@article {Manhart010082, author = {Michael Manhart and Alexandre V Morozov}, title = {Scaling properties of evolutionary paths in a biophysical model of protein adaptation}, elocation-id = {010082}, year = {2014}, doi = {10.1101/010082}, publisher = {Cold Spring Harbor Laboratory}, 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 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.}, URL = {https://www.biorxiv.org/content/early/2014/10/06/010082}, eprint = {https://www.biorxiv.org/content/early/2014/10/06/010082.full.pdf}, journal = {bioRxiv} }