Abstract
Computing the free energy of binding a ligand to a protein is a difficult task of essential importance for which purpose various theoretical/computational approaches have been pursued. In this paper, we develop a hybrid steered molecular dynamics (hSMD) method capable of resolving one ligand–protein complex within a few wall-clock days with high enough accuracy to compare with the experimental data. This hSMD approach is based on the relationship between the binding affinity and the potential of mean force (PMF) in the established literature. It involves simultaneously steering n (n = 1, 2, 3, ...) centers of mass of n selected segments of the ligand using n springs of infinite stiffness. Steering the ligand from a single initial state chosen from the bound state ensemble to the corresponding dissociated state, disallowing any fluctuations of the pulling centers along the way, one can determine a 3n-dimensional PMF curve connecting the two states by sampling a small number of forward and reverse pulling paths. This PMF constitutes a large but not the sole contribution to the binding free energy. Two other contributors are (1) the partial partition function containing the equilibrium fluctuations of the ligand at the binding site and the deviation of the initial state from the PMF minimum and (2) the partial partition function containing rotation and fluctuations of the ligand around one of the pulling centers that is fixed at a position far from the protein. We implement this hSMD approach for two ligand–protein complexes whose structures were determined and whose binding affinities were measured experimentally: caprylic acid binding to bovine β-lactoglobulin and glutathione binding to Schistosoma japonicum glutathione S-transferase tyrosine 7 to phenylalanine mutant. Our computed binding affinities agree with the experimental data within a factor of 1.5. The total time of computation for these two all-atom model systems (consisting of 96K and 114K atoms, respectively) was less than one wall-clock week using 512 cores (32 Xeon E5-2680 processors).