%0 Journal Article
%T Scaling properties of evolutionary paths in a biophysical model of protein adaptation
%A Michael Manhart
%A Alexandre V. Morozov
%J Quantitative Biology
%D 2014
%I arXiv
%R 10.1088/1478-3975/12/4/045001
%X The enormous size and complexity of genotypic sequence space frequently requires consideration of coarse-grained sequences in empirical models. We develop scaling relations to quantify the effect of this coarse-graining on properties of fitness landscapes and evolutionary paths. We first consider evolution on a simple Mount Fuji fitness landscape, focusing on how the length and predictability of evolutionary paths scale with the coarse-grained sequence length and alphabet. We obtain simple scaling relations for both the weak- and strong-selection limits, with a non-trivial crossover regime at intermediate selection strengths. We apply these results to evolution on a biophysical fitness landscape that describes how proteins evolve new binding interactions while maintaining their folding stability. We combine the scaling relations with numerical calculations for coarse-grained protein sequences to obtain quantitative properties of the model for realistic binding interfaces and a full amino acid alphabet.
%U http://arxiv.org/abs/1410.1493v2