Rare Event Rates From Probability Distributions*

In a rare event scenario, a system undergoes transitions between metastable states separated by large barriers. Calculating transition rate under this circumstances is difficult. However, it has been shown that if a bias can be engineered such that the transition state region is left untouched, transition rates can be nonetheless computed[1-3]. Here, we present a new method to build a bias that achieves this property in a relatively simple and transparent way. In this method, called Gaussian Mixture Based Enhanced Sampling, the metastable states are discriminated by a set of descriptors[4]. The fluctuations of these descriptors in the different metastable states are fitted to Gaussian Mixtures. From the fit, a bias can be built such that it allows the system to migrate from one metastable state to another. Yet, by construction, the bias is null in the transition state region. We exemplify the effectiveness of the method by calculating rates for chemical reaction, ligand unbinding and protein unfolding.
1.Voter,A. F., J. Chem. Phys., 1997, 106, 4665-4677
2.Tiwary,P.; Parrinello,M., Phys. Rev. Lett. 2013, 111, 230602
3.McCarty,J. et. al., Phys. Rev. Lett. 2015, 115, 070601
4.Debnath, J.; Parrinello M., J. Phys. Chem. Lett. 2020,11(13), 5076-5080