MOTIVATION: Genome-wide association studies (GWAS) have discovered thousands of significant genetic effects on disease phenotypes. By considering gene expression as the intermediary between genotype and disease phenotype, expression quantitative trait loci studies have interpreted many of these variants by their regulatory effects on gene expression. However, there remains a considerable gap between genotype-to-gene expression association and genotype-to-gene expression prediction. Accurate prediction of gene expression enables gene-based association studies to be performed post hoc for existing GWAS, reduces multiple testing burden, and can prioritize genes for subsequent experimental investigation. RESULTS: In this work, we develop gene expression prediction methods that relax the independence and additivity assumptions between genetic markers. First, we consider gene expression prediction from a regression perspective and develop the HAPLEXR algorithm which combines haplotype clusterings with allelic dosages. Second, we introduce the new gene expression classification problem, which focuses on identifying expression groups rather than continuous measurements; we formalize the selection of an appropriate number of expression groups using the principle of maximum entropy. Third, we develop the HAPLEXD algorithm that models haplotype sharing with a modified suffix tree data structure and computes expression groups by spectral clustering. In both models, we penalize model complexity by prioritizing genetic clusters that indicate significant effects on expression. We compare HAPLEXR and HAPLEXD with three state-of-the-art expression prediction methods and two novel logistic regression approaches across five GTEx v8 tissues. HAPLEXD exhibits significantly higher classification accuracy overall; HAPLEXR shows higher prediction accuracy on approximately half of the genes tested and the largest number of best predicted genes (r2>0.1) among all methods. We show that variant and haplotype features selected by HAPLEXR are smaller in size than competing methods (and thus more interpretable) and are significantly enriched in functional annotations related to gene regulation. These results demonstrate the importance of explicitly modeling non-dosage dependent and intragenic epistatic effects when predicting expression. AVAILABILITY AND IMPLEMENTATION: Source code and binaries are freely available at https://github.com/rapturous/HAPLEX. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Images form a rich information source, which remains underutilized in biomedical document classification. We present here work that uses both image- and text-based features in order to identify articles of interest, in this case, pertaining to cis-regulatory modules in the context of gene-networks. Extending on our new idea, which we have recently introduced, of using OCR-based features to identify DNA contents in images, we combine image and text based classifiers to categorize documents as relevant or irrelevant to cis-regulatory modules. Using a set of hundreds of articles, marked by experts as relevant or irrelevant to cis-regulatory modules, we train/test image and text based classifiers, as well as classifiers integrating both. Our results indicate that the latter show the best performance with Recall, F-measure and Utility measures all above 0.9, demonstrating the significance of incorporating image data, and specifically OCR-based features, into the document categorization process. Moreover, the use of character distribution properties to represent images is directly relevant to other biomedical images containing text (e.g. RNA, proteins). Diagrams and other images containing text are also prevalent outside the biomedical domain, hence the work stands to be applicable and beneficial in other application areas.

MOTIVATION: Genome-wide haplotype reconstruction from sequence data, or haplotype assembly, is at the center of major challenges in molecular biology and life sciences. For complex eukaryotic organisms like humans, the genome is vast and the population samples are growing so rapidly that algorithms processing high-throughput sequencing data must scale favorably in terms of both accuracy and computational efficiency. Furthermore, current models and methodologies for haplotype assembly (i) do not consider individuals sharing haplotypes jointly, which reduces the size and accuracy of assembled haplotypes, and (ii) are unable to model genomes having more than two sets of homologous chromosomes (polyploidy). Polyploid organisms are increasingly becoming the target of many research groups interested in the genomics of disease, phylogenetics, botany and evolution but there is an absence of theory and methods for polyploid haplotype reconstruction. RESULTS: In this work, we present a number of results, extensions and generalizations of compass graphs and our HapCompass framework. We prove the theoretical complexity of two haplotype assembly optimizations, thereby motivating the use of heuristics. Furthermore, we present graph theory-based algorithms for the problem of haplotype assembly using our previously developed HapCompass framework for (i) novel implementations of haplotype assembly optimizations (minimum error correction), (ii) assembly of a pair of individuals sharing a haplotype tract identical by descent and (iii) assembly of polyploid genomes. We evaluate our methods on 1000 Genomes Project, Pacific Biosciences and simulated sequence data. AVAILABILITY AND IMPLEMENTATION: HapCompass is available for download at http://www.brown.edu/Research/Istrail_Lab/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: The understanding of the genetic determinants of complex disease is undergoing a paradigm shift. Genetic heterogeneity of rare mutations with deleterious effects is more commonly being viewed as a major component of disease. Autism is an excellent example where research is active in identifying matches between the phenotypic and genomic heterogeneities. A considerable portion of autism appears to be correlated with copy number variation, which is not directly probed by single nucleotide polymorphism (SNP) array or sequencing technologies. Identifying the genetic heterogeneity of small deletions remains a major unresolved computational problem partly due to the inability of algorithms to detect them. RESULTS: In this article, we present an algorithmic framework, which we term DELISHUS, that implements three exact algorithms for inferring regions of hemizygosity containing genomic deletions of all sizes and frequencies in SNP genotype data. We implement an efficient backtracking algorithm-that processes a 1 billion entry genome-wide association study SNP matrix in a few minutes-to compute all inherited deletions in a dataset. We further extend our model to give an efficient algorithm for detecting de novo deletions. Finally, given a set of called deletions, we also give a polynomial time algorithm for computing the critical regions of recurrent deletions. DELISHUS achieves significantly lower false-positive rates and higher power than previously published algorithms partly because it considers all individuals in the sample simultaneously. DELISHUS may be applied to SNP array or sequencing data to identify the deletion spectrum for family-based association studies. AVAILABILITY: DELISHUS is available at http://www.brown.edu/Research/Istrail_Lab/.

We study the parsimony approach to haplotype inference, which calls for finding a set of haplotypes of minimum cardinality that explains an input set of genotypes. We prove that the problem is APX-hard even in very restricted cases. On the positive side, we identify islands of tractability for the problem, by focusing on instances with specific structure of haplotype sharing among the input genotypes. We exploit the structure of those instance to give polynomial and constant-approximation algorithms to the problem. We also show that the general parsimony haplotyping problem is fixed parameter tractable.

Recent sequencing of the human and other mammalian genomes has brought about the necessity to align them, to identify and characterize their commonalities and differences. Programs that align whole genomes generally use a seed-and-extend technique, starting from exact or near-exact matches and selecting a reliable subset of these, called anchors, and then filling in the remaining portions between the anchors using a combination of local and global alignment algorithms, but their choices for the parameters so far have been primarily heuristic. We present a statistical framework and practical methods for selecting a set of matches that is both sensitive and specific and can constitute a reliable set of anchors for a one-to-one mapping of two genomes from which a whole-genome alignment can be built. Starting from exact matches, we introduce a novel per-base repeat annotation, the $Z$-score, from which noise and repeat filtering conditions are explored. Dynamic programming-based chaining algorithms are also evaluated as context-based filters. We apply the methods described here to the comparison of two progressive assemblies of the human genome, NCBI build 28 and build 34 http://genome.ucsc.edu), and show that a significant portion of the two genomes can be found in selected exact matches, with very limited amount of sequence duplication.

It is widely hoped that variation in the human genome will provide a means of predicting risk of a variety of complex, chronic diseases. A major stumbling block to the successful identification of association between human DNA polymorphisms (SNPs) and variability in risk of complex diseases is the enormous number of SNPs in the human genome (4,9). The large number of SNPs results in unacceptably high costs for exhaustive genotyping, and so there is a broad effort to determine ways to select SNPs so as to maximize the informativeness of a subset.In this paper we contrast two methods for reducing the complexity of SNP variation: haplotype tagging, i.e. typing a subset of SNPs to identify segments of the genome that appear to be nearly unrecombined (haplotype blocks), and a new block-free model that we develop in this report. We present a statistic for comparing haplotype blocks and show that while the concept of haplotype blocks is reasonably robust there is substantial variability among block partitions. We develop a measure for selecting an informative subset of SNPs in a block free model. We show that the general version of this problem is NP-hard and give efficient algorithms for two important special cases of this problem.

With the consensus human genome sequenced and many other sequencing projects at varying stages of completion, greater attention is being paid to the genetic differences among individuals and the abilities of those differences to predict phenotypes. A significant obstacle to such work is the difficulty and expense of determining haplotypes--sets of variants genetically linked because of their proximity on the genome--for large numbers of individuals for use in association studies. This paper presents some algorithmic considerations in a new approach for haplotype determination: inferring haplotypes from localised polymorphism data gathered from short genome 'fragments.' Formalised models of the biological system under consideration are examined, given a variety of assumptions about the goal of the problem and the character of optimal solutions. Some theoretical results and algorithms for handling haplotype assembly given the different models are then sketched. The primary conclusion is that some important simplified variants of the problem yield tractable problems while more general variants tend to be intractable in the worst case.

Structure comparison is a fundamental problem for structural genomics. A variety of structure comparison methods were proposed and several protein structure classification servers e.g., SCOP, DALI, CATH, were designed based on them, and are extensively used in practice. This area of research continues to be very active, being energized bi-annually by the CASP folding competitions, but despite the extraordinary international research effort devoted to it, progress is slow. A fundamental dimension of this bottleneck is the absence of rigorous algorithmic methods. A recent excellent survey on structure comparison by Taylor et.al. [23] records the state of the art of the area: In structure comparison, we do not even have an algorithm that guarantees an optimal answer for pairs of structures …

Article Free Access Share on Statistical mechanics, three-dimensionality and NP-completeness: I. Universality of intracatability for the partition function of the Ising model across non-planar surfaces (extended abstract) Author: Sorin Istrail Sandia National Laboratories, Applied Mathematics Department, MS 1110, Albuquerque, NM Sandia National Laboratories, Applied Mathematics Department, MS 1110, Albuquerque, NMView Profile Authors Info & Claims STOC '00: Proceedings of the thirty-second annual ACM symposium on Theory of computingMay 2000 Pages 87–96https://doi.org/10.1145/335305.335316Published:01 May 2000Publication History 34citation1,337DownloadsMetricsTotal Citations34Total Downloads1,337Last 12 Months164Last 6 weeks29 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

We show that calculating contact map overlap (a measure of similarity of protein structures) is NP-hard, but can be solved in polynomial time for several interesting and relevant special cases. We identify an important special case of this problem corresponding to self-avoiding walks, and prove a decomposition theorem and a corollary approximation result for this special case. These are the first approximation algorithms with guaranteed error bounds, and NP-completeness results in the literature in the area of protein structure alignment/fold recognition for measures of structure similarity of practical interest.

We present performance-guaranteed approximation algorithms for the protein folding problem in the hydrophobic-hydrophilic model (Dill, 1985). Our algorithms are the first approximation algorithms in the literature with guaranteed performance for this model (Dill, 1994). The hydrophobic-hydrophilic model abstracts the dominant force of protein folding: the hydrophobic interaction. The protein is modeled as a chain of amino acids of length n that are of two types; H (hydrophobic, i.e., nonpolar) and P (hydrophilic, i.e., polar). Although this model is a simplification of more complex protein folding models, the protein folding structure prediction problem is notoriously difficult for this model. Our algorithms have conformation that has linear (3n) or quadratic time and achieve a three-dimensional protein a guaranteed free energy no worse than three-eighths of optimal. This result answers the open problem of Ngo et al. (1994) about the possible existence of an efficient approximation algorithm with guaranteed performance for protein structure prediction in any well-studied model of protein folding. By achieving speed and near-optimality simultaneously, our algorithms rigorously capture salient features of the recently proposed framework of protein folding by Sali et al. (1994). Equally important, the final conformations of our algorithms have significant secondary structure (antiparallel sheets, ^-sheets, compact hydrophobic core). Furthermore, hypothetical folding pathways can be described for our algorithms that fit within the framework of diffusion-collision protein folding proposed by Karplus and Weaver (1979). Computational limitations of algorithms that compute the optimal conformation have restricted their applicability to short sequences (length < 90). Because our algorithms trade computational accuracy for speed, they can construct near-optimal conformations in linear time for sequences of any size. 1.

In the concurrent language CCS, two programs are considered the same if they are bisimilar . Several years and many researchers have demonstrated that the theory of bisimulation is mathematically appealing and useful in practice. However, bisimulation makes too many distinctions between programs. We consider the problem of adding operations to CCS to make bisimulation fully abstract. We define the class of GSOS operations, generalizing the style and technical advantages of CCS operations. We characterize GSOS congruence in as a bisimulation-like relation called ready-simulation . Bisimulation is strictly finer than ready simulation, and hence not a congruence for any GSOS language.

In 1979, Bernhart and Kainen conjectured that graphs of fixed genus g ≥ 1 have unbounded pagenumber. In this paper, it is proven that genus g graphs can be embedded in O ( g ) pages, thus disproving the conjecture. An Ω( g 1/2 ) lower bound is also derived. The first algorithm in the literature for embedding an arbitrary graph in a book with a non-trivial upper bound on the number of pages is presented. First, the algorithm computes the genus g of a graph using the algorithm of Filotti, Miller, Reif (1979), which is polynomial-time for fixed genus. Second, it applies an optimal-time algorithm for obtaining an O ( g )-page book embedding. Separate book embedding algorithms are given for the cases of graphs embedded in orientable and nonorientable surfaces. An important aspect of the construction is a new decomposition theorem, of independent interest, for a graph embedded on a surface. Book embedding has application in several areas, two of which are directly related to the results obtained: fault-tolerant VLSI and complexity theory.

A generalized version of universal traversing sequences is constructed. The generalization preserves the features of the universal traversing sequences that make them attractive for applications to derandomizations and space-bounded computation. For every n, there is constructed a sequence that is used by a finite automaton with O(1) states in order to traverse all the n-vertex labeled undirected graphs. The automaton walks on the graph; when it is at a certain vertex, it uses the edge labels and the sequence in order to decide which edge to follow. When it is walking on an edge, the automaton can see the edge labeling. As a corollary, polynomial-size generalized universal traversing sequences constructible in DSpace(log n) are obtained for certain classes of graphs.>

Bisimulation is the primitive notion of equivalence between concurrent processes in Milner's Calculus of Communicating Systems (CCS); there is a nontrivial game-like protocol for distinguishing nonbisimular processes. In contrast, process distinguishability in Hoare's theory of Communicating Sequential Processes (CSP) is determined solely on the basis of traces of visible actions. We examine what additional operations are needed to explain bisimulation similarly—specifically in the case of finitely branching processes without silent moves. We formulate a general notion of Structured Operational Semantics for processes with Guarded recursion (GSOS), and demonstrate that bisimulation does not agree with trace congruence with respect to any set of GSOS-definable contexts. In justifying the generality and significance of GSOS's, we work out some of the basic proof theoretic facts which justify the SOS discipline.

The paper constructs the first polynomial universal traversing sequences for cycles, solving an open problem of S. Cook and R. Aleliunas, R. Karp, R. Lipton, L. Lovasz, C. Rackoff (1979) [2] in the case of 2-regular graphs. The existence of universal traversing sequences of size Ο(d2n3logn) for n-vertex d-regular graphs was established in [2] by a probabilistic argument, which was inherently non-constructive. For the cycles, the non-constructive upper bound was improved to Ο (n3) by Janowsky (1983) [13] and Cobham (1986) [8]. Previously, the best explicit constructions for cycles were due to Bridgland (1986) and A. Bar-Noy, A. Borodin, M. Karchmer, N. Linial, and M. Werman (1986), and have size Ο(nlog n).

This paper disproves the conjecture that graphs of fixed genus g ≤ 1 have unbounded pagenumber (Bernhart and Kainen, 1979). We show that genus g graphs can be embedded in Ο(g) pages, and derive an Ω(√g) lower bound. We present the first algorithm in the literature for embedding an arbitrary graph in a book with a non-trivial upper bound on the number of pages. We first compute the genus g of a graph using the algorithm of Filotti, Miller, Reif (1979), and then apply our (optimal-time) algorithm for obtaining an Ο(g) page embedding. An important aspect of our construction is a new decomposition theorem, of independent interest, for a graph embedded on a surface. Book embedding has application in several areas, two of which are directly related to the results we obtain: fault-tolerant VLSI and complexity theory.