Fast Equilibration of Water between Buried Sites and the Bulk by Molecular Dynamics with Parallel Monte Carlo Water Moves on Graphical Processing Units.

Molecular dynamics (MD) simulations of proteins are commonly used to sample from the Boltzmann distribution of conformational states, with wide-ranging applications spanning chemistry, biophysics, and drug discovery. However, MD can be inefficient at equilibrating water occupancy for buried cavities in proteins that are inaccessible to the surrounding solvent. Indeed, the time needed for water molecules to equilibrate between the bulk solvent and the binding site can be well beyond what is practical with standard MD, which typically ranges from hundreds of nanoseconds to a few microseconds. We recently introduced a hybrid Monte Carlo/MD (MC/MD) method, which speeds up the equilibration of water between buried cavities and the surrounding solvent, while sampling from the thermodynamically correct distribution of states. While the initial implementation of the MC functionality led to considerable slowing of the overall simulations, here we address this problem with a parallel MC algorithm implemented on graphical processing units. This results in speed-ups of 10-fold to 1000-fold over the original MC/MD algorithm, depending on the system and simulation parameters. The present method is available for use in the AMBER simulation software.

Enhancing water sampling of buried binding sites using nonequilibrium candidate Monte Carlo.

Water molecules can be found interacting with the surface and within cavities in proteins. However, water exchange between bulk and buried hydration sites can be slow compared to simulation timescales, thus leading to the inefficient sampling of the locations of water. This can pose problems for free energy calculations for computer-aided drug design. Here, we apply a hybrid method that combines nonequilibrium candidate Monte Carlo (NCMC) simulations and molecular dynamics (MD) to enhance sampling of water in specific areas of a system, such as the binding site of a protein. Our approach uses NCMC to gradually remove interactions between a selected water molecule and its environment, then translates the water to a new region, before turning the interactions back on. This approach of gradual removal of interactions, followed by a move and then reintroduction of interactions, allows the environment to relax in response to the proposed water translation, improving acceptance of moves and thereby accelerating water exchange and sampling. We validate this approach on several test systems including the ligand-bound MUP-1 and HSP90 proteins with buried crystallographic waters removed. We show that our BLUES (NCMC/MD) method enhances water sampling relative to normal MD when applied to these systems. Thus, this approach provides a strategy to improve water sampling in molecular simulations which may be useful in practical applications in drug discovery and biomolecular design.

Accounting for the Central Role of Interfacial Water in Protein-Ligand Binding Free Energy Calculations.

Rigorous binding free energy methods in drug discovery are growing in popularity because of a combination of methodological advances, improvements in computer hardware, and workflow automation. These calculations typically use molecular dynamics (MD) to sample from the Boltzmann distribution of conformational states. However, when part or all of the binding sites is inaccessible to the bulk solvent, the time needed for water molecules to equilibrate between bulk solvent and the binding site can be well beyond what is practical with standard MD. This sampling limitation is problematic in relative binding free energy calculations, which compute the reversible work of converting ligand 1 to ligand 2 within the binding site. Thus, if ligand 1 is smaller and/or more polar than ligand 2, the perturbation may allow additional water molecules to occupy a region of the binding site. However, this change in hydration may not be captured by standard MD simulations and may therefore lead to errors in the computed free energy. We recently developed a hybrid Monte Carlo/MD (MC/MD) method, which speeds up the equilibration of water between bulk solvent and buried cavities, while sampling from the intended distribution of states. Here, we report on the use of this approach in the context of alchemical binding free energy calculations. We find that using MC/MD markedly improves the accuracy of the calculations and also reduces hysteresis between the forward and reverse perturbations, relative to matched calculations using only MD with or without the crystallographic water molecules. The present method is available for use in AMBER simulation software.

Simulating Water Exchange to Buried Binding Sites.

Traditional molecular dynamics (MD) simulations of proteins, which relies on integration of Newton's equations of motion, cannot efficiently equilibrate water occupancy for buried cavities in proteins. This leads to slow convergence of thermodynamic averages for such systems. We have addressed this challenge by efficiently integrating standard Metropolis Monte Carlo (MC) translational water moves with MD in the AMBER simulation package. The translational moves allow water to easily enter or exit buried sites in a thermodynamically correct way during a simulation. To maximize efficiency, the algorithm avoids moves that only interchange waters within the bulk around the protein instead focusing on moves that can transfer water between bulk and the protein interior. In addition, a steric grid allows avoidance of moves that would lead to obvious steric clashes, and a fast grid-based energy evaluation is used to reduce the number of expensive full energy calculations. The potential energy distribution produced using MC/MD was found to be statistically indistinguishable from that of control simulations using only MD, and the algorithm effectively equilibrated water across steric barriers and into binding pockets that are not accessible with pure MD. The MC/MD method introduced here should be of increasing utility for applications spanning protein folding, the elucidation of protein mechanisms, and free energy calculations for computer-aided drug design. It is available in version 18 release of the widely disseminated AMBER simulation package.

Rigidity Theory-Based Approximation of Vibrational Entropy Changes upon Binding to Biomolecules.

We introduce a computationally efficient approximation of vibrational entropy changes (ΔSvib) upon binding to biomolecules based on rigidity theory. From constraint network representations of the binding partners, ΔSvib is estimated from changes in the number of low frequency ("spongy") modes with respect to changes in the networks' coordination number. Compared to ΔSvib computed by normal-mode analysis (NMA), our approach yields significant and good to fair correlations for data sets of protein-protein and protein-ligand complexes. Our approach could be a valuable alternative to NMA-based ΔSvib computation in end-point (free) energy methods.

Efficient Approximation of Ligand Rotational and Translational Entropy Changes upon Binding for Use in MM-PBSA Calculations.

A major uncertainty in binding free energy estimates for protein-ligand complexes by methods such as MM-PB(GB)SA or docking scores results from neglecting or approximating changes in the configurational entropies (ΔSconfig.) of the solutes. In MM/PB(GB)SA-type calculations, ΔSconfig. has usually been estimated in the rigid rotor, harmonic oscillator approximation. Here, we present the development of a computationally efficient method (termed BEERT) to approximate ΔSconfig. in terms of the reduction in translational and rotational freedom of the ligand upon protein-ligand binding (ΔSR/T), starting from the flexible molecule approach. We test the method successfully in binding affinity computations in connection with MM-PBSA effective energies describing changes in gas-phase interactions and solvation free energies. Compared to related work by Ruvinsky and co-workers, clustering bound ligand poses based on interactions with the protein rather than structural similarity of the poses, and an appropriate averaging over single entropies associated with an individual well of the energy landscape of the protein-ligand complex, were found to be crucial. Employing three data sets of protein-ligand complexes of pharmacologically relevant targets for validation, with up to 20, in part related ligands per data set, spanning binding free energies over a range of ≤7 kcal mol-1, reliable and predictive linear models to estimate binding affinities are obtained in all three cases (R2 = 0.54-0.72, p < 0.001, root mean squared error S = 0.78-1.44 kcal mol-1; q2 = 0.34-0.67, p < 0.05, root mean squared error sPRESS = 1.07-1.36 kcal mol-1). These models are markedly improved compared to considering MM-PBSA effective energies alone, scoring functions, and combinations with ΔSconfig. estimates based on the number of rotatable bonds, rigid rotor, harmonic oscillator approximation, or interaction entropy method. As a limitation, our method currently requires a target-specific training data set to identify appropriate scaling coefficients for the MM-PBSA effective energies and BEERT ΔSR/T. Still, our results suggest that the approach is a valuable, computationally more efficient complement to existing rigorous methods for estimating changes in binding free energy across structurally (weakly) related series of ligands binding to one target.