled image-patch grid, the at least one cell-specific location error for predicted locations of clusters of oligonucleotides; and identifying, from a subsampled grid cell of the subsampled grid cells, the at least one cellspecific location error for each grid cell of the image-patch grid.CLAUSE 16. The computer-implemented method of clause 15, further comprising determining, for a subsampled grid cell of the subsampled image-patch grid: an optical distortion vector that estimates optical distortion in a first direction and represents a first cell-specific location error; and a jitter vector that estimates jitter in a second direction and represents a second cell-specific location error.CLAUSE 17. The computer-implemented method of clause 16, further comprising determining, for the subsampled grid cell of the subsampled image-patch grid, the optical distortion vector and the jitter vector utilizing a least-squares model by: determining observed band-edge-region errors for the pair of band-edge spectral regions within the image; determining estimated band-edge-region errors for the pair of band-edge spectral regions based on the optical distortion vector and the jitter vector; and determining, utilizing the least-squares model, the optical distortion vector and the jitter vector resulting in a least squared error between the observed band-edge-region errors and the estimated band-edge-region errors.CLAUSE 18. The computer-implemented method of clause 15, further comprising identifying the subsampled image-patch grid by identifying a staggered and subsampled image-Attorney Docket No. IP-2805-PCT 72 Patent Applicationpatch grid in which the subsampled grid cells have been staggered and sections of the subsampled image-patch grid have been shifted according to a circular shift.

[0228] As shown in FIG. 18, the series of acts 1800 includes an act 1802 of identifying pairs of band-edge spectral regions within images depicting signals of a cluster of oligonucleotides at respective predicted locations within a nucleotide-sample slide, an act 1804 of determining a phase difference between respective pairs of band-edge spectral regions, an act 1806 of generating location errors in at least one direction for the respective predicted locations of the clusters of oligonucleotides based on the phase differences, and an act 1808 of determining adjusted locations of the clusters of oligonucleotides within the nucleotide-sample slide based on the location errors. For example, the series of acts 1800 can include acts to perform any of the operations described in the following clauses:CLAUSE 19. A computer-implemented method comprising: identifying, for a sequencing cycle, pairs of band-edge spectral regions within images depicting signals of a cluster of oligonucleotides at respective predicted locations within a nucleotide-sample slide; determining phase differences between respective pairs of band-edge spectral regions; generating, based on the respective phase differences, location errors in at least one direction for the respective predicted locations of the cluster of oligonucleotides; and determining based on the location errors and for the sequencing cycle, adjusted locations of the cluster of oligonucleotides within the nucleotide-sample slide.CLAUSE 20. The computer-implemented method of clause 19, further comprising: determining, for the sequencing cycle, intensity values for the signals of the cluster of oligonucleotides; and generating a base call for the cluster of oligonucleotides based on the adjusted locations of the cluster of oligonucleotides within the images depicting the signals of the cluster of oligonucleotides and the intensity values.CLAUSE 21. The computer-implemented method of clause 19 or 20, further comprising identifying, for the sequencing cycle, the pairs of band-edge spectral regions by: identifying, for the sequencing cycle in a first channel, a first pair of band-edge spectral regions from a first spatial frequency band within a first image depicting signals of the cluster of oligonucleotides at a first predicted location within the nucleotide-sample slide; and identifying, for the sequencing cycle in a second channel, a second pair of band-edge spectral regions from a second spatial frequency band within a second image depicting signals of the cluster of oligonucleotides at a second predicted location within the nucleotide-sample slide.Attorney Docket No. IP-2805-PCT 73 Patent ApplicationCLAUSE 22. The computer-implemented method of clause 21, further comprising determining the respective phase differences between the respective pairs of band-edge spectral regions by: determining a first phase difference between the first pair of band-edge spectral regions; and determining a second phase difference between the second pair of band-edge spectral regions.CLAUSE 23. The computer-implemented method of clause 22, further comprising determining the adjusted locations of the cluster of oligonucleotides within the nucleotide-sample slide by: generating a first location error in at least one direction for the first predicted location of the cluster of oligonucleotides based on the first phase difference; determining, based on the first location error and for the sequencing cycle, a first adjusted location of the cluster of oligonucleotides within the nucleotide-sample slide; generating a second location error in at least one direction for the second predicted location of the cluster of oligonucleotides based on the second phase difference; and determining, based on the second location error and for the sequencing cycle, a second adjusted location of the cluster of oligonucleotides within the nucleotide-sample slide.CLAUSE 24. The computer-implemented method of clause 23, further comprising: determining, for the sequencing cycle, intensity values for the signals of the cluster of oligonucleotides in the first image; determining, for the sequencing cycle, intensity values for the signals of the cluster of oligonucleotides in the second image; and generating a base call for the cluster of oligonucleotides based on the first adjusted location of the cluster of oligonucleotides within the first image, the intensity values for the signals of the cluster of oligonucleotides in the first image, the second adjusted location of the cluster of oligonucleotides within the second image, and the intensity values for the signals of the cluster of oligonucleotides in the second image.CLAUSE 25. The computer-implemented method of clause 19, further comprising: identifying the pairs of band-edge spectral regions from a spatial frequency band within the images depicting signals of the cluster of oligonucleotides and neighboring clusters of oligonucleotides adjacent to the cluster of oligonucleotides; and determining, based on the location errors, the adjusted locations for the cluster of oligonucleotides and the neighboring clusters of oligonucleotides.Attorney Docket No. IP-2805-PCT 74 Patent ApplicationCLAUSE 26. The computer-implemented method of clause 19, wherein identifying the pairs of band-edge spectral regions comprises identifying the pairs of band-edge spectral regions according to a geometric layout for cluster locations of clusters of oligonucleotides within a region of the nucleotide-sample slide.CLAUSE 27. The computer-implemented method of clause 26, wherein identifying the pairs of band-edge spectral regions comprises identifying the pairs of band-edge spectral regions according to a hexagon layout, a square layout, or a diamond layout for the cluster locations within the region of the nucleotide-sample slide.CLAUSE 28. The computer-implemented method of clause 19, wherein determining the phase differences comprises determining a respective phase difference between each pair of the pairs of band-edge spectral regions.CLAUSE 29. The computer-implemented method of clause 19, wherein generating the location errors in at least one direction comprises: determining phase angles between the respective pairs of band-edge spectral regions; and determining the location errors in at least one direction based on the respective phase angles and respective distances between clusters of oligonucleotides within the nucleotide-sample slide.CLAUSE 30. The computer-implemented method of clause 29, wherein determining the phase differences comprises determining a phase angle between a pair of band-edge spectral regions of the pairs of band-edge spectral regions by: extracting, from an image of the images depicting signals of a cluster of oligonucleotides, a first band-edge spectral region of the pair of band-edge spectral regions and a second band-edge spectral region of the pair of band-edge spectral regions; and determining a product of the first band-edge spectral region and a conjugate of the second band-edge spectral region.CLAUSE 31. The computer-implemented method of clause 19, wherein generating the location errors comprises generating a first location error and a second location error of the location errors by: determining a first phase angle between a pair of band-edge spectral regions of the pairs of band-edge spectral regions; determining the first location error in a first direction based on the first phase angle and a distance between clusters of oligonucleotides within the nucleotide-sample slide; determining a second phase angle between an additional pair of band-edge spectral regions of the pairs of band-edge spectral regions; and determining the second location error in a second direction based on the second phase angle and the distance between clusters of oligonucleotides within the nucleotide-sample slide.Attorney Docket No. IP-2805-PCT 75 Patent ApplicationCLAUSE 32. The computer-implemented method of clause 19, further comprising: accessing an image-patch grid comprising grid cells corresponding to image patches depicting subregions of a nucleotide-sample slide; determining, for each grid cell of the image-patch grid, cell-specific location errors for predicted locations of clusters of oligonucleotides; and determining, based on the cell-specific location errors, respective adjusted locations of the clusters of oligonucleotides within each grid cell of the image-patch grid.CLAUSE 33. The computer-implemented method of clause 32, further comprising: mapping image pixels for a grid cell of the image-patch grid to the predicted locations of clusters of oligonucleotides of a subset of clusters within the grid cell; placing a patch of an image, of the images depicting the signals of the cluster of oligonucleotides, within the grid cell of the image-patch grid; and determining, for each grid cell of the image-patch grid, the cell-specific location errors for the predicted locations of clusters of oligonucleotides.CLAUSE 34. The computer-implemented method of clause 19, further comprising: applying a smoothing model to cell-specific location errors in grid cells of an image-patch grid; generating, utilizing the smoothing model and a cell-specific location error in a grid cell for the cluster of oligonucleotides, smoothed location errors for the respective predicted locations of the cluster of oligonucleotides; and determining, based on the smoothed location errors, the adjusted locations of the cluster of oligonucleotides.CLAUSE 35. The computer-implemented method of clause 33, further comprising determining, for each grid cell of the image-patch grid, the cell-specific location errors for the predicted locations of clusters of oligonucleotides by: identifying a subsampled image-patch grid comprising subsampled grid cells corresponding to a subset of image patches; determining, for each subsampled grid cell of the subsampled image-patch grid, the cellspecific location errors for predicted locations of clusters of oligonucleotides; and identifying, from a subsampled grid cell of the subsampled grid cells, the cell-specific location errors for each grid cell of the image-patch grid.CLAUSE 36. The computer-implemented method of clause 35, further comprising determining, for a subsampled grid cell of the subsampled image-patch grid: an optical distortion vector that estimates optical distortion in a first direction and represents a first cell-specific location error; andAttorney Docket No. IP-2805-PCT 76 Patent Applicationa jitter vector that estimates jitter in a second direction and represents a second cell-specific location error.CLAUSE 37. The computer-implemented method of clause 36, further comprising determining, for the subsampled grid cell of the subsampled image-patch grid, the optical distortion vector and the jitter vector utilizing a least-squares model by: determining observed band-edge-region errors for a pair of band-edge spectral regions of the pairs of band-edge spectral regions within the images; determining estimated band-edge-region errors for the pair of band-edge spectral regions based on the optical distortion vector and the jitter vector; and determining, utilizing the least-squares model, the optical distortion vector and the jitter vector resulting in a least squared error between the observed band-edge-region errors and the estimated band-edge-region errors.CLAUSE 38. The computer-implemented method of clause 35, wherein identifying the subsampled image-patch grid comprises identifying a staggered and subsampled image-patch grid in which the subsampled grid cells have been staggered and sections of the subsampled imagepatch grid have been shifted according to a circular shift.

[0229] The methods described herein can be used in conjunction with a variety of nucleic acid sequencing techniques. Particularly applicable techniques are those wherein nucleic acids are attached at fixed locations in an array such that their relative positions do not change and wherein the array is repeatedly imaged. Embodiments in which images are obtained in different color channels, for example, coinciding with different labels used to distinguish one nucleobase type from another are particularly applicable. In some embodiments, the process to determine the nucleotide sequence of a target nucleic acid (i.e., a nucleic acid polymer) can be an automated process. Preferred embodiments include sequencing-by-synthesis (SBS) techniques.

[0230] SBS techniques generally involve the enzymatic extension of a nascent nucleic acid strand through the iterative addition of nucleotides against a template strand. In traditional methods of SBS, a single nucleotide monomer may be provided to a target nucleotide in the presence of a polymerase in each delivery. However, in the methods described herein, more than one type of nucleotide monomer can be provided to a target nucleic acid in the presence of a polymerase in a delivery.

[0231] SBS can utilize nucleotide monomers that have a terminator moiety or those that lack any terminator moieties. Methods utilizing nucleotide monomers lacking terminators include, for example, pyrosequencing and sequencing using y-phosphate-labeled nucleotides, as set forth in further detail below. In methods using nucleotide monomers lacking terminators, the number of nucleotides added in each cycle is generally variable and dependent upon the template sequenceAttorney Docket No. IP-2805-PCT 77 Patent Applicationand the mode of nucleotide delivery. For SBS techniques that utilize nucleotide monomers having a terminator moiety, the terminator can be effectively irreversible under the sequencing conditions used as is the case for traditional Sanger sequencing which utilizes dideoxynucleotides, or the terminator can be reversible as is the case for sequencing methods developed by Solexa (now Illumina, Inc.).

[0232] SBS techniques can utilize nucleotide monomers that have a label moiety or those that lack a label moiety. Accordingly, incorporation events can be detected based on a characteristic of the label, such as fluorescence of the label; a characteristic of the nucleotide monomer such as molecular weight or charge; a byproduct of incorporation of the nucleotide, such as release of pyrophosphate; or the like. In embodiments where two or more different nucleotides are present in a sequencing reagent, the different nucleotides can be distinguishable from each other, or alternatively, the two or more different labels can be the indistinguishable under the detection techniques being used. For example, the different nucleotides present in a sequencing reagent can have different labels and they can be distinguished using appropriate optics as exemplified by the sequencing methods developed by Solexa (now Illumina, Inc.).

[0233] Preferred embodiments include pyrosequencing techniques. Pyrosequencing detects the release of inorganic pyrophosphate (PPi) as particular nucleotides are incorporated into the nascent strand (Ronaghi, M., Karamohamed, S., Pettersson, B., Uhlen, M. and Nyren, P. (1996) "Real-time DNA sequencing using detection of pyrophosphate release." Analytical Biochemistry 242(1), 84-9; Ronaghi, M. (2001) "Pyrosequencing sheds light on DNA sequencing." Genome Res. 11(1), 3-11; Ronaghi, M., Uhlen, M. and Nyren, P. (1998) “A sequencing method based on realtime pyrophosphate.” Science 281(5375), 363; U.S. Pat. No. 6,210,891; U.S. Pat. No. 6,258,568 and U.S. Pat. No. 6,274,320, the disclosures of which are incorporated herein by reference in their entireties). In pyrosequencing, released PPi can be detected by being immediately converted to adenosine triphosphate (ATP) by ATP sulfurylase, and the level of ATP generated is detected via luciferase-produced photons. The nucleic acids to be sequenced can be attached to features in an array and the array can be imaged to capture the chemiluminescent signals that are produced due to incorporation of a nucleotides at the features of the array. An image can be obtained after the array is treated with a particular nucleotide type (e.g., A, T, C or G). Images obtained after addition of each nucleotide type will differ with regard to which features in the array are detected. These differences in the image reflect the different sequence content of the features on the array. However, the relative locations of each feature will remain unchanged in the images. The images can be stored, processed and analyzed using the methods set forth herein. For example, images obtained after treatment of the array with each different nucleotide type can be handled in the same way asAttorney Docket No. IP-2805-PCT 78 Patent Applicationexemplified herein for images obtained from different detection channels for reversible terminatorbased sequencing methods.

[0234] In another exemplary type of SBS, cycle sequencing is accomplished by stepwise addition of reversible terminator nucleotides containing, for example, a cleavable or photobleachable dye label as described, for example, in WO 04 / 018497 and U.S. Pat. No. 7,057,026, the disclosures of which are incorporated herein by reference. This approach is being commercialized by Solexa (now Illumina Inc.), and is also described in WO 91 / 06678 and WO 07 / 123,744, each of which is incorporated herein by reference. The availability of fluorescently labeled terminators in which both the termination can be reversed, and the fluorescent label cleaved facilitates efficient cyclic reversible termination (CRT) sequencing. Polymerases can also be coengineered to efficiently incorporate and extend from these modified nucleotides.

[0235] Preferably in reversible terminator-based sequencing embodiments, the labels do not substantially inhibit extension under SBS reaction conditions. However, the detection labels can be removable, for example, by cleavage or degradation. Images can be captured following incorporation of labels into arrayed nucleic acid features. In particular embodiments, each cycle involves simultaneous delivery of four different nucleotide types to the array and each nucleotide type has a spectrally distinct label. Four images can then be obtained, each using a detection channel that is selective for one of the four different labels. Alternatively, different nucleotide types can be added sequentially, and an image of the array can be obtained between each addition step. In such embodiments, each image will show nucleic acid features that have incorporated nucleotides of a particular type. Different features are present or absent in the different images due the different sequence content of each feature. However, the relative position of the features will remain unchanged in the images. Images obtained from such reversible terminator- SBS methods can be stored, processed and analyzed as set forth herein. Following the image capture step, labels can be removed, and reversible terminator moieties can be removed for subsequent cycles of nucleotide addition and detection. Removal of the labels after they have been detected in a particular cycle and prior to a subsequent cycle can provide the advantage of reducing background signal and crosstalk between cycles. Examples of useful labels and removal methods are set forth below.

[0236] In particular embodiments some or all of the nucleotide monomers can include reversible terminators. In such embodiments, reversible terminators / cleavable fluors can include fluor linked to the ribose moiety via a 3' ester linkage (Metzker, Genome Res. 15: 1767-1776 (2005), which is incorporated herein by reference). Other approaches have separated the terminator chemistry from the cleavage of the fluorescence label (Ruparel et al., Proc Natl Acad Sci USA 102: 5932-7 (2005), which is incorporated herein by reference in its entirety). Ruparel et al described the development of reversible terminators that used a small 3' allyl group to block extension butAttorney Docket No. IP-2805-PCT 79 Patent Applicationcould easily be deblocked by a short treatment with a palladium catalyst. The fluorophore was attached to the base via a photocleavable linker that could easily be cleaved by a 30 second exposure to long wavelength UV light. Thus, either disulfide reduction or photocleavage can be used as a cleavable linker. Another approach to reversible termination is the use of natural termination that ensues after placement of a bulky dye on a dNTP. The presence of a charged bulky dye on the dNTP can act as an effective terminator through steric and / or electrostatic hindrance. The presence of one incorporation event prevents further incorporations unless the dye is removed. Cleavage of the dye removes the fluor and effectively reverses the termination. Examples of modified nucleotides are also described in U.S. Pat. No. 7,427,673, and U.S. Pat. No. 7,057,026, the disclosures of which are incorporated herein by reference in their entireties.

[0237] Additional exemplary SBS systems and methods which can be utilized with the methods and systems described herein are described in U.S. Patent Application Publication No. 2007 / 0166705, U.S. Patent Application Publication No. 2006 / 0188901, U.S. Pat. No. 7,057,026, U.S. Patent Application Publication No. 2006 / 0240439, U.S. Patent Application Publication No. 2006 / 0281109, PCT Publication No. WO 05 / 065814, U.S. Patent Application Publication No. 2005 / 0100900, PCT Publication No. WO 06 / 064199, PCT Publication No. WO 07 / 010,251, U.S. Patent Application Publication No. 2012 / 0270305 and U.S. Patent Application Publication No. 2013 / 0260372, the disclosures of which are incorporated herein by reference in their entireties.

[0238] Some embodiments can utilize detection of four different nucleotides using fewer than four different labels. For example, SBS can be performed utilizing methods and systems described in the incorporated materials of U.S. Patent Application Publication No. 2013 / 0079232. As a first example, a pair of nucleotide types can be detected at the same wavelength, but distinguished based on a difference in intensity for one member of the pair compared to the other, or based on a change to one member of the pair (e.g. via chemical modification, photochemical modification or physical modification) that causes apparent signal to appear or disappear compared to the signal detected for the other member of the pair. As a second example, three of four different nucleotide types can be detected under particular conditions while a fourth nucleotide type lacks a label that is detectable under those conditions, or is minimally detected under those conditions (e.g., minimal detection due to background fluorescence, etc.). Incorporation of the first three nucleotide types into a nucleic acid can be determined based on presence of their respective signals and incorporation of the fourth nucleotide type into the nucleic acid can be determined based on absence or minimal detection of any signal. As a third example, one nucleotide type can include label(s) that are detected in two different channels, whereas other nucleotide types are detected in no more than one of the channels. The aforementioned three exemplary configurations are not considered mutually exclusive and can be used in various combinations. An exemplary embodiment that combines all three examples, isAttorney Docket No. IP-2805-PCT 80 Patent Applicationa fluorescent-based SBS method that uses a first nucleotide type that is detected in a first channel (e.g. dATP having a label that is detected in the first channel when excited by a first excitation wavelength), a second nucleotide type that is detected in a second channel (e.g. dCTP having a label that is detected in the second channel when excited by a second excitation wavelength), a third nucleotide type that is detected in both the first and the second channel (e.g. dTTP having at least one label that is detected in both channels when excited by the first and / or second excitation wavelength) and a fourth nucleotide type that lacks a label that is not, or minimally, detected in either channel (e.g. dGTP having no label).

[0239] Further, as described in the incorporated materials of U.S. Patent Application Publication No. 2013 / 0079232, sequencing data can be obtained using a single channel. In such so- called one-dye sequencing approaches, the first nucleotide type is labeled but the label is removed after the first image is generated, and the second nucleotide type is labeled only after a first image is generated. The third nucleotide type retains its label in both the first and second images, and the fourth nucleotide type remains unlabeled in both images.

[0240] Some embodiments can utilize sequencing by ligation techniques. Such techniques utilize DNA ligase to incorporate oligonucleotides and identify the incorporation of such oligonucleotides. The oligonucleotides typically have different labels that are correlated with the identity of a particular nucleotide in a sequence to which the oligonucleotides hybridize. As with other SBS methods, images can be obtained following treatment of an array of nucleic acid features with the labeled sequencing reagents. Each image will show nucleic acid features that have incorporated labels of a particular type. Different features are present or absent in the different images due the different sequence content of each feature, but the relative position of the features will remain unchanged in the images. Images obtained from ligation-based sequencing methods can be stored, processed and analyzed as set forth herein. Exemplary SBS systems and methods which can be utilized with the methods and systems described herein are described in U.S. Pat. No. 6,969,488, U.S. Pat. No. 6,172,218, and U.S. Pat. No. 6,306,597, the disclosures of which are incorporated herein by reference in their entireties.

[0241] Some embodiments can utilize nanopore sequencing (Deamer, D. W. & Akeson, M. "Nanopores and nucleic acids: prospects for ultrarapid sequencing." Trends Biotechnol. 18, 147- 151 (2000); Deamer, D. and D. Branton, "Characterization of nucleic acids by nanopore analysis". Acc. Chem. Res. 35:817-825 (2002); Li, J., M. Gershow, D. Stein, E. Brandin, and J. A. Golovchenko, "DNA molecules and configurations in a solid-state nanopore microscope" Nat. Mater. 2:611-615 (2003), the disclosures of which are incorporated herein by reference in their entireties). In such embodiments, the target nucleic acid passes through a nanopore. The nanopore can be a synthetic pore or biological membrane protein, such as a-hemolysin. As the target nucleicAttorney Docket No. IP-2805-PCT 81 Patent Applicationacid passes through the nanopore, each base-pair can be identified by measuring fluctuations in the electrical conductance of the pore. (U.S. Pat. No. 7,001,792; Soni, G. V. & Meller, "A. Progress toward ultrafast DNA sequencing using solid-state nanopores." Clin. Chem. 53, 1996-2001 (2007); Healy, K. "Nanopore-based single-molecule DNA analysis." Nanomed. 2, 459-481 (2007); Cockroft, S. L., Chu, J., Amorin, M. & Ghadiri, M. R. "A single-molecule nanopore device detects DNA polymerase activity with single-nucleotide resolution." J. Am. Chem. Soc. 130, 818-820 (2008), the disclosures of which are incorporated herein by reference in their entireties). Data obtained from nanopore sequencing can be stored, processed and analyzed as set forth herein. In particular, the data can be treated as an image in accordance with the exemplary treatment of optical images and other images that is set forth herein.

[0242] Some embodiments can utilize methods involving the real-time monitoring of DNA polymerase activity. Nucleotide incorporations can be detected through fluorescence resonance energy transfer (FRET) interactions between a fluorophore-bearing polymerase and y-phosphate- labeled nucleotides as described, for example, in U.S. Pat. No. 7,329,492 and U.S. Pat. No. 7,211,414 (each of which is incorporated herein by reference) or nucleotide incorporations can be detected with zero-mode waveguides as described, for example, in U.S. Pat. No. 7,315,019 (which is incorporated herein by reference) and using fluorescent nucleotide analogs and engineered polymerases as described, for example, in U.S. Pat. No. 7,405,281 and U.S. Patent Application Publication No. 2008 / 0108082 (each of which is incorporated herein by reference). The illumination can be restricted to a zeptoliter-scale volume around a surface-tethered polymerase such that incorporation of fluorescently labeled nucleotides can be observed with low background (Levene, M. J. et al. "Zero-mode waveguides for single-molecule analysis at high concentrations." Science 299, 682-686 (2003); Lundquist, P. M. et al. "Parallel confocal detection of single molecules in real time." Opt. Lett. 33, 1026-1028 (2008); Korlach, J. et al. "Selective aluminum passivation for targeted immobilization of single DNA polymerase molecules in zero-mode waveguide nano structures." Proc. Natl. Acad. Sci. USA 105, 1176-1181 (2008), the disclosures of which are incorporated herein by reference in their entireties). Images obtained from such methods can be stored, processed and analyzed as set forth herein.

[0243] Some SBS embodiments include detection of a proton released upon incorporation of a nucleotide into an extension product. For example, sequencing based on detection of released protons can use an electrical detector and associated techniques that are commercially available from Ion Torrent (Guilford, CT, a Life Technologies subsidiary) or sequencing methods and systems described in US 2009 / 0026082 Al; US 2009 / 0127589 Al; US 2010 / 0137143 Al; or US 2010 / 0282617 Al, each of which is incorporated herein by reference. Methods set forth herein for amplifying target nucleic acids using kinetic exclusion can be readily applied to substrates used forAttorney Docket No. IP-2805-PCT 82 Patent Applicationdetecting protons. More specifically, methods set forth herein can be used to produce clonal populations of amplicons that are used to detect protons.

[0244] The above SBS methods can be advantageously carried out in multiplex formats such that multiple different target nucleic acids are manipulated simultaneously. In particular embodiments, different target nucleic acids can be treated in a common reaction vessel or on a surface of a particular substrate. This allows convenient delivery of sequencing reagents, removal of unreacted reagents and detection of incorporation events in a multiplex manner. In embodiments using surface-bound target nucleic acids, the target nucleic acids can be in an array format. In an array format, the target nucleic acids can be typically bound to a surface in a spatially distinguishable manner. The target nucleic acids can be bound by direct covalent attachment, attachment to a bead or other particle or binding to a polymerase or other molecule that is attached to the surface. The array can include a single copy of a target nucleic acid at each site (also referred to as a feature) or multiple copies having the same sequence can be present at each site or feature. Multiple copies can be produced by amplification methods such as, bridge amplification or emulsion PCR as described in further detail below.

[0245] The methods set forth herein can use arrays having features at any of a variety of densities including, for example, at least about 10 features / cm2, 100 features / cm2, 500 features / cm2, 1,000 features / cm2, 5,000 features / cm2, 10,000 features / cm2, 50,000 features / cm2, 100,000 features / cm2, 1,000,000 features / cm2, 5,000,000 features / cm2, or higher.

[0246] An advantage of the methods set forth herein is that they provide for rapid and efficient detection of a plurality of target nucleic acid in parallel. Accordingly, the present disclosure provides integrated systems capable of preparing and detecting nucleic acids using techniques known in the art such as those exemplified above. Thus, an integrated system of the present disclosure can include fluidic components capable of delivering amplification reagents and / or sequencing reagents to one or more immobilized DNA fragments, the system comprising components such as pumps, valves, reservoirs, fluidic lines and the like. A flow cell can be configured and / or used in an integrated system for detection of target nucleic acids. Exemplary flow cells are described, for example, in US 2010 / 0111768 Al and US Ser. No. 13 / 273,666, each of which is incorporated herein by reference. As exemplified for flow cells, one or more of the fluidic components of an integrated system can be used for an amplification method and for a detection method. Taking a nucleic acid sequencing embodiment as an example, one or more of the fluidic components of an integrated system can be used for an amplification method set forth herein and for the delivery of sequencing reagents in a sequencing method such as those exemplified above. Alternatively, an integrated system can include separate fluidic systems to carry out amplification methods and to carry out detection methods. Examples of integrated sequencingAttorney Docket No. IP-2805-PCT 83 Patent Applicationsystems that are capable of creating amplified nucleic acids and also determining the sequence of the nucleic acids include, without limitation, the MiSeqTM platform (Illumina, Inc., San Diego, CA) and devices described in US Ser. No. 13 / 273,666, which is incorporated herein by reference. The sequencing system described above sequences nucleic acid polymers present in samples received by a sequencing device, as described further above.

[0247] Further, the methods and compositions disclosed herein may be useful to amplify a nucleic acid sample having low-quality nucleic acid molecules, such as degraded and / or fragmented genomic DNA from a forensic sample. In one embodiment, forensic samples can include nucleic acids obtained from a crime scene, nucleic acids obtained from a missing persons DNA database, nucleic acids obtained from a laboratory associated with a forensic investigation or include forensic samples obtained by law enforcement agencies, one or more military services or any such personnel. The nucleic acid sample may be a purified sample or a crude DNA containing lysate, for example derived from a buccal swab, paper, fabric or other substrate that may be impregnated with saliva, blood, or other bodily fluids. As such, in some embodiments, the nucleic acid sample may comprise low amounts of, or fragmented portions of DNA, such as genomic DNA. In some embodiments, target sequences can be present in one or more bodily fluids including but not limited to, blood, sputum, plasma, semen, urine and serum. In some embodiments, target sequences can be obtained from hair, skin, tissue samples, autopsy or remains of a victim. In some embodiments, nucleic acids including one or more target sequences can be obtained from a deceased animal or human. In some embodiments, target sequences can include nucleic acids obtained from non-human DNA such a microbial, plant or entomological DNA. In some embodiments, target sequences or amplified target sequences are directed to purposes of human identification. In some embodiments, the disclosure relates generally to methods for identifying characteristics of a forensic sample. In some embodiments, the disclosure relates generally to human identification methods using one or more target specific primers disclosed herein or one or more target specific primers designed using the primer design criteria outlined herein. In one embodiment, a forensic or human identification sample containing at least one target sequence can be amplified using any one or more of the target-specific primers disclosed herein or using the primer criteria outlined herein.

[0248] The components of the location-error-prediction system 106 can include software, hardware, or both. For example, the components of the location-error-prediction system 106 can include one or more instructions stored on a computer-readable storage medium and executable by processors of one or more computing devices (e.g., the client device 114, the local device 108, or the server device(s) 110). When executed by the one or more processors, the computer-executable instructions of the location-error-prediction system 106 can cause the computing devices to performAttorney Docket No. IP-2805-PCT 84 Patent Applicationthe bubble detection methods described herein. Alternatively, the components of the location-error- prediction system 106 can comprise hardware, such as special purpose processing devices to perform a certain function or group of functions. Additionally, or alternatively, the components of the location-error-prediction system 106 can include a combination of computer-executable instructions and hardware.

[0249] Furthermore, the components of the location-error-prediction system 106 performing the functions described herein with respect to the location-error-prediction system 106 may, for example, be implemented as part of a stand-alone application, as a module of an application, as a plug-in for applications, as a library function or functions that may be called by other applications, and / or as a cloud-computing model. Thus, components of the location-error-prediction system 106 may be implemented as part of a stand-alone application on a personal computing device or a mobile device. Additionally, or alternatively, the components of the location-error-prediction system 106 may be implemented in any application that provides sequencing services including, but not limited to hardware or software Illumina MiSeq, Illumina NextSeq, or Illumina NovaSeq. “Illumina,” “MiSeq,” “NextSeq,” and “NovaSeq,” are either registered trademarks or trademarks of Illumina, Inc. in the United States and / or other countries.

[0250] Embodiments of the present disclosure may comprise or utilize a special purpose or general-purpose computer including computer hardware, such as, for example, one or more processors and system memory, as discussed in greater detail below. Embodiments within the scope of the present disclosure also include physical and other computer-readable media for carrying or storing computer-executable instructions and / or data structures. In particular, one or more of the processes described herein may be implemented at least in part as instructions embodied in a non- transitory computer-readable medium and executable by one or more computing devices (e.g., any of the media content access devices described herein). In general, a processor (e.g., a microprocessor) receives instructions, from a non-transitory computer-readable medium, (e.g., a memory, etc.), and executes those instructions, thereby performing one or more processes, including one or more of the processes described herein.

[0251] Computer-readable media can be any available media that can be accessed by a general purpose or special purpose computer system. Computer-readable media that store computerexecutable instructions are non-transitory computer-readable storage media (devices). Computer- readable media that carry computer-executable instructions are transmission media. Thus, by way of example, and not limitation, embodiments of the disclosure can comprise at least two distinctly different kinds of computer-readable media: non-transitory computer-readable storage media (devices) and transmission media.Attorney Docket No. IP-2805-PCT 85 Patent Application

[0252] Non-transitory computer-readable storage media (devices) includes RAM, ROM, EEPROM, CD-ROM, solid state drives (SSDs) (e.g., based on RAM), Flash memory, phasechange memory (PCM), other types of memory, other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store desired program code means in the form of computer-executable instructions or data structures and which can be accessed by a general purpose or special purpose computer.

[0253] A “network” is defined as one or more data links that enable the transport of electronic data between computer systems and / or modules and / or other electronic devices. When information is transferred or provided over a network or another communications connection (either hardwired, wireless, or a combination of hardwired or wireless) to a computer, the computer properly views the connection as a transmission medium. Transmissions media can include a network and / or data links which can be used to carry desired program code means in the form of computer-executable instructions or data structures and which can be accessed by a general purpose or special purpose computer. Combinations of the above should also be included within the scope of computer- readable media.

[0254] Further, upon reaching various computer system components, program code means in the form of computer-executable instructions or data structures can be transferred automatically from transmission media to non-transitory computer-readable storage media (devices) (or vice versa). For example, computer-executable instructions or data structures received over a network or data link can be buffered in RAM within a network interface module (e.g., a NIC), and then eventually transferred to computer system RAM and / or to less volatile computer storage media (devices) at a computer system. Thus, it should be understood that non-transitory computer- readable storage media (devices) can be included in computer system components that also (or even primarily) utilize transmission media.

[0255] Computer-executable instructions comprise, for example, instructions and data which, when executed at a processor, cause a general-purpose computer, special purpose computer, or special purpose processing device to perform a certain function or group of functions. In some embodiments, computer-executable instructions are executed on a general-purpose computer to turn the general-purpose computer into a special purpose computer implementing elements of the disclosure. The computer executable instructions may be, for example, binaries, intermediate format instructions such as assembly language, or even source code. Although the subject matter has been described in language specific to structural features and / or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the described features or acts described above. Rather, the described features and acts are disclosed as example forms of implementing the claims.Attorney Docket No. IP-2805-PCT 86 Patent Application

[0256] Those skilled in the art will appreciate that the disclosure may be practiced in network computing environments with many types of computer system configurations, including, personal computers, desktop computers, laptop computers, message processors, hand-held devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, mobile telephones, PDAs, tablets, pagers, routers, switches, and the like. The disclosure may also be practiced in distributed system environments where local and remote computer systems, which are linked (either by hardwired data links, wireless data links, or by a combination of hardwired and wireless data links) through a network, both perform tasks. In a distributed system environment, program modules may be located in both local and remote memory storage devices.

[0257] Embodiments of the present disclosure can also be implemented in cloud computing environments. In this description, “cloud computing” is defined as a model for enabling on-demand network access to a shared pool of configurable computing resources. For example, cloud computing can be employed in the marketplace to offer ubiquitous and convenient on-demand access to the shared pool of configurable computing resources. The shared pool of configurable computing resources can be rapidly provisioned via virtualization and released with low management effort or service provider interaction, and then scaled accordingly.

[0258] A cloud-computing model can be composed of various characteristics such as, for example, on-demand self-service, broad network access, resource pooling, rapid elasticity, measured service, and so forth. A cloud-computing model can also expose various service models, such as, for example, Software as a Service (SaaS), Platform as a Service (PaaS), and Infrastructure as a Service (laaS). A cloud-computing model can also be deployed using different deployment models such as private cloud, community cloud, public cloud, hybrid cloud, and so forth. In this description and in the claims, a “cloud-computing environment” is an environment in which cloud computing is employed.

[0259] FIG. 19 illustrates a block diagram of a computing device 1900 that may be configured to perform one or more of the processes described above. One will appreciate that one or more computing devices such as the computing device 1900 may implement the location-error-prediction system 106 and the sequencing device system 104. As shown by FIG. 19, the computing device 1900 can comprise a processor 1902, a memory 1904, a storage device 1906, an I / O interface 1908, and a communication interface 1910, which may be communicatively coupled by way of a communication infrastructure 1912. In certain embodiments, the computing device 1900 can include fewer or more components than those shown in FIG. 19. The following paragraphs describe components of the computing device 1900 shown in FIG. 19 in additional detail.Attorney Docket No. IP-2805-PCT 87 Patent Application

[0260] In one or more embodiments, the processor 1902 includes hardware for executing instructions, such as those making up a computer program. As an example, and not by way of limitation, to execute instructions for dynamically modifying workflows, the processor 1902 may retrieve (or fetch) the instructions from an internal register, an internal cache, the memory 1904, or the storage device 1906 and decode and execute them. The memory 1904 may be a volatile or nonvolatile memory used for storing data, metadata, and programs for execution by the processor(s). The storage device 1906 includes storage, such as a hard disk, flash disk drive, or other digital storage device, for storing data or instructions for performing the methods described herein.

[0261] The I / O interface 1908 allows a user to provide input to, receive output from, and otherwise transfer data to and receive data from computing device 1900. The I / O interface 1908 may include a mouse, a keypad or a keyboard, a touch screen, a camera, an optical scanner, network interface, modem, other known I / O devices or a combination of such I / O interfaces. The I / O interface 1908 may include one or more devices for presenting output to a user, including, but not limited to, a graphics engine, a display (e.g., a display screen), one or more output drivers (e.g., display drivers), one or more audio speakers, and one or more audio drivers. In certain embodiments, the I / O interface 1908 is configured to provide graphical data to a display for presentation to a user. The graphical data may be representative of one or more graphical user interfaces and / or any other graphical content as may serve a particular implementation.

[0262] The communication interface 1910 can include hardware, software, or both. In any event, the communication interface 1910 can provide one or more interfaces for communication (such as, for example, packet-based communication) between the computing device 1900 and one or more other computing devices or networks. As an example, and not by way of limitation, the communication interface 1910 may include a network interface controller (NIC) or network adapter for communicating with an Ethernet or other wire-based network or a wireless NIC (WNIC) or wireless adapter for communicating with a wireless network, such as a WI-FI.

[0263] Additionally, the communication interface 1910 may facilitate communications with various types of wired or wireless networks. The communication interface 1910 may also facilitate communications using various communication protocols. The communication infrastructure 1912 may also include hardware, software, or both that couples components of the computing device 1900 to each other. For example, the communication interface 1910 may use one or more networks and / or protocols to enable a plurality of computing devices connected by a particular infrastructure to communicate with each other to perform one or more aspects of the processes described herein. To illustrate, the sequencing process can allow a plurality of devices (e.g., a client device, sequencing device, and server device(s)) to exchange information such as sequencing data and error notifications.Attorney Docket No. IP-2805-PCT 88 Patent Application

[0264] In the foregoing specification, the present disclosure has been described with reference to specific exemplary embodiments thereof. Various embodiments and aspects of the present disclosure(s) are described with reference to details discussed herein, and the accompanying drawings illustrate the various embodiments. The description above and drawings are illustrative of the disclosure and are not to be construed as limiting the disclosure. Numerous specific details are described to provide a thorough understanding of various embodiments of the present disclosure.

[0265] The present disclosure may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. For example, the methods described herein may be performed with less or more steps / acts or the steps / acts may be performed in differing orders. Additionally, the steps / acts described herein may be repeated or performed in parallel with one another or in parallel with different instances of the same or similar steps / acts. The scope of the present application is, therefore, indicated by the appended claims rather than by the foregoing description. All changes that come within the meaning and range of equivalency of the claims are to be embraced within their scope.

[0266] In the foregoing specification, the invention has been described with reference to specific example embodiments thereof. Various embodiments and aspects of the invention(s) are described with reference to details discussed herein, and the accompanying drawings illustrate the various embodiments. The description above and drawings are illustrative of the invention and are not to be construed as limiting the invention. Numerous specific details are described to provide a thorough understanding of various embodiments of the present invention.

[0267] The present invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. For example, the methods described herein may be performed with less or more steps / acts or the steps / acts may be performed in differing orders. Additionally, the steps / acts described herein may be repeated or performed in parallel to one another or in parallel to different instances of the same or similar steps / acts. The scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes that come within the meaning and range of equivalency of the claims are to be embraced within their scope.Attorney Docket No. IP-2805-PCT 89 Patent Application

Claims

CLAIMSWhat is claimed is:

1. A system comprising: at least one processor; and a non-transitory computer readable medium comprising instruction that, when executed by the at least one processor, cause the system to: identify, for a sequencing cycle, a pair of band-edge spectral regions from a spatial frequency band within an image depicting signals of at least one cluster of oligonucleotides at a predicted location within a nucleotide-sample slide; determine a phase difference between the pair of band-edge spectral regions; generate at least one location error in at least one direction for the predicted location of the at least one cluster of oligonucleotides based on the phase difference; and determine, based on the at least one location error and for the sequencing cycle, an adjusted location of the at least one cluster of oligonucleotides within the nucleotide-sample slide.

2. The system of claim 1, further comprising instructions that, when executed by the at least one processor, cause the system to determine, for the sequencing cycle, the adjusted location of the at least one cluster of oligonucleotides by: identifying an additional pair of band-edge spectral regions from an additional portion of the spatial frequency band within the image; determining an additional phase difference between the additional pair of band-edge spectral regions; generating a first location error in a first direction and a second location error in a second direction for the predicted location of the at least one cluster of oligonucleotides based on the additional phase difference; and determining, for the sequencing cycle, the adjusted location of the at least one cluster of oligonucleotides based on the first location error in the first direction and second location error the second direction.

3. The system of claim 1, further comprising instructions that, when executed by the at least one processor, cause the system to: determine, for a first channel of the image depicting signals of the at least one cluster of oligonucleotides, the at least one location error in the at least one direction for the predicted location of the at least one cluster of oligonucleotides based on the phase difference; determine, based on the at least one location error for the first channel, the adjusted location of the at least one cluster of oligonucleotides;Attorney Docket No. IP-2805-PCT 90 Patent Applicationdetermine, for a second channel of an additional image depicting additional signals of the at least one cluster of oligonucleotides, at least one additional location error in the at least one direction for the predicted location of the at least one cluster of oligonucleotides based on the phase difference; and determine, based on the at least one additional location error for the second channel, an additional adjusted location of the at least one cluster of oligonucleotides.

4. The system of claim 3, further comprising instructions that, when executed by the at least one processor, cause the system to generate a base call for the at least one cluster of oligonucleotides based on the adjusted location within the image, the additional adjusted location within the additional image, and intensity values for the signals of the at least one cluster of oligonucleotides.

5. The system of claim 1, further comprising instructions that, when executed by the at least one processor, cause the system to: identify the pair of band-edge spectral regions from the spatial frequency band within the image depicting signals of a target cluster of oligonucleotides and neighboring clusters of oligonucleotides adjacent to the target cluster of oligonucleotides; and determine, based on the at least one location error, the adjusted location for the target cluster of oligonucleotides and the neighboring clusters of oligonucleotides.

6. The system of claim 1, further comprising instructions that, when executed by the at least one processor, cause the system to identify the pair of band-edge spectral regions according to a geometric layout for cluster locations of clusters of oligonucleotides within a region of the nucleotide-sample slide.

7. The system of claim 6, further comprising instructions that, when executed by the at least one processor, cause the system to identify the pair of band-edge spectral regions according to a hexagon layout, a square layout, or a diamond layout for the cluster locations within the region of the nucleotide-sample slide.

8. The system of claim 6, further comprising instructions that, when executed by the at least one processor, cause the system to: identify a set of pairs of band-edge spectral regions based on the geometric layout for cluster locations within the region of the nucleotide-sample slide; and determine a respective phase difference between each pair of the set of pairs of band-edge spectral regions.

9. The system of claim 1, further comprising instructions that, when executed by the at least one processor, cause the system to generate the at least one location error in at least one direction by:Attorney Docket No. IP-2805-PCT 91 Patent Applicationdetermining a phase angle between the pair of band-edge spectral regions; and determining the at least one location error in at least one direction based on the phase angle and a distance between clusters of oligonucleotides within the nucleotide-sample slide.

10. The system of claim 9, further comprising instructions that, when executed by the at least one processor, cause the system to determine the phase angle between the pair of band-edge spectral regions by: extracting, from the image, a first band-edge spectral region of the pair of band-edge spectral regions and a second band-edge spectral region of the pair of band-edge spectral regions; and determining a product of the first band-edge spectral region and a conjugate of the second band-edge spectral region.

11. The system of claim 1, further comprising instructions that, when executed by the at least one processor, cause the system to generate the at least one location error in at least one direction by: determining a first phase angle between the pair of band-edge spectral regions; determining a first location error in a first direction based on the first phase angle and a distance between clusters of oligonucleotides within the nucleotide-sample slide; determining a second phase angle between an additional pair of band-edge spectral regions from the spatial frequency band within the image; and determining a second location error in a second direction based on the second phase angle and the distance between clusters of oligonucleotides within the nucleotide-sample slide.

12. The system of claim 1, further comprising instructions that, when executed by the at least one processor, cause the system to: access an image-patch grid comprising grid cells corresponding to image patches depicting subregions of a nucleotide-sample slide; determine, for each grid cell of the image-patch grid, at least one cell-specific location error for predicted locations of clusters of oligonucleotides; and determine, based on the at least one cell-specific location error, adjusted locations of the clusters of oligonucleotides within each grid cell of the image-patch grid.

13. The system of claim 12, further comprising instructions that, when executed by the at least one processor, cause the system to: map image pixels for a grid cell of the image-patch grid to the predicted locations of clusters of oligonucleotides of a subset of clusters within the grid cell; place a patch of the image within the grid cell of the image-patch grid; andAttorney Docket No. IP-2805-PCT 92 Patent Applicationdetermine, for each grid cell of the image-patch grid, the at least one cell-specific location error for the predicted locations of clusters of oligonucleotides.

14. The system of claim 1, further comprising instructions that, when executed by the at least one processor, cause the system to: apply a smoothing model to cell-specific location errors in grid cells of an image-patch grid; generate, utilizing the smoothing model and a cell-specific location error in a grid cell for the at least one cluster of oligonucleotides, at least one smoothed location error for the predicted location of the at least one cluster of oligonucleotides; and determine, based on the at least one smoothed location error, the adjusted location of the at least one cluster of oligonucleotides.

15. The system of claim 13, further comprising instructions that, when executed by the at least one processor, cause the system to determine, for each grid cell of the image-patch grid, the at least one cell-specific location error for the predicted locations of clusters of oligonucleotides by: identifying a subsampled image-patch grid comprising subsampled grid cells corresponding to a subset of image patches; determining, for each subsampled grid cell of the subsampled image-patch grid, the at least one cell-specific location error for predicted locations of clusters of oligonucleotides; and identifying, from a subsampled grid cell of the subsampled grid cells, the at least one cellspecific location error for each grid cell of the image-patch grid.

16. The system of claim 15, further comprising instructions that, when executed by the at least one processor, cause the system to determine, for a subsampled grid cell of the subsampled image-patch grid: an optical distortion vector that estimates optical distortion in a first direction and represents a first cell-specific location error; and a jitter vector that estimates jitter in a second direction and represents a second cell-specific location error.

17. The system of claim 16, further comprising instructions that, when executed by the at least one processor, cause the system to determine, for the subsampled grid cell of the subsampled image-patch grid, the optical distortion vector and the jitter vector utilizing a leastsquares model by: determining observed band-edge-region errors for the pair of band-edge spectral regions within the image;Attorney Docket No. IP-2805-PCT 93 Patent Applicationdetermining estimated band-edge-region errors for the pair of band-edge spectral regions based on the optical distortion vector and the jitter vector; and determining, utilizing the least-squares model, the optical distortion vector and the jitter vector resulting in a least squared error between the observed band-edge-region errors and the estimated band-edge-region errors.

18. The system of claim 15, further comprising instructions that, when executed by the at least one processor, cause the system to identify the subsampled image-patch grid by identifying a staggered and subsampled image-patch grid in which the subsampled grid cells have been staggered and sections of the subsampled image-patch grid have been shifted according to a circular shift.

19. A computer-implemented method comprising: identifying, for a sequencing cycle, a pair of band-edge spectral regions from a spatial frequency band within an image depicting signals of at least one cluster of oligonucleotides at a predicted location within a nucleotide-sample slide; determining a phase difference between the pair of band-edge spectral regions; generating at least one location error in at least one direction for the predicted location of the at least one cluster of oligonucleotides based on the phase difference; and determining, based on the at least one location error and for the sequencing cycle, an adjusted location of the at least one cluster of oligonucleotides within the nucleotide-sample slide.

20. A non-transitory computer readable medium comprising instructions that, when executed by at least one processor, cause a system to: identify, for a sequencing cycle, a pair of band-edge spectral regions from a spatial frequency band within an image depicting signals of at least one cluster of oligonucleotides at a predicted location within a nucleotide-sample slide; determine a phase difference between the pair of band-edge spectral regions; generate at least one location error in at least one direction for the predicted location of the at least one cluster of oligonucleotides based on the phase difference; and determine, based on the at least one location error and for the sequencing cycle, an adjusted location of the at least one cluster of oligonucleotides within the nucleotide-sample slide.

21. A system comprising: at least one processor; and a non-transitory computer readable medium comprising instructions that, when executed by the at least one processor, cause the system to:Attorney Docket No. IP-2805-PCT 94 Patent Applicationidentify, for a sequencing cycle, pairs of band-edge spectral regions within images depicting signals of a cluster of oligonucleotides at respective predicted locations within a nucleotide-sample slide; determine phase differences between respective pairs of band-edge spectral regions; generate, based on the respective phase differences, location errors in at least one direction for the respective predicted locations of the cluster of oligonucleotides; and determine, based on the location errors and for the sequencing cycle, adjusted locations of the cluster of oligonucleotides within the nucleotide-sample slide.

22. The system of claim 21, further comprising instructions that, when executed by the at least one processor, cause the system to: determine, for the sequencing cycle, intensity values for the signals of the cluster of oligonucleotides; and generate a base call for the cluster of oligonucleotides based on the adjusted locations of the cluster of oligonucleotides within the images depicting the signals of the cluster of oligonucleotides and the intensity values.

23. The system of claim 21, further comprising instructions that, when executed by the at least one processor, cause the system to identify, for the sequencing cycle, the pairs of band-edge spectral regions by: identifying, for the sequencing cycle in a first channel, a first pair of band-edge spectral regions from a first spatial frequency band within a first image depicting signals of the cluster of oligonucleotides at a first predicted location within the nucleotide-sample slide; and identifying, for the sequencing cycle in a second channel, a second pair of band-edge spectral regions from a second spatial frequency band within a second image depicting signals of the cluster of oligonucleotides at a second predicted location within the nucleotide-sample slide.

24. The system of claim 23, further comprising instructions that, when executed by the at least one processor, cause the system to determine the respective phase differences between the respective pairs of band-edge spectral regions by: determining a first phase difference between the first pair of band-edge spectral regions; and determining a second phase difference between the second pair of band-edge spectral regions.

25. The system of claim 24, further comprising instructions that, when executed by the at least one processor, cause the system to determine the adjusted locations of the cluster of oligonucleotides within the nucleotide-sample slide by:Attorney Docket No. IP-2805-PCT 95 Patent Applicationgenerating a first location error in at least one direction for the first predicted location of the cluster of oligonucleotides based on the first phase difference; determining, based on the first location error and for the sequencing cycle, a first adjusted location of the cluster of oligonucleotides within the nucleotide-sample slide; generating a second location error in at least one direction for the second predicted location of the cluster of oligonucleotides based on the second phase difference; and determining, based on the second location error and for the sequencing cycle, a second adjusted location of the cluster of oligonucleotides within the nucleotide-sample slide.

26. The system of claim 25, further comprising instructions that, when executed by the at least one processor, cause the system to: determine, for the sequencing cycle, intensity values for the signals of the cluster of oligonucleotides in the first image; determine, for the sequencing cycle, intensity values for the signals of the cluster of oligonucleotides in the second image; and generate a base call for the cluster of oligonucleotides based on the first adjusted location of the cluster of oligonucleotides within the first image, the intensity values for the signals of the cluster of oligonucleotides in the first image, the second adjusted location of the cluster of oligonucleotides within the second image, and the intensity values for the signals of the cluster of oligonucleotides in the second image.

27. The system of claim 21, further comprising instructions that, when executed by the at least one processor, cause the system to: identify the pairs of band-edge spectral regions from a spatial frequency band within the images depicting signals of the cluster of oligonucleotides and neighboring clusters of oligonucleotides adjacent to the cluster of oligonucleotides; and determine, based on the location errors, the adjusted locations for the cluster of oligonucleotides and the neighboring clusters of oligonucleotides.

28. The system of claim 21, further comprising instructions that, when executed by the at least one processor, cause the system to identify the pairs of band-edge spectral regions according to a geometric layout for cluster locations of clusters of oligonucleotides within a region of the nucleotide-sample slide.

29. The system of claim 28, further comprising instructions that, when executed by the at least one processor, cause the system to identify the pairs of band-edge spectral regions according to a hexagon layout, a square layout, or a diamond layout for the cluster locations within the region of the nucleotide-sample slide.Attorney Docket No. IP-2805-PCT 96 Patent Application30. The system of claim 21, further comprising instructions that, when executed by the at least one processor, cause the system to determine a respective phase difference between each pair of the pairs of band-edge spectral regions.

31. The system of claim 21 , further comprising instructions that, when executed by the at least one processor, cause the system to generate the location errors in at least one direction by: determining phase angles between the respective pairs of band-edge spectral regions; and determining the location errors in at least one direction based on the respective phase angles and respective distances between clusters of oligonucleotides within the nucleotide-sample slide.

32. The system of claim 31, further comprising instructions that, when executed by the at least one processor, cause the system to determine a phase angle between a pair of band-edge spectral regions of the pairs of band-edge spectral regions by: extracting, from an image of the images depicting signals of a cluster of oligonucleotides, a first band-edge spectral region of the pair of band-edge spectral regions and a second band-edge spectral region of the pair of band-edge spectral regions; and determining a product of the first band-edge spectral region and a conjugate of the second band-edge spectral region.

33. The system of claim 21, further comprising instructions that, when executed by the at least one processor, cause the system to generate a first location error and a second location error of the location errors by: determining a first phase angle between a pair of band-edge spectral regions of the pairs of band-edge spectral regions; determining the first location error in a first direction based on the first phase angle and a distance between clusters of oligonucleotides within the nucleotide-sample slide; determining a second phase angle between an additional pair of band-edge spectral regions of the pairs of band-edge spectral regions; and determining the second location error in a second direction based on the second phase angle and the distance between clusters of oligonucleotides within the nucleotide-sample slide.

34. The system of claim 21, further comprising instructions that, when executed by the at least one processor, cause the system to: access an image-patch grid comprising grid cells corresponding to image patches depicting subregions of a nucleotide-sample slide; determine, for each grid cell of the image-patch grid, cell-specific location errors for predicted locations of clusters of oligonucleotides; and determine, based on the cell-specific location errors, respective adjusted locations of the clusters of oligonucleotides within each grid cell of the image-patch grid.Attorney Docket No. IP-2805-PCT 97 Patent Application35. The system of claim 34, further comprising instructions that, when executed by the at least one processor, cause the system to: map image pixels for a grid cell of the image-patch grid to the predicted locations of clusters of oligonucleotides of a subset of clusters within the grid cell; place a patch of an image, of the images depicting the signals of the cluster of oligonucleotides, within the grid cell of the image-patch grid; and determine, for each grid cell of the image-patch grid, the cell-specific location errors for the predicted locations of clusters of oligonucleotides.

36. The system of claim 21, further comprising instructions that, when executed by the at least one processor, cause the system to: apply a smoothing model to cell-specific location errors in grid cells of an image-patch grid; generate, utilizing the smoothing model and a cell-specific location error in a grid cell for the cluster of oligonucleotides, smoothed location errors for the respective predicted locations of the cluster of oligonucleotides; and determine, based on the smoothed location errors, the adjusted locations of the cluster of oligonucleotides.

37. The system of claim 35, further comprising instructions that, when executed by the at least one processor, cause the system to determine, for each grid cell of the image-patch grid, the cell-specific location errors for the predicted locations of clusters of oligonucleotides by: identifying a subsampled image-patch grid comprising subsampled grid cells corresponding to a subset of image patches; determining, for each subsampled grid cell of the subsampled image-patch grid, the cellspecific location errors for predicted locations of clusters of oligonucleotides; and identifying, from a subsampled grid cell of the subsampled grid cells, the cell-specific location errors for each grid cell of the image-patch grid.

38. The system of claim 37, further comprising instructions that, when executed by the at least one processor, cause the system to determine, for a subsampled grid cell of the subsampled image-patch grid: an optical distortion vector that estimates optical distortion in a first direction and represents a first cell-specific location error; and a jitter vector that estimates jitter in a second direction and represents a second cell-specific location error.

39. The system of claim 38, further comprising instructions that, when executed by the at least one processor, cause the system to determine, for the subsampled grid cell of theAttorney Docket No. IP-2805-PCT 98 Patent Applicationsubsampled image-patch grid, the optical distortion vector and the jitter vector utilizing a leastsquares model by: determining observed band-edge-region errors for a pair of band-edge spectral regions of the pairs of band-edge spectral regions within the images; determining estimated band-edge-region errors for the pair of band-edge spectral regions based on the optical distortion vector and the jitter vector; and determining, utilizing the least-squares model, the optical distortion vector and the jitter vector resulting in a least squared error between the observed band-edge-region errors and the estimated band-edge-region errors.

40. The system of claim 37, further comprising instructions that, when executed by the at least one processor, cause the system to identify the subsampled image-patch grid by identifying a staggered and subsampled image-patch grid in which the subsampled grid cells have been staggered and sections of the subsampled image-patch grid have been shifted according to a circular shift.

41. A computer-implemented method comprising: identifying, for a sequencing cycle, pairs of band-edge spectral regions within images depicting signals of a cluster of oligonucleotides at respective predicted locations within a nucleotide-sample slide; determining phase differences between respective pairs of band-edge spectral regions; generating, based on the respective phase differences, location errors in at least one direction for the respective predicted locations of the cluster of oligonucleotides; and determining, based on the location errors and for the sequencing cycle, adjusted locations of the cluster of oligonucleotides within the nucleotide-sample slide.

42. A non-transitory computer readable medium comprising instructions that, when executed by at least one processor, cause a system to: identify, for a sequencing cycle, pairs of band-edge spectral regions within images depicting signals of a cluster of oligonucleotides at respective predicted locations within a nucleotide-sample slide; determine phase differences between respective pairs of band-edge spectral regions; generate, based on the respective phase differences, location errors in at least one direction for the respective predicted locations of the cluster of oligonucleotides; and determine, based on the location errors and for the sequencing cycle, adjusted locations of the cluster of oligonucleotides within the nucleotide-sample slide.Attorney Docket No. IP-2805-PCT 99 Patent Application

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