PT  - JOURNAL ARTICLE
AU  - Michael Manhart
AU  - Alexandre V Morozov
TI  - Scaling properties of evolutionary paths in a biophysical model of protein adaptation
AID  - 10.1101/010082
DP  - 2015 Jan 01
TA  - bioRxiv
PG  - 010082
4099  - http://biorxiv.org/content/early/2015/03/13/010082.short
4100  - http://biorxiv.org/content/early/2015/03/13/010082.full
AB  - 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.