Surveying a local fitness landscape of a protein with epistatic sites for the study of directed evolution.

We present a method for analysis of a fitness landscape of a biopolymer with significantly epistatic sites. The analysis is based on a quasi-additive fitness model. The fitness model is constructed with additive terms conducted by "site-fitness" and epistatic terms conducted by "pair-fitness," where the site-fitness is a fitness contribution from an independent residue and the pair-fitness is a fitness contribution from a pair of epistatic residues. As a case study, we analyzed the sequence-fitness data for 45 clones of thermostable prolyl endopeptidase mutants. They were generated by a mutation scrambling method, which can accumulate advantageous mutations. The fitness contributions from 14 single-point mutations including E67Q and Q656R were identified by the analysis. As a result, we found that the fitness model with a significant epistatic term by a pair of the 67th site and 656th site was in good agreement with the experimental data and that the explored landscape in the binary 14-dimensional sequence space is still a mountainous landscape with twin peaks. The validity was supported by the analysis of mutant fitness distributions derived from another mutation scrambling experiment and by (3D) structural data. Copyright 2002 Wiley Periodicals, Inc.