Expectation maximized molecular dynamics: Toward efficient learning of rarely sampled features in free energy surfaces from unbiased simulations.

Biophysical processes often encounter high energy transition states that lie in regions of the free energy landscape (FEL) inaccesible to conventional molecular dynamics simulations. Various enhanced sampling methods have been developed to handle the inherent quasi-nonergodicity, either by adding a biasing potential to the underlying Hamiltonian or by forcing the transitions with parallel tempering. However, when attempting to probe systems of increasing complexity with limited computational resources, there arises an imminent need for fast and efficient FEL exploration with sufficient accuracy. Herein, we present a computationally efficient algorithm based on statistical inference for fast estimation of key features in the two-dimensional FEL. Unlike conventional enhanced sampling methods, this newly developed method avoids direct sampling of high free energy states. Rather, the transition states connecting metastable regions of comparable free energies are estimated using Bayesian likelihood maximization. Furthermore, the method incorporates a tunable self-feedback mechanism with classical molecular dynamics for preventing unnecessary sampling that no more effectively contributes to the underlying distributions of metastable states. We have applied this novel protocol in three independent case studies and compared the results against a conventional method. We conclude with the scope of further developments for improved accuracy of the new method and its generalization toward estimation of features in more complex FELs.