TY - JOUR T1 - Scaling properties of evolutionary paths in a biophysical model of protein adaptation JF - bioRxiv DO - 10.1101/010082 SP - 010082 AU - Michael Manhart AU - Alexandre V Morozov Y1 - 2014/01/01 UR - http://biorxiv.org/content/early/2014/10/06/010082.abstract N2 - 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 number of alleles. 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 designed to describe how proteins evolve new binding interactions while maintaining their folding stability. We combine numerical calculations for coarse-grained protein sequences with the scaling relations to obtain quantitative properties of the model for realistic binding interfaces and a full amino acid alphabet. ER -