(384b) Erroneous Reduction of Energy Barriers By One-Dimensional Potentials of Mean Force

A common approach to measurement of activation barriers for rare events is to enhance sampling of the system configurations in a neighborhood of the energy barrier. This can be accomplished by various methods ranging from umbrella sampling to forward flux simulations. Most of these methods yield the potential of mean force (PMF) acting on a key degree of freedom (reaction coordinate).

In this talk we discuss a possible pitfall associated with application of PMF parametrized by a single reaction coordinate to determine the height of the energy barrier. As a test case we consider transport of a hydrophobic nanoparticle into a lipid bilayer studied by coarse grained molecular dynamics (CGMD) simulations. The PMF acting on the nanoparticle and the nanoparticle diffusion coefficient are obtained from constrained MD simulations. Solution of the Langevin equation with thus obtained PMF and diffusivity predicts the mean transport time of 40 ns. This timescale is readily accessible by CGMD and therefore we can verify the prediction of the Langevin equation by a series of direct (unbiased and unconstrained) MD simulations. Surprisingly, the mean transport time observed in the direct simulations is 2 microseconds, i.e. almost two order of magnitude slower than that predicted by the one-dimensional Langevin model.

This discrepancy is caused by an inability of a one-dimensional PMF to capture the true energy barrier experienced by the nanoparticle. We show that the true energy barrier becomes hidden when one averages over all degrees of freedom transversal to the reaction coordinate. This apparent reduction of the energy barrier is caused by bistability of the system in a small neigborhood of the barrier. In order to determine the true barrier, it is necessary to account for an additional degree of freedom (in this case, the membrane deformation) and consider a multi-dimensional free energy landscape.

In conclusion of the talk, we present evidence that this situation is relatively common and discuss possible approaches to detection of such hidden energy barriers and modifications to the constrained MD simulations to determine the true barrier height.