Genome aliquoting with double cut and join

<p>Abstract</p> <p>Background</p> <p>The <it>genome aliquoting probem </it>is, given an observed genome <it>A </it>with <it>n </it>copies of each gene, presumed to descend from an <it>n</it>-way polyploidization event from an ordinary diploid genome <it>B</it>, followed by a history of chromosomal rearrangements, to reconstruct the identity of the original genome <it>B'</it>. The idea is to construct <it>B'</it>, containing exactly one copy of each gene, so as to minimize the number of rearrangements <it>d</it>(<it>A, B' </it>⊕ <it>B' </it>⊕ ... ⊕ <it>B'</it>) necessary to convert the observed genome <it>B' </it>⊕ <it>B' </it>⊕ ... ⊕ <it>B' </it>into <it>A</it>.</p> <p>Results</p> <p>In this paper we make the first attempt to define and solve the genome aliquoting problem. We present a heuristic algorithm for the problem as well the data from our experiments demonstrating its validity.</p> <p>Conclusion</p> <p>The heuristic performs well, consistently giving a non-trivial result. The question as to the existence or non-existence of an exact solution to this problem remains open.</p

Sorting by reversals, block interchanges, tandem duplications, and deletions

<p>Abstract</p> <p>Background</p> <p>Finding sequences of evolutionary operations that transform one genome into another is a classic problem in comparative genomics. While most of the genome rearrangement algorithms assume that there is exactly one copy of each gene in both genomes, this does not reflect the biological reality very well – most of the studied genomes contain duplicated gene content, which has to be removed before applying those algorithms. However, dealing with unequal gene content is a very challenging task, and only few algorithms allow operations like duplications and deletions. Almost all of these algorithms restrict these operations to have a fixed size.</p> <p>Results</p> <p>In this paper, we present a heuristic algorithm to sort an ancestral genome (with unique gene content) into a genome of a descendant (with arbitrary gene content) by reversals, block interchanges, tandem duplications, and deletions, where tandem duplications and deletions are of arbitrary size.</p> <p>Conclusion</p> <p>Experimental results show that our algorithm finds sorting sequences that are close to an optimal sorting sequence when the ancestor and the descendant are closely related. The quality of the results decreases when the genomes get more diverged or the genome size increases. Nevertheless, the calculated distances give a good approximation of the true evolutionary distances.</p

Multichromosomal median and halving problems under different genomic distances

<p>Abstract</p> <p>Background</p> <p>Genome median and genome halving are combinatorial optimization problems that aim at reconstructing ancestral genomes as well as the evolutionary events leading from the ancestor to extant species. Exploring complexity issues is a first step towards devising efficient algorithms. The complexity of the median problem for unichromosomal genomes (permutations) has been settled for both the breakpoint distance and the reversal distance. Although the multichromosomal case has often been assumed to be a simple generalization of the unichromosomal case, it is also a relaxation so that complexity in this context does not follow from existing results, and is open for all distances.</p> <p>Results</p> <p>We settle here the complexity of several genome median and halving problems, including a surprising polynomial result for the breakpoint median and guided halving problems in genomes with circular and linear chromosomes, showing that the multichromosomal problem is actually easier than the unichromosomal problem. Still other variants of these problems are NP-complete, including the DCJ double distance problem, previously mentioned as an open question. We list the remaining open problems.</p> <p>Conclusion</p> <p>This theoretical study clears up a wide swathe of the algorithmical study of genome rearrangements with multiple multichromosomal genomes.</p

Tandem halving problems by DCJ

This paper has been withdrawn by the author.Comment: This paper has been withdrawn by the autho

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The Problem of Chromosome Reincorporation in DCJ Sorting and Halving

Kovac J, Dias Vieira Braga M, Stoye J. The Problem of Chromosome Reincorporation in DCJ Sorting and Halving. In: Proc. of Recomb-CG 2010. LNBI. Vol 6398. 2010: 13-24

SCJ: A Variant of Breakpoint Distance for Which Sorting, Genome Median and Genome Halving Problems Are Easy

Feijão P, Meidanis J. SCJ: A Variant of Breakpoint Distance for Which Sorting, Genome Median and Genome Halving Problems Are Easy. In: Salzberg SL, Warnow T, eds. Algorithms in Bioinformatics. Lecture Notes in Computer Science. Vol 5724. Berlin, Heidelberg: Springer Berlin Heidelberg; 2009: 85-96