Hostname: page-component-76d6cb85b7-lcgwf Total loading time: 0 Render date: 2026-07-13T01:57:20.885Z Has data issue: false hasContentIssue false
  • English
  • Français

Calculations of electrostatic interactions in biological systems and in solutions

Published online by Cambridge University Press:  17 March 2009

Arieh Warshel  and
Stephen T. Russell
Arieh Warshel
Affiliation:
Department of Chemistry, University of Southern California, Los Angeles, California 90007
Stephen T. Russell
Affiliation:
Department of Chemistry, University of Southern California, Los Angeles, California 90007
Get access Rights & Permissions [Opens in a new window]

Extract

Correlating the structure and action of biological molecules requires knowledge of the corresponding relation between structure and energy. Probably the most important factors in such a structure– energy correlation are associated with electrostatic interactions. Thus the key requirement for quantative understanding of the action of biological molecules is the ability to correlate electrostatic interactions with structural information. To appreciate this point it is useful to compare the electrostatic energy of a charged amino acid in a polar solvent to the corresponding van der Waals energy. The electrostatic free energy, ΔGel, can be approximated (as will be shown in Section II) by the Born formula (ΔGel = –(166Q2/ā) (I – I/E)). Where ΔGel is given in kcal/mol, Qis the charge of the given group, in units of electron charge, āis the effective radius of the group, and E is the dielectric constant of the solvent. With an effective radius of charged amino acids of approximately 2 Å, Born's formula gives about – 80 kcal/mol for their energy in polar solvents where E is larger than 10. This energy is two orders of magnitude larger than the van der Waals interaction of such groups and their surroundings.

Information

Type
Research Article
Information
Quarterly Reviews of Biophysics , Volume 17 , Issue 3 , August 1984 , pp. 283 - 422
Copyright
Copyright © Cambridge University Press 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Adams, D. J. (1980). Computer simulation of highly polar liquids: the hard sphere plus point dipole potential. Molec. Phys. 40, 1261–1271.CrossRefGoogle Scholar
Adelman, S. A. & Deutch, J. M. (1974). Exact solution of the mean spherical model for strong electrolytes in polar solvents. J. Chem. Phys. 60, 3935–3949.CrossRefGoogle Scholar
Adman, E. T. (1979). A comparison of the structure of electron transfer proteins. Biochim. biophys. acta 549, 107–144.CrossRefGoogle ScholarPubMed
Alder, B. J. & Pollock, E. L. (1981). Simulation of polar and polarizable fluids. A. Rev. phys. Chem. 32, 311–329.CrossRefGoogle Scholar
Alkaitis, S. A., Gratzel, M. & Henglein, A. (1975). Laser photoionization of phenothiazine in micellar solution. II. Mechanism and light induced redox reactions with quinones. Ber. BunsenGes. phys. Chem. 79, 541–546.CrossRefGoogle Scholar
Allen, L. C. (1981). The catalytic function of active site side chains in well-characterized enzymes. Ann. N. Y. Acad. Sci. 367, 383–406.CrossRefGoogle ScholarPubMed
Amos, A. T. & Burrows, B. L. (1973). Solvent-shift effects on electronic spectra and excited-state dipole moments and polarizabilities. Adv. Quantum Chem. I, 289–313.CrossRefGoogle Scholar
Anderson, J. B. (1973). Statistical theories of chemical reactions. Distributions in the transition region. J. chem. Phys. 58, 4684–4697.CrossRefGoogle Scholar
Angyan, J. & Naray-Szabo., G. (1983). Comparison of protein electrostatic potential along the catalytic triad of serine proteinases. J. theor. Biol. 103, 349–356.CrossRefGoogle ScholarPubMed
Barker, J. A. & Watts, R. O. (1969). Structure of water; a Monte Carlo calculation. Chem. Phys. Lett. 3, 144–145.CrossRefGoogle Scholar
Barnes, P., Pinney, J. L., Nicholas, J. D. & Quinn, J. E. (1979). Cooperative effects in simulated water. Nature, Lond. 282, 459–464.CrossRefGoogle Scholar
Bartmess, J. E. & JrMcIver, R. T. (1979). The gas-phase acidity scale. In Gas-Phase Ion Chemistry, vol. 2 (ed. Bowers, M. T.), pp. 2, 87–121. Academic Press.Google Scholar
Berendsen, H. J. C., Postma, J. P. M., Van Gunsteren, W. F. & Hermans, J. (1981). Interaction models for water in relation to protein hydration. In Jerusalem Symp. Quantum Chem. Biochem., no. 14 (ed. Pullman, B.), pp. 331–342. Dordrecht, Holland: Reidel.Google Scholar
Berens, P. H., Mackay, D. H. J., White, G. M. & Wilson, K. R. (1983). Thermodynamics and quantum corrections from molecular dynamics for liquid water. J. chem. Phys. 79, 2375–2389.CrossRefGoogle Scholar
Bernhard, S. A. & Lau, S. -J. (1972). Spectrophotometric and structural evidence as to the mechanism of protease catalysis at chemical bonding resolution. Cold Spring Harb. Symp. quant. Biol. 36, 75–83.CrossRefGoogle Scholar
Bolis, G., Ragazzi, M., Salvaderi, D., Ferro, D. R. & Clementi, E. (1978). A preliminary attempt to follow the enthalpy of an enzymic reaction by ab initio computations. The catalytic action of papain. Gazz. chim. Ital. 108, 425–443.Google Scholar
Born, M. (1920). Volumen and Hydrationswärme der lonen. Z. Phys. I, 45–48.CrossRefGoogle Scholar
Born, M. & Huang, K. (1954). Dynamical Theory of Crystal Lattices, p. 248. Oxford University Press.Google Scholar
Bosshard, H. & Zurrer, M. (1980). The conformation of cytochrome c in solution. Localization of a conformational difference between ferri-and ferrocytochrome c on the surface of the molecule. J. biol. Chem. 255, 6694–6699.CrossRefGoogle ScholarPubMed
Botelho, L. H., Friend, S. H., Matthew, J. B., Lehman, L. D., Hanania, G. I. H. & Gurd, F. R. N. (1978). Proton nuclear magnetic resonance study of histidine ionizations in myoglobin of various species. Comparison of observed and computed pK values. Biochemistry 17, 5197–5205.CrossRefGoogle ScholarPubMed
Brand, L. & Gohlke, J. R. (1971). Nanosecond time-resolved fluorescence spectra of a protein-dye complex. J. biol. Chem. 246, 2317–2319.CrossRefGoogle ScholarPubMed
Butler, P. J. G. & Klug, A. (1978). The assembly of a virus. Scient. Am. 239, 62–69.Google ScholarPubMed
Careri, G., Fasella, P. & Gratton, E. (1979). Enzyme dynamics: the Statistical physics approach. A. Rev. Biophys. Bioeng. 8, 69–97.CrossRefGoogle ScholarPubMed
Carey, P. R. (1982). Biochemical Applications of Raman and Resonance Raman Spectroscopies. New York: Academic Press.Google Scholar
Carey, P. R. & Storer, A. C. (1983). Molecular details of enzyme-substrate transients by resonance Raman spectroscophy. Acc. chem. Res. 16, 455–460.CrossRefGoogle Scholar
Chandrasekhar, J. & Jorgensen, W. L. (1982). The nature of dilute solutions of sodium ions in water, methanol and tetrahydrofuran. J. chem. Phys. 77, 5080–5089.CrossRefGoogle Scholar
Choux, G. & Benoit, R. L. (1969). Solvation in dipolar aprotic solvents. Ionic enthalpies of transfer. J. Am. chem. Soc. 91, 6221–6224.CrossRefGoogle Scholar
Churg, A. K., Weiss, R. M., Warshel, A. & Takano, T. (1983). On the action of cytochrome c: correlating geometry changes upon oxidation with activation energies of electron transfer. J. phys. Chem. 87, 1683–1693.CrossRefGoogle Scholar
Clementi, E., Cavallone, F. & Schordamaglia, R. (1977). Analytical potential functions from ‘ab initio’ computations for the interaction between biomolecules. I. Water with amino acids. J. Am. chem. Soc. 99, 5531–5544.CrossRefGoogle Scholar
Conway, B. E., Bockris, J. O'M. & Ammar, I. A. (1951). The dielectric constant of the solution in the diffusion and Helmholtz double layers at a charged interface in aqueous solution. Trans. Faraday Soc. 47, 756–766.CrossRefGoogle Scholar
Cooper, A. (1979). Energy uptake in the first step of the visual excitation. Nature, Lond. 282, 531–533.CrossRefGoogle ScholarPubMed
Coulson, C. A. & Danielsson, U. (1954). Ionic and covalent contributions to the hydrogen bond. Part II. Ark. Fys. 8, 245–255.Google Scholar
Cremaschi, P., Gamba, A. & Simonetta, M. (1977). Geometry and electronic structure of intimate and solvent-separated ion pairs of fluoromethane in water. J. chem. Soc., Perkin II, 162–166.Google Scholar
Dawson, R. M. C., Elliot, D. C., Elliot, W. H. & Jones, K. M. (eds) (1974). Data for Biochemical Research, 2nd ed.Oxford: Clarendon Press.Google Scholar
Debye, P. (1912). Einige Resultate einer kinetischen Theorie der Isolatoren. Phys. Z. 13, 97–100.Google Scholar
Debye, P. (1929). Polar Molecules. New York: Dover.Google Scholar
Deisenhofer, J. & Steigemann, W. (1975). Crystallographic refinement of the structure of bovine pancreatic trypsin inhibitor at 1·5 Ångstroms. Acta Crystallogr. B 31, 238–250.CrossRefGoogle Scholar
Dunmur, D. A. (1972). The local electric field in anisotropic molecular crystals. Molec. Phys. 23, 109–115.CrossRefGoogle Scholar
Dunn, M. F., Dietrich, H., MacGibbon, A. K. H., Koerber, S. C. & Zeppezauer, M. (1982). Investigation of intermediates and transition states in the catalytic mechanisms of active site substituted cobalt(II), nickel(II), zinc(II) and cadmium(II) horse liver alcohol dehydrogenase. Biochemistry 21, 354–363.CrossRefGoogle ScholarPubMed
Fernandez, M. S. & Fromherz, P. (1977). Lipid pH indicators as probes of electrical potential and polarity in micelles. J. phys. Chem. 81, 1755–1761.CrossRefGoogle Scholar
Fersht, A. R. (1972). Conformational equilibria in α- and δ-chymotrypsin. The energetics and importance of the salt bridge. J. molec. Biol. 64, 497–509.CrossRefGoogle Scholar
Frahm, J., Diekmann, S. & Haase, A. (1980). Electrostatic properties of ionic micelles in aqueous solutions. Ber. BunsenGes. phys. Chem. 84, 566–571.CrossRefGoogle Scholar
Friedman, H. L. & Krishnan, C. V. (1973). Thermodynamics of Ion Hydration in Water, A Comprehensive Treatise, vol. 3 (ed. Franks, F.), pp. 1–118. New York: Plenum.Google Scholar
Frohlich, H. (1958). Theory of Dielectrics. London: Oxford University Press.Google Scholar
Gafni, A., Detoma, R. P., Manrow, R. E. & Brand, L. (1977). Nanosecond decay studies of a fluorescence probe bound to apomyoglobin. Biophys. J. 17, 155–168.CrossRefGoogle ScholarPubMed
Gavish, B. & Werber, M. M. (1979). Viscosity-dependent structural fluctuations in enzyme catalysis. Biochemistry 18, 1269–1275.CrossRefGoogle ScholarPubMed
Gelin, B. R. & Karplus, M. (1979). Side-chain torsional potentials: effect of dipeptide, protein and solvent environment. Biochemistry 18, 1256–1268.CrossRefGoogle ScholarPubMed
Gready, J. E., Bacskay, G. B. & Hush, N. S. (1977). Finite-field method calculations. III. Dipole moment gradients, polarizability gradients in field-induced shifts in bond lengths, vibrational levels, spectroscopic constants and dipole functions – applications to LiH. Chem. Phys. 24, 333–341.CrossRefGoogle Scholar
Gready, J. E., Bacskay, G. B. & Hush, N. S. (1978). Finite-field method calculations. IV. Higher-order moments, dipole moment gradients, polarizability gradients and field-induced shifts in molecular properties: application to N2, CO, CN-, HCN and HNC. Chem. Phys. 31, 467–483.CrossRefGoogle Scholar
Greenberg, D. A., Barry, C. D. & Marshall, G. R. (1978). Investigation and parametrization of molecular dielectric function. J. Am. chem. Soc. 100, 4020–4026.CrossRefGoogle Scholar
Grimmelmann, E. K., Tully, J. C. & Helfand, E. (1981). Molecular dynamics of infrequent events: thermal desorption of xenon from a platinum surface. J. chem. Phys. 74, 5300–5310.CrossRefGoogle Scholar
Hagler, A. T., Huler, E. & Lifson, S. (1974). Energy functions for peptides and proteins. I. Derivation of a consistent force field including the hydrogen bond from amide crystals. J. Am. chem. Soc. 96, 5319–5327.CrossRefGoogle ScholarPubMed
Hagler, A. T. & Moult, J. (1978). Computer simulation of solvent structure around biological macromolecules. Nature 272, 222–226.CrossRefGoogle ScholarPubMed
Hayes, D. M. & Kollman, P. A. (1976). Electrostatic potentials of proteins. I. Carboxypeptidase A. J. Am. chem. Soc. 98, 3335–3345.CrossRefGoogle ScholarPubMed
Henderson, R. (1977). The purple membrane from Halobacterium halobium. A. Rev. Biophys. Bioeng. 6, 87–109.CrossRefGoogle ScholarPubMed
Hill, T. L. (1962). An Introduction to Statistical Thermodynamics, pp. 205–209. Addison-Wesley.Google Scholar
Hirata, F., Rossky, P. J. & Montgomery, P. (1983). The inter-ionic potential of mean force in a molecular polar solvent from an extended RISM equation. J. chem. Phys. 78, 4133–4144.CrossRefGoogle Scholar
Hirshfelder, J. O., Curtiss, C. F. & Bird, R. B. (1954). Molecular Theory of Gases and Liquids. New York: Wiley.Google Scholar
Hol, W. G. J., Van Duijnen, P. T. & Berendson, H. J. C. (1978). The α-helix dipole and the properties of proteins. Nature, Lond. 273, 443–446.CrossRefGoogle ScholarPubMed
Honig, B., Greenberg, A. D., Dinur, U. & Ebrey, T. G. (1976). Visual pigment spectra: implications of the protonation of the retinal Schiff base. Biochemistry 15, 4593–4599.CrossRefGoogle ScholarPubMed
Honig, B., Dinur, U., Nakanishi, K., Balogh-Nair, V., Gawinowicz, M. A., Arnaboldi, M. & Motto, M. G. (1979). An external pointcharge model for wavelength regulation in visual pigment. J. Am. chem. Soc. 101, 7084–7086.CrossRefGoogle Scholar
Honig, B. H. & Hubbell, W. L. (1983). Do ‘Salt-Bridges’ exist in membrane proteins. Biophys. J. 41, 203.Google Scholar
Hopfinger, A. J. (1974). Studies of some empiricial functions used in peptide conformational analysis. In Peptides, Polypeptides and Proteins (ed. Blout, E. R., Bovey, F. A., Goodman, M. and Lotan, N.), pp. 71–78. New York: Wiley.Google Scholar
Irving, C. S., Byers, G. W. & Leermakers, P. A. (1970). Spectroscopic model for the visual pigments. Influence of microenvironmental polarizability. Biochemistry 9, 858–864.CrossRefGoogle ScholarPubMed
Jackson, J. D. (1975). Classical Electrodynamics. New York: Wiley.Google Scholar
Johannin, G. & Kellershohn, N. (1972). An estimate of intraproteic electrostatic fields values originated by the peptide groups in α-chymotrypsin. Biochem. biophys. Res. Commun. 49, 321–327.CrossRefGoogle Scholar
Johnson, F. A., Lewis, S. D. & Shafer, J. A. (1981). Perturbations in the free energy and enthalpy of ionization of histidine-159 at the active site of papin as determined by fluorescence spectroscopy. Biochemistry 20, 52–58.CrossRefGoogle Scholar
Jordan, P. C. (1981). Energy barriers for passage of ions through channels. Exact solution of two electrostatic problems. Biophys. Chem. 13, 203–212.CrossRefGoogle ScholarPubMed
Jorgensen, W. L. (1978). Ab initio molecular orbital study of the geometric properties and protonation of alkyl chloride. J. Am. chem. Soc. 100, 1057–1061.CrossRefGoogle Scholar
Jorgensen, W. L. (1981). Transferable intermolecular potential functions for water, alcohols, and ethers. Application to liquid water. J. Am. chem. Soc. 103, 335–340.CrossRefGoogle Scholar
Jorgensen, W. L. (1982). Revised TIPS for simulations of liquid water and aqueous solutions. J. chem. Phys. 77, 4156–4163.CrossRefGoogle Scholar
Jorgensen, W. L. & Madura, J. D. (1983). Solvation and conformations of methanol in water. J. Am. chem. Soc. 105, 1407–1413.CrossRefGoogle Scholar
Kassner, R. J. (1972). Effects of non-polar environments on the Redox potentials of heme complexes. Proc. natn. Acad. Sci. U.S.A. 69, 2263–2267.CrossRefGoogle Scholar
Kassner, R. J. (1973). A theoretical model for the effects of local nonpolar heme environments on the Redox potentials in cytochromes. J. Am. chem. Soc. 95, 2674–2677.CrossRefGoogle ScholarPubMed
Kassner, R. J. & Yang, W. (1977). A theoretical model for the effects of solvent and protein dielectric on the Redox potentials of iron–sulfur clusters. J. Am. chem. Soc. 99, 4351–4355.CrossRefGoogle ScholarPubMed
Kebarle, P. (1977). Ion thermochemistry and solvation from gas phase ion equilibria. A. Rev. phys. Chem. 28, 445–476.CrossRefGoogle Scholar
Keck, J. C. (1962). Statistical investigation of dissociation cross-sections for diatoms. Discuss. Faraday Soc. 33, 173–182.CrossRefGoogle Scholar
Kessler, H. & Feigel, M. (1982). Direct observation of recombination of ion pairs by dynamic NMR spectroscopy. Acc. chem. Res. 15, 2–8.CrossRefGoogle Scholar
Kilmartin, J. V., Fogg, J. H. & Perutz, M. F. (1980). Role of C-terminal histidine in the alkaline Bohr effect of human hemoglobin. Biochemistry 19, 3189–3193.CrossRefGoogle ScholarPubMed
Kirkwood, J. G. (1934). Theory of solutions of molecules containing widely separated charges with special application to zwitterions. J. chem. Phys. 2, 351–361.CrossRefGoogle Scholar
Kirkwood, J. G. & Westheimer, F. H. (1938). The electrostatic influence of substituents on the dissociation constants of organic acids: I. J. chem. Phys. 6, 506–512.CrossRefGoogle Scholar
Kirkwood, J. G. (1939). The dielectric polarization of polar liquids. J. chem. Phys. 7, 911–919.CrossRefGoogle Scholar
Kitagawa, T., Ozaki, Y. & Kyogoku, Y. (1978). Resonance Raman studies on the ligand–iron interactions in hemoproteins and metalloporphyrins. Adv. Biophys. II, 153–196.Google Scholar
Kliger, D. S., Milder, S. J. & Dratz, E. A. (1977). Solvent effects on the spectra of retinal Schiff bases. I. Models for the bathochromic shift of thechromophore spectrum in visual pigments. Photochem. Photobiol. 25, 277–286.CrossRefGoogle ScholarPubMed
Klymkowsky, M. W. & Stroud, R. M. (1979). Immunospecific identification and three-dimensional structure of a membrane-bound acetyl-choline receptor from Torpedo californica. y. molec. Biol. 128, 319–334.CrossRefGoogle Scholar
Kollman, P. A. & Haves, D. M. (1981). Theoretical calculations on proton-transfer energetics: studies of methanol, imidazole, formic acid and methanethiol as models for the serine and cysteine proteases. J. Am. chem. Soc. 103, 2955–2961.CrossRefGoogle Scholar
Kollman, P. A., Weiner, P. K. & Dearing, A. (1981). Studies of nucleotide conformations and interactions. The relative stability of double helical β–DNA sequence isomers. Biopolymers 20, 2583–2621.CrossRefGoogle Scholar
Koppenol, W. H., Vroonland, C. A. J. & Braams, R. (1978). The electric potential field around cytochrome c and the effect of ionic strength on reaction rates of horse cytochrome c. Biochim. biophys. Acta 503, 499–508.CrossRefGoogle ScholarPubMed
Kosower, E. M. (1982). Intramolecular donor–acceptor Systems. 9. Photophysics of (phenylamino)naphthalenesulfonates: a paradigm for excited-state intramolecular charge transfer. Acc. chem. Res. 15, 259–266.CrossRefGoogle Scholar
Levesque, D., Weiss, J. J. & Patey, G. M. (1980). Charged hard spheres in dipolar hard sphere solvents. A model for electrolyte solutions. J. chem. Phys. 72, 1887–1899.CrossRefGoogle Scholar
Levitt, D. G. (1978). Electrostatic calculations for an ion channel. I. Energy and potential profiles and interactions between ions. Biophys. J. 22, 209–219.CrossRefGoogle ScholarPubMed
Lewis, S. D., Johnson, F. A. & Shafer, J. A. (1981). Effect of cystein-25 on the ionization of histidine-159 in papain as determined by proton nuclear magnetic resonance spectroscopy. Evidence for a His-159–Cys-25 ion pair and its possible role in catalysis. Biochemistry 20, 48–58.CrossRefGoogle ScholarPubMed
Lifson, S. & Warshel, A. (1968). A consistent force field for calculation on conformations, vibrational spectra and enthalpies of cycloalkanes and n-alkane molecules. J. chem. Phys. 49, 5116–5129.CrossRefGoogle Scholar
Linderstrom-Lang, K. (1924). On the ionization of proteins. C.r. Trav. Lab. Carlsberg 15, 1–29.Google Scholar
Locke, M. J. & McIver, R. T. Jr. (1983). Effect of solvation on the acid/base properties of glycine. J. Am. chem. Soc. 105, 4226–4232.CrossRefGoogle Scholar
Loew, G. H. & Thomas, D. D. (1972). Molecular orbital calculations of the catalytic effect of lysozyme. I. Glu 35 as general acid catalyst. J. theor. Biol. 36, 89–104.CrossRefGoogle ScholarPubMed
Lorentz, H. A. (1909). Theory of Electrons. Leipzig: Teubner.Google Scholar
McDonald, I. R. & Rasaiah, J. C. (1975). Monte Carlo simulation of the average force between two ions in a Stockmayer solvent. Chem. Phys. Lett. 34, 382–386.CrossRefGoogle Scholar
McDonald, I. R. & Klein, M. (1978). Intermolecular potentials and the simulation of liquid water. J. chem. Phys. 68, 4875–4877.CrossRefGoogle Scholar
McRae, E. G. (1957). Theory of solvent effects on molecular electronic spectra. Frequency shifts. J. phys. Chem. 61, 562–572.CrossRefGoogle Scholar
Marcus, R. A. (1964). Chemical and electrochemical electron-transfer theory. A. Rev. phys. Chem. 15, 155–196.CrossRefGoogle Scholar
Mataga, N. & Kubota, T. (1970). Molecular Interactions and Electronic Spectra. New York: Marcel Dekker.Google Scholar
Matthew, J. B., Hanania, G. I. H. & Gurd, F. R. N. (1979). Electrostatic effects in hemoglobin: hydrogen ion equilibrium in human deoxy- and oxyhemoglobin A. Biochemistry 18, 1919–1928.CrossRefGoogle Scholar
Matthew, J. B., Weber, P. C., Salemme, F. R. & Richards, F. M. (1983). Electrostatic orientation during electron transfer between flavodoxin and cytochrome c. Nature, Lond. 301, 169–171.CrossRefGoogle ScholarPubMed
Mehrotra, P. K., Mezei, M. & Beveridge, D. L. (1983). Convergence acceleration in Monte Carlo computer simulation on water and aqueous solutions. J. chem. Phys. 78, 3156–3166.CrossRefGoogle Scholar
Merzbacher, E. (1970). Quantum Mechanics, 2nd ed.New York: ohn Wiley.Google Scholar
Metzger, R. M. (1981). INDO and MINDO/3 atom-in-molecule polarizabilities. J. chem. Phys. 74, 3444–3457.CrossRefGoogle Scholar
Metzger, R. M. & Rhee, C. H. (1982). CNDO/2-FPP polarizabilities. Molec. Cryst. Liq. Cryst. 85, 81–87.CrossRefGoogle Scholar
Mezei, M. & Beveridge, D. L. (1982). Further quasicomponent distribution function analysis of liquid water. Temperature dependent of the results. J. chem. Phys. 76, 593–600.CrossRefGoogle Scholar
Mitchell, P. (1977). Epilogue: from energetic abstraction to biochemical mechanism. In Symposia of the Society for General Microbiology, no. 27, pp. 384–423.Google Scholar
Nagel, J. F. & Mille, M. (1981). Molecular models of proton pumps. J. chem. Phys. 74, 1367–1372.CrossRefGoogle Scholar
Naray-Szabo, G. & Bleha, T. (1982). Quantum chemical studies on the mechanism of enzyme action, molecular structure and conformation: recent advances. In Progress in Theoretical Organic Chemistry, vol. 3 (ed. Csizmadia, I. G.), pp. 267–336. Amsterdam: Elsevier.Google Scholar
Onsager, L. (1936). Electric moments of molecules in liquids. J. Am. chem. Soc. 58, 1486–1493.CrossRefGoogle Scholar
Orttung, W. H. (1969). Interpretation of the titration curve of oxyhemo-globin. Detailed consideration of Coulomb interactions at low ionic strength. J. Am. chem. Soc. 91, 162–167.CrossRefGoogle Scholar
Orttung, W. H. (1977). Direct solution of the Poisson equation for biomolecules of arbitrary shape, polarizability density and charge distribution. Ann. N. Y. Acad. Sci. 303, 22–37.CrossRefGoogle Scholar
Orttung, W. H. (1978). Extension of the Kirkwood-Westheimer model of substituent effects to general shapes, charges, and polarizabilities. Application to substituted bicyclo [2.2.2] octanes. J. Am. chem. Soc. 100, 4369–4375.CrossRefGoogle Scholar
Owicki, J. C. & Scheraga, H. A. (1977). Monte Carlo calculations in the isothermal isobaric ensemble. I. Liquid water. J. Am. chem. Soc. 99, 7403–7412.CrossRefGoogle Scholar
Pangali, C., Rao, M. & Berne, B. J. (1979). A Monte Carlo simulation of the hydrophobic interaction. J. chem. Phys. 71, 2975–2981.CrossRefGoogle Scholar
Parsegian, A. (1969). Energy of an ion crossing a low dielectric membrane: solutions to four relevant electrostatic problems. Nature, Lond. 221, 844–846.CrossRefGoogle Scholar
Parsegian, A. (1975). Ion–membrane interactions as structural forces. Ann. N.Y. Acad. Sci. 264, 161–179.CrossRefGoogle ScholarPubMed
Parson, S. M. & Rafferty, M. A. (1972). Ionization behavior of the catalytic carboxyls of lysozymes. Biochemistry II, 1623–1633.CrossRefGoogle Scholar
Patey, G. N. & Carnie, S. L. (1983). Theoretical results for aqueous electrolytes. Ion–ion potentials of mean force and the solute-dependent dielectric constant. J. chem. Phys. 78, 5183–5190.CrossRefGoogle Scholar
Patey, G. N. & Valleau, J. P. (1975). A Monte Carlo method for obtaining the interionic potential of mean force in ionic solutions. J. chem. Phys. 63, 2334–2339.CrossRefGoogle Scholar
Perutz, M. F. (1970). Stereochemistry of cooperative effects in haemoglobin. Nature, Lond. 228, 726–739.CrossRefGoogle ScholarPubMed
Perutz, M. F. (1978). Electrostatic effects in proteins. Science, N. Y. 201, 1187–1191.CrossRefGoogle ScholarPubMed
Phelps, D. J., Schneider, H. & Carey, P. R. (1981). Correlation between reactivity and structure of some chromophoric acylchymotrypsins by resonance Ramam spectroscopy. Biochemistry 20, 3447–3959.CrossRefGoogle Scholar
Pollock, E. L. & Alder, B. J. (1977). Effective field of a dipole in polarizable fluids. Phys. Rev. Lett. 39, 299–302.CrossRefGoogle Scholar
Pollock, E. L. & Alder, B. J. (1978). Changed particles in polarizable fluids. Phys. Rev. Lett. 41, 903–906.CrossRefGoogle Scholar
Pollock, E. L. & Alder, B. J. (1980). Static dielectric properties of Stockmayer fluids. Physica 102 A, 1–21.Google Scholar
Pollock, E. L., Alder, B. J. & Patey, G. N. (1981). Static dielectric properties of polarizable Stockmayer fluids. Physica 108 A, 14–26.CrossRefGoogle Scholar
Pollock, E. L., Alder, B. J. & Pratt, L. R. (1980). Relation between the local field at large distances from a charge or dipole and the dielectric constant. Proc. natn. Acad. Sci. U.S.A. 77, 49–51.CrossRefGoogle ScholarPubMed
Pople, J. A. (1954). The statistical mechanics of assemblies of axially symmetric molecules. I. General theory. Proc. R. Soc. Lond. A 221, 498–507.Google Scholar
Pullman, A. & Etchebest, C. (1983). The gramicidin A channel: the energy profile for single and double-occupancy in a head-to-head β6333-helical dimer backbone. FEBS Lett. 163, 199–202.CrossRefGoogle Scholar
Pullman, A. & Pullman, B. (1975). New paths in the molecular orbital approach to solvation in biological molecules. Q. Rev. Biophys. 7, 506–566.Google Scholar
Purcell, E. M. (1965). Electricity and Magnetism. New York: McGraw-Hill.Google Scholar
Rahman, A. & Stillinger, F. H. (1971). Molecular dynamics study of liquid water. J. chem. Phys. 55, 3336–3359.CrossRefGoogle Scholar
Rao, M., Pangali, C. & Berne, B. J. (1979). On the force bias Monte Carlo simulation of water: methodology, optimization and comparison with molecular dynamics. Molec. Phys. 37, 1773–1798.CrossRefGoogle Scholar
Rees, D. C. (1980). Experimental evaluation of the effective dielectric constant of proteins. J. molec. Biol. 141, 323–326.CrossRefGoogle ScholarPubMed
Revetllat, J. A. & Bertran, J. (1978). Theoretical study of lithium-fluoride ion pair in aqueous solution. Gazz. chim. Ital. 108, 149–151.Google Scholar
Ross, M. J., Klymkowsky, M. W., Agard, D. A. & Stroud, R. M. (1977). Structural studies of a membrane-bound acetylcholine-receptor from Torpedo californica. J. molec. Biol. 116, 635–659.CrossRefGoogle ScholarPubMed
Salem, L. (1982). Electrons in Chemical Reactions; First Principles, pp. 240–242. New York: Wiley.Google Scholar
Salemme, F. R. (1977). Structure and function of cytochrome c. A. Rev. Biochem. 46, 299–329.CrossRefGoogle Scholar
Scheiner, S., Kleier, D. A. & Lipscomb, W. N. (1975). Molecular orbital studies of enzyme activity. I. Charge relay System and tetrahedral intermediate in acylation of serine proteinases. Proc. natn. Acad. Sci. U.S.A. 72, 2606–2610.CrossRefGoogle ScholarPubMed
Scheiner, S. & Lipscomb, W. N. (1976). Molecular orbital studies of enzyme activity: catalytic mechanism of serine proteinases. Proc. natn. Acad. Sci. U.S.A. 73, 432–436.CrossRefGoogle ScholarPubMed
Scheiner, S. & Lipscomb, W. N. (1977). Molecular orbital studies of enzyme activity. IV. Hydrolysis of peptides by carboxypeptidase A. J. Am. chem. Soc. 99, 3466–3472.CrossRefGoogle Scholar
Scheraga, H. A. (1979). Interactions in aqueous solution. Acct chem. Res. 12, 7–13.CrossRefGoogle Scholar
Schultan, K. & Tavan, P. (1978). A mechanism for the light-driven proton pump of Halobacterium halobiwn. Nature, Lond. 272, 85–86.CrossRefGoogle Scholar
Sheridan, R. P. & Allen, L. C. (1980 a). The nature of hydrogen bonding in electron-transport proteins. Chem. Phys. Lett. 69, 600–603.CrossRefGoogle Scholar
Sheridan, R. P. & Allen, L. C. (1980 b). The electrostatic potential of the alpha helix. Biophys. Chem. II, 133–136.CrossRefGoogle Scholar
Sheridan, R. P. & Allen, L. C. (1981). The active site electrostatic potential of human carbonic anhydrase. J. Am. chem. Soc. 103, 1544–1550.CrossRefGoogle Scholar
Sheridan, R. P., Allen, L. C. & Carter, C. W. Jr. (1981). Coupling between oxidation state and hydrogen bond conformation in high potential iron–sulfur protein. J. biol. Chem. 256, 5052–5057.CrossRefGoogle ScholarPubMed
Shire, S. J., Hanania, G. I. H. & Gurd, F. R. N. (1975). Electrostatic effects in myoglobin. Application of the modified Tanford–Kirkwood theory to myoglobins from horse, California gray whale, harbor seal and California sea lion. Biochemistry 14, 1352–1358.CrossRefGoogle ScholarPubMed
Stillinger, F. H. & Rahman, A. (1974). Improved simulation of liquid water by molecular dynamics. J. chem. Phys. 60, 1545–1557.CrossRefGoogle Scholar
Stillinger, F. H. (1977). Theoretical approaches to the intermolecular nature of water. Phil. Trans. R. Soc. Lond. 278, 97–110.Google Scholar
Stockmayer, W. H. (1941). Second virial coefficients of polar gases. J. chem. Phys. 9, 398–402.CrossRefGoogle Scholar
Stoeckenius, W., Lozier, R. H. & Bogomolni, R. A. (1979). Bacteriorhodopsin and the purple membrane of halobacteria. Biochim. biophys. Acta 505, 215–278.CrossRefGoogle ScholarPubMed
Suzuki, H., Komatsu, T. & Kitojima, H. (1974). Theory of the optical property of visual pigment. J. phys. Soc. Japan 37, 177–185.CrossRefGoogle Scholar
Tanford, C. & Kirkwood, J. G. (1957). Theory of protein titration curves. I. General equations for impenetrable spheres. J. Am. chem. Soc. 79, 5333–5339.CrossRefGoogle Scholar
Tanford, C. & Roxby, R. (1972). Interpretation of protein titration curves. Application to lysozyme. Biochemistry II, 2192–2198.CrossRefGoogle Scholar
Tapia, O. & Johannin, G. (1981). An inhomogeneous self-consistent reaction field theory of protein core effects. Towards a quantum scheme for describing enzyme reactions. J. chem. Phys. 75, 3624–3635.CrossRefGoogle Scholar
Thoma, J. A. (1974). Separation of factors responsible for lysozyme catalysis. J. theor. Biol. 44, 305–317.CrossRefGoogle ScholarPubMed
Umeyama, H., Imamura, A., Nagata, C. & Hanano, M. (1973). A molecular orbital study on the enzymic reaction mechanism of chymotrypsin. J. theor. Biol. 41, 485–502.CrossRefGoogle Scholar
Valleau, J. P. & Whittington, S. G. (1977). A guide to Monte Carlo for statistical mechanics. I. Highways. In Modern Theoretical Chemistry, vol. 5 (ed. Berne, B. J.), pp. 137–168. New York: Plenum.Google Scholar
Valleau, J. P. & Torrie, G. M. (1977). A guide to Monte Carlo for statistical mechanics. 2. Byways. In Modern Theoretical Chemistry, vol. 5 (ed. Berne, B. J.), pp. 169–194. New York: Plenum.Google Scholar
Van Der Zwan, G. & Hynes, J. T. (1983). Nonequilibrium solvation dynamics in solution reactions. J. chem. Phys. 78, 4174–4184.CrossRefGoogle Scholar
Van Duijnen, P. TH., Thole, B. TH., Broer, R. & Nieuwpoort, W. C. (1980). Active-site α-helix in papain and the stability of the ion pair RS-…ImH+. Ab initio molecular orbital study. Int. J. Quantum Chem. 17, 651–671.CrossRefGoogle Scholar
Van Duijnen, P. Th., Thole, B. TH. & Hol, W. G. J. (1979). On the role of the active site helix in papain. An ab initia molecular orbital study. Biophys. Chem. 9, 273–280.CrossRefGoogle Scholar
Van Gunsteren, W. F., Berendsen, H. J. C., Hermans, J., Hol, W. G. J. & Postma, J. P. M. (1983). Computer-simulation of the dynamics of hydrated protein crystals and its comparison with X-ray data. Proc. natn. Acad. Sci. U.S.A. 80, 4315–4319.CrossRefGoogle ScholarPubMed
Van Gunsteren, W. F., Berendsen, H. J. C. & Rullmann, J. A. C. (1978). Inclusion of reaction fields in molecular dynamics: application to liquid water. Faraday Discuss. chem. Soc. 66, 58–70.CrossRefGoogle Scholar
Wada, A. (1976). The α-helix as an electric macro-dipole. Adv. Biophys. 9, 1–63.Google Scholar
Waleh, A. & Ingraham, L. L. (1973). A molecular orbital study of the protein-controlled bathochromic shift in a model of rhodopsin. Archs Biochem. Biophys. 156, 261–266.CrossRefGoogle Scholar
Warshel, A. (1976). Bicycle-pedal model for the first step of the vision process. Nature, Lond. 260, 679–683.CrossRefGoogle ScholarPubMed
Warshel, A. (1977 a). The consistent force field and its quantum mechanical extension. In Modern Theoretical Chemistry, vol. 7 (ed. Segal, G. A.), pp. 133–171. New York: Plenum Press.Google Scholar
Warshel, A. (1977 b). A microscopic dielectric model for reactions in water. Phil. Trans. R. Soc. Lond. 278, 111–112.Google Scholar
Warshel, A. (1977 c). Interpretation of resonance Raman spectra of biological molecules. Ann. Rev. Biophys. Bioeng. 6, 273–300.CrossRefGoogle ScholarPubMed
Warshel, A. (1978 a). A macroscopic model for calculations of chemical processes in aqueous solutions. Chem. Phys. Lett. 55, 454–458.CrossRefGoogle Scholar
Warshel, A. (1978 b). Energetics of enzyme catalysis. Proc. natn. Acad. Sci. U.S.A. 75, 5250–5254.CrossRefGoogle ScholarPubMed
Warshel, A. (1978 c). Charge stabilization mechanism in the visual and purple membrane pigments. Proc. natn. Acad. Sci. U.S.A. 75, 2558–2562.CrossRefGoogle ScholarPubMed
Warshel, A. (1979 a). Calculations of chemical processes in solutions. J. phys. Chem. 83, 1640–1652.CrossRefGoogle Scholar
Warshel, A. (1979 b). Conversion of light energy to electrostatic energy in the proton pump of Halobacterium halobium. Photochem. Photobiol. 30, 285–290.CrossRefGoogle ScholarPubMed
Warshel, A. (1981 a). Calculations of enzymic reactions: calculations of pKa, proton transfer reactions and general acid catalysis in enzymes. Biochemistry 20, 3167–3177.CrossRefGoogle ScholarPubMed
Warshel, A. (1981 b). Energetic of light-induced charge separation across membranes. Israel J. Chem. 21, 341–347.CrossRefGoogle Scholar
Warshel, A. (1981 c). Electrostatic basis of structure-function correlation in proteins. Acc. Chem. Res. 14, 284–290.CrossRefGoogle Scholar
Warshel, A. (1982 a). Dynamics of reactions in polar solvents. Semiclassical trajectory studies of electron transfer and proton transfer reactions. J. phys. Chem. 86, 2218–2224.CrossRefGoogle Scholar
Warshel, A. & Barboy, N. (1982 b). Energy storage and reaction pathways in the first step of the vision process. J. Am. chem. Soc. 104, 1469–1475.CrossRefGoogle Scholar
Warshel, A. (1982 c). Optimal protein relaxation for electron transfer in bacterial photosynthesis. In Electron Transport and Oxygen Utilization (ed. Ho, Chien), pp. 112–115. North Holland: Elsevier.Google Scholar
Warshel, A. (1984 a). Dynamics of enzymatic reactions. Proc. natn. Acad. Sci. 81, 444–448.CrossRefGoogle ScholarPubMed
Warshel, A. (1984 b). Simulating the energetics and dynamics of enzymatic reactions. In Specificity in Biological Interactions, Pontificiae Academiae Scientiarum Scripta varia, ed. Chagas, C. & Pullman, B. 55, 58–81.CrossRefGoogle Scholar
Warshel, A. & King, G. (1985). Electrostatic surface constraints in dynamical studies of polar solvents (in preparation).Google Scholar
Warshel, A. & Lappicirella, A. (1981). Calculations of ground and excited state potential surfaces for conjugated heteroatomic molecules. J. Am. chem. Soc. 103, 4664–4673.CrossRefGoogle Scholar
Warshel, A. & Levitt, M. (1976). Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. J. molec. Biol. 103, 227–249.CrossRefGoogle ScholarPubMed
Warshel, A. & Lifson, S. (1970). Consistent force field calculations. II. Crystal structures, sublimation energies, molecular and lattice vibrations, molecular conformations, and enthalpies of alkanes. J. chem. Phys. 53, 582–594.CrossRefGoogle Scholar
Warshel, A., Russell, S. T. & Churg, A. K. (1984). Macroscopic models in studies of electrostatic interactions in proteins; Limitations and applicability. Proc. natn Acad. Sci. U.S.A. (In the Press.)CrossRefGoogle Scholar
Warshel, A., Russell, S. & Weiss, R. M. (1982). Correlation of X-ray structures of enzymes with their catalytic activity; the catalytic reaction of serine proteases. Biomimatic Chemistry and Transition State Analogs (ed. Green, B. S., Ashani, Y. and Chipman, D.), pp. 267–273. Amsterdam: Elsevier.Google Scholar
Warshel, A. & Schlosser, D. W. (1981). Electrostatic control of the efficiency of light-induced electron transfer across membranes. Proc. natn. Acad. Sci. U.S.A. 78, 5564–5568.CrossRefGoogle ScholarPubMed
Warshel, A. & Weiss, R. M. (1980). An empirical valence bond approach for comparing reactions in solutions and in enzymes. J. Am. chem. Soc. 102, 6218–6226.CrossRefGoogle Scholar
Warshel, A. & Weiss, R. M. (1981 e). Energetics of heme-protein interactions in hemoglobin. J. Am. chem. Soc. 103, 446–451.CrossRefGoogle Scholar
Watts, R. O. (1974). Monte Carlo studies of liquid water. Molec. Phys. 28, 1069–1083.CrossRefGoogle Scholar
Webb, T. J. (1920). The free energy of hydration of ions and the electrostriction of the solvent. J. Am. chem. Soc. 48, 2589–2603.CrossRefGoogle Scholar
White, G. M. & Wilson, K. R. (1984). Free energy, entropy and quantum corrections from molecular dynamics for liquid water. J. chem. Phys. (In the Press.)Google Scholar
Williams, R. J. P. (1974). The separation of electrons and protons during electron transfer: the distinction between membrane potentials and transmembrane gradients. Ann. N. Y. Acad. Sci. 227, 98–107.CrossRefGoogle ScholarPubMed
Winstein, S., Clippinger, E., Fainberg, A. H. & Robinson, G. C. (1954). The nature and behavior of ion pairs in acetolysis. Chem. and Ind. 664–665.Google Scholar
Wolfenden, R., Anderson, L., Cullis, P. M. & Southgate, C. C. B. (1981). Affinities of amino acid side chains for solvent water. Bio-chemistry 20, 849–855.Google ScholarPubMed
Wüthrich, K. & Wagner, G. (1979). Nuclear magnetic resonance of labile protons in the basic pancreatic trypsin inhibitor. J. molec. Biol. 130, 1–18.CrossRefGoogle ScholarPubMed