Linear Interaction Energy (LIE) Models for Ligand Binding in Implicit Solvent:  Theory and Application to the Binding...

Expressions for Linear Interaction Energy (LIE) estimators for the binding of ligands to a protein receptor in implicit solvent are derived based on linear response theory and the cumulant expansion expression for the free energy. Using physical arguments, values of the LIE linear response proportionality coefficients are predicted for the explicit and implicit solvent electrostatic and van der Waals terms. Motivated by the fact that the receptor and solution media may respond differently to the introduction of the ligand, a novel form of the LIE regression equation is proposed to model independently the processes of insertion of the ligand in the receptor and in solution. We apply these models to the problem of estimating the binding free energy of two non-nucleoside classes of inhibitors of HIV-1 RT (HEPT and TIBO analogues). We develop novel regression models with greater predictive ability than more standard LIE formulations. The values of the regression coefficients generally conform to linear response predictions, and we use this fact to develop a LIE regression equation with only one adjustable parameter (excluding the intercept parameter) which is superior to the other models we tested and to previous results in terms of predictive accuracy for the HEPT and TIBO compounds individually. The new models indicate that, due to the different effects of induced steric strain of the receptor, an increase of ligand size alone opposes binding for ligands of the HEPT class, whereas it favors binding for ligands of the TIBO class.