The elusive evidence for chromothripsis.

The chromothripsis hypothesis suggests an extraordinary one-step catastrophic genomic event allowing a chromosome to 'shatter into many pieces' and reassemble into a functioning chromosome. Recent efforts have aimed to detect chromothripsis by looking for a genomic signature, characterized by a large number of breakpoints (50-250), but a limited number of oscillating copy number states (2-3) confined to a few chromosomes. The chromothripsis phenomenon has become widely reported in different cancers, but using inconsistent and sometimes relaxed criteria for determining rearrangements occur simultaneously rather than progressively. We revisit the original simulation approach and show that the signature is not clearly exceptional, and can be explained using only progressive rearrangements. For example, 3.9% of progressively simulated chromosomes with 50-55 breakpoints were dominated by two or three copy number states. In addition, by adjusting the parameters of the simulation, the proposed footprint appears more frequently. Lastly, we provide an algorithm to find a sequence of progressive rearrangements that explains all observed breakpoints from a proposed chromothripsis chromosome. Thus, the proposed signature cannot be considered a sufficient proof for this extraordinary hypothesis. Great caution should be exercised when labeling complex rearrangements as chromothripsis from genome hybridization and sequencing experiments

Approximating the double-cut-and-join distance between unsigned genomes

In this paper we study the problem of sorting unsigned genomes by double-cut-and-join operations, where genomes allow a mix of linear and circular chromosomes to be present. First, we formulate an equivalent optimization problem, called maximum cycle/path decomposition, which is aimed at finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths in a breakpoint graph. Then, we show that the problem of finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths of length no more than l can be reduced to the well-known degree-bounded k-set packing problem with k = 2l. Finally, a polynomial-time approximation algorithm for the problem of sorting unsigned genomes by double-cut-and-join operations is devised, which achieves the approximation ratio for any positive ε. For the restricted variation where each genome contains only one linear chromosome, the approximation ratio can be further improved t

Can a permutation be sorted by best short swaps?

A short swap switches two elements with at most one element caught between them. Sorting permutation by short swaps asks to find a shortest short swap sequence to transform a permutation into another. A short swap can eliminate at most three inversions. It is still open for whether a permutation can be sorted by short swaps each of which can eliminate three inversions. In this paper, we present a polynomial time algorithm to solve the problem, which can decide whether a permutation can be sorted by short swaps each of which can eliminate 3 inversions in O(n) time, and if so, sort the permutation by such short swaps in O(n^2) time, where n is the number of elements in the permutation. A short swap can cause the total length of two element vectors to decrease by at most 4. We further propose an algorithm to recognize a permutation which can be sorted by short swaps each of which can cause the element vector length sum to decrease by 4 in O(n) time, and if so, sort the permutation by such short swaps in O(n^2) time. This improves upon the O(n^2) algorithm proposed by Heath and Vergara to decide whether a permutation is so called lucky

Elucidating Genome Structure Evolution by Analysis of Isoapostatic Gene Clusters using Statistics of Variance of Gene Distances

Identifying genomic regions that descended from a common ancestor is important for understanding the function and evolution of genomes. In related genomes, clusters of homologous gene pairs serve as evidence for candidate homologous regions, which make up genomic core. Previous studies on the structural organization of bacterial genomes revealed that basic backbone of genomic core is interrupted by genomic islands. Here, we applied statistics using variance of distances as a measure to classify conserved genes within a set of genomes according to their “isoapostatic” relationship, which keeps nearly identical distances of genes. The results of variance statistics analysis of cyanobacterial genomes including Prochlorococcus, Synechococcus, and Anabaena indicated that the conserved genes are classified into several groups called “virtual linkage groups (VLGs)” according to their positional conservation of orthologs over the genomes analyzed. The VLGs were used to define mosaic domain structure of the genomic core. The current model of mosaic genomic domains can explain global evolution of the genomic core of cyanobacteria. It also visualizes islands of lateral gene transfer. The stability and the robustness of the variance statistics are discussed. This method will also be useful in deciphering the structural organization of genomes in other groups of bacteria