On pairwise distances and median score of three genomes under DCJ

In comparative genomics, the rearrangement distance between two genomes (equal the minimal number of genome rearrangements required to transform them into a single genome) is often used for measuring their evolutionary remoteness. Generalization of this measure to three genomes is known as the median score (while a resulting genome is called median genome). In contrast to the rearrangement distance between two genomes which can be computed in linear time, computing the median score for three genomes is NP-hard. This inspires a quest for simpler and faster approximations for the median score, the most natural of which appears to be the halved sum of pairwise distances which in fact represents a lower bound for the median score. In this work, we study relationship and interplay of pairwise distances between three genomes and their median score under the model of Double-Cut-and-Join (DCJ) rearrangements. Most remarkably we show that while a rearrangement may change the sum of pairwise distances by at most 2 (and thus change the lower bound by at most 1), even the most "powerful" rearrangements in this respect that increase the lower bound by 1 (by moving one genome farther away from each of the other two genomes), which we call strong, do not necessarily affect the median score. This observation implies that the two measures are not as well-correlated as one's intuition may suggest. We further prove that the median score attains the lower bound exactly on the triples of genomes that can be obtained from a single genome with strong rearrangements. While the sum of pairwise distances with the factor 2/3 represents an upper bound for the median score, its tightness remains unclear. Nonetheless, we show that the difference of the median score and its lower bound is not bounded by a constant.Comment: Proceedings of the 10-th Annual RECOMB Satellite Workshop on Comparative Genomics (RECOMB-CG), 2012. (to appear

Hidden breakpoints in genome alignments

During the course of evolution, an organism's genome can undergo changes that affect the large-scale structure of the genome. These changes include gene gain, loss, duplication, chromosome fusion, fission, and rearrangement. When gene gain and loss occurs in addition to other types of rearrangement, breakpoints of rearrangement can exist that are only detectable by comparison of three or more genomes. An arbitrarily large number of these "hidden" breakpoints can exist among genomes that exhibit no rearrangements in pairwise comparisons. We present an extension of the multichromosomal breakpoint median problem to genomes that have undergone gene gain and loss. We then demonstrate that the median distance among three genomes can be used to calculate a lower bound on the number of hidden breakpoints present. We provide an implementation of this calculation including the median distance, along with some practical improvements on the time complexity of the underlying algorithm. We apply our approach to measure the abundance of hidden breakpoints in simulated data sets under a wide range of evolutionary scenarios. We demonstrate that in simulations the hidden breakpoint counts depend strongly on relative rates of inversion and gene gain/loss. Finally we apply current multiple genome aligners to the simulated genomes, and show that all aligners introduce a high degree of error in hidden breakpoint counts, and that this error grows with evolutionary distance in the simulation. Our results suggest that hidden breakpoint error may be pervasive in genome alignments.Comment: 13 pages, 4 figure

Phylogenetic reconstruction from transpositions

Background Because of the advent of high-throughput sequencing and the consequent reduction in the cost of sequencing, many organisms have been completely sequenced and most of their genes identified. It thus has become possible to represent whole genomes as ordered lists of gene identifiers and to study the rearrangement of these entities through computational means. As a result, genome rearrangement data has attracted increasing attentions from both biologists and computer scientists as a new type of data for phylogenetic analysis. The main events of genome rearrangements include inversions, transpositions and transversions. To date, GRAPPA and MGR are the most accurate methods for rearrangement phylogeny, both assuming inversion as the only event. However, due to the complexity of computing transposition distance, it is very difficult to analyze datasets when transpositions are dominant. Results We extend GRAPPA to handle transpositions. The new method is named GRAPPA-TP, with two major extensions: a heuristic method to estimate transposition distance, and a new transposition median solver for three genomes. Although GRAPPA-TP uses a greedy approach to compute the transposition distance, it is very accurate when genomes are relatively close. The new GRAPPA-TP is available from http://phylo.cse.sc.edu/ Conclusion Our extensive testing using simulated datasets shows that GRAPPA-TP is very accurate in terms of ancestor genome inference and phylogenetic reconstruction. Simulation results also suggest that model match is critical in genome rearrangement analysis: it is not accurate to simulate transpositions with other events including inversions

FPGA Acceleration of Gene Rearrangement Analysis

In this paper we present our work toward FPGA acceleration of phylogenetic reconstruction, a type of analysis that is commonly performed in the fields of systematic biology and comparative genomics. In our initial study, we have targeted a specific application that reconstructs maximum-parsimony (MP) phylogenies for gene-rearrangement data. Like other prevalent applications in computational biology, this application relies on a control-dependent, memory-intensive, and non-arithmetic combinatorial optimization algorithm. To achieve hardware acceleration, we developed an FPGA core design that implements the application\u27s primary bottleneck computation. Because our core is lightweight, we are able to synthesize multiple cores on a single FPGA. By using several cores in parallel, we have achieved a 25X end-to-end application speedup using simulated input data

A New Implementation and Detailed Study of Breakpoint Analysis

Phylogenies derived from gene order data may prove crucial in answering some fundamental open questions in biomolecular evolution. Yet very few techniques are available for such phylogenetic reconstructions. One method is breakpoint analysis, developed by Blanchette and Sankoff 2 for solving the breakpoint phylogeny.\u27 Our earlier studies 5;6 confirmed the usefulness of this approach, but also found that BPAnalysis, the implementation developed by Sankoff and Blanchette, was too slow to use on all but very small datasets. We report here on a reimplementation of BPAnalysis using the principles of algorithmic engineering. Our faster (by 2 to 3 orders of magnitude) and flexible implementation allowed us to conduct studies on the characteristics of breakpoint analysis, in terms of running time, quality, and robustness, as well as to analyze datasets that had so far been considered out of reach. We report on these findings and also discuss future directions for our new implementation.\u2

Limited Lifespan of Fragile Regions in Mammalian Evolution

An important question in genome evolution is whether there exist fragile regions (rearrangement hotspots) where chromosomal rearrangements are happening over and over again. Although nearly all recent studies supported the existence of fragile regions in mammalian genomes, the most comprehensive phylogenomic study of mammals (Ma et al. (2006) Genome Research 16, 1557-1565) raised some doubts about their existence. We demonstrate that fragile regions are subject to a "birth and death" process, implying that fragility has limited evolutionary lifespan. This finding implies that fragile regions migrate to different locations in different mammals, explaining why there exist only a few chromosomal breakpoints shared between different lineages. The birth and death of fragile regions phenomenon reinforces the hypothesis that rearrangements are promoted by matching segmental duplications and suggests putative locations of the currently active fragile regions in the human genome

A fast algorithm for the multiple genome rearrangement problem with weighted reversals and transpositions

<p>Abstract</p> <p>Background</p> <p>Due to recent progress in genome sequencing, more and more data for phylogenetic reconstruction based on rearrangement distances between genomes become available. However, this phylogenetic reconstruction is a very challenging task. For the most simple distance measures (the breakpoint distance and the reversal distance), the problem is NP-hard even if one considers only three genomes.</p> <p>Results</p> <p>In this paper, we present a new heuristic algorithm that directly constructs a phylogenetic tree w.r.t. the weighted reversal and transposition distance. Experimental results on previously published datasets show that constructing phylogenetic trees in this way results in better trees than constructing the trees w.r.t. the reversal distance, and recalculating the weight of the trees with the weighted reversal and transposition distance. An implementation of the algorithm can be obtained from the authors.</p> <p>Conclusion</p> <p>The possibility of creating phylogenetic trees directly w.r.t. the weighted reversal and transposition distance results in biologically more realistic scenarios. Our algorithm can solve today's most challenging biological datasets in a reasonable amount of time.</p

Maximum likelihood estimates of pairwise rearrangement distances

Accurate estimation of evolutionary distances between taxa is important for many phylogenetic reconstruction methods. In the case of bacteria, distances can be estimated using a range of different evolutionary models, from single nucleotide polymorphisms to large-scale genome rearrangements. In the case of sequence evolution models (such as the Jukes-Cantor model and associated metric) have been used to correct pairwise distances. Similar correction methods for genome rearrangement processes are required to improve inference. Current attempts at correction fall into 3 categories: Empirical computational studies, Bayesian/MCMC approaches, and combinatorial approaches. Here we introduce a maximum likelihood estimator for the inversion distance between a pair of genomes, using the group-theoretic approach to modelling inversions introduced recently. This MLE functions as a corrected distance: in particular, we show that because of the way sequences of inversions interact with each other, it is quite possible for minimal distance and MLE distance to differently order the distances of two genomes from a third. This has obvious implications for the use of minimal distance in phylogeny reconstruction. The work also tackles the above problem allowing free rotation of the genome. Generally a frame of reference is locked, and all computation made accordingly. This work incorporates the action of the dihedral group so that distance estimates are free from any a priori frame of reference.Comment: 21 pages, 7 figures. To appear in the Journal of Theoretical Biolog