Neural Network and Nearest Neighbor Algorithms for Enhancing Sampling of Molecular Dynamics.

The free energy calculations of complex chemical and biological systems with molecular dynamics (MD) are inefficient due to multiple local minima separated by high-energy barriers. The minima can be escaped using an enhanced sampling method such as metadynamics, which apply bias (i.e., importance sampling) along a set of collective variables (CV), but the maximum number of CVs (or dimensions) is severely limited. We propose a high-dimensional bias potential method (NN2B) based on two machine learning algorithms: the nearest neighbor density estimator (NNDE) and the artificial neural network (ANN) for the bias potential approximation. The bias potential is constructed iteratively from short biased MD simulations accounting for correlation among CVs. Our method is capable of achieving ergodic sampling and calculating free energy of polypeptides with up to 8-dimensional bias potential.