Calculation of the Relative Binding Affinity of Enzyme Inhibitors Using the Generalized Linear Response Method

The generalized linear response (GLR) method initially developed for hydration free energy calculations has been adapted for binding free energy calculations. The calculations employ the concept of thermodynamic cycle. To obtain the value of the relative binding free energy between two ligands, we run molecular dynamics simulations at only four "midpoint" states along the thermodynamic pathways connecting the two ligands in the unbound and bound states, respectively. This approach significantly simplifies and accelerates the calculations as compared to the traditional free energy simulations where significantly more intermediate states are usually sampled. We show that each of these "midpoint" states can be approximately defined by a modified force field function in which both the van der Waals and electrostatic interactions between the variant part of a ligand and its environment, either binding site or aqueous solution, are scaled by a factor of 0.5. We tested this new approach to relative binding affinity calculations on the HIV-1 protease complex with its inhibitor JG365 as a starting point for the following two structural transformations:  (a) the critical chiral center on the central residue was changed from (S) to (R) configuration, and (b) the C terminal valine residue was deleted. In both cases, the GLR method afforded calculated values that were in good agreement with the experimental data.