Universal global imprints of genome growth and evolution--equivalent length and cumulative mutation density

Segmental duplication is widely held to be an important mode of genome growth and evolution. Yet how this would affect the global structure of genomes has been little discussed.

Here, we show that equivalent length, or L(e), a quantity determined by the variance of fluctuating part of the distribution of the k-mer frequencies in a genome, characterizes the latter's global structure. We computed the L(e)s of 865 complete chromosomes and found that they have nearly universal but (k-dependent) values. The differences among the L(e) of a chromosome and those of its coding and non-coding parts were found to be slight.

We verified that these non-trivial results are natural consequences of a genome growth model characterized by random segmental duplication and random point mutation, but not of any model whose dominant growth mechanism is not segmental duplication. Our study also indicates that genomes have a nearly universal cumulative "point" mutation density of about 0.73 mutations per site that is compatible with the relatively low mutation rates of (1-5) x 10(-3)/site/Mya previously determined by sequence comparison for the human and E. coli genomes.