Protein Cold Denaturation in Implicit Solvent Simulations: A Transfer Free Energy Approach

Proteins are stable over a narrow temperature range, with hot and cold denaturation occurring outside of this window, both of which adversely affect protein function. While hot unfolding is entropically driven, cold denaturation, on the other hand, results from a more favorable free energy associated with the interaction of water with apolar groups at low temperature. Because of the key role of water in this latter process, capturing cold denaturation using implicit solvent models is challenging. We propose here a novel computational approach to develop an implicit solvent model that accounts for both hot and cold denaturation in simulations involving atomistically detailed protein representations. By mining a large number of protein structures solved by nuclear magnetic resonance, we derive transfer free energy contributions for the backbone and amino acids side chains representing the transfer of these moieties between water at two different temperatures. Using Trp-cage as a model system, we show that the implicit solvent model constructed using these temperature-dependent free energies of transfer recovers the parabolic temperature dependence of protein stability, capturing both hot and cold denaturation. The resulting cold-unfolded conformations show reduced secondary structure content but preserve most of their internal hydrogen-bonding network, in contrast to the extended configurations with no hydrogen-bonding populated during heat-induced denaturation.