Predictability of evolutionary trajectories in fitness landscapes

TL;DR

This study provides an exhaustive analysis of protein fitness landscapes using a model based on protein folding, revealing that these landscapes are smoother and more robust to mutation than random landscapes, influencing evolutionary trajectories.

Contribution

The paper introduces a comprehensive off-lattice model of protein folding to analyze fitness landscapes, highlighting their smoothness and robustness, and introduces mean path divergence as a new measure.

Findings

Fitness landscapes are smoother than random landscapes.

Global landscape roughness predicts path divergence.

Protein landscapes are robust to mutations and have fewer peaks.

Abstract

Experimental studies on enzyme evolution show that only a small fraction of all possible mutation trajectories are accessible to evolution. However, these experiments deal with individual enzymes and explore a tiny part of the fitness landscape. We report an exhaustive analysis of fitness landscapes constructed with an off-lattice model of protein folding where fitness is equated with robustness to misfolding. This model mimics the essential features of the interactions between amino acids, is consistent with the key paradigms of protein folding and reproduces the universal distribution of evolutionary rates among orthologous proteins. We introduce mean path divergence as a quantitative measure of the degree to which the starting and ending points determine the path of evolution in fitness landscapes. Global measures of landscape roughness are good predictors of path divergence in all studied landscapes: the mean path divergence is greater in smooth landscapes than in rough ones. The model-derived and experimental landscapes are significantly smoother than random landscapes and resemble additive landscapes perturbed with moderate amounts of noise; thus, these landscapes are substantially robust to mutation. The model landscapes show a deficit of suboptimal peaks even compared with noisy additive landscapes with similar overall roughness. We suggest that smoothness and the substantial deficit of peaks in the fitness landscapes of protein evolution are fundamental consequences of the physics of protein folding.