DYNAMICAL MODEL FOR DNA-SEQUENCES

We address the problem of DNA sequences, developing a ''dynamical'' me thod based on the assumption that the statistical properties of DNA pa ths are determined by the joint action of two processes, one determini stic with long-range correlations and the other random and delta-funct ion correlated. The generator of the deterministic evolution is a nonl inear map belonging to a class of maps recently tailored to mimic the processes of weak chaos responsible for the birth of anomalous diffusi on. It is assumed that the deterministic process corresponds to unknow n biological rules that determine the DNA path, whereas the noise mimi cs the influence of an infinite-dimensional environment on the biologi cal process under study. We prove that the resulting diffusion process , if the effect of the random process is neglected, is an cu-stable Le vy process with 1 < alpha < 2. We also show that, if the diffusion pro cess is determined by the joint action of the deterministic and the ra ndom process, the correlation effects of the ''deterministic dynamics' ' are canceled on the short-range scale, but show up in the long-range one. We denote our prescription to generate statistical sequences as the copying mistake map (CMM). We carry out our analysis of several DN A sequences and their CMM realizations with a variety of techniques an d we especially focus on a method of regression to equilibrium, which we call the Onsager analysis. With these techniques we establish the s tatistical equivalence of the real DNA sequences with their CMM realiz ations. We show that long-range correlations are present in exons as w ell as in introns, but are difficult to detect, since the exon ''dynam ics'' is shown to be determined by the entanglement of three distinct and independent CMM's.