Breakage-fusion-bridge (BFB) is a mechanism of genomic instability characterized by the joining and subsequent tearing apart of sister chromatids. When this process is repeated during multiple rounds of cell division, it leads to patterns of copy number increases of chromosomal segments as well as fold-back inversions where duplicated segments are arranged head-to-head. These structural variations can then drive tumorigenesis. BFB can be observed in progress using cytogenetic techniques, but generally BFB must be inferred from data such as microarrays or sequencing collected after BFB has ceased. Making correct inferences from this data is not straightforward, particularly given the complexity of some cancer genomes and BFB's ability to generate a wide range of rearrangement patterns. Here we present algorithms to aid the interpretation of evidence for BFB. We first pose the BFB countvector problem: given a chromosome segmentation and segment copy numbers, decide whether BFB can yield a chromosome with the given segment counts. We present a linear time algorithm for the problem, in contrast to a previous exponential time algorithm. We then combine this algorithm with fold-back inversions to develop tests for BFB. We show that, contingent on assumptions about cancer genome evolution, count vectors and fold-back inversions are sufficient evidence for detecting BFB. We apply the presented techniques to paired-end sequencing data from pancreatic tumors and confirm a previous finding of BFB as well as identify a chromosomal region likely rearranged by BFB cycles, demonstrating the practicality of our approach.bioinformatics | cancer genomics | combinatorial pattern matching | gene amplification

The currently fastest algorithm for RNA Single Strand Folding requires O (nZ) time and Θ(n 2 ) space, where n denotes the length of the input string and Z is a sparsity parameter satisfying n Z < n 2 . We show how to reduce the time and space complexities of this algorithm in the sparse case. The space reduction is based on the observation that some solutions for sub-instances are not examined after a certain stage of the algorithm, and may be discarded from memory. The running time speed up is achieved by combining two independent sparsification criteria, which restrict the number of expressions that need to be examined in bottleneck computations of the algorithm. This yields an O (n 2 + P Z) time and Θ(Z ) space algorithm, where P is a sparsity parameter satisfying P < n Z n(P + 1). For the base-pairing maximization variant, the time complexity is further reduced to O (L Z), where L denotes the maximum number of base-pairs in a folding of the input string and satisfies L n\2. The presented techniques also extend to the related RNA Simultaneous Alignment and Folding problem. For an input composed of two strings of lengths n and m, the time and space complexities are reduced from O (nmZ ) and Θ(n 2 m 2 ) down to O (n 2 m 2 +PZ ) and Θ(nm 2 +Z ) respectively, whereZ andP are sparsity parameters satisfyingP < nm Z < nm(P + 3).A preliminary extended abstract of this work previously appeared in Backofen et al. (2009) [5]. Code implementations (in Java) may be downloaded from: http://www.cs.bgu.ac.il/ zakovs/RNAfold/SparseFold.zip.

BackgroundRNA secondary structure prediction is a mainstream bioinformatic domain, and is key to computational analysis of functional RNA. In more than 30 years, much research has been devoted to defining different variants of RNA structure prediction problems, and to developing techniques for improving prediction quality. Nevertheless, most of the algorithms in this field follow a similar dynamic programming approach as that presented by Nussinov and Jacobson in the late 70's, which typically yields cubic worst case running time algorithms. Recently, some algorithmic approaches were applied to improve the complexity of these algorithms, motivated by new discoveries in the RNA domain and by the need to efficiently analyze the increasing amount of accumulated genome-wide data.ResultsWe study Valiant's classical algorithm for Context Free Grammar recognition in sub-cubic time, and extract features that are common to problems on which Valiant's approach can be applied. Based on this, we describe several problem templates, and formulate generic algorithms that use Valiant's technique and can be applied to all problems which abide by these templates, including many problems within the world of RNA Secondary Structures and Context Free Grammars.ConclusionsThe algorithms presented in this paper improve the theoretical asymptotic worst case running time bounds for a large family of important problems. It is also possible that the suggested techniques could be applied to yield a practical speedup for these problems. For some of the problems (such as computing the RNA partition function and base-pair binding probabilities), the presented techniques are the only ones which are currently known for reducing the asymptotic running time bounds of the standard algorithms.

Methods for detecting the genomic signatures of natural selection have been heavily studied, and they have been successful in identifying many selective sweeps. For most of these sweeps, the favored allele remains unknown, making it difficult to distinguish carriers of the sweep from non-carriers. In an ongoing selective sweep, carriers of the favored allele are likely to contain a future most recent common ancestor. Therefore, identifying them may prove useful in predicting the evolutionary trajectory—for example, in contexts involving drug-resistant pathogen strains or cancer subclones. The main contribution of this paper is the development and analysis of a new statistic, the Haplotype Allele Frequency (HAF) score. The HAF score, assigned to individual haplotypes in a sample, naturally captures many of the properties shared by haplotypes carrying a favored allele. We provide a theoretical framework for computing expected HAF scores under different evolutionary scenarios, and we validate the theoretical predictions with simulations. As an application of HAF score computations, we develop an algorithm (PreCIOSS: Predicting Carriers of Ongoing Selective Sweeps) to identify carriers of the favored allele in selective sweeps, and we demonstrate its power on simulations of both hard and soft sweeps, as well as on data from well-known sweeps in human populations.

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Background: RNA secondary structure prediction is a mainstream bioinformatic domain, and is key to computational analysis of functional RNA. In more than 30 years, much research has been devoted to defining different variants of RNA structure prediction problems, and to developing techniques for improving prediction quality. Nevertheless, most of the algorithms in this field follow a similar dynamic programming approach as that presented by Nussinov and Jacobson in the late 70's, which typically yields cubic worst case running time algorithms. Recently, some algorithmic approaches were applied to improve the complexity of these algorithms, motivated by new discoveries in the RNA domain and by the need to efficiently analyze the increasing amount of accumulated genome-wide data.

With the remarkable development in inexpensive sequencing technologies and supporting computational tools, we have the promise of medicine being personalized by knowledge of the individual genome. Current technologies provide high throughput, but short reads. Reconstruction of the donor genome is based either on de novo assembly of the (short) reads, or on mapping donor reads to a standard reference. While such techniques demonstrate high success rates for inferring 'simple' genomic segments, they are confounded by segments with complex duplication patterns, including regions of direct medical relevance, like the HLA and the KIR regions.In this work, we address this problem with a method for assessing the quality of a predicted genome sequence for complex regions of the genome. This method combines two natural types of evidence: sequence similarity of the mapped reads to the predicted donor genome, and distribution of reads across the predicted genome. We define a new scoring function for read-to-genome matchings, which penalizes for sequence dissimilarities and deviations from expected read location distribution, and present an efficient algorithm for finding matchings that minimize the penalty. The algorithm is based on a formal problem, first defined in this paper, called Coverage Sensitive many-to-many min-cost bipartite Matching (CSM). This new problem variant generalizes the standard (one-to-one) weighted bipartite matching problem, and can be solved using network flows. The resulting Java-based tool, called SAGE (Scoring function for Assembled GEnomes), is freely available upon request. We demonstrate over simulated data that SAGE can be used to infer correct haplotypes of the highly repetitive KIR region on the Human chromosome 19.

The currently fastest algorithm for RNA Single Strand Folding requires O (nZ) time and Θ(n 2 )space, where n denotes the length of the input string and Z is a sparsity parameter satisfying n Z < n 2 . We show how to reduce the time and space complexities of this algorithm in the sparse case. The space reduction is based on the observation that some solutions for sub-instances are not examined after a certain stage of the algorithm, and may be discarded from memory. The running time speed up is achieved by combining two independent sparsification criteria, which restrict the number of expressions that need to be examined in bottleneck computations of the algorithm. This yields an O (n 2 + P Z) time and Θ(Z ) space algorithm, where P is a sparsity parameter satisfying P < n Z n(P + A preliminary extended abstract of this work previously appeared in Backofen et al. (2009) [5]. Code implementations (in Java) may be downloaded from: http://www.cs.bgu.ac.il/ zakovs/RNAfold/SparseFold.zip.1