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Genome Rearrangement - Introduction

9 Nov 2011, Wed, 16:00
Max Alekseyev


Basically I will cover two papers:
Max A. Alekseyev and Pavel A. Pevzner "Multi-Break Rearrangements and
Chromosomal Evolution". Theoretical Computer Science 395(2-3) (2008),
pp. 193-202. doi:10.1016/j.tcs.2008.01.013
Most genome rearrangements (e.g., reversals and translocations) can be
represented as 2-breaks that break a genome at 2 points
and glue the resulting fragments in a new order. Multi-break
rearrangements break a genome into multiple fragments and further
glue them together in a new order. While multi-break rearrangements
were studied in depth for k = 2 breaks, the k-break distance
problem for arbitrary k remains unsolved. We prove a duality theorem
for multi-break distance problem and give a polynomial
algorithm for computing this distance.
Shuai Jiang and Max A. Alekseyev "Weighted genomic distance can hardly
impose a bound on the proportion of transpositions". Lecture Notes in
Computer Science 6577 (2011), pp. 124-133.
Genomic distance between two genomes, i.e., the smallest number of
genome rearrangements required to transform one genome into the other,
is often used as a measure of evolutionary closeness of the genomes in
comparative genomics studies. However, in models that include
rearrangements of significantly different "power" such as reversals
(that are "weak" and most frequent rearrangements) and transpositions
(that are more "powerful" but rare), the genomic distance typically
corresponds to a transformation with a large proportion of
transpositions, which is not biologically adequate.
Weighted genomic distance is a traditional approach to bounding the
proportion of transpositions by assigning them a relative weight
{\alpha} > 1. A number of previous studies addressed the problem of
computing weighted genomic distance with {\alpha} \leq 2.
Employing the model of multi-break rearrangements on circular genomes,
that captures both reversals (modelled as 2-breaks) and transpositions
(modelled as 3-breaks), we prove that for {\alpha} \in (1,2], a
minimum-weight transformation may entirely consist of transpositions,
implying that the corresponding weighted genomic distance does not
actually achieve its purpose of bounding the proportion of
transpositions. We further prove that for {\alpha} \in (1,2), the
minimum-weight transformations do not depend on a particular choice of
{\alpha} from this interval. We give a complete characterization of
such transformations and show that they coincide with the
transformations that at the same time have the shortest length and
make the smallest number of breakages in the genomes.
Our results also provide a theoretical foundation for the empirical
observation that for {\alpha} < 2, transpositions are favored over
reversals in the minimum-weight transformations.