Dynamical Degrees of Freedom of DNA Sequences by Local and Global Short-Range Prediction

The dynamical properties of DNA sequence samples have been analyzed on the basis of a procedure able to distinguish chaos from randomness. The procedure relies on the concept of short-term (range) predictability of low-dimensional chaotic motions and can distinguish merely linear stochastic processes, e.g. fractional Brownian motion, from truly nonlinear deterministic systems. The method consists in obtaining forecasts on the basis of past events in the sequence. Two forecasting strategies are used. The local strategy views the sequence as the outcome of a nonlinear process, whereas the global approach considers the series as the outcome of a linear stochastic process. For both approaches, the predictive skill is computed and their inter-comparison allows us to get insight into and an understanding of the structure of DNA sequences. Nucleotidic sequences belonging to different taxonomic and functional groups have been analyzed. Different behaviors have been detected according to the existence of finite correlation dimension for specific groups of sequences.