Scaling properties of evolutionary paths in a biophysical model of protein adaptation

TL;DR

This paper develops scaling relations to understand how coarse-graining affects evolutionary paths and fitness landscapes in protein evolution models, bridging simple theoretical landscapes and realistic biophysical scenarios.

Contribution

It introduces scaling relations that connect coarse-grained models to detailed biophysical protein evolution landscapes, enabling quantitative predictions.

Findings

Scaling relations for path length and predictability across selection regimes

Application to biophysical protein models with realistic sequence complexity

Quantitative predictions for protein evolution dynamics

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.