Parking functions, labeled trees and DCJ sorting scenarios

In genome rearrangement theory, one of the elusive questions raised in recent years is the enumeration of rearrangement scenarios between two genomes. This problem is related to the uniform generation of rearrangement scenarios, and the derivation of tests of statistical significance of the properties of these scenarios. Here we give an exact formula for the number of double-cut-and-join (DCJ) rearrangement scenarios of co-tailed genomes. We also construct effective bijections between the set of scenarios that sort a cycle and well studied combinatorial objects such as parking functions and labeled trees.Comment: 12 pages, 3 figure

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

Karyotypic Determinants of Chromosome Instability in Aneuploid Budding Yeast

Recent studies in cancer cells and budding yeast demonstrated that aneuploidy, the state of having abnormal chromosome numbers, correlates with elevated chromosome instability (CIN), i.e. the propensity of gaining and losing chromosomes at a high frequency. Here we have investigated ploidy- and chromosome-specific determinants underlying aneuploidy-induced CIN by observing karyotype dynamics in fully isogenic aneuploid yeast strains with ploidies between 1N and 2N obtained through a random meiotic process. The aneuploid strains exhibited various levels of whole-chromosome instability (i.e. chromosome gains and losses). CIN correlates with cellular ploidy in an unexpected way: cells with a chromosomal content close to the haploid state are significantly more stable than cells displaying an apparent ploidy between 1.5 and 2N. We propose that the capacity for accurate chromosome segregation by the mitotic system does not scale continuously with an increasing number of chromosomes, but may occur via discrete steps each time a full set of chromosomes is added to the genome. On top of such general ploidy-related effect, CIN is also associated with the presence of specific aneuploid chromosomes as well as dosage imbalance between specific chromosome pairs. Our findings potentially help reconcile the divide between gene-centric versus genome-centric theories in cancer evolution

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