Comparative Genomics

This paper investigates the problem of conservation of combinatorial structures in genome rearrangement scenarios. We give a characterization of a class of scenarios that conserve all common intervals, called commuting scenarios, and a characterization of permutations for which commuting scenarios exist. We show that measuring conservation of common intervals can be useful tool in assessing the quality of rearrangement scenarios, by investigating in detail three specific scenarios involving the mouse, rat and human X chromosomes.

High-throughput DNA sequencing is now producing collections of genomes from moderately or closely related organisms. Such a collection may be represented as a multiple alignment M of orthologous sequences, which induces a phylogenetic tree τ. Long-range genomic alignments with phylogenies have not yet found a prominent place in BLAST-like similarity search algorithms, though using them directly as databases can potentially yield more accurate and more informative alignments.

This work describes how to construct local alignments between a query and a multiple alignment in a way that explicitly uses a phylogenetic tree τ. We give an EM algorithm to find a locally optimal alignment when the location of the query on the tree τ is not known. An initial implementation of the method is tested on a large multiple alignment of sequences from eight vertebrate genomes.

We have developed a multiple genome alignment algorithm by using a sequence clustering algorithm to combine local pairwisegenome sequence matches produced by pairwise genome alignments, e.g, BLASTZ. Sequence clustering algorithms often generate clusters of sequences such that there exists a common shared region among all sequences in each cluster. To use a sequence clustering algorithm for genome alignment, it is necessary to handle numerous local alignments between a pair of genomes. We propose a multiple genome alignment method that converts the multiple genome alignment problem to the sequence clustering problem. This method does not need to make a guide tree to determine the order of multiple alignment, and it accurately detects multiple homologous regions. As a result, our multiple genome alignment algorithm performs competitively over existing algorithms. This is shown using an experiment which compares the performance of TBA, MultiPipMaker (MPM) and our algorithm in aligning 12 groups of 56 microbial genomes and by evaluating the number of common COGs detected.

In this paper we present an extended model related to reconciliation concepts. It is based on gene duplications, gene losses and speciation events. We define an evolutionary scenario (called a DLS-tree) which informally can represent an evolution of genes in species. We are interested in all scenarios – not only parsimonious ones. We propose a system of rules for transforming the scenarios. We prove that the system is confluent, sound and strongly normalizing. We show that a scenario in normal form (i.e. non-reducible) is unique and minimal in the sense of the cost computed as the total number of gene duplications and losses. Moreover, we present a classification of the scenarios and analyze their hierarchy. Finally, we prove that the tree in normal form could be easily transformed into the reconciled tree [12] in duplication-loss model. This solves some open problems stated in [13].

Identifying gene clusters, genomic regions that share local similarities in gene organization, is a prerequisite for many different types of genomic analyses, including operon prediction, reconstruction of chromosomal rearrangements, and detection of whole-genome duplications. A number of formal definitions of gene clusters have been proposed, as well as methods for finding such clusters and/or statistical tests for determining their significance. Unfortunately, there is very little overlap between previously published rigorous analytical statistical tests and the definitions used in practice. In this paper, we consider the max-gap cluster: a contiguous region containing a maximal set of homologs, where the number of non-homologous genes between pairs of adjacent homologs is never greater than a predefined, fixed parameter, g. Although this is one of the models most widely used in practice, currently the statistical significance of max-gap clusters can only be evaluated using Monte Carlo simulations because no analytical statistical tests have been developed for it. We give exact expressions for the probability of observing such a cluster by chance, assuming a simple reference-region scenario and random gene order, as well as more efficient methods for approximating this probability. We use these methods to identify which regions of the parameter space yield clusters that are statistically significant. Finally, we discuss some of the challenges in extending this model to whole-genome comparison.

In the first part of this paper, we investigate gene orders of closely related mitochondrial genomes for studying the properties of mutations rearranging genes in mitochondria. Our conclusions are that the evolution of mitochondrial genomes is more complicated than it is considered in recent methods, and stochastic modelling is necessary for its deeper understanding and more accurate inferring. The second part is a review on the Markov chain Monte Carlo approaches for the stochastic modelling of genome rearrangement, which seem to be the only computationally tractable way to this problem. We introduce the concept of partial importance sampling, which yields a class of Markov chains being efficient both in terms of mixing and computational time. We also give a list of open algorithmic problems whose solution might help improve the efficiency of partial importance samplers.

The distribution of the lengths of genomic segments inverted during the evolutionary divergence of two species cannot be inferred directly from the output of genome rearrangement algorithms, due to the rapid loss of signal from all but the shortest inversions. The number of short inversions produced by these algorithms, however, particularly those involving a single gene, is relatively reliable. To gain some insight into the shape of the inversion-length distribution we first apply a genome rearrangement algorithm to each of 32 pairs of bacterial genomes. For each pair we then simulate their divergence using a test distribution to generate the inversions and use the simulated genomes as input to the reconstruction algorithm. It is the comparison between the algorithm output for the real pair of genomes and the simulated pair which is used to assess the test distribution. We find that simulations based on the exponential distribution cannot provide a good fit, but that simulations based on a gamma distribution can account for both single-gene inversions and short inversions involving at most 20 genes, and we conclude that the shape of latter distribution corresponds well to the true distribution at least for small inversion lengths.

In a comparative map, the number of translocations in the evolutionary history of a chromosome can be estimated solely on the basis of the conserved syntenies it contains. This estimate, subtracted from the number of conserved segments, then allows the estimation of the number of inversions that have affected the chromosome. Summing these estimates over all chromosomes provides a startlingly accurate estimator (as assessed by simulation) of the total number of rearrangements of each type occurring in the evolutionary divergence of two genomes.