We address the problem of DNA sequences, developing a "dynamical" method based on the assumption that the statistical properties of DNA paths are determined by the joint action of two processes, one deterministic with long-range correlations and the other random and b-function correlated. The generator of the deterministic evolution is a nonlinear map belonging to a class of maps recently tailored to mimic the processes of weak chaos responsible for the birth of anomalous diffusion. It is assumed that the deterministic process corresponds to unknown biological rules that determine the DNA path, whereas the noise mimics the inQuence of an infinite-dimensional environment on the biological process under study. We prove that the resulting diffusion process, if the effect of the random process is neglected, is an o.-stable Levy process with 1 ( o. ( 2. We also show that, if the diffusion process is determined by the joint action of the deterministic and the random process, the correlation effects of the "deterministic dynamics" are canceled on the shortrange 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 DNA sequences and their CMM realizations with a variety of techniques and we especially focus on a method of regression to equilibrium, which we call the Onsager analysis. With these techniques we establish the statistical equivalence of the real DNA sequences with their CMM realizations. We show that long-range correlations are present in exons as well as in introns, but are diKcult to detect, since the exon "dynamics" is shown to be determined by the entanglement of three distinct and independent CMM's.

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The random sequence of openings and closings of single ion channels and the channel conductances have been the object of intense study over the past two decades with a view toward illuminating the underlying kinetics of the channel protein molecules. Channels that are sensitive to voltage, such as many K(+)-selective channels, have been particularly useful, because the kinetic rates can be manipulated by changing the membrane voltage. Most such studies have been performed under stationary conditions and usually at a single temperature. Here we report the results of experiments with sinusoidal modulation of the membrane potential performed at several temperatures. Dwell time and cycle histograms, objects not normally associated with ion channel experiments, are herein reported. From the last, the transition probability densities for channel opening and closing events are obtained. A new and unusual phase anticipation is observed in the cycle histograms, and its temperature dependence is measured.