Evolutionary constraints on coding sequences at the nucleotidic level: A statistical physics approach

Selection at the molecular level is generally measured by amino-acid alterations, for instance, through the ratio of non-synonymous and synonymous substitutions. While it is known that codons coding for identical amino acids are not perfectly identical in terms of fitness cost, e.g. Due to differences in the kinetics of the associated t-RNAs, mechanisms exist for selection acting at the nucleotide level rather than the amino-acid level. In this work, we consider two such mechanisms. The first is the action of the innate immune system, with pattern recognition receptors capable of recognizing small nucleotidic motifs, such as CpG dinucleotides. Pathogens such as viruses are under this selective pressure while strongly constrained by the fact that their short genomes must code for essential proteins. A second tentative mechanism, referred to as the Ambush Hypothesis, suggests that codons are optimized to favor the presence of off-frame stop codons, which are useful to abort translation of non-functional proteins in case of accidental ribosomal frame-shift. We show how the same statistical physics inspired formalism can be applied to both questions to compute selective pressure or make predictions in a null model, called random codon model, in which the coding nature of the genomic sequence and its essential statistical features are retained. Our formalism is based on the notion of transfer matrix, developed in statistical physics to deal with systems of particles with short-range interactions; here, particles are codons and interactions result from the presence of selection mechanism acting at the nucleotidic level, possibly on contiguous codons along the sequence. Our approach is computationally efficient as it requires a computation time growing only linearly with the length of the sequence under study.