Protein sites present different amino acids during their evolution, whose number reflects the selective constraints operating on them. This evolutionary variability is strongly influenced by the structural properties of the site in the native structure, and it is quantified either through sequence entropy or through substitution rates. However, while the sequence entropy only depends on the equilibrium frequencies of the amino acids, the substitution rate also depends on the exchangeability matrix that describes mutations in the mathematical model of the substitution process.
Here we apply a mathematical model of protein evolution with selection for protein stability, both against unfolding and against misfolding, and find that sites with the same sequence entropy present different substitution rates depending on whether the site is prevalently hydrophobic or hydrophylic. For equal sequence entropy, polar sites evolve faster than hydrophobic sites. This is a consequence of the differential exchangeability associated with hydrophobic or polar amino acids. Accordingly, the model predicts that more polar proteins present, on the average, a faster substitution rate. However, these results change if we compare proteins that evolve under different mutation biases, such as orthologous proteins in different bacterial genomes. In this case, the substitution rates are faster in genomes that evolve under mutational bias that favour hydrophobic amino acids by preferentially incorporating the nucleotide Thymine that is more frequent in hydrophobic codons. In our model, the mutation bias influences both the sequence entropies and the substitution rates of protein sites. The sequence entropy is maximal for the mutational biases that reproduce the observed amino acid distributions and strongly decreases when extreme mutational biases are approached. The hydrophobicity for which the entropy is maximal is close to the mean hydrophobicity of the twenty amino acids and independent of the mutation bias. In contrast, the substitution rate and the hydrophobicity for which the substitution rate is maximal tend to increase when the mutation bias favours hydrophobic amino acids. Thus, changes of the mutational bias lead to deep effects on the biophysical properties of the protein (hydrophobicity) and on its evolutionary properties (sequence entropy and substitution rate) at the same time. The program Prot_evol is freely available for download at the url https://ub.cbm.uam.es/prot_fold_evol/prot_fold_evol_soft_main.php#Prot_Evol.[p]
Mutational Bias Affects Protein Evolution in Flowering Plants
