Context dependent evolution and noninformative biological sequences

Abstract

Most of current stochastic models of noncoding DNA sequence evolution assume that neighbor¬ing nucleotides evolve independently [1,2]. However independent evolution implies that distribu¬tion of nucleotides in DNA sequences is independent of the rest of the sequence. Therefore the importance of neighbor dependencies in the substitution process has long been recognized, and several models of these dependencies have been proposed [1,2,4,5]. The properties they impose on the sequences (Markovity, reversibility, long range dependence [3], etc.) are rather contradic¬tory [6]. The validity of these properties in noncoding sequences of bacterial genomes is tested by making use of statistical methods. One can assume that mutations in noncoding regions of primitive organisms do not directly affect their vitality and hence nucleotides in these regions evolve entirely under the influence of random factors. Thus the noncoding regions can be treated as noninformative DNA sequences or genetic noise. Mathematically noninformative distribution of genetic sequences (noise) is denned as a stationary distribution of some evolutionary process of genetic sequences. In view of the statistical analysis of the bacterial genomes a simple context dependent Markov evolutionary process is proposed and properties of its stationary distribution are investigated. In particular, it is shown that in general case the genetic noise produced by this process is non-Markov random sequence. Some results of computer simulations are also presented.