title: Scaling properties of evolutionary paths in a biophysical model of protein adaptation.
abstract: 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.
authors.affiliation: Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854, USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Manhart
authors.forename: Alexandre V
authors.initials: AV
authors.lastname: Morozov
mesh_terms: D000595:Amino Acid Sequence; D055592:Biophysical Phenomena; D019143:Evolution, Molecular; D008957:Models, Genetic; D011506:Proteins / Q000737:chemistry*
chemical_list: D011506:Proteins