Information-Theoretic Model of Evolution over Protein Communication Channel
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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We develop a mathematical model of the genetic information storage and transmission system and investigate its properties. Breaking with tradition, whereas the genetic information storage and transmission apparatus is conventionally modelled as an engineering communication system with the DNA sequence as the input and the amino acid chain as the output, in this paper the genetic communication model is viewed as one between proteins. A connection in a series of protein communication systems is equivalent to a channel through time: the Channel of Evolution. We investigate the dynamics of the channel of evolution in both cases of a constant and time-variant point mutation rates. We prove that the distribution of amino acids converges geometrically to a specific distribution which matches nearly perfectly an estimate of the natural abundance of amino acids in Nature today. Moreover, based on the highly redundant structure of the encoded genetic message (i.e., DNA), we demonstrate that the role of introns in eukaryotic genomes is to maintain a fine balance between two competing yet complementary forces: stability and adaptability. The stability role is evaluated by showing that introns play the role of a decoy in absorbing mutations. We derive the optimal exon length distribution, which minimizes the probability of error in eukaryotic genomes. Furthermore, to understand how Nature can physically achieve such a distribution, we propose a diffusive random walk model for exon generation throughout evolution. This model results in an alpha stable distribution, which is asymptotically equivalent to the optimal distribution. Experimental results on various eukaryotic organisms spanning the phylogenetic tree from unicellular organisms to plants to vertebrates show that both distributions accurately fit the biological data.