Nonequilibrium friction and free energy estimates for kinetic coarse-graining—Driven particles in responsive media

Predicting the molecular friction and energy landscapes under nonequilibrium conditions is key to coarse-graining the dynamics of selective solute transport through complex, fluctuating, and responsive media, e.g., polymeric materials such as hydrogels, cellular membranes, or ion channels. The analysis of equilibrium ensembles already allows such a coarse-graining for very mild nonequilibrium conditions. However, in the presence of stronger external driving and/or inhomogeneous setups, the transport process is governed apart from a potential of mean force also by a nontrivial position- and velocity-dependent friction. It is therefore important to find suitable and efficient methods to estimate the mean force and the friction landscape, which can then be used in a low-dimensional, coarse-grained Langevin framework to predict the system's transport properties and timescales. In this work, we evaluate different coarse-graining approaches based on constant-velocity constraint simulations for generating such estimates using two model systems, which are a 1D responsive barrier as a minimalistic model and a single tracer driven through a 3D bead-spring polymer membrane as a more sophisticated problem. Finally, we demonstrate that the estimates from 3D constant-velocity simulations yield the correct velocity-dependent friction, which can be directly utilized for coarse-grained (1D) Langevin simulations with constant external driving forces.