4,034 research outputs found
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
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
Genome Halving by Block Interchange
We address the problem of finding the minimal number of block interchanges
(exchange of two intervals) required to transform a duplicated linear genome
into a tandem duplicated linear genome. We provide a formula for the distance
as well as a polynomial time algorithm for the sorting problem
The distribution of cycles in breakpoint graphs of signed permutations
Breakpoint graphs are ubiquitous structures in the field of genome
rearrangements. Their cycle decomposition has proved useful in computing and
bounding many measures of (dis)similarity between genomes, and studying the
distribution of those cycles is therefore critical to gaining insight on the
distributions of the genomic distances that rely on it. We extend here the work
initiated by Doignon and Labarre, who enumerated unsigned permutations whose
breakpoint graph contains cycles, to signed permutations, and prove
explicit formulas for computing the expected value and the variance of the
corresponding distributions, both in the unsigned case and in the signed case.
We also compare these distributions to those of several well-studied distances,
emphasising the cases where approximations obtained in this way stand out.
Finally, we show how our results can be used to derive simpler proofs of other
previously known results
Phylogeny of Prokaryotes and Chloroplasts Revealed by a Simple Composition Approach on All Protein Sequences from Complete Genomes Without Sequence Alignment
The complete genomes of living organisms have provided much information on their phylogenetic relationships. Similarly, the complete genomes of chloroplasts have helped to resolve the evolution of this organelle in photosynthetic eukaryotes. In this paper we propose an alternative method of phylogenetic analysis using compositional statistics for all protein sequences from complete genomes. This new method is conceptually simpler than and computationally as fast as the one proposed by Qi et al. (2004b) and Chu et al. (2004). The same data sets used in Qi et al. (2004b) and Chu et al. (2004) are analyzed using the new method. Our distance-based phylogenic tree of the 109 prokaryotes and eukaryotes agrees with the biologists tree of life based on 16S rRNA comparison in a predominant majority of basic branching and most lower taxa. Our phylogenetic analysis also shows that the chloroplast genomes are separated to two major clades corresponding to chlorophytes s.l. and rhodophytes s.l. The interrelationships among the chloroplasts are largely in agreement with the current understanding on chloroplast evolution
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