Improved Ligand Binding Energies Derived from Molecular Dynamics: Replicate Sampling Enhances the Search of Conformational Space

Abstract

Does a single molecular trajectory provide an adequate sample conformational space? Our calculations indicate that for Molecular Mechanics--Poisson-Boltzmann Surface Area (MM-PBSA) measurement of protein ligand binding, a single molecular dynamics trajectory does not provide a representative sampling of phase space. For a single trajectory, the binding energy obtained by averaging over a number of molecular dynamics frames in an equilibrated system will converge after an adequate simulation time. A separate trajectory with nearly identical starting coordinates (1% randomly perturbed by 0.001 Å), however, can lead to a significantly different calculated binding energy. Thus, even though the calculated energy converges for a single molecular dynamics run, the variation across separate runs implies that a single run inadequately samples the system. The divergence in the trajectories is reflected in the individual energy components, such as the van der Waals and the electrostatics terms. These results indicate that the trajectories sample different conformations that are not in rapid exchange. Extending the length of the dynamics simulation does not resolve the energy differences observed between different trajectories. By averaging over multiple simulations, each with a nearly equivalent starting structure, we find the standard deviation in the calculated binding energy to be ∼1.3 kcal/mol. The work presented here indicates that combining MM-PBSA with multiple samples of the initial starting coordinates will produce more precise and accurate estimates of protein/ligand affinity.