Stochastic Analysis of Amino Acid Substitution in Protein Synthesis
D. Bosnacki, H.M.M. ten Eikelder, M.N. Steijaert & E.P. de Vink

We present a formal analysis of amino acid replacement during mRNA
translation. Building on an abstract stochastic model of arrival of tRNAs and
their processing at the ribosome, we compute probabilities of the insertion of
amino acids into the nascent polypeptide chain. To this end, we integrate the
probabilistic model checker Prism in the Matlab environment. We construct the
substitution matrix containing the probabilities of an amino acid replacing
another. The resulting matrix depends on various parameters, including
availability and concentration of tRNA species, as well as their assignment to
individual codons. We draw a parallel with the standard mutation matrices like
Dayhoff and PET91, and analyze the mutual replacement of biologically similar
amino acids.