An efficient genotyper and star-allele caller for pharmacogenomics.

High-throughput sequencing provides sufficient means for determining genotypes of clinically important pharmacogenes that can be used to tailor medical decisions to individual patients. However, pharmacogene genotyping, also known as star-allele calling, is a challenging problem that requires accurate copy number calling, structural variation identification, variant calling, and phasing within each pharmacogene copy present in the sample. Here we introduce Aldy 4, a fast and efficient tool for genotyping pharmacogenes that uses combinatorial optimization for accurate star-allele calling across different sequencing technologies. Aldy 4 adds support for long reads and uses a novel phasing model and improved copy number and variant calling models. We compare Aldy 4 against the current state-of-the-art star-allele callers on a large and diverse set of samples and genes sequenced by various sequencing technologies, such as whole-genome and targeted Illumina sequencing, barcoded 10x Genomics, and Pacific Biosciences (PacBio) HiFi. We show that Aldy 4 is the most accurate star-allele caller with near-perfect accuracy in all evaluated contexts, and hope that Aldy remains an invaluable tool in the clinical toolbox even with the advent of long-read sequencing technologies.

Comparison of high-throughput sequencing data compression tools.

High-throughput sequencing (HTS) data are commonly stored as raw sequencing reads in FASTQ format or as reads mapped to a reference, in SAM format, both with large memory footprints. Worldwide growth of HTS data has prompted the development of compression methods that aim to significantly reduce HTS data size. Here we report on a benchmarking study of available compression methods on a comprehensive set of HTS data using an automated framework.

Fast characterization of segmental duplications in genome assemblies.

Motivation: Segmental duplications (SDs) or low-copy repeats, are segments of DNA > 1 Kbp with high sequence identity that are copied to other regions of the genome. SDs are among the most important sources of evolution, a common cause of genomic structural variation and several are associated with diseases of genomic origin including schizophrenia and autism. Despite their functional importance, SDs present one of the major hurdles for de novo genome assembly due to the ambiguity they cause in building and traversing both state-of-the-art overlap-layout-consensus and de Bruijn graphs. This causes SD regions to be misassembled, collapsed into a unique representation, or completely missing from assembled reference genomes for various organisms. In turn, this missing or incorrect information limits our ability to fully understand the evolution and the architecture of the genomes. Despite the essential need to accurately characterize SDs in assemblies, there has been only one tool that was developed for this purpose, called Whole-Genome Assembly Comparison (WGAC); its primary goal is SD detection. WGAC is comprised of several steps that employ different tools and custom scripts, which makes this strategy difficult and time consuming to use. Thus there is still a need for algorithms to characterize within-assembly SDs quickly, accurately, and in a user friendly manner. Results: Here we introduce SEgmental Duplication Evaluation Framework (SEDEF) to rapidly detect SDs through sophisticated filtering strategies based on Jaccard similarity and local chaining. We show that SEDEF accurately detects SDs while maintaining substantial speed up over WGAC that translates into practical run times of minutes instead of weeks. Notably, our algorithm captures up to 25% 'pairwise error' between segments, whereas previous studies focused on only 10%, allowing us to more deeply track the evolutionary history of the genome. Availability and implementation: SEDEF is available at https://github.com/vpc-ccg/sedef.

Computational identification of micro-structural variations and their proteogenomic consequences in cancer.

Motivation: Rapid advancement in high throughput genome and transcriptome sequencing (HTS) and mass spectrometry (MS) technologies has enabled the acquisition of the genomic, transcriptomic and proteomic data from the same tissue sample. We introduce a computational framework, ProTIE, to integratively analyze all three types of omics data for a complete molecular profile of a tissue sample. Our framework features MiStrVar, a novel algorithmic method to identify micro structural variants (microSVs) on genomic HTS data. Coupled with deFuse, a popular gene fusion detection method we developed earlier, MiStrVar can accurately profile structurally aberrant transcripts in tumors. Given the breakpoints obtained by MiStrVar and deFuse, our framework can then identify all relevant peptides that span the breakpoint junctions and match them with unique proteomic signatures. Observing structural aberrations in all three types of omics data validates their presence in the tumor samples. Results: We have applied our framework to all The Cancer Genome Atlas (TCGA) breast cancer Whole Genome Sequencing (WGS) and/or RNA-Seq datasets, spanning all four major subtypes, for which proteomics data from Clinical Proteomic Tumor Analysis Consortium (CPTAC) have been released. A recent study on this dataset focusing on SNVs has reported many that lead to novel peptides. Complementing and significantly broadening this study, we detected 244 novel peptides from 432 candidate genomic or transcriptomic sequence aberrations. Many of the fusions and microSVs we discovered have not been reported in the literature. Interestingly, the vast majority of these translated aberrations, fusions in particular, were private, demonstrating the extensive inter-genomic heterogeneity present in breast cancer. Many of these aberrations also have matching out-of-frame downstream peptides, potentially indicating novel protein sequence and structure. Availability and implementation: MiStrVar is available for download at https://bitbucket.org/compbio/mistrvar, and ProTIE is available at https://bitbucket.org/compbio/protie. Contact: cenksahi@indiana.edu. Supplementary information: Supplementary data are available at Bioinformatics online.

Discovery and genotyping of novel sequence insertions in many sequenced individuals.

MOTIVATION: Despite recent advances in algorithms design to characterize structural variation using high-throughput short read sequencing (HTS) data, characterization of novel sequence insertions longer than the average read length remains a challenging task. This is mainly due to both computational difficulties and the complexities imposed by genomic repeats in generating reliable assemblies to accurately detect both the sequence content and the exact location of such insertions. Additionally, de novo genome assembly algorithms typically require a very high depth of coverage, which may be a limiting factor for most genome studies. Therefore, characterization of novel sequence insertions is not a routine part of most sequencing projects. RESULT: Here, we present Pamir, a new algorithm to efficiently and accurately discover and genotype novel sequence insertions using either single or multiple genome sequencing datasets. Pamir is able to detect breakpoint locations of the insertions and calculate their zygosity (i.e. heterozygous versus homozygous) by analyzing multiple sequence signatures, matching one-end-anchored sequences to small-scale de novo assemblies of unmapped reads, and conducting strand-aware local assembly. We test the efficacy of Pamir on both simulated and real data, and demonstrate its potential use in accurate and routine identification of novel sequence insertions in genome projects. AVAILABILITY AND IMPLEMENTATION: Pamir is available at https://github.com/vpc-ccg/pamir . CONTACT: fhach@{sfu.ca, prostatecentre.com } or calkan@cs.bilkent.edu.tr. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Cypiripi: exact genotyping of CYP2D6 using high-throughput sequencing data.

MOTIVATION: CYP2D6 is highly polymorphic gene which encodes the (CYP2D6) enzyme, involved in the metabolism of 20-25% of all clinically prescribed drugs and other xenobiotics in the human body. CYP2D6 genotyping is recommended prior to treatment decisions involving one or more of the numerous drugs sensitive to CYP2D6 allelic composition. In this context, high-throughput sequencing (HTS) technologies provide a promising time-efficient and cost-effective alternative to currently used genotyping techniques. To achieve accurate interpretation of HTS data, however, one needs to overcome several obstacles such as high sequence similarity and genetic recombinations between CYP2D6 and evolutionarily related pseudogenes CYP2D7 and CYP2D8, high copy number variation among individuals and short read lengths generated by HTS technologies. RESULTS: In this work, we present the first algorithm to computationally infer CYP2D6 genotype at basepair resolution from HTS data. Our algorithm is able to resolve complex genotypes, including alleles that are the products of duplication, deletion and fusion events involving CYP2D6 and its evolutionarily related cousin CYP2D7. Through extensive experiments using simulated and real datasets, we show that our algorithm accurately solves this important problem with potential clinical implications. AVAILABILITY AND IMPLEMENTATION: Cypiripi is available at http://sfu-compbio.github.io/cypiripi.

ORMAN: optimal resolution of ambiguous RNA-Seq multimappings in the presence of novel isoforms.

MOTIVATION: RNA-Seq technology is promising to uncover many novel alternative splicing events, gene fusions and other variations in RNA transcripts. For an accurate detection and quantification of transcripts, it is important to resolve the mapping ambiguity for those RNA-Seq reads that can be mapped to multiple loci: >17% of the reads from mouse RNA-Seq data and 50% of the reads from some plant RNA-Seq data have multiple mapping loci. In this study, we show how to resolve the mapping ambiguity in the presence of novel transcriptomic events such as exon skipping and novel indels towards accurate downstream analysis. We introduce ORMAN ( O ptimal R esolution of M ultimapping A mbiguity of R N A-Seq Reads), which aims to compute the minimum number of potential transcript products for each gene and to assign each multimapping read to one of these transcripts based on the estimated distribution of the region covering the read. ORMAN achieves this objective through a combinatorial optimization formulation, which is solved through well-known approximation algorithms, integer linear programs and heuristics. RESULTS: On a simulated RNA-Seq dataset including a random subset of transcripts from the UCSC database, the performance of several state-of-the-art methods for identifying and quantifying novel transcripts, such as Cufflinks, IsoLasso and CLIIQ, is significantly improved through the use of ORMAN. Furthermore, in an experiment using real RNA-Seq reads, we show that ORMAN is able to resolve multimapping to produce coverage values that are similar to the original distribution, even in genes with highly non-uniform coverage. AVAILABILITY: ORMAN is available at http://orman.sf.net

Geny: A Genotyping Tool for Allelic Decomposition of Killer Cell Immunoglobulin-Like Receptor Genes.

Accurate genotyping of Killer cell Immunoglobulin-like Receptor (KIR) genes plays a pivotal role in enhancing our understanding of innate immune responses, disease correlations, and the advancement of personalized medicine. However, due to the high variability of the KIR region and high level of sequence similarity among different KIR genes, the currently available genotyping methods are unable to accurately infer copy numbers, genotypes and haplotypes of individual KIR genes from next-generation sequencing data. Here we introduce Geny, a new computational tool for precise genotyping of KIR genes. Geny utilizes available KIR haplotype databases and proposes a novel combination of expectation-maximization filtering schemes and integer linear programming-based combinatorial optimization models to resolve ambiguous reads, provide accurate copy number estimation and estimate the haplotype of each copy for the genes within the KIR region. We evaluated Geny on a large set of simulated short-read datasets covering the known validated KIR region assemblies and a set of Illumina short-read samples sequenced from 25 validated samples from the Human Pangenome Reference Consortium collection and showed that it outperforms the existing genotyping tools in terms of accuracy, precision and recall. We envision Geny becoming a valuable resource for understanding immune system response and consequently advancing the field of patient-centric medicine.

SCALCE: boosting sequence compression algorithms using locally consistent encoding.

MOTIVATION: The high throughput sequencing (HTS) platforms generate unprecedented amounts of data that introduce challenges for the computational infrastructure. Data management, storage and analysis have become major logistical obstacles for those adopting the new platforms. The requirement for large investment for this purpose almost signalled the end of the Sequence Read Archive hosted at the National Center for Biotechnology Information (NCBI), which holds most of the sequence data generated world wide. Currently, most HTS data are compressed through general purpose algorithms such as gzip. These algorithms are not designed for compressing data generated by the HTS platforms; for example, they do not take advantage of the specific nature of genomic sequence data, that is, limited alphabet size and high similarity among reads. Fast and efficient compression algorithms designed specifically for HTS data should be able to address some of the issues in data management, storage and communication. Such algorithms would also help with analysis provided they offer additional capabilities such as random access to any read and indexing for efficient sequence similarity search. Here we present SCALCE, a 'boosting' scheme based on Locally Consistent Parsing technique, which reorganizes the reads in a way that results in a higher compression speed and compression rate, independent of the compression algorithm in use and without using a reference genome. RESULTS: Our tests indicate that SCALCE can improve the compression rate achieved through gzip by a factor of 4.19-when the goal is to compress the reads alone. In fact, on SCALCE reordered reads, gzip running time can improve by a factor of 15.06 on a standard PC with a single core and 6 GB memory. Interestingly even the running time of SCALCE + gzip improves that of gzip alone by a factor of 2.09. When compared with the recently published BEETL, which aims to sort the (inverted) reads in lexicographic order for improving bzip2, SCALCE + gzip provides up to 2.01 times better compression while improving the running time by a factor of 5.17. SCALCE also provides the option to compress the quality scores as well as the read names, in addition to the reads themselves. This is achieved by compressing the quality scores through order-3 Arithmetic Coding (AC) and the read names through gzip through the reordering SCALCE provides on the reads. This way, in comparison with gzip compression of the unordered FASTQ files (including reads, read names and quality scores), SCALCE (together with gzip and arithmetic encoding) can provide up to 3.34 improvement in the compression rate and 1.26 improvement in running time. AVAILABILITY: Our algorithm, SCALCE (Sequence Compression Algorithm using Locally Consistent Encoding), is implemented in C++ with both gzip and bzip2 compression options. It also supports multithreading when gzip option is selected, and the pigz binary is available. It is available at http://scalce.sourceforge.net. CONTACT: fhach@cs.sfu.ca or cenk@cs.sfu.ca SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Sequre: a high-performance framework for secure multiparty computation enables biomedical data sharing.

Secure multiparty computation (MPC) is a cryptographic tool that allows computation on top of sensitive biomedical data without revealing private information to the involved entities. Here, we introduce Sequre, an easy-to-use, high-performance framework for developing performant MPC applications. Sequre offers a set of automatic compile-time optimizations that significantly improve the performance of MPC applications and incorporates the syntax of Python programming language to facilitate rapid application development. We demonstrate its usability and performance on various bioinformatics tasks showing up to 3-4 times increased speed over the existing pipelines with 7-fold reductions in codebase sizes.

Computational pharmacogenotype extraction from clinical next-generation sequencing.

Background: Next-generation sequencing (NGS), including whole genome sequencing (WGS) and whole exome sequencing (WES), is increasingly being used for clinic care. While NGS data have the potential to be repurposed to support clinical pharmacogenomics (PGx), current computational approaches have not been widely validated using clinical data. In this study, we assessed the accuracy of the Aldy computational method to extract PGx genotypes from WGS and WES data for 14 and 13 major pharmacogenes, respectively. Methods: Germline DNA was isolated from whole blood samples collected for 264 patients seen at our institutional molecular solid tumor board. DNA was used for panel-based genotyping within our institutional Clinical Laboratory Improvement Amendments- (CLIA-) certified PGx laboratory. DNA was also sent to other CLIA-certified commercial laboratories for clinical WGS or WES. Aldy v3.3 and v4.4 were used to extract PGx genotypes from these NGS data, and results were compared to the panel-based genotyping reference standard that contained 45 star allele-defining variants within CYP2B6, CYP2C8, CYP2C9, CYP2C19, CYP2D6, CYP3A4, CYP3A5, CYP4F2, DPYD, G6PD, NUDT15, SLCO1B1, TPMT, and VKORC1. Results: Mean WGS read depth was >30x for all variant regions except for G6PD (average read depth was 29 reads), and mean WES read depth was >30x for all variant regions. For 94 patients with WGS, Aldy v3.3 diplotype calls were concordant with those from the genotyping reference standard in 99.5% of cases when excluding diplotypes with additional major star alleles not tested by targeted genotyping, ambiguous phasing, and CYP2D6 hybrid alleles. Aldy v3.3 identified 15 additional clinically actionable star alleles not covered by genotyping within CYP2B6, CYP2C19, DPYD, SLCO1B1, and NUDT15. Within the WGS cohort, Aldy v4.4 diplotype calls were concordant with those from genotyping in 99.7% of cases. When excluding patients with CYP2D6 copy number variation, all Aldy v4.4 diplotype calls except for one CYP3A4 diplotype call were concordant with genotyping for 161 patients in the WES cohort. Conclusion: Aldy v3.3 and v4.4 called diplotypes for major pharmacogenes from clinical WES and WGS data with >99% accuracy. These findings support the use of Aldy to repurpose clinical NGS data to inform clinical PGx.

Fast characterization of segmental duplication structure in multiple genome assemblies.

MOTIVATION: The increasing availability of high-quality genome assemblies raised interest in the characterization of genomic architecture. Major architectural elements, such as common repeats and segmental duplications (SDs), increase genome plasticity that stimulates further evolution by changing the genomic structure and inventing new genes. Optimal computation of SDs within a genome requires quadratic-time local alignment algorithms that are impractical due to the size of most genomes. Additionally, to perform evolutionary analysis, one needs to characterize SDs in multiple genomes and find relations between those SDs and unique (non-duplicated) segments in other genomes. A naïve approach consisting of multiple sequence alignment would make the optimal solution to this problem even more impractical. Thus there is a need for fast and accurate algorithms to characterize SD structure in multiple genome assemblies to better understand the evolutionary forces that shaped the genomes of today. RESULTS: Here we introduce a new approach, BISER, to quickly detect SDs in multiple genomes and identify elementary SDs and core duplicons that drive the formation of such SDs. BISER improves earlier tools by (i) scaling the detection of SDs with low homology to multiple genomes while introducing further 7-33[Formula: see text] speed-ups over the existing tools, and by (ii) characterizing elementary SDs and detecting core duplicons to help trace the evolutionary history of duplications to as far as 300 million years. AVAILABILITY AND IMPLEMENTATION: BISER is implemented in Seq programming language and is publicly available at https://github.com/0xTCG/biser .

Analytical Validation of a Computational Method for Pharmacogenetic Genotyping from Clinical Whole Exome Sequencing.

Germline whole exome sequencing from molecular tumor boards has the potential to be repurposed to support clinical pharmacogenomics. However, accurately calling pharmacogenomics-relevant genotypes from exome sequencing data remains challenging. Accordingly, this study assessed the analytical validity of the computational tool, Aldy, in calling pharmacogenomics-relevant genotypes from exome sequencing data for 13 major pharmacogenes. Germline DNA from whole blood was obtained for 164 subjects seen at an institutional molecular solid tumor board. All subjects had whole exome sequencing from Ashion Analytics and panel-based genotyping from an institutional pharmacogenomics laboratory. Aldy version 3.3 was operationalized on the LifeOmic Precision Health Cloud with copy number fixed to two copies per gene. Aldy results were compared with those from genotyping for 56 star allele-defining variants within CYP2B6, CYP2C8, CYP2C9, CYP2C19, CYP2D6, CYP3A4, CYP3A5, CYP4F2, DPYD, G6PD, NUDT15, SLCO1B1, and TPMT. Read depth was >100× for all variants except CYP3A4∗22. For 75 subjects in the validation cohort, all 3393 Aldy variant calls were concordant with genotyping. Aldy calls for 736 diplotypes containing alleles assessed by both platforms were also concordant. Aldy identified additional star alleles not covered by targeted genotyping for 139 diplotypes. Aldy accurately called variants and diplotypes for 13 major pharmacogenes, except for CYP2D6 variants involving copy number variations, thus allowing repurposing of whole exome sequencing to support clinical pharmacogenomics.

CYP2C8, CYP2C9, and CYP2C19 Characterization Using Next-Generation Sequencing and Haplotype Analysis: A GeT-RM Collaborative Project.

Pharmacogenetic tests typically target selected sequence variants to identify haplotypes that are often defined by star (∗) allele nomenclature. Due to their design, these targeted genotyping assays are unable to detect novel variants that may change the function of the gene product and thereby affect phenotype prediction and patient care. In the current study, 137 DNA samples that were previously characterized by the Genetic Testing Reference Material (GeT-RM) program using a variety of targeted genotyping methods were recharacterized using targeted and whole genome sequencing analysis. Sequence data were analyzed using three genotype calling tools to identify star allele diplotypes for CYP2C8, CYP2C9, and CYP2C19. The genotype calls from next-generation sequencing (NGS) correlated well to those previously reported, except when novel alleles were present in a sample. Six novel alleles and 38 novel suballeles were identified in the three genes due to identification of variants not covered by targeted genotyping assays. In addition, several ambiguous genotype calls from a previous study were resolved using the NGS and/or long-read NGS data. Diplotype calls were mostly consistent between the calling algorithms, although several discrepancies were noted. This study highlights the utility of NGS for pharmacogenetic testing and demonstrates that there are many novel alleles that are yet to be discovered, even in highly characterized genes such as CYP2C9 and CYP2C19.

Improved haplotype inference by exploiting long-range linking and allelic imbalance in RNA-seq datasets.

Haplotype reconstruction of distant genetic variants remains an unsolved problem due to the short-read length of common sequencing data. Here, we introduce HapTree-X, a probabilistic framework that utilizes latent long-range information to reconstruct unspecified haplotypes in diploid and polyploid organisms. It introduces the observation that differential allele-specific expression can link genetic variants from the same physical chromosome, thus even enabling using reads that cover only individual variants. We demonstrate HapTree-X's feasibility on in-house sequenced Genome in a Bottle RNA-seq and various whole exome, genome, and 10X Genomics datasets. HapTree-X produces more complete phases (up to 25%), even in clinically important genes, and phases more variants than other methods while maintaining similar or higher accuracy and being up to 10×  faster than other tools. The advantage of HapTree-X's ability to use multiple lines of evidence, as well as to phase polyploid genomes in a single integrative framework, substantially grows as the amount of diverse data increases.

Seq: A High-Performance Language for Bioinformatics.

The scope and scale of biological data are increasing at an exponential rate, as technologies like next-generation sequencing are becoming radically cheaper and more prevalent. Over the last two decades, the cost of sequencing a genome has dropped from $100 million to nearly $100-a factor of over 106-and the amount of data to be analyzed has increased proportionally. Yet, as Moore's Law continues to slow, computational biologists can no longer rely on computing hardware to compensate for the ever-increasing size of biological datasets. In a field where many researchers are primarily focused on biological analysis over computational optimization, the unfortunate solution to this problem is often to simply buy larger and faster machines. Here, we introduce Seq, the first language tailored specifically to bioinformatics, which marries the ease and productivity of Python with C-like performance. Seq starts with a subset of Python-and is in many cases a drop-in replacement-yet also incorporates novel bioinformatics- and computational genomics-oriented data types, language constructs and optimizations. Seq enables users to write high-level, Pythonic code without having to worry about low-level or domain-specific optimizations, and allows for the seamless expression of the algorithms, idioms and patterns found in many genomics or bioinformatics applications. We evaluated Seq on several standard computational genomics tasks like reverse complementation, k-mer manipulation, sequence pattern matching and large genomic index queries. On equivalent CPython code, Seq attains a performance improvement of up to two orders of magnitude, and a 160× improvement once domain-specific language features and optimizations are used. With parallelism, we demonstrate up to a 650× improvement. Compared to optimized C++ code, which is already difficult for most biologists to produce, Seq frequently attains up to a 2× improvement, and with shorter, cleaner code. Thus, Seq opens the door to an age of democratization of highly-optimized bioinformatics software.

Statistical Binning for Barcoded Reads Improves Downstream Analyses.

Sequencing technologies are capturing longer-range genomic information at lower error rates, enabling alignment to genomic regions that are inaccessible with short reads. However, many methods are unable to align reads to much of the genome, recognized as important in disease, and thus report erroneous results in downstream analyses. We introduce EMA, a novel two-tiered statistical binning model for barcoded read alignment, that first probabilistically maps reads to potentially multiple "read clouds" and then within clouds by newly exploiting the non-uniform read densities characteristic of barcoded read sequencing. EMA substantially improves downstream accuracy over existing methods, including phasing and genotyping on 10x data, with fewer false variant calls in nearly half the time. EMA effectively resolves particularly challenging alignments in genomic regions that contain nearby homologous elements, uncovering variants in the pharmacogenomically important CYP2D region, and clinically important genes C4 (schizophrenia) and AMY1A (obesity), which go undetected by existing methods. Our work provides a framework for future generation sequencing.

Optimal compressed representation of high throughput sequence data via light assembly.

The most effective genomic data compression methods either assemble reads into contigs, or replace them with their alignment positions on a reference genome. Such methods require significant computational resources, but faster alternatives that avoid using explicit or de novo-constructed references fail to match their performance. Here, we introduce a new reference-free compressed representation for genomic data based on light de novo assembly of reads, where each read is represented as a node in a (compact) trie. We show how to efficiently build such tries to compactly represent reads and demonstrate that among all methods using this representation (including all de novo assembly based methods), our method achieves the shortest possible output. We also provide an lower bound on the compression rate achievable on uniformly sampled genomic read data, which is approximated by our method well. Our method significantly improves the compression performance of alternatives without compromising speed.

Publisher Correction: Optimal compressed representation of high throughput sequence data via light assembly.

The original version of this Article contained errors in the affiliations of the authors Ibrahim Numanagic and Thomas A. Courtade, which were incorrectly given as 'Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA' and 'Computer Science & Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA', respectively. Also, the hyperlink for the source code in the Data Availability section was incorrectly given as https://github.iu.edu/kzhu/assembltrie , which links to a page that is not publicly accessible. The source code is publicly accessible at https://github.com/kyzhu/assembltrie . Furthermore, in the PDF version of the Article, the right-hand side of Figure 3 was inadvertently cropped. These errors have now been corrected in both the PDF and HTML versions of the Article.