Funnel-like protein energy landscapes emerge from functional evolution under thermal fluctuations

Abstract

Foldable proteins exhibit funnel-like energy landscapes, but their evolution under selection for function remains unclear. We study this in a lattice protein model, defining fitness as the equilibrium probability of a fixed active-site motif and using multicanonical sequence sampling. At intermediate temperature, rare high-fitness sequences show funnel-like energy and double-well free-energy landscapes. At very low temperature, abundant high-fitness sequences retain glass-like landscapes. Thus, thermal fluctuations turn a local functional requirement into a global structural constraint.