Kinetics and Free Energy of Protein-Ligand Interaction Using Weighted Ensemble Milestoning (WEM)

Protein-ligand interactions are pivotal to the functioning of biological processes. However, their timescales often reach beyond μs-ms, making them difficult to probe using computional methods like all-atom molecular dynamics (MD) simulation. Weighted ensemble (WE) and milestoning are two powerful path sampling techniques to study such rare events, although both require significant computational effort. We developed the weighted ensemble milestoning (WEM) scheme, which combines the strength of these two methods to calculate the kinetics and the free energy profile from short and low cost MD trajectories. We study the unbinding and binding of 4-hydroxy-2-butanone (BUT) ligand to FKBP protein using the WEM protocol. We also propose an analytical diffusion model to calculate the binding rate constant and free energy, utilizing the WEM trajectories within the milestoning framework. Ligand binding and unbinding kinetics, and the binding free energy, obtained from 30 μs conventional MD simulation, are accurately reproduced using less than 100 ns of WEM calculation. Thus, WEM provides an inexpensive computational approach, to predict multiple important properties of protein-ligand interactions, for potential application in in-silico drug design.