Optimizing Molecular Electrostatic Interactions: Binding Affinity and Specificity

Chapter 3: Electrostatic Affinity Optimization: General Principles

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 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 examine 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 can not 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.

Methods have been developed to design optimal electrostatic interactions for molecular binding for situations in which the charge distribution of one binding partner is fixed, the other is adjustable, and the system can be described by the Poisson equation [L.-P. Lee and B. Tidor, J. Chem. Phys. 106, 8681 (1997)]. In some fields of interest (e.g., rational drug design), the solvent contains mobile ions, and the system is adequately described by the linearized Poisson--Boltzmann equation. Here the analytical framework for electrostatic optimization is extended to such situations. The case of spherical molecular geometries with an ion-excluding Stern layer has been treated in detail. Calculational results are reported for a variety of model receptors and ionic strengths. The effects of increasing the ionic strength up to 1.0 M causes a substantial weakening of the optimal binding affinity but a negligible change to the optimal ligand-charge distributions.

Variational optimization of molecular electrostatic charge distributions is a tool for the study of association reactions of molecules in solution. In principle, this method can be used in drug design and protein folding to analyze and improve molecular interactions and to provide electrostatic templates for molecular design. This optimization problem reduces to an inverse source problem in classical electrostatics, where the sources are determined by a combination of external and self-polarization potentials. In this chapter, we show that the electrostatic portion of the free energy of association for electrostatically optimized molecules has an upper bound of zero in many situations of physical interest. That is, variational optimization provides a ligand charge distribution that contributes favorably to the energetics of binding (even in a strongly polar medium), stabilizing association reactions contrary to the usual role of electrostatics in aqueous complexes (in which desolvation effects generally dominate). We also show the existence and non-uniqueness of the variational solution and make a connection to the electrostatic image charge problem.

Recently developed electrostatic charge optimization methods allow the calculation of a set of partial atomic charges for one molecule that provide it with a minimum electrostatic free energy contribution for binding its partner molecule. Charge optimization methods were applied here to the binding of the Bacillus subtilis chorismate mutase enzyme by its endo-oxabicyclic transition state analog. In particular, electrostatically optimized templates for the twelve different active sites in the X-ray crystal structure were used to define regions of the transition state analog whose electrostatic properties are particularly non-optimal for binding. Structural variations of the analog that could improve its electrostatic affinity for the enzyme are suggested by changes that more closely mimic the optimal charge distributions. Results indicate that the replacement of one of the analog's carboxylate groups with a nitro group may improve the electrostatic component of the binding free energy by up to about 3.1 kcal/mol. The principal mechanism is a decrease in the desolvation penalty of the ligand without a significant loss in ligand--enzyme interactions. This work shows that charge optimization techniques are capable of identifying chemically reasonable substitutions to known ligands that produce substantial improvements in computed binding affinity through electrostatic enhancement. In the current case, much of the electrostatic enhancement comes from the removal of a formal charge and might be better termed an electrostatic re-balancing. Comparison of the results across twelve crystallographically independent active sites confirms that the approach is not overly sensitive to subtle structural variation. Additionally, results indicate that the mean square residual surface potential correlates well with the improvement in electrostatic binding free energy for all variations examined.

Designing ligand molecules that bind with high affinity and specificity to a target molecule (or a family of related targets) is a fundamental goal of molecular biophysical research. While it is generally recognized that electrostatic interactions can contribute to binding specificity, it is unclear whether the inclusion of interactions that result in tight binding also necessarily lead to highly specific binding. Here we make use of recently developed charge-optimization techniques to explore the affinity-specificity relation in the context of electrostatic interactions. Using model problems we find that affinity-optimized electrostatic interactions do not necessarily create specificity. Furthermore, we develop several rigorous methods that indicate how best to perturb affinity-optimized ligand-charge distributions to increase specificity with minimal sacrifice in affinity for the target or target set. We provide a theoretical framework for improving specificity against any number of known receptors and/or binding modes as well as against uncharacterized receptors.

Analytic and numerical methods now allow optimization of the electrostatic contribution to the free energy of association of two molecules in solution. Using a continuum electrostatic approximation based on the linearized Poisson-Boltzmann equation, the electrostatic free energy of rigid bimolecular association becomes a quadratic function of the reactant-charge distributions. By optimizing the charge distribution of one reactant, we find that the electrostatic free energy can be minimized, and made favorable in many cases. Furthermore, a rigorous method for visualizing the extent of electrostatic complementarity between two molecules has been developed. In this paper we review the framework and progress of charge optimization and discuss some of the implications emerging to date.

Appears in Optimization in Computational Chemistry and Molecular Biology: Erik Kangas and Bruce Tidor, Electrostatic Optimization in Ligand Complementarity Design Nonconvex Optimization and Its Applications (series). Optimization in Computational Chemistry and Molecular Biology: Local and Global Approaches 40:231-242 (2000).