Evaluation of Electrostatic Interactions
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- Abstract
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Abstract
Described here are several computational procedures for the analysis of electrostatic interactions in molecular complexes, all based on a continuum model of solvation. The first section describes how to compute the residual potential, a measure of how electrostatically complementary a ligand is for its receptor. The second procedure describes electrostatic component analysis, a method by which the electrostatic contribution to the binding free energy can be broken up into terms directly attributable to individual chemical groups. Finally, electrostatic affinity optimization is described. This procedure is particularly useful in determining what portions of a ligand are the most suboptimal, and thus provide the greatest opportunity for the design of improvements.
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- Basic Protocol 1: Analysis of Electrostatic Complementarity
- Basic Protocol 2: Electrostatic Component Analysis
- Basic Protocol 3: Electrostatic Affinity Optimization
- Guidelines for Understanding Results
- Commentary
- Literature Cited
- Figures
- Tables
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Basic Protocol 1: Analysis of Electrostatic Complementarity
Necessary Resources
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Figure 8.3.1 (A ) Example of a charge file for the complex of interest in DelPhi format. Each line of this file contains one charge entry. The first column is the atom name, the second the residue name, the third the residue ID, the fourth column the chain ID, and the fifth column the partial atomic charge. Two example lines are shown for a backbone NH group, with the nitrogen having a partial charge of −0.4 and the hydrogen +0.4. (B ) Example of a radius file for the complex of interest. Each line of this file contains one radius entry. The first column is the atom name, the second is the residue name, and the third is the atomic radius. Again, two example lines are shown, the nitrogen having a radius of 1.5 Å, the hydrogen 1.0 Å. View Image -
Figure 8.3.2 Increased electrostatic complementarity is indicated by a smaller magnitude residual potential. The large negative residual potential on the left‐hand side is reduced in the right‐hand figure. The ligand on the right has a several additional positively charged residues that interact with negative groups on the receptor. View Image -
Figure 8.3.3 The electrostatic binding free energy (Δ G es ) varies quadratically with ligand charge ( Q l ). The desolvation free energy of the ligand (D G hyd l ) varies with the square of the charges on the ligand, while the free energy of interaction with the receptor (Δ G int l,r ) varies linearly with the ligand charges. As the receptor desolvation free energy (Δ G hyd r ) is independent of the ligand charges, the net electrostatic binding free energy is a quadratic function of the ligand charge distribution. As a result, there is a single minimum on the free energy surface, corresponding to the optimal ligand charge distribution. View Image
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Literature Cited
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| Hendsch, Z.S. and Tidor, B. 1994. Do salt bridges stabilize proteins? A continuum electrostatics analysis. Protein Sci. 3:211‐226. | |
| Hendsch, Z.S. and Tidor, B. 1999. Electrostatic interactions in the GCN4 leucine zipper: Substantial contributions arise from intramolecular interactions enhanced on binding. Protein Sci. 8:1381‐1392. | |
| Hendsch, Z.S., Jonsson, T., Sauer, R.T., and Tidor, B. 1996. Protein stabilization by removal of unsatisfied polar groups: Computational approaches and experimental tests. Biochemistry 35:7621‐7625. | |
| Kangas, E. and Tidor, B. 1998. Optimizing electrostatic affinity in ligand–receptor binding: Theory, computation, and ligand properties. J. Chem. Phys. 109:7522‐7545. | |
| Kangas, E. and Tidor, B. 1999. Charge optimization leads to favorable electrostatic binding free energy. Phys. Rev. E 59:5958‐5961. | |
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| Kangas, E. and Tidor, B. 2001. Electrostatic complementarity at ligand binding sites: Application to chorismate mutase. J. Phys. Chem. B. 105:880‐888. | |
| Lee, L.‐P. and Tidor, B. 1997. Optimization of electrostatic binding free energy. J. Chem. Phys. 106:8681‐8690. | |
| Lee, L.‐P. and Tidor, B. 2001a. Barstar is electrostatically optimized for tight binding to barnase. Nat. Struct. Biol. 8:73‐76. | |
| Lee, L.‐P. and Tidor, B. 2001b. Optimization of binding electrostatics: Charge complementarity in the barnase‐barstar protein complex. Protein Sci. 10:362‐377. | |
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| Nohaile, M.J., Hendsch, Z.S., Tidor, B., and Sauer, R.T. 2001. Altering dimerization specificity by changes in surface electrostatics. Proc. Natl. Acad. Sci. U.S.A. 98:3109‐3114. | |
| Potter, M.J., Gilson, M.K., and McCammon, J.A. 1994. Molecule pK(a) prediction with continuum electrostatics. J. Am. Chem. Soc. 116:10298‐10299. | |
| Sarkar, C.A., Lowenhaupt, K., Horan, T., Boone, T.C., Tidor, B., and Lauffenbuger, D.A. 2002. Rational cytokine design for increased lifetime and enhanced potency using pH‐activated “histidine switching.” Nat. Biotech. 20:908‐913. | |
| Sharp, K.A. and Honig, B. 1990. Electrostatic interactions in macromolecules: Theory and applications. Annu. Rev. Biophys. Biophys. Chem. 19: 301‐332. | |
| Sharp, K.A., Nicholls, A., Fine, R.F., and Honig, B. 1991. Reconciling the magnitude of the microscopic and macroscopic hydrophobic effects. Science 252:106‐109. | |
| Spector, S., Wang, M.H., Carp, S.A., Robblee, J., Hendsch, Z.S., Fairman, R., Tidor, B., and Raleigh, D.P. 2000. Rational modification of protein stability by the mutation of charged surface residues. Biochemistry 39:872‐879. | |
| Sulea, T. and Purisima, E.O. 2001. Optimizing ligand charges for maximum binding affinity. A solvated interaction energy approach. J. Phys. Chem. B 105:889‐899. | |
| van Vlijmen, H.W.T., Schaefer, M., and Karplus, M. 1998. Improving the accuracy of protein pK(a) calculations: Conformational averaging versus the average structure. Proteins 33:145‐158. | |
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| Warwicker, J. and Watson, H.C. 1982. Calculation of the electric potential in the active site cleft due to α‐helix dipoles. J. Mol. Biol. 157:671‐679. | |
| Xiao, L. and Honig, B. 1999. Electrostatic contributions to the stability of hyperthermophilic proteins. J. Mol. Biol. 289:1435‐1444. | |
| Yang, A.S., Gunner, M.R., Sampogna, R., Sharp, K., and Honig, B. 1993. On the calculation of pK(a)s in proteins. Proteins 15:252‐265. | |
| Zacharias, M., Luty, B.A., Davis, M.E., and McCammon, J.A. 1992. Poisson–Boltzmann analysis of the lambda‐repressor‐operator interaction. Biophys. J. 63:1280‐1285. | |
| Key References | |
| Hendsch and Tidor, 1999. See above. | |
| Contains a detailed description of the implementation of component analysis and its application to the GCN4 leucine zipper. | |
| Lee and Tidor, 1997. See above. | |
| Outlines the theory behind the optimization of electrostatic binding free energy. | |
| Kangas and Tidor, 1998. See above. | |
| A detailed description of the electrostatic optimization procedure, including a definition of electrostatic complementarity. | |
| Internet Resources | |
| http://web.mit.edu/tidor/www/residual | |
| Obtaining the Residual Potential Web site. | |
| http://trantor.bioc.columbia.edu/grasp | |
| The Grasp Web site. | |
| http://trantor.bioc.columbia.edu/delphi | |
| The DelPhi Web site. |
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