Fitness Landscape of a Biopolymer Participating in a Multi-step Reaction

A biopolymer such as an enzyme participates in a multi-step reaction. When we take such a biopolymer as a target of evolutionary molecular engineering, the problem of frustration or interference among partial-fitness landscapes for elementary reaction steps arises. We examined the effect of the frustration on a fitness landscape for the whole reaction. From the results of a previous paper we assumed that each partial-fitness landscape is of the Mt. Fuji-type, based on the mutational additivity. Computer simulation for two-step or three-step reactions showed that the fitness landscape for a whole reaction was of the rough Mt. Fuji-type, in which optima were located near the top. However, there were fitter double-point mutants around each local optimum. This conclusion was supported by the result of the mathematical analysis of a simplified landscape for anL-step reaction: even if there are local optima on the fitness landscape, several fitter sequences exist at the Hamming distance ofLfrom every local optimum in almost all cases. Fitness distributions around the global optimum also showed that the fitness landscape can be approximated to a Mt. Fuji-type landscape.