Optimizing electrostatic affinity in ligand–receptor binding: Theory, computation, and ligand properties

The design of a tight-binding molecular ligand involves a tradeoff between an unfavorable electrostatic desolvation penalty incurred when the ligand binds a receptor in aqueous solution and the generally favorable intermolecular interactions made in the bound state. Using continuum electrostatic models we have developed a theoretical framework for analyzing this problem and have shown that the ligand-charge distribution can be optimized to produce the most favorable balance of these opposing free energy contributions L.-P. Lee and B. Tidor, J. Chem. Phys. 106, 8681 (1997). Herein the theoretical framework is extended and calculations are performed for a wide range of model receptors. We examine methods for computing optimal ligands (including cases where there is conformational change) and the resulting properties of optimized ligands. In particular, indicators are developed to aid in the determination of the deficiencies in a specific ligand or basis. A connection is established between the optimization problem here and a generalized image problem, from which an inverse-image basis set can be defined; this basis is shown to perform very well in optimization calculations. Furthermore, the optimized ligands are shown to have favorable electrostatic binding free energies (in contrast to many natural ligands), there is a strong correlation between the receptor desolvation penalty and the optimized binding free energy for fixed geometry, and the ligand and receptor cannot generally be mutually optimal. Additionally, we introduce the display of complementary desolvation and interaction potentials and the deviation of their relationship from ideal as a useful tool for judging effective complementarity. Scripts for computing and displaying these potentials with GRASP are available at http://mit.edu/tidor.