Evolvability and single-genotype fluctuation in phenotypic properties: a simple heteropolymer model.

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, R(N)(2), as an example conformational property, we study how the thermal fluctuation of a sequence's R(N)(2) may be predictive of the changes in the Boltzmann average R(N)(2) caused by single-point mutations on that sequence. We found that sequences with the same ground-state (R(N)(2))(0) exhibit a funnel-like organization under conditions favorable to chain collapse or folding: fluctuation (standard deviation sigma) of R(N)(2) tends to increase with mutational distance from a prototype sequence whose R(N)(2) deviates little from its (R(N)(2))(0). In general, large mutational decreases in R(N)(2) or in sigma are only possible for some, though not all, sequences with large sigma values. This finding suggests that single-genotype phenotypic fluctuation is a necessary, though not sufficient, indicator of evolvability toward genotypes with less phenotypic fluctuations.