35 research outputs found
A Computational Method for the Rate Estimation of Evolutionary Transpositions
Genome rearrangements are evolutionary events that shuffle genomic
architectures. Most frequent genome rearrangements are reversals,
translocations, fusions, and fissions. While there are some more complex genome
rearrangements such as transpositions, they are rarely observed and believed to
constitute only a small fraction of genome rearrangements happening in the
course of evolution. The analysis of transpositions is further obfuscated by
intractability of the underlying computational problems.
We propose a computational method for estimating the rate of transpositions
in evolutionary scenarios between genomes. We applied our method to a set of
mammalian genomes and estimated the transpositions rate in mammalian evolution
to be around 0.26.Comment: Proceedings of the 3rd International Work-Conference on
Bioinformatics and Biomedical Engineering (IWBBIO), 2015. (to appear
Ordering Metro Lines by Block Crossings
A problem that arises in drawings of transportation networks is to minimize
the number of crossings between different transportation lines. While this can
be done efficiently under specific constraints, not all solutions are visually
equivalent. We suggest merging crossings into block crossings, that is,
crossings of two neighboring groups of consecutive lines. Unfortunately,
minimizing the total number of block crossings is NP-hard even for very simple
graphs. We give approximation algorithms for special classes of graphs and an
asymptotically worst-case optimal algorithm for block crossings on general
graphs. That is, we bound the number of block crossings that our algorithm
needs and construct worst-case instances on which the number of block crossings
that is necessary in any solution is asymptotically the same as our bound
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
On Weighting Schemes for Gene Order Analysis
Gene order analysis aims at extracting phylogenetic information from the comparison of the order and orientation of the genes on the genomes of different species. This can be achieved by computing parsimonious rearrangement scenarios, i.e. to determine a sequence of rearrangements events that transforms one given gene order into another such that the sum of weights of the included rearrangement events is minimal. In this sequence only certain types of rearrangements, given by the rearrangement model, are admissible and weights are assigned with respect to the rearrangement type. The choice of a suitable rearrangement model and corresponding weights for the included rearrangement types is important for the meaningful reconstruction. So far the analysis of weighting schemes for gene order analysis has not been considered sufficiently. In this paper weighting schemes for gene order analysis are considered for two
rearrangement models: 1) inversions, transpositions, and inverse
transpositions; 2) inversions, block interchanges, and inverse transpositions. For both rearrangement models we determined properties of the weighting functions that exclude certain types of rearrangements from parsimonious rearrangement scenarios
A barrier for further approximating Sorting By Transpositions
The Transposition Distance Problem (TDP) is a classical problem in genome
rearrangements which seeks to determine the minimum number of transpositions
needed to transform a linear chromosome into another represented by the
permutations and , respectively. This paper focuses on the
equivalent problem of Sorting By Transpositions (SBT), where is the
identity permutation . Specifically, we investigate palisades, a family
of permutations that are "hard" to sort, as they require numerous
transpositions above the celebrated lower bound devised by Bafna and Pevzner.
By determining the transposition distance of palisades, we were able to provide
the exact transposition diameter for -permutations (TD3), a special subset
of the Symmetric Group , essential for the study of approximate solutions
for SBT using the simplification technique. The exact value for TD3 has
remained unknown since Elias and Hartman showed an upper bound for it. Another
consequence of determining the transposition distance of palisades is that,
using as lower bound the one by Bafna and Pevzner, it is impossible to
guarantee approximation ratios lower than when approximating SBT. This
finding has significant implications for the study of SBT, as this problem has
been subject of intense research efforts for the past 25 years
Permutation entropy of of weakly noise-affected
L.R. and A.P. contributed equally to this work. Funding: This research received no external funding.Peer reviewedPublisher PD