Limits of Free Energy Computation for Protein-Ligand Interactions

Abstract

A detailed error analysis is presented for the computation of protein-ligand interaction energies. In particular, we show that it is probable that even highly accurate computed binding free energies have errors that represent a large percentage of the target free energies of binding. This is due to the observation that the error for computed energies quasi-linearly increases with the increasing number of interactions present in a protein-ligand complex. This principle is expected to hold true for any system that involves an ever increasing number of inter or intra-molecular interactions (e.g. ab initio protein folding). We introduce the concept of best-case scenario errors (BCS(errors)) that can be routinely applied to docking and scoring exercises and used to provide errors bars for the computed binding free energies. These BCS(errors) form a basis by which one can evaluate the outcome of a docking and scoring exercise. Moreover, the resultant error analysis enables the formation of an hypothesis that defines the best direction to proceed in order to improve scoring functions used in molecular docking studies.

Figure 1

Thermodyamic cycle to estimate the free energy of binding of a drug molecule to a protein receptor. P=Protein, S=small molecule/substrate and PS=protein-small molecule/substrate complex.

Figure 2

The LigPlot diagram of Indinavir bound to HIV-1 protease.

Scheme 1

Thermodynamic Cycle