Discriminant Analysis Optimizes Progress Coordinate in Weighted Ensemble Simulations of Rare Event Kinetics

Calculating the kinetics of rare-but-important conformational transitions in complex biomolecules is a significant challenge in computational biophysics. Because of the long timescales needed to observe such processes, regular molecular dynamics simulations are too slow to sample these events by direct integration of the equations of motion. Recently, the weighted ensemble method has gained significant popularity for its ability to compute the rates of conformational transitions in biomolecular systems using unbiased simulations. However, the progress coordinate(s) of the weighted ensemble simulation should be carefully designed to capture the slow degrees of freedom of the system. Here, we demonstrate the application of a machine learning approach, harmonic linear discriminant analysis, which builds a predictive model for class membership, to design progress coordinates for weighted ensemble simulations. We test the accuracy and efficiency of this technique for computing the kinetics of the conformational transition of alanine dipeptide and the unfolding of a small protein. The key advantage of our data-driven approach is its minimal system knowledge requirement, which potentially extends its applicability to more complex and physiologically relevant systems.