In a binding process such as that shown in Figure 1, two molecules
(a ligand and a receptor) associate in solution to form a complex. If
each of the three individual molecules exist predominantly in a single
conformation, then the free energy change due to the
binding process can be separated into electrostatic and non-polar
components [1,2]. The electrostatic component of the binding free energy
is, in the continuum electrostatic approximation, quadratic [3,5] with
respect to the ligand- and receptor-charge distributions. If the
electrostatic charge distribution of the ligand is varied while the ligand
and receptor shapes and the binding conformation are kept fixed (i.e., all
non-polar aspects of binding are held constant), then an optimum set of
electrostatic charges can be found for the ligand that make the
electrostatic component of the binding free energy as favorable (negative)
as possible [3-5].
- Residual Potential
- The sum of 1) the total bound-state electrostatic potential due to
the receptor charges (sometimes called the interaction potential) and 2)
the change in the electrostatic potential of the ligand charges due to
binding (also known as the desolvation potential). The Residual potential
should be exactly zero everywhere within and on the ligand's molecular
surface if the ligand is complementary to the receptor.
The Residual potential allows one to rigorously determine and analyze
ligand regions that are not complementarity to a given receptor. This can
be done explicitly by plotting or contouring the Residual Potential on the
ligand's surface to discern regions where it is significantly non-zero, as
shown in the section Example of Employing
the Residual Potential. With the Residual Potential, one can
- Discern regions of significant non-complementary.
- Possibly improve such regions through mutagenesis or redesign of
the ligand.
- Add basis points in such regions to improve the optimization
process.
- Suggest specificity-determining regions of the ligand-receptor
interface.
Analysis through the Residual Potential is inherently asymmetric
because receptor and ligand cannot generally be mutually complementary.
As a result, the degree of complementarity observed using the Residual
Potential may depend on which of the two associating molecules is labeled
the ligand and which the receptor. When actually optimizing the ligand,
this choice is unambiguous; however, for natural complexes, it is not. In
fact, by considering both possibilities, one may be able to determine
which of the associating species is more complementary to the other and
thus gain insight into the evolutionary history of the system in question
[5].
In the next section, Examples, we show
how the Residual potential can be used to analyze complementarity and
compare this method to the usual method used by structural biophysicists,
which involves only examining the surface electrostatic potentials of the
free ligand and receptor. In the section Software, we give scripts for computing and
displaying the Residual Potential using the GRASP [6] software
package.
References
[1] Classical Electrostatics in Biology and Chemistry.
B. Honig and A. Nicholls.
Science (Washington D. C.)
268: 1144-1149 (1995).
[2] Macroscopic Models of Aqueous Solutions: Biological and Chemical Applications.
B. Honig, K. Sharp, and A.-S. Yang.
J. Phys. Chem.
97: 1101-1109 (1993).
[3] Optimization of Electrostatic Binding Free Energy.
L.-P. Lee and B. Tidor.
J. Chem. Phys.
106: 8681-8690 (1997).
[4] Computation of Electrostatic Complements to Proteins: A Case of Charge Stabilized Binding.
L. T. Chong, S. E. Dempster, Z. S. Hendsch, L.-P. Lee, and B. Tidor.
Protein Sci.
7: 206-210 (1998).
[5] Optimizing Electrostatic Affinity in Ligand-Receptor Binding: Theory, Computation, and Ligand Properties.
E. Kangas and B. Tidor.
J. Chem. Phys.
109: 7522-7545 (1998).
[6] Protein Folding and Association: Insights From the Interfacial and Thermodynamic Properties of Hydrocarbons.
A. Nicholls, K. A. Sharp, and B. Honig.
Proteins: Struct., Funct., Genet.
11: 281-296 (1991).