Chen T, Vernazobres D, Yomo T, Bornberg-Bauer E and Chan HS
Evolvability and Single-Genotype Fluctuation in Phenotypic Properties: A Simple Heteropolymer Model
Biophysical Journal,98:2487-2496, 2010
Experiment showed that the response of a genotype to mutation, i.e., the magnitude of mutational change in a phenotypic property, can be correlated with the extent of phenotypic fluctuation among genetic clones. To address a possible statistical mechanical basis for such phenomena at the protein level, we consider a simple hydrophobic-polar lattice protein-chain model with an exhaustive mapping between sequence (genotype) and conformational (phenotype) spaces. Using squared end-to-end distance, RN2, as an example conformational property, we study how the thermal fluctuation of a sequence's RN2 may be predictive of the changes in the Boltzmann average 〈RN2〉 caused by single-point mutations on that sequence. We found that sequences with the same ground-state (RN2)0 exhibit a funnel-like organization under conditions favorable to chain collapse or folding: fluctuation (standard deviation σ) of RN2 tends to increase with mutational distance from a prototype sequence whose 〈RN2〉 deviates little from its (RN2)0. In general, large mutational decreases in 〈RN2〉 or in σ are only possible for some, though not all, sequences with large σ values. This finding suggests that single-genotype phenotypic fluctuation is a necessary, though not sufficient, indicator of evolvability toward genotypes with less phenotypic fluctuations.