title: Path-based approach to random walks on networks characterizes how proteins evolve new functions.
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.
authors.affiliation: Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Manhart
authors.forename: Alexandre V
authors.initials: AV
authors.lastname: Morozov
mesh_terms: D000465:Algorithms; D008954:Models, Biological; D008956:Models, Chemical; D011506:Proteins / Q000737:chemistry* / Q000502:physiology*; D013269:Stochastic Processes; D013816:Thermodynamics
chemical_list: D011506:Proteins