THE DISTANCE BETWEEN RANDOMLY CONSTRUCTED GENOMES

摘要

In this paper, we study the exact probability distribution of the number of cycles c in the breakpoint graph of two random genomes with n genes or markers and X1 and X2 linear chromosomes, respectively. The genomic distance d between the two genomes is d = n - c. In the limit we find that the expectation of d is n (2x1x2)/(2x1+2x2-1)-1/2(n+min(x1,x2))/(ln(x1+x2)) The study of genome rearrangements has developed a sophisticated technology for inferring a minimizing sequence of operations necessary totransform one genome into another, where the genomes are represented by signed permutations on 1. ..., n and the operations are modeled on the biological processes of inversion, reciprocal translocation, chromosome fusion and fission, transposition of chromosomal segments, excision and reintegration of circular chromosomal segments, among others. Once these inferences are made, however, there is a need for some way to statistically validate both the inferences and the assumptions of the evolutionary model.