Biological Evolution: Distribution and Convergence Analysis of Amino Acids

We propose a protein communication system where the transmitted messages are protein sequences and the encoded message is the DNA. A series connection of the protein communication channel is equivalent to a channel through time: the channel of evolution. We study the evolutionary dynamics of this channel in both cases of constant and time-varying point mutation rate. We establish, using matrix analysis, that stochastic messages sent through the channel of evolution are received according to a fixed probability distribution, which is independent of the original message