We study the mean first-passage time τ for the barrier crossing of a single massive particle with non-Markovian memory by Langevin simulations in one dimension. In the Markovian limit of short memory time τ, the expected Kramers turnover between the overdamped (high-friction) and the inertial (low-friction) limits is recovered. Compared to the Markovian case, we find barrier crossing to be accelerated for intermediate memory time, while for long memory time, barrier crossing is slowed down and τ increases with τ as a power law τ∼τ. Both effects are derived from an asymptotic propagator analysis: while barrier crossing acceleration at intermediate memory can be understood as an effective particle mass reduction, slowing down for long memory is caused by the slow kinetics of energy diffusion. A simple and globally accurate heuristic formula for τ in terms of all relevant time scales of the system is presented and used to establish a scaling diagram featuring the Markovian overdamped and the Markovian inertial regimes, as well as the non-Markovian intermediate memory time regime where barrier crossing is accelerated and the non-Markovian long memory time regime where barrier crossing is slowed down.

SignificanceThe interpretation of rates of reactions that take place in a solvent is complicated because of the entanglement of free-energy and history-dependent friction effects. In this context, the dihedral dynamics of butane has played a paradigmatic role since it is simple yet relevant for conformational transitions in polymers and proteins. We directly extract the friction that governs the dihedral dynamics in butane from simulations. We show that ∼89% of the total friction cannot be described as solvent friction and is caused by degrees of freedom that are orthogonal to the dihedral reaction coordinate. This shows that the hydrodynamic estimate of friction severely fails, even in the simplest molecular reaction.

We extract the folding free energy landscape and the time-dependent friction function, the two ingredients of the generalized Langevin equation (GLE), from explicit-water molecular dynamics (MD) simulations of the α-helix forming polypeptide alanine9 for a one-dimensional reaction coordinate based on the sum of the native H-bond distances. Folding and unfolding times from numerical integration of the GLE agree accurately with MD results, which demonstrate the robustness of our GLE-based non-Markovian model. In contrast, Markovian models do not accurately describe the peptide kinetics and in particular, cannot reproduce the folding and unfolding kinetics simultaneously, even if a spatially dependent friction profile is used. Analysis of the GLE demonstrates that memory effects in the friction significantly speed up peptide folding and unfolding kinetics, as predicted by the Grote–Hynes theory, and are the cause of anomalous diffusion in configuration space. Our methods are applicable to any reaction coordinate and in principle, also to experimental trajectories from single-molecule experiments. Our results demonstrate that a consistent description of protein-folding dynamics must account for memory friction effects.

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The viscous properties of nanoscopically confined water are important when hydrated surfaces in close contact are sheared against each other. Numerous experiments have probed the friction between atomically flat hydrated surfaces in the subnanometer separation regime and suggested an increased water viscosity, but the value of the effective viscosity of ultraconfined water, the mechanism of hydration layer friction, and the crossover to the dry friction limit are unclear. We study the shear friction between polar surfaces by extensive nonequilibrium molecular dynamics simulations in the linear-response regime at low shearing velocity, which is the relevant regime for typical biological applications. With decreasing water film thickness we find three consecutive friction regimes: For thick films friction is governed by bulk water viscosity. At separations of about a nanometer the highly viscous interfacial water layers dominate and increase the surface friction, while at the transition to the dry friction limit interfacial slip sets in. Based on our simulation results, we construct a confinement-dependent friction model which accounts for the additive friction contributions from bulklike water, interfacial water layers, and interfacial slip and which is valid for arbitrary water film thickness.