Computing Protein-Ligand Binding Association Rate Constants by Combining Brownian Dynamics and Molecular Dynamics Simulations

Abstract

Understanding the detailed molecular kinetics of protein-ligand association is of fundamental importance in biomedical research - increasingly so, as the kinetic characteristics of drugs become more widely appreciated as key to their efficacy. Conventional unbiased all-atom molecular dynamics (MD) simulations can now accurately sample the millisecond timescale allowing detailed kinetic properties of binding, conformational changes and protein folding to be reconstructed from large ensembles of simulations. However, it still remains a major computational hurdle to calculate protein-ligand binding kinetics for even moderately sized drugs and/or large receptor targets, especially if the binding pathway is coupled to conformational changes in either, or if the kinetics are too slow. Binding timescales for clinically relevant ligands usually extend far beyond those that can be simulated by conventional MD methods. Implicit solvent, rigid-body Brownian dynamics (BD) methods are promising because calculations are computationally feasible. However, whilst such methods have been successful for computing diffusional association rate constants, a rigid-body approach cannot capture all the various ligand/protein conformations that are often involved along binding pathways. Here, we develop a multiscale method that integrates conventional MD with rigid-body BD and thereby allows target-ligand flexibility to be integrated into calculations of association rate constants (kon). Our approach involves pre-computing the conformational kinetics of the apo-protein ensemble using MD simulations and Markov state models and then integrating a set of kinetically distinct conformers within the framework of the BD calculations. Based on this approach, we compute kon values for a set of inhibitors with known experimental kinetics, that bind to the conformationally flexible protein HIV-1 protease. The method also allows us to compute and analyze ligand gating effects mediated by the major conformational changes in flexible proteins.