The accurate prediction of the binding affinities of ligands to proteins is a major goal in drug discovery and personalized medicine. The time taken to make such predictions is of similar importance to their accuracy, precision, and reliability. In the past few years, an ensemble based molecular dynamics approach has been proposed that provides a route to reliable predictions of free energies based on the molecular mechanics Poisson-Boltzmann surface area method which meets the requirements of speed, accuracy, precision, and reliability. Here, we describe an equivalent methodology based on thermodynamic integration to substantially improve the speed, accuracy, precision, and reliability of calculated relative binding free energies. We report the performance of the method when applied to a diverse set of protein targets and ligands. The results are in very good agreement with experimental data (90% of calculations agree to within 1 kcal/mol), while the method is reproducible by construction. Statistical uncertainties of the order of 0.5 kcal/mol or less are achieved. We present a systematic account of how the uncertainty in the predictions may be estimated.

The purpose of statistical mechanics is to provide a route to the calculation of macroscopic properties of matter from their constituent microscopic components. It is well known that the macrostates emerge as ensemble averages of microstates. However, this is more often stated than implemented in computer simulation studies. Here we consider foundational aspects of statistical mechanics which are overlooked in most textbooks and research articles that purport to compute macroscopic behaviour from microscopic descriptions based on classical mechanics and show how due attention to these issues leads in directions which have not been widely appreciated in the field of molecular dynamics simulation.

The presentation of potentially pathogenic peptides by major histocompatibility complex (MHC) molecules is one of the most important processes in adaptive immune defense. Prediction of peptide-MHC (pMHC) binding affinities is therefore a principal objective of theoretical immunology. Machine learning techniques achieve good results if substantial experimental training data are available. Approaches based on structural information become necessary if sufficiently similar training data are unavailable for a specific MHC allele, although they have often been deemed to lack accuracy. In this study, we use a free energy method to rank the binding affinities of 12 diverse peptides bound by a class I MHC molecule HLA-A*02:01. The method is based on enhanced sampling of molecular dynamics calculations in combination with a continuum solvent approximation and includes estimates of the configurational entropy based on either a one or a three trajectory protocol. It produces precise and reproducible free energy estimates which correlate well with experimental measurements. If the results are combined with an amino acid hydrophobicity scale, then an extremely good ranking of peptide binding affinities emerges. Our approach is rapid, robust, and applicable to a wide range of ligand-receptor interactions without further adjustment.

Binding free energies of bromodomain inhibitors are calculated with recently formulated approaches, namely ESMACS (enhanced sampling of molecular dynamics with approximation of continuum solvent) and TIES (thermodynamic integration with enhanced sampling). A set of compounds is provided by GlaxoSmithKline, which represents a range of chemical functionality and binding affinities. The predicted binding free energies exhibit a good Spearman correlation of 0.78 with the experimental data from the 3-trajectory ESMACS, and an excellent correlation of 0.92 from the TIES approach where applicable. Given access to suitable high end computing resources and a high degree of automation, we can compute individual binding affinities in a few hours with precisions no greater than 0.2 kcal/mol for TIES, and no larger than 0.34 and 1.71 kcal/mol for the 1- and 3-trajectory ESMACS approaches.