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.