Analysis of a local fitness landscape with a model of the rough Mt. Fuji-type landscape: application to prolyl endopeptidase and thermolysin

A method of analysis of a local fitness landscape for a current biopolymer is presented. Based on the assumption of additivity of mutational effects in the biopolymer, we assigned a site-fitness to each residue at each site. The assigned values of site-fitnesses were obtained by the least-squares method to minimize discrepancies between experimental fitnesses and theoretical ones. As test cases, we analyzed a section of a local landscape for the thermostability of prolyl endopeptidase and that for the enzymatic activity of thermolysin. These sections were proved to be of the rough Mt. Fuji-type with straight theta values of larger than 1.0, where straight theta is defined as the ratio of the "mean slope" to the "degree of roughness" on the fitness surface. Furthermore, we theoretically explained discrepancies between the fitnesses of multiple mutants and those predicted based on strict additivity of the component mutations by using a model of the rough Mt. Fuji-type landscape. According to this model, the discrepancies depend on the local landscape property (such as the straight theta value) and the location of the wild type on the landscape and the mean change in fitness by the component mutations. Our results suggest that this model may provide a good approximation of real sections of local landscapes for current biopolymers phenomenologically.