A safety framework for flow decomposition problems via integer linear programming

MOTIVATION

Many important problems in Bioinformatics (e.g. assembly or multiassembly) admit multiple solutions, while the final objective is to report only one. A common approach to deal with this uncertainty is finding "safe" partial solutions (e.g. contigs) which are common to all solutions. Previous research on safety has focused on polynomially time solvable problems, whereas many successful and natural models are NP-hard to solve, leaving a lack of "safety tools" for such problems. We propose the first method for computing all safe solutions for an NP-hard problem, "minimum flow decomposition" (MFD). We obtain our results by developing a "safety test" for paths based on a general integer linear programming (ILP) formulation. Moreover, we provide implementations with practical optimizations aimed to reduce the total ILP time, the most efficient of these being based on a recursive group-testing procedure.

RESULTS

Experimental results on transcriptome datasets show that all safe paths for MFDs correctly recover up to 90% of the full RNA transcripts, which is at least 25% more than previously known safe paths. Moreover, despite the NP-hardness of the problem, we can report all safe paths for 99.8% of the over 27 000 non-trivial graphs of this dataset in only 1.5 h. Our results suggest that, on perfect data, there is less ambiguity than thought in the notoriously hard RNA assembly problem.

AVAILABILITY AND IMPLEMENTATION

https://github.com/algbio/mfd-safety.

Flow Decomposition With Subpath Constraints

Flow network decomposition is a natural model for problems where we are given a flow network arising from superimposing a set of weighted paths and would like to recover the underlying data, i.e., decompose the flow into the original paths and their weights. Thus, variations on flow decomposition are often used as subroutines in multiassembly problems such as RNA transcript assembly. In practice, we frequently have access to information beyond flow values in the form of subpaths, and many tools incorporate these heuristically. But despite acknowledging their utility in practice, previous work has not formally addressed the effect of subpath constraints on the accuracy of flow network decomposition approaches. We formalize the flow decomposition with subpath constraints problem, give the first algorithms for it, and study its usefulness for recovering ground truth decompositions. For finding a minimum decomposition, we propose both a heuristic and an FPT algorithm. Experiments on RNA transcript datasets show that for instances with larger solution path sets, the addition of subpath constraints finds 13% more ground truth solutions when minimal decompositions are found exactly, and 30% more ground truth solutions when minimal decompositions are found heuristically.

Safety in Multi-Assembly via Paths Appearing in All Path Covers of a DAG

A multi-assembly problem asks to reconstruct multiple genomic sequences from mixed reads sequenced from all of them. Standard formulations of such problems model a solution as a path cover in a directed acyclic graph, namely a set of paths that together cover all vertices of the graph. Since multi-assembly problems admit multiple solutions in practice, we consider an approach commonly used in standard genome assembly: output only partial solutions (contigs, or safe paths), that appear in all path cover solutions. We study constrained path covers, a restriction on the path cover solution that incorporate practical constraints arising in multi-assembly problems. We give efficient algorithms finding all maximal safe paths for constrained path covers. We compute the safe paths of splicing graphs constructed from transcript annotations of different species. Our algorithms run in less than 15 seconds per species and report RNA contigs that are over 99% precise and are up to 8 times longer than unitigs. Moreover, RNA contigs cover over 70% of the transcripts and their coding sequences in most cases. With their increased length to unitigs, high precision, and fast construction time, maximal safe paths can provide a better base set of sequences for transcript assembly programs.

Efficient Minimum Flow Decomposition via Integer Linear Programming

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.

Genetic dissection of natural variation in oilseed traits of camelina by whole-genome resequencing and QTL mapping

Camelina [Camelina sativa (L.) Crantz] is an oilseed crop in the Brassicaceae family that is currently being developed as a source of bioenergy and healthy fatty acids. To facilitate modern breeding efforts through marker-assisted selection and biotechnology, we evaluated genetic variation among a worldwide collection of 222 camelina accessions. We performed whole-genome resequencing to obtain single nucleotide polymorphism (SNP) markers and to analyze genomic diversity. We also conducted phenotypic field evaluations in two consecutive seasons for variations in key agronomic traits related to oilseed production such as seed size, oil content (OC), fatty acid composition, and flowering time. We determined the population structure of the camelina accessions using 161,301 SNPs. Further, we identified quantitative trait loci (QTL) and candidate genes controlling the above field-evaluated traits by genome-wide association studies (GWAS) complemented with linkage mapping using a recombinant inbred line (RIL) population. Characterization of the natural variation at the genome and phenotypic levels provides valuable resources to camelina genetic studies and crop improvement. The QTL and candidate genes should assist in breeding of advanced camelina varieties that can be integrated into the cropping systems for the production of high yield of oils of desired fatty acid composition.

Maximal Perfect Haplotype Blocks with Wildcards

Recent work provides the first method to measure the relative fitness of genomic variants within a population that scales to large numbers of genomes. A key component of the computation involves finding maximal perfect haplotype blocks from a set of genomic samples for which SNPs (single-nucleotide polymorphisms) have been called. Often, owing to low read coverage and imperfect assemblies, some of the SNP calls can be missing from some of the samples. In this work, we consider the problem of finding maximal perfect haplotype blocks where some missing values may be present. Missing values are treated as wildcards, and the definition of maximal perfect haplotype blocks is extended in a natural way. We provide an output-linear time algorithm to identify all such blocks and demonstrate the algorithm on a large population SNP dataset. Our software is publicly available.

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Defined haplotype blocks to study SNP population data with missing values

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Developed a fast software tool to find these blocks

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Tested on a human chromosome 22 dataset of 5,008 samples and over one million SNPs

Extending Maximal Perfect Haplotype Blocks to the Realm of Pangenomics

Recent work provides the first method to measure the relative fitness of genomic variants within a population that scales to large numbers of genomes. A key component of the computation involves finding conserved haplotype blocks, which can be done in linear time. Here, we extend the notion of conserved haplotype blocks to pangenomes, which can store more complex variation than a single reference genome. We define a maximal perfect pangenome haplotype block and give a linear-time, suffix tree based approach to find all such blocks from a set of pangenome haplotypes. We demonstrate the method by applying it to a pangenome built from yeast strains.

Exploring Frequented Regions in Pan-Genomic Graphs

We consider the problem of identifying regions within a pan-genome De Bruijn graph that are traversed by many sequence paths. We define such regions and the subpaths that traverse them as frequented regions (FRs). In this work, we formalize the FR problem and describe an efficient algorithm for finding FRs. Subsequently, we propose some applications of FRs based on machine-learning and pan-genome graph simplification. We demonstrate the effectiveness of these applications using data sets for the organisms Staphylococcus aureus (bacterium) and Saccharomyces cerevisiae (yeast). We corroborate the biological relevance of FRs such as identifying introgressions in yeast that aid in alcohol tolerance, and show that FRs are useful for classification of yeast strains by industrial use and visualizing pan-genomic space.

Physiological dynamic compression regulates central energy metabolism in primary human chondrocytes

Chondrocytes use the pathways of central metabolism to synthesize molecular building blocks and energy for cartilage homeostasis. An interesting feature of the in vivo chondrocyte environment is the cyclical loading generated in various activities (e.g., walking). However, it is unknown whether central metabolism is altered by mechanical loading. We hypothesized that physiological dynamic compression alters central metabolism in chondrocytes to promote production of amino acid precursors for matrix synthesis. We measured the expression of central metabolites (e.g., glucose, its derivatives, and relevant co-factors) for primary human osteoarthritic chondrocytes in response to 0-30 minutes of compression. To analyze the data, we used principal components analysis and ANOVA-simultaneous components analysis, as well as metabolic flux analysis. Compression-induced metabolic responses consistent with our hypothesis. Additionally, these data show that chondrocyte samples from different patient donors exhibit different sensitivity to compression. Most importantly, we find that grade IV osteoarthritic chondrocytes are capable of synthesizing non-essential amino acids and precursors in response to mechanical loading. These results suggest that further advances in metabolic engineering of chondrocyte mechanotransduction may yield novel translational strategies for cartilage repair.

Cooperative group provisioning with latency guarantees in multi-cloud deployments

Given a set of datacenters and groups of application clients, well-connected datacenters can be rented as traffic proxies to reduce client latency. Rental costs must be minimized while meeting the application specific latency needs. Here, we formally define the Cooperative Group Provisioning problem and show it is NP-hard to approximate within a constant factor. We introduce a novel greedy approach and demonstrate its promise through extensive simulation using real cloud network topology measurements and realistic client churn. We find that multi-cloud deployments dramatically increase the likelihood of meeting group latency thresholds with minimal cost increase compared to single-cloud deployments.

Antigen-antibody interface properties: composition, residue interactions, and features of 53 non-redundant structures

The structures of protein antigen-antibody (Ag-Ab) interfaces contain information about how Ab recognize Ag as well as how Ag are folded to present surfaces for Ag recognition. As such, the Ab surface holds information about Ag folding that resides with the Ab-Ag interface residues and how they interact. In order to gain insight into the nature of such interactions, a data set comprised of 53 non-redundant 3D structures of Ag-Ab complexes was analyzed. We assessed the physical and biochemical features of the Ag-Ab interfaces and the degree to which favored interactions exist between amino acid residues on the corresponding interface surfaces. Amino acid compositional analysis of the interfaces confirmed the dominance of TYR in the Ab paratope-containing surface (PCS), with almost two fold greater abundance than any other residue. Additionally TYR had a much higher than expected presence in the PCS compared to the surface of the whole antibody (defined as the occurrence propensity), along with aromatics PHE, TRP, and to a lesser degree HIS and ILE. In the Ag epitope-containing surface (ECS), there were slightly increased occurrence propensities of TRP and TYR relative to the whole Ag surface, implying an increased significance over the compositionally most abundant LYS>ASN>GLU>ASP>ARG. This examination encompasses a large, diverse set of unique Ag-Ab crystal structures that help explain the biological range and specificity of Ag-Ab interactions. This analysis may also provide a measure of the significance of individual amino acid residues in phage display analysis of Ag binding.

Towards a consensus on datasets and evaluation metrics for developing B-cell epitope prediction tools

A B-cell epitope is the three-dimensional structure within an antigen that can be bound to the variable region of an antibody. The prediction of B-cell epitopes is highly desirable for various immunological applications, but has presented a set of unique challenges to the bioinformatics and immunology communities. Improving the accuracy of B-cell epitope prediction methods depends on a community consensus on the data and metrics utilized to develop and evaluate such tools. A workshop, sponsored by the National Institute of Allergy and Infectious Disease (NIAID), was recently held in Washington, DC to discuss the current state of the B-cell epitope prediction field. Many of the currently available tools were surveyed and a set of recommendations was devised to facilitate improvements in the currently existing tools and to expedite future tool development. An underlying theme of the recommendations put forth by the panel is increased collaboration among research groups. By developing common datasets, standardized data formats, and the means with which to consolidate information, we hope to greatly enhance the development of B-cell epitope prediction tools.

C-Terminal Tail Phosphorylation of N-Formyl Peptide Receptor: Differential Recognition of Two Neutrophil Chemoattractant Receptors by Monoclonal Antibodies NFPR1 and NFPR2

The N-formyl peptide receptor (FPR), a G protein-coupled receptor that binds proinflammatory chemoattractant peptides, serves as a model receptor for leukocyte chemotaxis. Recombinant histidine-tagged FPR (rHis-FPR) was purified in lysophosphatidyl glycerol (LPG) by Ni(2+)-NTA agarose chromatography to >95% purity with high yield. MALDI-TOF mass analysis (>36% sequence coverage) and immunoblotting confirmed the identity as FPR. The rHis-FPR served as an immunogen for the production of 2 mAbs, NFPR1 and NFPR2, that epitope map to the FPR C-terminal tail sequences, 305-GQDFRERLI-313 and 337-NSTLPSAEVE-346, respectively. Both mAbs specifically immunoblotted rHis-FPR and recombinant FPR (rFPR) expressed in Chinese hamster ovary cells. NFPR1 also recognized recombinant FPRL1, specifically expressed in mouse L fibroblasts. In human neutrophil membranes, both Abs labeled a 45-75 kDa species (peak M(r) approximately 60 kDa) localized primarily in the plasma membrane with a minor component in the lactoferrin-enriched intracellular fractions, consistent with FPR size and localization. NFPR1 also recognized a band of M(r) approximately 40 kDa localized, in equal proportions to the plasma membrane and lactoferrin-enriched fractions, consistent with FPRL1 size and localization. Only NFPR2 was capable of immunoprecipitation of rFPR in detergent extracts. The recognition of rFPR by NFPR2 is lost after exposure of cellular rFPR to f-Met-Leu-Phe (fMLF) and regained after alkaline phosphatase treatment of rFPR-bearing membranes. In neutrophils, NFPR2 immunofluorescence was lost upon fMLF stimulation. Immunoblotting approximately 60 kDa species, after phosphatase treatment of fMLF-stimulated neutrophil membranes, was also enhanced. We conclude that the region 337-346 of FPR becomes phosphorylated after fMLF activation of rFPR-expressing Chinese hamster ovary cells and neutrophils.

Constraints on the conformation of the cytoplasmic face of dark-adapted and light-excited rhodopsin inferred from antirhodopsin antibody imprints

Rhodopsin is the best-understood member of the large G protein-coupled receptor (GPCR) superfamily. The G-protein amplification cascade is triggered by poorly understood light-induced conformational changes in rhodopsin that are homologous to changes caused by agonists in other GPCRs. We have applied the "antibody imprint" method to light-activated rhodopsin in native membranes by using nine monoclonal antibodies (mAbs) against aqueous faces of rhodopsin. Epitopes recognized by these mAbs were found by selection from random peptide libraries displayed on phage. A new computer algorithm, FINDMAP, was used to map the epitopes to discontinuous segments of rhodopsin that are distant in the primary sequence but are in close spatial proximity in the structure. The proximity of a segment of the N-terminal and the loop between helices VI and VIII found by FINDMAP is consistent with the X-ray structure of the dark-adapted rhodopsin. Epitopes to the cytoplasmic face segregated into two classes with different predicted spatial proximities of protein segments that correlate with different preferences of the antibodies for stabilizing the metarhodopsin I or metarhodopsin II conformations of light-excited rhodopsin. Epitopes of antibodies that stabilize metarhodopsin II indicate conformational changes from dark-adapted rhodopsin, including rearrangements of the C-terminal tail and altered exposure of the cytoplasmic end of helix VI, a portion of the C-3 loop, and helix VIII. As additional antibodies are subjected to antibody imprinting, this approach should provide increasingly detailed information on the conformation of light-excited rhodopsin and be applicable to structural studies of other challenging protein targets.

A fast heuristic algorithm for a probe mapping problem

A new heuristic algorithm is presented for mapping probes to locations along the genome, given noisy pairwise distance data as input. The model considered is quite general: The input consists of a collection of probe pairs and a confidence interval for the genomic distance separating each pair. Because the distance intervals are only known with some confidence level, some may be erroneous and must be removed in order to find a consistent map. A novel randomized technique for detecting and removing bad distance intervals is described. The technique could be useful in other contexts where partially erroneous data is inconsistent with the remaining data. These algorithms were motivated by the goal of making probe maps with inter-probe distance confidence intervals estimated from fluorescence in-situ hybridization (FISH) experiments. Experimentation was done on synthetic data sets (with and without errors) and FISH data from a region of human chromosome 4. Problems with up to 100 probes could be solved in several minutes on a fast workstation. In addition to FISH mapping, we describe some other possible applications that fall within the problem model. These include: mapping a backbone structure in folded DNA, finding consensus maps between independent maps covering the same genomic region, and ordering clones in a clone library.