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 i n the biopolymer, we assigned a site-fitness to each residue at each site. The assigned values of the site-fitnesses were obtained by the least-square s method to minimize discrepancies between experimental fitnesses and theor etical ones. As test cases, we analyzed a section of a local landscape for the thermostability of prolyl endopeptidase and that for the enzymatic acti vity of thermolysin. These sections were proved to be of the rough Mt. Fuji -type with theta values of larger than 1.0, where theta is defined as the r atio of the "mean slope" to the "degree of roughness" on the fitness surfac e. Furthermore, we theoretically explained discrepancies between the fitnes s 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 p roperty (such as the theta value) and the location of the wild type on the landscape and the mean change in fitness by the component mutations. Our re sults suggest that this model may provide a good approximation of real sect ions of local landscapes for current biopolymers phenomenologically. (C) 20 00 John Wiley & Sons, Inc. Biopoly 54: 64-70, 2000.