A path-based approach to random walks on networks characterizes how proteins evolve new function

TL;DR

This paper introduces a path-based method for analyzing continuous-time random walks on weighted networks, applied to biophysical models of protein evolution, revealing distinct adaptation regimes based on energetics.

Contribution

It presents an efficient numerical algorithm for stochastic path analysis and applies it to model protein evolution, uncovering new insights into adaptation dynamics.

Findings

Proteins exhibit two distinct adaptation regimes.

The methodology reproduces key features of directed evolution.

Proteins' evolutionary behavior depends on binding and folding energetics.

Abstract

We develop a path-based approach to continuous-time random walks on networks with arbitrarily weighted edges. We describe an efficient numerical algorithm for calculating statistical properties of the stochastic path ensemble. After demonstrating our approach on two reaction rate problems, we present a biophysical model that describes how proteins evolve new functions while maintaining thermodynamic stability. We use our methodology to characterize dynamics of evolutionary adaptation, reproducing several key features observed in directed evolution experiments. We find that proteins generally fall into two qualitatively different regimes of adaptation depending on their binding and folding energetics.