Sketching Methods with Small Window Guarantee Using Minimum Decycling Sets.

Most sequence sketching methods work by selecting specific k-mers from sequences so that the similarity between two sequences can be estimated using only the sketches. Because estimating sequence similarity is much faster using sketches than using sequence alignment, sketching methods are used to reduce the computational requirements of computational biology software. Applications using sketches often rely on properties of the k-mer selection procedure to ensure that using a sketch does not degrade the quality of the results compared with using sequence alignment. Two important examples of such properties are locality and window guarantees, the latter of which ensures that no long region of the sequence goes unrepresented in the sketch. A sketching method with a window guarantee, implicitly or explicitly, corresponds to a decycling set of the de Bruijn graph, which is a set of unavoidable k-mers. Any long enough sequence, by definition, must contain a k-mer from any decycling set (hence, the unavoidable property). Conversely, a decycling set also defines a sketching method by choosing the k-mers from the set as representatives. Although current methods use one of a small number of sketching method families, the space of decycling sets is much larger and largely unexplored. Finding decycling sets with desirable characteristics (e.g., small remaining path length) is a promising approach to discovering new sketching methods with improved performance (e.g., with small window guarantee). The Minimum Decycling Sets (MDSs) are of particular interest because of their minimum size. Only two algorithms, by Mykkeltveit and Champarnaud, are previously known to generate two particular MDSs, although there are typically a vast number of alternative MDSs. We provide a simple method to enumerate MDSs. This method allows one to explore the space of MDSs and to find MDSs optimized for desirable properties. We give evidence that the Mykkeltveit sets are close to optimal regarding one particular property, the remaining path length. A number of conjectures and computational and theoretical evidence to support them are presented. Code available at https://github.com/Kingsford-Group/mdsscope.

How has the AI boom impacted algorithmic biology?

This Voices piece will highlight the impact of artificial intelligence on algorithm development among computational biologists. How has worldwide focus on AI changed the path of research in computational biology? What is the impact on the algorithmic biology research community?

Revisiting the complexity of and algorithms for the graph traversal edit distance and its variants.

The graph traversal edit distance (GTED), introduced by Ebrahimpour Boroojeny et al. (2018), is an elegant distance measure defined as the minimum edit distance between strings reconstructed from Eulerian trails in two edge-labeled graphs. GTED can be used to infer evolutionary relationships between species by comparing de Bruijn graphs directly without the computationally costly and error-prone process of genome assembly. Ebrahimpour Boroojeny et al. (2018) propose two ILP formulations for GTED and claim that GTED is polynomially solvable because the linear programming relaxation of one of the ILPs always yields optimal integer solutions. The claim that GTED is polynomially solvable is contradictory to the complexity results of existing string-to-graph matching problems. We resolve this conflict in complexity results by proving that GTED is NP-complete and showing that the ILPs proposed by Ebrahimpour Boroojeny et al. do not solve GTED but instead solve for a lower bound of GTED and are not solvable in polynomial time. In addition, we provide the first two, correct ILP formulations of GTED and evaluate their empirical efficiency. These results provide solid algorithmic foundations for comparing genome graphs and point to the direction of heuristics. The source code to reproduce experimental results is available at https://github.com/Kingsford-Group/gtednewilp/ .

Detecting m6A RNA modification from nanopore sequencing using a semi-supervised learning framework.

Direct nanopore-based RNA sequencing can be used to detect post-transcriptional base modifications, such as m6A methylation, based on the electric current signals produced by the distinct chemical structures of modified bases. A key challenge is the scarcity of adequate training data with known methylation modifications. We present Xron, a hybrid encoder-decoder framework that delivers a direct methylation-distinguishing basecaller by training on synthetic RNA data and immunoprecipitation-based experimental data in two steps. First, we generate data with more diverse modification combinations through in silico cross-linking. Second, we use this dataset to train an end-to-end neural network basecaller followed by fine-tuning on immunoprecipitation-based experimental data with label-smoothing. The trained neural network basecaller outperforms existing methylation detection methods on both read-level and site-level prediction scores. Xron is a standalone, end-to-end m6A-distinguishing basecaller capable of detecting methylated bases directly from raw sequencing signals, enabling de novo methylome assembly.

Density and Conservation Optimization of the Generalized Masked-Minimizer Sketching Scheme.

Minimizers and syncmers are sketching methods that sample representative k-mer seeds from a long string. The minimizer scheme guarantees a well-spread k-mer sketch (high coverage) while seeking to minimize the sketch size (low density). The syncmer scheme yields sketches that are more robust to base substitutions (high conservation) on random sequences, but do not have the coverage guarantee of minimizers. These sketching metrics are generally adversarial to one another, especially in the context of sketch optimization for a specific sequence, and thus are difficult to be simultaneously achieved. The parameterized syncmer scheme was recently introduced as a generalization of syncmers with more flexible sampling rules and empirically better coverage than the original syncmer variants. However, no approach exists to optimize parameterized syncmers. To address this shortcoming, we introduce a new scheme called masked minimizers that generalizes minimizers in manner analogous to how parameterized syncmers generalize syncmers and allows us to extend existing optimization techniques developed for minimizers. This results in a practical algorithm to optimize the masked minimizer scheme with respect to both density and conservation. We evaluate the optimization algorithm on various benchmark genomes and show that our algorithm finds sketches that are overall more compact, well-spread, and robust to substitutions than those found by previous methods. Our implementation is released at https://github.com/Kingsford-Group/maskedminimizer. This new technique will enable more efficient and robust genomic analyses in the many settings where minimizers and syncmers are used.

Sketching methods with small window guarantee using minimum decycling sets.

Most sequence sketching methods work by selecting specific k-mers from sequences so that the similarity between two sequences can be estimated using only the sketches. Because estimating sequence similarity is much faster using sketches than using sequence alignment, sketching methods are used to reduce the computational requirements of computational biology software packages. Applications using sketches often rely on properties of the k-mer selection procedure to ensure that using a sketch does not degrade the quality of the results compared with using sequence alignment. Two important examples of such properties are locality and window guarantees, the latter of which ensures that no long region of the sequence goes unrepresented in the sketch. A sketching method with a window guarantee, implicitly or explicitly, corresponds to a Decycling Set, an unavoidable sets of k-mers. Any long enough sequence, by definition, must contain a k-mer from any decycling set (hence, it is unavoidable). Conversely, a decycling set also defines a sketching method by choosing the k-mers from the set as representatives. Although current methods use one of a small number of sketching method families, the space of decycling sets is much larger, and largely unexplored. Finding decycling sets with desirable characteristics (e.g., small remaining path length) is a promising approach to discovering new sketching methods with improved performance (e.g., with small window guarantee). The Minimum Decycling Sets (MDSs) are of particular interest because of their minimum size. Only two algorithms, by Mykkeltveit and Champarnaud, are previously known to generate two particular MDSs, although there are typically a vast number of alternative MDSs. We provide a simple method to enumerate MDSs. This method allows one to explore the space of MDSs and to find MDSs optimized for desirable properties. We give evidence that the Mykkeltveit sets are close to optimal regarding one particular property, the remaining path length. A number of conjectures and computational and theoretical evidence to support them are presented. Code available at https://github.com/Kingsford-Group/mdsscope.

Improving Hi-C contact matrices using genome graphs.

Three-dimensional chromosome structure plays an important role in fundamental genomic functions. Hi-C, a high-throughput, sequencing-based technique, has drastically expanded our comprehension of 3D chromosome structures. The first step of Hi-C analysis pipeline involves mapping sequencing reads from Hi-C to linear reference genomes. However, the linear reference genome does not incorporate genetic variation information, which can lead to incorrect read alignments, especially when analyzing samples with substantial genomic differences from the reference such as cancer samples. Using genome graphs as the reference facilitates more accurate mapping of reads, however, new algorithms are required for inferring linear genomes from Hi-C reads mapped on genome graphs and constructing corresponding Hi-C contact matrices, which is a prerequisite for the subsequent steps of the Hi-C analysis such as identifying topologically associated domains and calling chromatin loops. We introduce the problem of genome sequence inference from Hi-C data mediated by genome graphs. We formalize this problem, show the hardness of solving this problem, and introduce a novel heuristic algorithm specifically tailored to this problem. We provide a theoretical analysis to evaluate the efficacy of our algorithm. Finally, our empirical experiments indicate that the linear genomes inferred from our method lead to the creation of improved Hi-C contact matrices. These enhanced matrices show a reduction in erroneous patterns caused by structural variations and are more effective in accurately capturing the structures of topologically associated domains.

Creating and Using Minimizer Sketches in Computational Genomics.

Processing large data sets has become an essential part of computational genomics. Greatly increased availability of sequence data from multiple sources has fueled breakthroughs in genomics and related fields but has led to computational challenges processing large sequencing experiments. The minimizer sketch is a popular method for sequence sketching that underlies core steps in computational genomics such as read mapping, sequence assembling, k-mer counting, and more. In most applications, minimizer sketches are constructed using one of few classical approaches. More recently, efforts have been put into building minimizer sketches with desirable properties compared with the classical constructions. In this survey, we review the history of the minimizer sketch, the theories developed around the concept, and the plethora of applications taking advantage of such sketches. We aim to provide the readers a comprehensive picture of the research landscape involving minimizer sketches, in anticipation of better fusion of theory and application in the future.

Revisiting the Complexity of and Algorithms for the Graph Traversal Edit Distance and Its Variants.

The graph traversal edit distance (GTED), introduced by Ebrahimpour Boroojeny et al. (2018), is an elegant distance measure defined as the minimum edit distance between strings reconstructed from Eulerian trails in two edge-labeled graphs. GTED can be used to infer evolutionary relationships between species by comparing de Bruijn graphs directly without the computationally costly and error-prone process of genome assembly. Ebrahimpour Boroojeny et al. (2018) propose two ILP formulations for GTED and claim that GTED is polynomially solvable because the linear programming relaxation of one of the ILPs always yields optimal integer solutions. The claim that GTED is polynomially solvable is contradictory to the complexity results of existing string-to-graph matching problems. We resolve this conflict in complexity results by proving that GTED is NP-complete and showing that the ILPs proposed by Ebrahimpour Boroojeny et al. do not solve GTED but instead solve for a lower bound of GTED and are not solvable in polynomial time. In addition, we provide the first two, correct ILP formulations of GTED and evaluate their empirical efficiency. These results provide solid algorithmic foundations for comparing genome graphs and point to the direction of heuristics.

Differentiable Learning of Sequence-Specific Minimizer Schemes with DeepMinimizer.

Minimizers are widely used to sample representative k-mers from biological sequences in many applications, such as read mapping and taxonomy prediction. In most scenarios, having the minimizer scheme select as few k-mer positions as possible (i.e., having a low density) is desirable to reduce computation and memory cost. Despite the growing interest in minimizers, learning an effective scheme with optimal density is still an open question, as it requires solving an apparently challenging discrete optimization problem on the permutation space of k-mer orderings. Most existing schemes are designed to work well in expectation over random sequences, which have limited applicability to many practical tools. On the other hand, several methods have been proposed to construct minimizer schemes for a specific target sequence. These methods, however, only approximate the original objective with likewise discrete surrogate tasks that are not able to significantly improve the density performance. This article introduces the first continuous relaxation of the density minimizing objective, DeepMinimizer, which employs a novel Deep Learning twin architecture to simultaneously ensure both validity and performance of the minimizer scheme. Our surrogate objective is fully differentiable and, therefore, amenable to efficient gradient-based optimization using GPU computing. Finally, we demonstrate that DeepMinimizer discovers minimizer schemes that significantly outperform state-of-the-art constructions on human genomic sequences.

The effect of genome graph expressiveness on the discrepancy between genome graph distance and string set distance.

MOTIVATION: Intra-sample heterogeneity describes the phenomenon where a genomic sample contains a diverse set of genomic sequences. In practice, the true string sets in a sample are often unknown due to limitations in sequencing technology. In order to compare heterogeneous samples, genome graphs can be used to represent such sets of strings. However, a genome graph is generally able to represent a string set universe that contains multiple sets of strings in addition to the true string set. This difference between genome graphs and string sets is not well characterized. As a result, a distance metric between genome graphs may not match the distance between true string sets. RESULTS: We extend a genome graph distance metric, Graph Traversal Edit Distance (GTED) proposed by Ebrahimpour Boroojeny et al., to FGTED to model the distance between heterogeneous string sets and show that GTED and FGTED always underestimate the Earth Mover's Edit Distance (EMED) between string sets. We introduce the notion of string set universe diameter of a genome graph. Using the diameter, we are able to upper-bound the deviation of FGTED from EMED and to improve FGTED so that it reduces the average error in empirically estimating the similarity between true string sets. On simulated T-cell receptor sequences and actual Hepatitis B virus genomes, we show that the diameter-corrected FGTED reduces the average deviation of the estimated distance from the true string set distances by more than 250%. AVAILABILITY AND IMPLEMENTATION: Data and source code for reproducing the experiments are available at: https://github.com/Kingsford-Group/gtedemedtest/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Deriving Ranges of Optimal Estimated Transcript Expression due to Nonidentifiability.

Current expression quantification methods suffer from a fundamental but undercharacterized type of error: the most likely estimates for transcript abundances are not unique. This means multiple estimates of transcript abundances generate the observed RNA-seq reads with equal likelihood, and the underlying true expression cannot be determined. This is called nonidentifiability in probabilistic modeling. It is further exacerbated by incomplete reference transcriptomes where reads may be sequenced from unannotated transcripts. Graph quantification is a generalization to transcript quantification, accounting for the reference incompleteness by allowing exponentially many unannotated transcripts to express reads. We propose methods to calculate a "confidence range of expression" for each transcript, representing its possible abundance across equally optimal estimates for both quantification models. This range informs both whether a transcript has potential estimation error due to nonidentifiability and the extent of the error. Applying our methods to the Human Body Map data, we observe that 35%-50% of transcripts potentially suffer from inaccurate quantification caused by nonidentifiability. When comparing the expression between isoforms in one sample, we find that the degree of inaccuracy of 20%-47% transcripts can be so large that the ranking of expression between the transcript and other isoforms from the same gene cannot be determined. When comparing the expression of a transcript between two groups of RNA-seq samples in differential expression analysis, we observe that the majority of detected differentially expressed transcripts are reliable with a few exceptions after considering the ranges of the optimal expression estimates.

VariantStore: an index for large-scale genomic variant search.

Efficiently scaling genomic variant search indexes to thousands of samples is computationally challenging due to the presence of multiple coordinate systems to avoid reference biases. We present VariantStore, a system that indexes genomic variants from multiple samples using a variation graph and enables variant queries across any sample-specific coordinate system. We show the scalability of VariantStore by indexing genomic variants from the TCGA project in 4 h and the 1000 Genomes project in 3 h. Querying for variants in a gene takes between 0.002 and 3 seconds using memory only 10% of the size of the full representation.

Practical selection of representative sets of RNA-seq samples using a hierarchical approach.

MOTIVATION: Despite numerous RNA-seq samples available at large databases, most RNA-seq analysis tools are evaluated on a limited number of RNA-seq samples. This drives a need for methods to select a representative subset from all available RNA-seq samples to facilitate comprehensive, unbiased evaluation of bioinformatics tools. In sequence-based approaches for representative set selection (e.g. a k-mer counting approach that selects a subset based on k-mer similarities between RNA-seq samples), because of the large numbers of available RNA-seq samples and of k-mers/sequences in each sample, computing the full similarity matrix using k-mers/sequences for the entire set of RNA-seq samples in a large database (e.g. the SRA) has memory and runtime challenges; this makes direct representative set selection infeasible with limited computing resources. RESULTS: We developed a novel computational method called 'hierarchical representative set selection' to handle this challenge. Hierarchical representative set selection is a divide-and-conquer-like algorithm that breaks representative set selection into sub-selections and hierarchically selects representative samples through multiple levels. We demonstrate that hierarchical representative set selection can achieve summarization quality close to that of direct representative set selection, while largely reducing runtime and memory requirements of computing the full similarity matrix (up to 8.4× runtime reduction and 5.35× memory reduction for 10 000 and 12 000 samples respectively that could be practically run with direct subset selection). We show that hierarchical representative set selection substantially outperforms random sampling on the entire SRA set of RNA-seq samples, making it a practical solution to representative set selection on large databases like the SRA. AVAILABILITY AND IMPLEMENTATION: The code is available at https://github.com/Kingsford-Group/hierrepsetselection and https://github.com/Kingsford-Group/jellyfishsim. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Sequence-specific minimizers via polar sets.

MOTIVATION: Minimizers are efficient methods to sample k-mers from genomic sequences that unconditionally preserve sufficiently long matches between sequences. Well-established methods to construct efficient minimizers focus on sampling fewer k-mers on a random sequence and use universal hitting sets (sets of k-mers that appear frequently enough) to upper bound the sketch size. In contrast, the problem of sequence-specific minimizers, which is to construct efficient minimizers to sample fewer k-mers on a specific sequence such as the reference genome, is less studied. Currently, the theoretical understanding of this problem is lacking, and existing methods do not specialize well to sketch specific sequences. RESULTS: We propose the concept of polar sets, complementary to the existing idea of universal hitting sets. Polar sets are k-mer sets that are spread out enough on the reference, and provably specialize well to specific sequences. Link energy measures how well spread out a polar set is, and with it, the sketch size can be bounded from above and below in a theoretically sound way. This allows for direct optimization of sketch size. We propose efficient heuristics to construct polar sets, and via experiments on the human reference genome, show their practical superiority in designing efficient sequence-specific minimizers. AVAILABILITY AND IMPLEMENTATION: A reference implementation and code for analyses under an open-source license are at https://github.com/kingsford-group/polarset. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Constructing small genome graphs via string compression.

MOTIVATION: The size of a genome graph-the space required to store the nodes, node labels and edges-affects the efficiency of operations performed on it. For example, the time complexity to align a sequence to a graph without a graph index depends on the total number of characters in the node labels and the number of edges in the graph. This raises the need for approaches to construct space-efficient genome graphs. RESULTS: We point out similarities in the string encoding mechanisms of genome graphs and the external pointer macro (EPM) compression model. We present a pair of linear-time algorithms that transform between genome graphs and EPM-compressed forms. The algorithms result in an upper bound on the size of the genome graph constructed in terms of an optimal EPM compression. To further reduce the size of the genome graph, we propose the source assignment problem that optimizes over the equivalent choices during compression and introduce an ILP formulation that solves that problem optimally. As a proof-of-concept, we introduce RLZ-Graph, a genome graph constructed based on the relative Lempel-Ziv algorithm. Using RLZ-Graph, across all human chromosomes, we are able to reduce the disk space to store a genome graph on average by 40.7% compared to colored compacted de Bruijn graphs constructed by Bifrost under the default settings. The RLZ-Graph scales well in terms of running time and graph sizes with an increasing number of human genome sequences compared to Bifrost and variation graphs produced by VGtoolkit. AVAILABILITY: The RLZ-Graph software is available at: https://github.com/Kingsford-Group/rlzgraph. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Exact transcript quantification over splice graphs.

BACKGROUND: The probability of sequencing a set of RNA-seq reads can be directly modeled using the abundances of splice junctions in splice graphs instead of the abundances of a list of transcripts. We call this model graph quantification, which was first proposed by Bernard et al. (Bioinformatics 30:2447-55, 2014). The model can be viewed as a generalization of transcript expression quantification where every full path in the splice graph is a possible transcript. However, the previous graph quantification model assumes the length of single-end reads or paired-end fragments is fixed. RESULTS: We provide an improvement of this model to handle variable-length reads or fragments and incorporate bias correction. We prove that our model is equivalent to running a transcript quantifier with exactly the set of all compatible transcripts. The key to our method is constructing an extension of the splice graph based on Aho-Corasick automata. The proof of equivalence is based on a novel reparameterization of the read generation model of a state-of-art transcript quantification method. CONCLUSION: We propose a new approach for graph quantification, which is useful for modeling scenarios where reference transcriptome is incomplete or not available and can be further used in transcriptome assembly or alternative splicing analysis.

HARVESTMAN: a framework for hierarchical feature learning and selection from whole genome sequencing data.

BACKGROUND: Supervised learning from high-throughput sequencing data presents many challenges. For one, the curse of dimensionality often leads to overfitting as well as issues with scalability. This can bring about inaccurate models or those that require extensive compute time and resources. Additionally, variant calls may not be the optimal encoding for a given learning task, which also contributes to poor predictive capabilities. To address these issues, we present HARVESTMAN, a method that takes advantage of hierarchical relationships among the possible biological interpretations and representations of genomic variants to perform automatic feature learning, feature selection, and model building. RESULTS: We demonstrate that HARVESTMAN scales to thousands of genomes comprising more than 84 million variants by processing phase 3 data from the 1000 Genomes Project, one of the largest publicly available collection of whole genome sequences. Using breast cancer data from The Cancer Genome Atlas, we show that HARVESTMAN selects a rich combination of representations that are adapted to the learning task, and performs better than a binary representation of SNPs alone. We compare HARVESTMAN to existing feature selection methods and demonstrate that our method is more parsimonious-it selects smaller and less redundant feature subsets while maintaining accuracy of the resulting classifier. CONCLUSION: HARVESTMAN is a hierarchical feature selection approach for supervised model building from variant call data. By building a knowledge graph over genomic variants and solving an integer linear program , HARVESTMAN automatically and optimally finds the right encoding for genomic variants. Compared to other hierarchical feature selection methods, HARVESTMAN is faster and selects features more parsimoniously.

Maximum likelihood reconstruction of ancestral networks by integer linear programming.

MOTIVATION: The study of the evolutionary history of biological networks enables deep functional understanding of various bio-molecular processes. Network growth models, such as the Duplication-Mutation with Complementarity (DMC) model, provide a principled approach to characterizing the evolution of protein-protein interactions (PPIs) based on duplication and divergence. Current methods for model-based ancestral network reconstruction primarily use greedy heuristics and yield sub-optimal solutions. RESULTS: We present a new Integer Linear Programming (ILP) solution for maximum likelihood reconstruction of ancestral PPI networks using the DMC model. We prove the correctness of our solution that is designed to find the optimal solution. It can also use efficient heuristics from general-purpose ILP solvers to obtain multiple optimal and near-optimal solutions that may be useful in many applications. Experiments on synthetic data show that our ILP obtains solutions with higher likelihood than those from previous methods, and is robust to noise and model mismatch. We evaluate our algorithm on two real PPI networks, with proteins from the families of bZIP transcription factors and the Commander complex. On both the networks, solutions from our ILP have higher likelihood and are in better agreement with independent biological evidence from other studies. AVAILABILITY AND IMPLEMENTATION: A Python implementation is available at https://bitbucket.org/cdal/network-reconstruction. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Lower Density Selection Schemes via Small Universal Hitting Sets with Short Remaining Path Length.

Universal hitting sets (UHS) are sets of words that are unavoidable: every long enough sequence is hit by the set (i.e., it contains a word from the set). There is a tight relationship between UHS and minimizer schemes, where minimizer schemes with low density (i.e., efficient schemes) correspond to UHS of small size. Local schemes are a generalization of minimizer schemes that can be used as replacement for minimizer scheme with the possibility of being much more efficient. We establish the link between efficient local schemes and the minimum length of a string that must be hit by a UHS. We give bounds for the remaining path length of the Mykkeltveit UHS. In addition, we create a local scheme with the lowest known density that is only a log factor away from the theoretical lower bound.