On a chain of fragmentation equations for duplication-mutation dynamics in DNA sequences

Abstract: Recent studies have revealed that for the majority of species the length distributions of duplicated sequences in natural DNA follow a power-law tail. We study duplication-mutation models for processes in natural DNA sequences and the length distributions of exact matches computed from both synthetic and natural sequences. Here we present a hierarchy of equations for various number of exact matches for these models. The reduction of these equations to one equation for pairs of exact repeats is found. Quantitative correspondence of solutions of the equation to simulations is demonstrated.