Electrostatic Binding Free Energy Research Articles

Charge optimization leads to favorable electrostatic binding free energy.

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 paper, 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. This stabilizing effect on association reactions is contrary to the usual role of electrostatics in aqueous complexes, in which desolvation effects generally dominate. We also show the existence and nonuniqueness of the variational solution and make a connection to the electrostatic image charge problem.

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.

Monovalent and Divalent Salt Effects on Electrostatic Free Energies Defined by the Nonlinear Poisson−Boltzmann Equation: Application to DNA Binding Reactions

We have extended the finite-difference Poisson−Boltzmann (FDPB) equation method to incorporate the treatment of mixed salts (i.e. NaCl/MgCl2). In this context, we have derived an expression for the total electrostatic free energy for mixed salt systems. We use the theory to study nonspecific mixed salt effects on the binding free energies of the minor groove binding antibiotic DAPI, and λ repressor, with DNA. We find that in a pure salt solution the electrostatic contribution to binding varies linearly with log[Mn+], (where Mn+ represents an n-valent cation) and that the effect is uncorrelated with either the valence of the binding ligand or the number of counterions in the binding site. In mixed salt solution, the monovalent and divalent counterions “compete” for the immediate vicinity of the DNA. As experimentally observed in mixed salt solutions, a pronounced curvature appears in the plot of the electrostatic binding free energy vs log[Mn+]. The curvature for DAPI−DNA binding in mixed salts reflects th...

Optimization of electrostatic binding free energy

An analytic result is derived that defines the charge distribution of the tightest-binding ligand given a receptor charge distribution and spherical geometries. Using the framework of continuum electrostatics, the optimal distribution is expressed as a set of multipoles determined by minimizing the electrostatic free energy of binding. Results for two simple receptor systems are presented to illustrate applications of the theory.

Binding Data Analysis of the Interaction of Bovine Hemoglobin with Dodecyltrimethylammonium Bromide

Abstract The interaction of dodecyltrimethylammonium bromide, as a cationic surfactant, with bovine hemoglobin, as a biopolymer, has been investigated at different temperatures by an equilibrium dialysis technique. The obtained binding isotherms have been analyzed and interpreted by the Wyman binding potential model and other thermodynamic parameters which have been extracted on the basis of this model. A new method of analysis for evaluating the binding isotherms and estimating the free energy change, ΔGt, per mole of ligand has been proposed. The unusual behavior of the Scatchard plot at 300 K was analyzed in terms of two sets of binding sites. The first set of binding sites was considered as electrostatic and the second as hydrophobic. The free energy of interaction () from the Wyman model was also resolved according to electrostatic and hydrophobic binding free energies.

Calculations of the electrostatic free energy contributions to the binding free energy of sulfonamides to carbonic anhydrase

The interactions between biologically important enzymes and drugs are of great interest. In order to address some aspects of these interactions we have initiated a program to investigate enzymedrug interactions. Specifically, the interactions between one of the isozymes of carbonic anhydrase and a family of drugs known as sulfonamides have been studied using computational methods. In particular the electrostatic free energy of binding of carbonic anhydrase II with acetazolamide, methazolamide,p-chlorobenzenesulfonamide,p-aminobenzenesulfonamide and three new compounds (MK1, MK2, and MK3) has been computed using finite-difference Poisson-Boltzmann (FDPB) [1] method and the semimacroscopic version [2, 3] of the protein dipole Langevin dipole (PDLD) method [4]. Both methods, FDPB and PDLD, give similar results for the electrostatic free energy of binding even though different charges and different treatments were used for the protein. The calculated electrostatic binding free energies are in reasonable agreement with the experimental data. The potential and the limitation of electrostatic models for studies of binding energies are discussed.

On the magnitude of the electrostatic contribution to ligand-DNA interactions.

A model based on the nonlinear Poisson-Boltzmann equation is used to study the electrostatic contribution to the binding free energy of a simple intercalating ligand, 3,8-diamino-6-phenylphenanthridine, to DNA. We find that the nonlinear Poisson-Boltzmann model accurately describes both the absolute magnitude of the pKa shift of 3,8-diamino-6-phenylphenanthridine observed upon intercalation and its variation with bulk salt concentration. Since the pKa shift is directly related to the total electrostatic binding free energy of the charged and neutral forms of the ligand, the accuracy of the calculations implies that the electrostatic contributions to binding are accurately predicted as well. Based on our results, we have developed a general physical description of the electrostatic contribution to ligand-DNA binding in which the electrostatic binding free energy is described as a balance between the coulombic attraction of a ligand to DNA and the disruption of solvent upon binding. Long-range coulombic forces associated with highly charged nucleic acids provide a strong driving force for the interaction of cationic ligands with DNA. These favorable electrostatic interactions are, however, largely compensated for by unfavorable changes in the solvation of both the ligand and the DNA upon binding. The formation of a ligand-DNA complex removes both charged and polar groups at the binding interface from pure solvent while it displaces salt from around the nucleic acid. As a result, the total electrostatic binding free energy is quite small. Consequently, nonpolar interactions, such as tight packing and hydrophobic forces, must play a significant role in ligand-DNA stability.

Salt Effects on Protein-DNA Interactions: The λcI Repressor and EcoRI Endonuclease

In this paper, finite-difference solutions to the nonlinear Poisson-Boltzmann (NLPB) equation are used to calculate the salt dependent contribution to the electrostatic DNA binding free energy for both the λcI repressor and the EcoRI endonuclease. For the protein-DNA systems studied, the NLPB method describes nonspecific univalent salt dependent effects on the binding free energy which are in excellent agreement with experimental results. In these systems, the contribution of the ion atmosphere to the binding free energy substantially destabilizes the protein-DNA complexes. The magnitude of this effect involves a macromolecular structure dependent redistribution of both cations and anions around the protein and the DNA which is dominated by long range electrostatic interactions. We find that the free energy associated with global ion redistribution upon binding is more important than changes associated with local protein-DNA interactions (ion-pairs) in determining salt effects. The NLPB model reveals how long range salt effects can play a significant role in the relative stability of protein-DNA complexes with different structures.

Salt Effects on Ligand-DNA Binding: Minor Groove Binding Antibiotics

Salt dependent electrostatic effects play a central role in intermolecular interactions involving nucleic acids. In this paper, the finite-difference solution to the nonlinear Poisson-Boltzmann (NLPB) equation is used to evaluate the salt dependent contribution to the electrostatic binding free energy of the minor groove binding antibiotics DAPI, Hoechst 33258 and netropsin to DNA using detailed molecular structures of the complexes. For each of these systems, a treatment based on the NLPB equation accurately describes the variation of the experimentally observed binding constant with bulk salt concentration. A solvation formalism is developed in which salt effects are described in terms of three free energy contributions: the electrostatic ion-molecule interaction free energy, ΔΔ G o im; the electrostatic ion-ion interaction free energy, ΔΔ G o ii; and the entropic ion organization free energy, ΔΔ G o org. The electrostatic terms, ΔΔ G o im and ΔΔ G o ii, have both enthalpic and entropic components, while the term ΔΔ G o org is purely a cratic entropy. Each of these terms depends significantly on salt dependent changes in the counterion and coion concentrations around the DNA. In each of the systems studied, univalent ions substantially destabilize charged ligand-DNA complexes at physiological salt concentrations. This effect involves a salt dependent redistribution of counterions near the DNA. The free energy associated with the redistribution of counterions upon binding is dominated by the unfavorable change in the electrostatic ion-molecule interactions, ΔΔ G o im, rather than the change in the cratic entropy of ion organization, ΔΔ G o org. In addition, the observed slope of the salt dependence of the free energy is determined by electrostatic ion-molecule and ion-ion interactions as well as the cratic entropy of ion release. These findings are in contrast to models in which the cratic entropy of counterion release drives binding.