Information-theoretic bounds of evolutionary processes modeled as a protein communication system

In this paper, we investigate the information theoretic bounds of the channel of evolution introduced in [1]. The channel of evolution is modeled as the iteration of protein communication channels over time, where the transmitted messages are protein sequences and the encoded message is the DNA. We compute the capacity and the rate-distortion functions of the protein communication system for the three domains of life: Achaea, Prokaryotes and Eukaryotes. We analyze the trade-off between the transmission rate and the distortion in noisy protein communication channels. As expected, comparison of the optimal transmission rate with the channel capacity indicates that the biological fidelity does not reach the Shannon optimal distortion. However, the relationship between the channel capacity and rate distortion achieved for different biological domains provides tremendous insight into the dynamics of the evolutionary processes. We rely on these results to provide a model of protein sequence evolution based on the two major evolutionary processes: mutations and unequal crossover.