Paths and cycles in breakpoint graph of random multichromosomal genomes

摘要

We study the probability distribution of the distance d = n + chi - kappa - psi between two genomes with n markers distributed on chi chromosomes and with breakpoint graphs containing kappa cycles and psi " good" paths, under the hypothesis of random gene order. We interpret the random order assumption in terms of a stochastic method for constructing the bicolored breakpoint graph. We show that the limiting expectation of E[d] = n - 1/2 chi - 1/2 log n+chi/2 chi. We also calculate the variance, the effect of different numbers of chromosomes in the two genomes, and the number of plasmids, or circular chromosomes, generated by the random breakpoint graph construction. A more realistic model allows intra- and interchromosomal operations to have different probabilities, and simulations show that for a fixed number of rearrangements, kappa and d depend on the relative proportions of the two kinds of operation.