Calculation of Protein-Protein Binding Free Energies using Umbrella Sampling with Dual Resolution Water Models

Abstract

The binding free energy between two proteins is a measure of how strongly they will interact under physiological conditions. All-atom statistical-mechanics-based free energy calculation methods have the potential to accurately calculate binding free energy but are completely unfeasible for large-scale applications due to their high computational cost. This motivates the development of efficient and accurate free energy calculation approaches. Dual-resolution molecular simulation approach allows one to simulate at the atomic level in the regions of interest and at a coarser level, but much faster, in less relevant parts of the biomolecular systems. This hybrid approach has shown a substantial reduction of computational cost without compromising accuracy in a classical molecular dynamics simulations. Here, we investigate whether combining the statistical-mechanics-based free energy calculation method, umbrella sampling, with dual resolution water models provides a good trade-off between speed and accuracy. We chose Barnase-Barstar protein-protein complex as a test system since it is relatively small to allow convergence of the simulations, has a known structure, and empirical relative binding free energy difference values (ΔΔG) of their observed mutations are reported in the literature. We selected eight different mutations occurring at the different sites with broadly varying empirical ΔΔG values. We then calculated ΔΔG values for each mutation using umbrella sampling simulations, where we treated protein-protein complex and one surrounding water layer at an atomic level and the bulk of the water using WT4 coarse-grained water model. We obtained a high correlation between experimental and calculated ΔΔG values. This dual resolution free energy calculation approach has the potential for future high-throughput studies of protein-protein binding.