Entropy and long-range correlations in DNA sequences

We analyze the structure of DNA molecules of different organisms by using the additive Markov chain approach. Transforming nucleotide sequences into binary strings, we perform statistical analysis of the corresponding “texts”. We develop the theory of N-step additive binary stationary ergodic Markov chains and analyze their differential entropy. Supposing that the correlations are weak we express the conditional probability function of the chain by means of the pair correlation function and represent the entropy as a functional of the pair correlator. Since the model uses two point correlators instead of probability of block occurring, it makes possible to calculate the entropy of subsequences at much longer distances than with the use of the standard methods. We utilize the obtained analytical result for numerical evaluation of the entropy of coarse-grained DNA texts. We believe that the entropy study can be used for biological classification of living species.