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

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.

9 pages, 7 figures

References in corpus (3)

• First-passage times in complex scale-invariant media
• Predictability of evolutionary trajectories in fitness landscapes
• Random Walks on Complex Networks

Cited by in corpus (7)

• Protein folding and binding can emerge as evolutionary spandrels through structural coupling
• Biophysical Fitness Landscapes for Transcription Factor Binding Sites
• Path Factorization Approach to Stochastic Simulations
• Statistical Physics of Evolutionary Trajectories on Fitness Landscapes
• Path statistics, memory, and coarse-graining of continuous-time random walks on networks
• Scaling properties of evolutionary paths in a biophysical model of protein adaptation
• Spectral analysis and clustering of large stochastic networks. Application to the Lennard-Jones-75 cluster