Accurately predicting protein-ligand binding affinities and binding modes is a major goal in computational chemistry, but even the prediction of ligand binding modes in proteins poses major challenges. Here, we focus on solving the binding mode prediction problem for rigid fragments. That is, we focus on computing the dominant placement, conformation, and orientations of a relatively rigid, fragment-like ligand in a receptor, and the populations of the multiple binding modes which may be relevant. This problem is important in its own right, but is even more timely given the recent success of alchemical free energy calculations. Alchemical calculations are increasingly used to predict binding free energies of ligands to receptors. However, the accuracy of these calculations is dependent on proper sampling of the relevant ligand binding modes. Unfortunately, ligand binding modes may often be uncertain, hard to predict, and/or slow to interconvert on simulation timescales, so proper sampling with current techniques can require prohibitively long simulations. We need new methods which dramatically improve sampling of ligand binding modes. Here, we develop and apply a nonequilibrium candidate Monte Carlo (NCMC) method to improve sampling of ligand binding modes. In this technique, the ligand is rotated and subsequently allowed to relax in its new position through alchemical perturbation before accepting or rejecting the rotation and relaxation as a nonequilibrium Monte Carlo move. When applied to a T4 lysozyme model binding system, this NCMC method shows over two orders of magnitude improvement in binding mode sampling efficiency compared to a brute force molecular dynamics simulation. This is a first step towards applying this methodology to pharmaceutically-relevant binding of fragments and, eventually, drug-like molecules. We are making this approach available via our new Binding Modes of Ligands using Enhanced Sampling (BLUES) package which is freely available on GitHub.

Biomolecular simulations are typically performed in an aqueous environment where the number of ions remains fixed for the duration of the simulation, generally with either a minimally neutralizing ion environment or a number of salt pairs intended to match the macroscopic salt concentration. In contrast, real biomolecules experience local ion environments where the salt concentration is dynamic and may differ from bulk. The degree of salt concentration variability and average deviation from the macroscopic concentration remains, as yet, unknown. Here, we describe the theory and implementation of a Monte Carlo osmostat that can be added to explicit solvent molecular dynamics or Monte Carlo simulations to sample from a semigrand canonical ensemble in which the number of salt pairs fluctuates dynamically during the simulation. The osmostat reproduces the correct equilibrium statistics for a simulation volume that can exchange ions with a large reservoir at a defined macroscopic salt concentration. To achieve useful Monte Carlo acceptance rates, the method makes use of nonequilibrium candidate Monte Carlo (NCMC) moves in which monovalent ions and water molecules are alchemically transmuted using short nonequilibrium trajectories, with a modified Metropolis-Hastings criterion ensuring correct equilibrium statistics for an ( Δμ, N, p, T) ensemble to achieve a ∼10× boost in acceptance rates. We demonstrate how typical protein (DHFR and the tyrosine kinase Src) and nucleic acid (Drew-Dickerson B-DNA dodecamer) systems exhibit salt concentration distributions that significantly differ from fixed-salt bulk simulations and display fluctuations that are on the same order of magnitude as the average.

Alchemical free energy methods with molecular mechanics (MM) force fields are now widely used in the prioritization of small molecules for synthesis in structure-enabled drug discovery projects because of their ability to deliver 1–2 kcal mol−1 accuracy in well-behaved protein-ligand systems. Surpassing this accuracy limit would significantly reduce the number of compounds that must be synthesized to achieve desired potencies and selectivities in drug design campaigns. However, MM force fields pose a challenge to achieving higher accuracy due to their inability to capture the intricate atomic interactions of the physical systems they model. A major limitation is the accuracy with which ligand intramolecular energetics—especially torsions—can be modeled, as poor modeling of torsional profiles and coupling with other valence degrees of freedom can have a significant impact on binding free energies. Here, we demonstrate how a new generation of hybrid machine learning / molecular mechanics (ML/MM) potentials can deliver significant accuracy improvements in modeling protein-ligand binding affinities. Using a nonequilibrium perturbation approach, we can correct a standard, GPU-accelerated MM alchemical free energy calculation in a simple post-processing step to efficiently recover ML/MM free energies and deliver a significant accuracy improvement with small additional computational effort. To demonstrate the utility of ML/MM free energy calculations, we apply this approach to a benchmark system for predicting kinase:inhibitor binding affinities—a congeneric ligand series for non-receptor tyrosine kinase TYK2 (Tyk2)—wherein state-of-the-art MM free energy calculations (with OPLS2.1) achieve inaccuracies of 0.93±0.12 kcal mol−1 in predicting absolute binding free energies. Applying an ML/MM hybrid potential based on the ANI2x ML model and AMBER14SB/TIP3P with the OpenFF 1.0.0 (“Parsley”) small molecule force field as an MM model, we show that it is possible to significantly reduce the error in absolute binding free energies from 0.97 [95% CI: 0.68, 1.21] kcal mol−1 (MM) to 0.47 [95% CI: 0.31, 0.63] kcal mol−1 (ML/MM).