2016/12/30 by Miyazawa, Sanzo
#Biomolecules (q-bio.BM) #FOS: Biological sciences #Populations and Evolution (q-bio.PE)
paper · doi:10.48550/arxiv.1612.09378
The probability distribution of sequences with maximum entropy that satisfies a given amino acid composition at each site and a given pairwise amino acid frequency at each site pair is a Boltzmann distribution with exp(-ψN), where the total interaction ψN is represented as the sum of one body and pairwise interactions. A protein folding theory based on the random energy model (REM) indicates that the equilibrium ensemble of natural protein sequences is a canonical ensemble characterized by exp(-ΔGND/kB Ts) or by exp(- GN/kB Ts) if an amino acid composition is kept constant, meaning ψN = ΔGND/kB Ts + constant, where ΔGND ≡ GN - GD, GN and GD are the native and denatured free energies, and Ts is the effective temperature of natural selection. Here, we examine interaction changes (ΔψN) due to single nucleotide nonsynonymous mutations, and have found that the variance of their ΔψN over all sites hardly depends on the ψN of each homologous sequence, indicating that the variance of ΔGN (= kB Ts ΔψN) is nearly constant irrespective of protein families. As a result, Ts is estimated from the ratio of the variance of ΔψN to that of a reference protein, which is determined by a direct comparison between ΔΔψND (≃ ΔψN) and experimental ΔΔGND. Based on the REM, glass transition temperature Tg and ΔGND are estimated from Ts and experimental melting temperatures (Tm) for 14 protein domains. The estimates of ΔGND agree well with their experimental values for 5 proteins, and those of Ts and Tg are all within a reasonable range. This method is coarse-grained but much simpler in estimating Ts, Tg and ΔΔGND than previous methods.