A framework for orthology assignment from gene rearrangement data

Abstract. Gene rearrangements have successfully been used in phylogenetic reconstruction and comparative genomics, but usually under the assumption that all genomes have the same gene content and that no gene is duplicated. While these assumptions allow one to work with organellar genomes, they are too restrictive when comparing nuclear genomes. The main challenge is how to deal with gene families, specifically, how to identify orthologs. While searching for orthologies is a common task in computational biology, it is usually done using sequence data. We approach that problem using gene rearrangement data, provide an optimization framework in which to phrase the problem, and present some preliminary theoretical results.

Linear programming for phylogenetic reconstruction based on gene rearrangements

Phylogenetic reconstruction from gene rearrangements has attracted increasing attention from biologists and computer scientists over the last few years. Methods used in reconstruction include distance-based methods, parsimony methods using sequence-based encodings, and direct optimization. The latter, pioneered by Sankoff and extended by us with the software suite GRAPPA, is the most accurate approach, but has been limited to small genomes because the running time of its scoring algorithm grows exponentially with the number of genes in the genome. We report here on a new method to compute a tight lower bound on the score of a given tree, using a set of linear constraints generated through selective applications of the triangle inequality. Our method generates an integer linear program with a carefully limited number of constraints, rapidly solves its relaxed version, and uses the result to provide a tight lower bound. Since this bound is very close to the optimal tree score, it can be used directly as a selection criterion, thereby enabling us to bypass entirely the expensive scoring procedure. We have implemented this method within our GRAPPA software and run several series of experiments on both biological and simulated datasets to assess its accuracy. Our results show that using the bound as a selection criterion yields excellent trees, with error rates below 5 % up to very large evolutionary distances, consistently beating the baseline Neighbor-Joining. Our new method enables us to extend the range of applicability of the direct optimization method to chromosomes of size comparable to those of bacteria, as well as to datasets with complex combinations of evolutionary events.

Phylogenetic reconstruction from gene rearrangement data with unequal gene contents

Abstract. Phylogenetic reconstruction from gene-rearrangement data has seen increased attention over the last five years. Existing methods are limited computationally and by the assumption (highly unrealistic in practice) that all genomes have the same gene content. We have recently shown that we can scale our reconstruction tool, GRAPPA, to instances with up to a thousand genomes with no loss of accuracy and at minimal computational cost. Computing genomic distances between two genomes with unequal gene contents has seen much progress recently, but that progress has not yet been reflected in phylogenetic reconstruction methods. In this paper, we present extensions to our GRAPPA approach that can handle limited numbers of duplications (one of the main requirements for analyzing genomic data from organelles) and a few deletions. Although GRAPPA is based on exhaustive search, we show that, in practice, our bounding functions suffice to prune away almost all of the search space (our pruning rates never fall below 99.995%), resulting in high accuracy and fast running times. The range of values within which we have tested our approach encompasses mitochondria and chloroplast organellar genomes, whose phylogenetic analysis is providing new insights on evolution. Keywords computational biology, phylogenetic reconstruction, gene-order data, whole-genome data, signe

Quartet-Based Phylogeny Reconstruction from Gene Orders

Phylogenetic reconstruction from gene-rearrangement data is attracting increasing attention from biologists and computer scientists. Methods used in reconstruction include distance-based methods, parsimony methods using sequence encodings, and direct optimization. The latter, pioneered by Sankoff and extended by us with the software suiteGRAPPA, is the most accurate approach; however, its exhaustive approach means that it can be applied only to small datasets of fewer than 15 taxa. While we have successfully scaled it up to 1,000 genomes by integrating it with a disk-covering method (DCM-GRAPPA), the recursive decomposition may need many levels of recursion to handle datasets with 1,000 or more genomes. We thus investigated quartet-based approaches, which directly decompose the datasets into subsets of four taxa each; such approaches have been well studied for sequence data, but not for gene-rearrangement data. We give an optimization algorithm for the NP-hard problem of computing optimal trees for each quartet, present a variation of the dyadic method (using heuristics to choose suitable short quartets), and use both in simulation studies. We find that our quartet-based method can handle more genomes than the base version of GRAPPA, thus enabling us to reduce the number of levels of recursion in DCM-GRAPPA, but is more sensitive to the rate of evolution, with error rates rapidly increasing when saturation is approached

Quartet methods for phylogeny reconstruction from gene orders

Abstract. Phylogenetic reconstruction from gene-rearrangement data has attracted increasing attention from biologists and computer scientists. Methods used in reconstruction include distance-based methods, parsimony methods using sequence-based encodings, and direct optimization. The latter, pioneered by Sankoff and extended by us with the software suite GRAPPA, is the most accurate approach; however, its exhaustive approach means that it can be applied only to small datasets of fewer than 15 taxa. While we have successfully scaled it up to 1,000 genomes by integrating it with a diskcovering method (DCM-GRAPPA), the recursive decomposition may need many levels of recursion to handle datasets with 1,000 or more genomes. We thus investigated quartet-based approaches, which directly decompose the datasets into subsets of four taxa each; such approaches have been well studied for sequence data, but not for gene-rearrangement data. We give an optimization algorithm for the NP-hard problem of computing optimal trees for each quartet, present a variation of the dyadic method (using heuristics to choose suitable short quartets), and use both in simulation studies. We find that our quartet-based method can handle more genomes than the base version of GRAPPA, thus enabling us to reduce the number of levels of recursion in DCM-GRAPPA, but is more sensitive to the rate of evolution, with error rates rapidly increasing when saturation is approached.