Shannon information and self-similarity in whole genomes

The Shannon information (SI) in distributions of occurrence frequency of short words in whole genomes is shown to exhibit universality. For given word length, the SI in genomes of all lengths is the same as that in random sequences of a universal lengths Lr. For the shorter words Lr is far shorter than the genome. For example, Lr∼1000 bases for three-letter words. We further show that whole genomes are highly self-similar in the sense that any segment of the genome down to a length of Λsim, about twice Lr, also shares the universal property. We devise a simple genome growth model in which genome-size sequences grown by maximally stochastic segmental duplication and random mutation possess the universal and self-similar properties of genomes.