Simple, Intuitive Calculations of Free Energy of Binding for Protein−Ligand Complexes. 1. Models without Explicit Constrained Water

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Abstract
The prediction of the binding affinity between a protein and ligands is one of the most challenging issues for computational biochemistry and drug discovery. While the enthalpic contribution to binding is routinely available with molecular mechanics methods, the entropic contribution is more difficult to estimate. We describe and apply a relatively simple and intuitive calculation procedure for estimating the free energy of binding for 53 protein−ligand complexes formed by 17 proteins of known three-dimensional structure and characterized by different active site polarity. HINT, a software model based on experimental LogPo/w values for small organic molecules, was used to evaluate and score all atom−atom hydropathic interactions between the protein and the ligands. These total scores (HTOTAL), which have been previously shown to correlate with ΔGinteraction for protein−protein interactions, correlate with ΔGbinding for protein−ligand complexes in the present study with a standard error of ±2.6 kcal mol-1 from the equation ΔGbinding = −0.001 95 HTOTAL − 5.543. A more sophisticated model, utilizing categorized (by interaction class) HINT scores, produces a superior standard error of ±1.8 kcal mol-1. It is shown that within families of ligands for the same protein binding site, better models can be obtained with standard errors approaching ±1.0 kcal mol-1. Standardized methods for preparing crystallographic models for hydropathic analysis are also described. Particular attention is paid to the relationship between the ionization state of the ligands and the pH conditions under which the binding measurements are made. Sources and potential remedies of experimental and modeling errors affecting prediction of ΔGbinding are discussed.

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