A Mutation Model from First Principles of the Genetic Code

The paper presents a neutral Codons Probability Mutations (CPM) model of molecular evolution and genetic decay of an organism. The CPM model uses a Markov process with a 20-dimensional state space of probability distributions over amino acids. The transition matrix of the Markov process includes the mutation rate and those single point mutations compatible with the genetic code. This is an alternative to the standard Point Accepted Mutation (PAM) and BLOcks of amino acid SUbstitution Matrix (BLOSUM). Genetic decay is quantified as a similarity between the amino acid distribution of proteins from a (group of) species on one hand, and the equilibrium distribution of the Markov chain on the other. Amino acid data for the eukaryote, bacterium, and archaea families are used to illustrate how both the CPM and PAM models predict their genetic decay towards the equilibrium value of 1. A family of bacteria is studied in more detail. It is found that warm environment organisms on average have a higher degree of genetic decay compared to those species that live in cold environments. The paper addresses a new codon-based approach to quantify genetic decay due to single point mutations compatible with the genetic code. The present work may be seen as a first approach to use codon-based Markov models to study how genetic entropy increases with time in an effectively neutral biological regime. Various extensions of the model are also discussed.