Analysis of transition rates from variational flooding using analytical theory

Variational flooding is an enhanced sampling method for obtaining kinetic rates from molecular dynamics simulations. This method is inspired by the idea of conformational flooding that employs a boost potential acting along a chosen reaction coordinate to accelerate rare events. In this work, we show how the empirical distribution of crossing times from variational flooding simulations can be modeled with analytical Kramers' time-dependent rate (KTR) theory. An optimized bias potential that fills metastable free energy basins is constructed from the variationally enhanced sampling (VES) method. This VES-derived flooding potential is then augmented by a switching function that determines the fill level of the boost. Having a prescribed time-dependent fill rate of the flooding potential gives an analytical expression for the distribution of crossing times from KTR theory that is used to extract unbiased rates. In the case of a static boost potential, the distribution of barrier crossing times follows an expected exponential distribution, and unbiased rates are extracted from a series of boosted simulations at discrete fill levels. Introducing a time-dependent boost that increases the fill level gradually over the simulation time leads to a simplified procedure for fitting the biased distribution of crossing times to analytical theory. We demonstrate the approach for the paradigmatic cases of alanine dipeptide in vacuum, the asymmetric SN2 reaction, and the folding of chignolin in explicit solvent.