Myriad mechanisms diversify the sequence content of eukaryotic transcripts at the DNA and RNA level with profound functional consequences. Examples include diversity generated by RNA splicing and V(D)J recombination. Today, these and other events are detected with fragmented bioinformatic tools that require predefining a form of transcript diversification; moreover, they rely on alignment to a necessarily incomplete reference genome, filtering out unaligned sequences which can be among the most interesting. Each of these steps introduces blindspots for discovery. Here, we develop NOMAD+, a new analytic method that performs unified, reference-free statistical inference directly on raw sequencing reads, extending the core NOMAD algorithm to include a micro-assembly and interpretation framework. NOMAD+ discovers broad and new examples of transcript diversification in single cells, bypassing genome alignment and without requiring cell type metadata and impossible with current algorithms. In 10,326 primary human single cells in 19 tissues profiled with SmartSeq2, NOMAD+ discovers a set of splicing and histone regulators with highly conserved intronic regions that are themselves targets of complex splicing regulation and unreported transcript diversity in the heat shock protein HSP90AA1. NOMAD+ simultaneously discovers diversification in centromeric RNA expression, V(D)J recombination, RNA editing, and repeat expansions missed by or impossible to measure with existing bioinformatic methods. NOMAD+ is a unified, highly efficient algorithm enabling unbiased discovery of an unprecedented breadth of RNA regulation and diversification in single cells through a new paradigm to analyze the transcriptome.

Unsupervised reference-free inference reveals unrecognized regulated transcriptomic complexity in human single cells

Decomposing a network flow into weighted paths is a problem with numerous applications, ranging from networking, transportation planning, to bioinformatics. In some applications we look for a decomposition that is optimal with respect to some property, such as the number of paths used, robustness to edge deletion, or length of the longest path. However, in many bioinformatic applications, we seek a specific decomposition where the paths correspond to some underlying data that generated the flow. In these cases, no optimization criteria guarantee the identification of the correct decomposition. Therefore, we propose to instead report the safe paths, which are subpaths of at least one path in every flow decomposition. In this work, we give the first local characterization of safe paths for flow decompositions in directed acyclic graphs, leading to a practical algorithm for finding the complete set of safe paths. In addition, we evaluate our algorithm on RNA transcript data sets against a trivial safe algorithm (extended unitigs), the recently proposed safe paths for path covers (TCBB 2021) and the popular heuristic greedy-width. On the one hand, we found that besides maintaining perfect precision, our safe and complete algorithm reports a significantly higher coverage (≈50% more) compared with the other safe algorithms. On the other hand, the greedy-width algorithm although reporting a better coverage, it also reports a significantly lower precision on complex graphs (for genes expressing a large number of transcripts). Overall, our safe and complete algorithm outperforms (by ≈20%) greedy-width on a unified metric (F-score) considering both coverage and precision when the evaluated data set has a significant number of complex graphs. Moreover, it also has a superior time (4−5×) and space performance (1.2−2.2×), resulting in a better and more practical approach for bioinformatic applications of flow decomposition.

Improving RNA Assembly via Safety and Completeness in Flow Decompositions

Minimum flow decomposition (MFD) is an NP-hard problem asking to decompose a network flow into a minimum set of paths (together with associated weights). Variants of it are powerful models in multiassembly problems in Bioinformatics, such as RNA assembly. Owing to its hardness, practical multiassembly tools either use heuristics or solve simpler, polynomial time-solvable versions of the problem, which may yield solutions that are not minimal or do not perfectly decompose the flow. Here, we provide the first fast and exact solver for MFD on acyclic flow networks, based on Integer Linear Programming (ILP). Key to our approach is an encoding of all the exponentially many solution paths using only a quadratic number of variables. We also extend our ILP formulation to many practical variants, such as incorporating longer or paired-end reads, or minimizing flow errors. On both simulated and real-flow splicing graphs, our approach solves any instance in <13 seconds. We hope that our formulations can lie at the core of future practical RNA assembly tools. Our implementations are freely available on Github.

Efficient Minimum Flow Decomposition via Integer Linear Programming

Hepatitis B virus (HBV) remains a global public health concern, with over 250 million individuals living with chronic HBV infection (CHB) and no curative therapy currently available. Viral diversity is associated with CHB pathogenesis and immunological control of infection. Improved methods to characterize the viral genome at both the population and intra-host level could aid drug development efforts. Conventionally, HBV sequencing data are aligned to a linear reference genome and only sequences capable of aligning to the reference are captured for analysis. Reference selection has additional consequences, including sample-specific ‘consensus’ sequence construction. It remains unclear how to select a reference from available sequences and whether a single reference is sufficient for genetic analyses. Using simulated short-read sequencing data generated from full-length publicly available HBV genome sequences and HBV sequencing data from a longitudinally sampled individual with CHB, we investigate alternative graph-based alignment approaches. We demonstrate that using a phylogenetically representative ‘genome graph’ for alignment, rather than linear reference sequences, avoids issues of reference ambiguity, improves alignment, and facilitates the construction of sample-specific consensus sequences genetically similar to an individual’s infection. Graph-based methods can therefore improve efforts to characterize the genetics of viral pathogens, including HBV, and may have broad implications in host pathogen research.

/pdf/a-hepatitis-b-virus-hbv-sequence-variation-graph-improves-17p218yq.pdf

A hepatitis B virus (HBV) sequence variation graph improves sequence alignment and sample-specific consensus sequence construction for genetic analysis of HBV

Elementary flux modes (EFMs) are minimal, steady state pathways characterizing a flux network. Fundamentally, all steady state fluxes in a network are decomposable into a linear combination of EFMs. While there is typically no unique set of EFM weights that reconstructs these fluxes, several optimization-based methods have been proposed to constrain the solution space by enforcing some notion of parsimony. However, it has long been recognized that optimization-based approaches may fail to uniquely identify EFM weights and return different feasible solutions across objective functions and solvers. Here we show that, for flux networks only involving single molecule transformations, these problems can be avoided by imposing a Markovian constraint on EFM weights. Our Markovian constraint guarantees a unique solution to the flux decomposition problem, and that solution is arguably more biophysically plausible than other solutions. We describe an algorithm for computing Markovian EFM weights via steady state analysis of a certain discrete-time Markov chain, based on the flux network, which we call the cycle-history Markov chain. We demonstrate our method with a differential analysis of EFM activity in a lipid metabolic network comparing healthy and Alzheimer’s disease patients. Our method is the first to uniquely decompose steady state fluxes into EFM weights for any unimolecular metabolic network.

/pdf/a-markov-constraint-to-uniquely-identify-elementary-flux-181a78yh.pdf

A Markov constraint to uniquely identify elementary flux mode weights in unimolecular metabolic networks

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. 

Deriving Ranges of Optimal Estimated Transcript Expression due to Nonidentifiability

Abstract 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 TCR sequences and 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 Data and source code for reproducing the experiments are available at: https://github.com/Kingsford-Group/gtedemedtest/ Contact carlk@cs.cmu.edu 

Lucio Maria Valletta

Papers

Deriving Ranges of Optimal Estimated Transcript Expression due to Nonidentifiability

The Effect of Genome Graph Expressiveness on the Discrepancy Between Genome Graph Distance and String Set Distance