Modeling gene's length distribution in genomes

We show, that the specific distribution of gene's length, which is observed in natural genomes, might be a result of a growth process, in which a single length scale $L(t)$ develops that grows with time as $t^{1/3}$. This length scale could be associated with the length of the longest gene in an evolving genome. The growth kinetics of the genes resembles the one observed in physical systems with conserved ordered parameter. We show, that in genome this conservation is guaranteed by compositional compensation along DNA strands of the purine-like trends introduced by genes. The presented mathematical model is the modified Bak-Sneppen model of critical self-organization applied to the one-dimensional system of $N$ spins. The spins take discrete values, which represent gene's length.