Simulation of protein evolution: evidence for a non-linear aminoacidic substitution rate

Protein evolution is characterized by several processes. In the theory of neutral evolution the rate of mutation is considered a linear process in which the amount of aminoacidic substitutions in proteins is constant in time. A simulation approach has been developed by using a model of amino-acidic substitution. The frequency of spontaneous mutations has been assumed to be equal to about 10(-9)/base/year. The aim of the present work is to show that starting from a constant mutation rate (nucleotide substitutions) the corresponding process of aminoacidic substitutions becomes non-linear if some criteria of mutation selection are introduced. The basic criteria used are the physical-chemical characteristics of aminoacids, the same criteria that have made it possible to classify aminoacids. Different classifications based on differences in such criteria give different results, indicating that the degenerate nature of the genetic code determines a non-linear behaviour of protein evolution. Simulations have been performed on short protein subsequences of five aminoacids. A further analysis has been made to verify, on the basis of the code structure and of accepted selection criteria, the mechanisms of aminoacidic substitutions and the existence of preferential paths. We have concluded that aminoacidic substitution is not a simple stochastic process, but that complex Markov's chains are involved. The consequences are important, although generally ignored.