FITNESS SPECTRUM AMONG RANDOM MUTANTS ON MT FUJI-TYPE FITNESS LANDSCAPE

Statistical properties of a Mt. Fuji-type fitness landscape on a multi -valued sequence space were analysed. We constructed the model landsca pe based on additivity of the free energy contributed by each residue on a biopolymer, introducing ''tolerance functions'' that describe tol erance to residue substitution at each site. The fitness spectrum amon g a random mutant population around a wild-type sequence was theoretic ally obtained as the probability density distribution function of fitn ess. As the Hamming distance from the wild-type to the mutants increas es, the mean fitness of the mutant population gradually decreases, and the variance of the fitness increases. These features are originated from the anisotropy of the landscape. On the assumption that the free energy is statistically additive around a wild-type in a sequence spac e of a real biopolymer, one can estimate the Hamming distance from the wild-type to the optimal biopolymer and the fitness of the optimum. T wo sets of experimental data were analysed: (1) a promoter strength sp ectrum of a mutant population produced by the random mutagenesis of a wild-type lac promoter; (2) four stepwise optimization processes of di fferent peptide mixtures evaluated with ligand binding affinity. Analy sis of both experiments showed the compatibility with the hypothesis t hat local fitness landscapes around contemporary biopolymers are near Mt. Fuji-type. The mean slope of each of the four affinity landscapes for (2) was estimated as Delta In (K) over bar(d)/Delta d = 1.3 simila r to 2.3, where d denotes the Hamming distance from the optimum and (K ) over bar(d) represents the mean dissociation constant of sequences l ocated at the Hamming distance of d.Mt. Fuji-type landscape can be reg arded as a zero-th order approximation to the real local landscape jus t like an ''ideal gas''. We showed a method to gauge statistically the shape of a near Mt. Fuji-type landscape by measuring mutant fitness s pectra. (C) 1996 Academic Press Limited