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Calculations of electrostatic interactions in biological systems and in solutions

  • Arieh Warshel (a1) and Stephen T. Russell (a1)
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.

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Adams, D. J. (1980). Computer simulation of highly polar liquids: the hard sphere plus point dipole potential. Molec. Phys. 40, 12611271.
Adelman, S. A. & Deutch, J. M. (1974). Exact solution of the mean spherical model for strong electrolytes in polar solvents. J. Chem. Phys. 60, 39353949.
Adman, E. T. (1979). A comparison of the structure of electron transfer proteins. Biochim. biophys. acta 549, 107144.
Alder, B. J. & Pollock, E. L. (1981). Simulation of polar and polarizable fluids. A. Rev. phys. Chem. 32, 311329.
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, 541546.
Allen, L. C. (1981). The catalytic function of active site side chains in well-characterized enzymes. Ann. N. Y. Acad. Sci. 367, 383406.
Amos, A. T. & Burrows, B. L. (1973). Solvent-shift effects on electronic spectra and excited-state dipole moments and polarizabilities. Adv. Quantum Chem. I, 289313.
Anderson, J. B. (1973). Statistical theories of chemical reactions. Distributions in the transition region. J. chem. Phys. 58, 46844697.
Angyan, J. & Naray-Szabo., G. (1983). Comparison of protein electrostatic potential along the catalytic triad of serine proteinases. J. theor. Biol. 103, 349356.
Barker, J. A. & Watts, R. O. (1969). Structure of water; a Monte Carlo calculation. Chem. Phys. Lett. 3, 144145.
Barnes, P., Pinney, J. L., Nicholas, J. D. & Quinn, J. E. (1979). Cooperative effects in simulated water. Nature, Lond. 282, 459464.
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, 87121. Academic Press.
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. 331342. Dordrecht, Holland: Reidel.
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, 23752389.
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, 7583.
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, 425443.
Born, M. (1920). Volumen and Hydrationswärme der lonen. Z. Phys. I, 4548.
Born, M. & Huang, K. (1954). Dynamical Theory of Crystal Lattices, p. 248. Oxford University Press.
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, 66946699.
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, 51975205.
Brand, L. & Gohlke, J. R. (1971). Nanosecond time-resolved fluorescence spectra of a protein-dye complex. J. biol. Chem. 246, 23172319.
Butler, P. J. G. & Klug, A. (1978). The assembly of a virus. Scient. Am. 239, 6269.
Careri, G., Fasella, P. & Gratton, E. (1979). Enzyme dynamics: the Statistical physics approach. A. Rev. Biophys. Bioeng. 8, 6997.
Carey, P. R. (1982). Biochemical Applications of Raman and Resonance Raman Spectroscopies. New York: Academic Press.
Carey, P. R. & Storer, A. C. (1983). Molecular details of enzyme-substrate transients by resonance Raman spectroscophy. Acc. chem. Res. 16, 455460.
Chandrasekhar, J. & Jorgensen, W. L. (1982). The nature of dilute solutions of sodium ions in water, methanol and tetrahydrofuran. J. chem. Phys. 77, 50805089.
Choux, G. & Benoit, R. L. (1969). Solvation in dipolar aprotic solvents. Ionic enthalpies of transfer. J. Am. chem. Soc. 91, 62216224.
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, 16831693.
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, 55315544.
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, 756766.
Cooper, A. (1979). Energy uptake in the first step of the visual excitation. Nature, Lond. 282, 531533.
Coulson, C. A. & Danielsson, U. (1954). Ionic and covalent contributions to the hydrogen bond. Part II. Ark. Fys. 8, 245255.
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, 162166.
Dawson, R. M. C., Elliot, D. C., Elliot, W. H. & Jones, K. M. (eds) (1974). Data for Biochemical Research, 2nd ed.Oxford: Clarendon Press.
Debye, P. (1912). Einige Resultate einer kinetischen Theorie der Isolatoren. Phys. Z. 13, 97100.
Debye, P. (1929). Polar Molecules. New York: Dover.
Deisenhofer, J. & Steigemann, W. (1975). Crystallographic refinement of the structure of bovine pancreatic trypsin inhibitor at 1·5 Ångstroms. Acta Crystallogr. B 31, 238250.
Dunmur, D. A. (1972). The local electric field in anisotropic molecular crystals. Molec. Phys. 23, 109115.
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, 354363.
Fernandez, M. S. & Fromherz, P. (1977). Lipid pH indicators as probes of electrical potential and polarity in micelles. J. phys. Chem. 81, 17551761.
Fersht, A. R. (1972). Conformational equilibria in α- and δ-chymotrypsin. The energetics and importance of the salt bridge. J. molec. Biol. 64, 497509.
Frahm, J., Diekmann, S. & Haase, A. (1980). Electrostatic properties of ionic micelles in aqueous solutions. Ber. BunsenGes. phys. Chem. 84, 566571.
Friedman, H. L. & Krishnan, C. V. (1973). Thermodynamics of Ion Hydration in Water, A Comprehensive Treatise, vol. 3 (ed. Franks, F.), pp. 1118. New York: Plenum.
Frohlich, H. (1958). Theory of Dielectrics. London: Oxford University Press.
Gafni, A., Detoma, R. P., Manrow, R. E. & Brand, L. (1977). Nanosecond decay studies of a fluorescence probe bound to apomyoglobin. Biophys. J. 17, 155168.
Gavish, B. & Werber, M. M. (1979). Viscosity-dependent structural fluctuations in enzyme catalysis. Biochemistry 18, 12691275.
Gelin, B. R. & Karplus, M. (1979). Side-chain torsional potentials: effect of dipeptide, protein and solvent environment. Biochemistry 18, 12561268.
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, 333341.
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, 467483.
Greenberg, D. A., Barry, C. D. & Marshall, G. R. (1978). Investigation and parametrization of molecular dielectric function. J. Am. chem. Soc. 100, 40204026.
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, 53005310.
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, 53195327.
Hagler, A. T. & Moult, J. (1978). Computer simulation of solvent structure around biological macromolecules. Nature 272, 222226.
Hayes, D. M. & Kollman, P. A. (1976). Electrostatic potentials of proteins. I. Carboxypeptidase A. J. Am. chem. Soc. 98, 33353345.
Henderson, R. (1977). The purple membrane from Halobacterium halobium. A. Rev. Biophys. Bioeng. 6, 87109.
Hill, T. L. (1962). An Introduction to Statistical Thermodynamics, pp. 205209. Addison-Wesley.
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, 41334144.
Hirshfelder, J. O., Curtiss, C. F. & Bird, R. B. (1954). Molecular Theory of Gases and Liquids. New York: Wiley.
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, 443446.
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, 45934599.
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, 70847086.
Honig, B. H. & Hubbell, W. L. (1983). Do ‘Salt-Bridges’ exist in membrane proteins. Biophys. J. 41, 203.
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. 7178. New York: Wiley.
Irving, C. S., Byers, G. W. & Leermakers, P. A. (1970). Spectroscopic model for the visual pigments. Influence of microenvironmental polarizability. Biochemistry 9, 858864.
Jackson, J. D. (1975). Classical Electrodynamics. New York: Wiley.
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, 321327.
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, 5258.
Jordan, P. C. (1981). Energy barriers for passage of ions through channels. Exact solution of two electrostatic problems. Biophys. Chem. 13, 203212.
Jorgensen, W. L. (1978). Ab initio molecular orbital study of the geometric properties and protonation of alkyl chloride. J. Am. chem. Soc. 100, 10571061.
Jorgensen, W. L. (1981). Transferable intermolecular potential functions for water, alcohols, and ethers. Application to liquid water. J. Am. chem. Soc. 103, 335340.
Jorgensen, W. L. (1982). Revised TIPS for simulations of liquid water and aqueous solutions. J. chem. Phys. 77, 41564163.
Jorgensen, W. L. & Madura, J. D. (1983). Solvation and conformations of methanol in water. J. Am. chem. Soc. 105, 14071413.
Kassner, R. J. (1972). Effects of non-polar environments on the Redox potentials of heme complexes. Proc. natn. Acad. Sci. U.S.A. 69, 22632267.
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, 26742677.
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, 43514355.
Kebarle, P. (1977). Ion thermochemistry and solvation from gas phase ion equilibria. A. Rev. phys. Chem. 28, 445476.
Keck, J. C. (1962). Statistical investigation of dissociation cross-sections for diatoms. Discuss. Faraday Soc. 33, 173182.
Kessler, H. & Feigel, M. (1982). Direct observation of recombination of ion pairs by dynamic NMR spectroscopy. Acc. chem. Res. 15, 28.
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, 31893193.
Kirkwood, J. G. (1934). Theory of solutions of molecules containing widely separated charges with special application to zwitterions. J. chem. Phys. 2, 351361.
Kirkwood, J. G. & Westheimer, F. H. (1938). The electrostatic influence of substituents on the dissociation constants of organic acids: I. J. chem. Phys. 6, 506512.
Kirkwood, J. G. (1939). The dielectric polarization of polar liquids. J. chem. Phys. 7, 911919.
Kitagawa, T., Ozaki, Y. & Kyogoku, Y. (1978). Resonance Raman studies on the ligand–iron interactions in hemoproteins and metalloporphyrins. Adv. Biophys. II, 153196.
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, 277286.
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, 319334.
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, 29552961.
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, 25832621.
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, 499508.
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, 259266.
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, 18871899.
Levitt, D. G. (1978). Electrostatic calculations for an ion channel. I. Energy and potential profiles and interactions between ions. Biophys. J. 22, 209219.
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, 4858.
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, 51165129.
Linderstrom-Lang, K. (1924). On the ionization of proteins. C.r. Trav. Lab. Carlsberg 15, 129.
Locke, M. J. & McIver, R. T. Jr. (1983). Effect of solvation on the acid/base properties of glycine. J. Am. chem. Soc. 105, 42264232.
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, 89104.
Lorentz, H. A. (1909). Theory of Electrons. Leipzig: Teubner.
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, 382386.
McDonald, I. R. & Klein, M. (1978). Intermolecular potentials and the simulation of liquid water. J. chem. Phys. 68, 48754877.
McRae, E. G. (1957). Theory of solvent effects on molecular electronic spectra. Frequency shifts. J. phys. Chem. 61, 562572.
Marcus, R. A. (1964). Chemical and electrochemical electron-transfer theory. A. Rev. phys. Chem. 15, 155196.
Mataga, N. & Kubota, T. (1970). Molecular Interactions and Electronic Spectra. New York: Marcel Dekker.
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, 19191928.
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, 169171.
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, 31563166.
Merzbacher, E. (1970). Quantum Mechanics, 2nd ed.New York: ohn Wiley.
Metzger, R. M. (1981). INDO and MINDO/3 atom-in-molecule polarizabilities. J. chem. Phys. 74, 34443457.
Metzger, R. M. & Rhee, C. H. (1982). CNDO/2-FPP polarizabilities. Molec. Cryst. Liq. Cryst. 85, 8187.
Mezei, M. & Beveridge, D. L. (1982). Further quasicomponent distribution function analysis of liquid water. Temperature dependent of the results. J. chem. Phys. 76, 593600.
Mitchell, P. (1977). Epilogue: from energetic abstraction to biochemical mechanism. In Symposia of the Society for General Microbiology, no. 27, pp. 384423.
Nagel, J. F. & Mille, M. (1981). Molecular models of proton pumps. J. chem. Phys. 74, 13671372.
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. 267336. Amsterdam: Elsevier.
Onsager, L. (1936). Electric moments of molecules in liquids. J. Am. chem. Soc. 58, 14861493.
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, 162167.
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, 2237.
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, 43694375.
Owicki, J. C. & Scheraga, H. A. (1977). Monte Carlo calculations in the isothermal isobaric ensemble. I. Liquid water. J. Am. chem. Soc. 99, 74037412.
Pangali, C., Rao, M. & Berne, B. J. (1979). A Monte Carlo simulation of the hydrophobic interaction. J. chem. Phys. 71, 29752981.
Parsegian, A. (1969). Energy of an ion crossing a low dielectric membrane: solutions to four relevant electrostatic problems. Nature, Lond. 221, 844846.
Parsegian, A. (1975). Ion–membrane interactions as structural forces. Ann. N.Y. Acad. Sci. 264, 161179.
Parson, S. M. & Rafferty, M. A. (1972). Ionization behavior of the catalytic carboxyls of lysozymes. Biochemistry II, 16231633.
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, 51835190.
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, 23342339.
Perutz, M. F. (1970). Stereochemistry of cooperative effects in haemoglobin. Nature, Lond. 228, 726739.
Perutz, M. F. (1978). Electrostatic effects in proteins. Science, N. Y. 201, 11871191.
Phelps, D. J., Schneider, H. & Carey, P. R. (1981). Correlation between reactivity and structure of some chromophoric acylchymotrypsins by resonance Ramam spectroscopy. Biochemistry 20, 34473959.
Pollock, E. L. & Alder, B. J. (1977). Effective field of a dipole in polarizable fluids. Phys. Rev. Lett. 39, 299302.
Pollock, E. L. & Alder, B. J. (1978). Changed particles in polarizable fluids. Phys. Rev. Lett. 41, 903906.
Pollock, E. L. & Alder, B. J. (1980). Static dielectric properties of Stockmayer fluids. Physica 102 A, 121.
Pollock, E. L., Alder, B. J. & Patey, G. N. (1981). Static dielectric properties of polarizable Stockmayer fluids. Physica 108 A, 1426.
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, 4951.
Pople, J. A. (1954). The statistical mechanics of assemblies of axially symmetric molecules. I. General theory. Proc. R. Soc. Lond. A 221, 498507.
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, 199202.
Pullman, A. & Pullman, B. (1975). New paths in the molecular orbital approach to solvation in biological molecules. Q. Rev. Biophys. 7, 506566.
Purcell, E. M. (1965). Electricity and Magnetism. New York: McGraw-Hill.
Rahman, A. & Stillinger, F. H. (1971). Molecular dynamics study of liquid water. J. chem. Phys. 55, 33363359.
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, 17731798.
Rees, D. C. (1980). Experimental evaluation of the effective dielectric constant of proteins. J. molec. Biol. 141, 323326.
Revetllat, J. A. & Bertran, J. (1978). Theoretical study of lithium-fluoride ion pair in aqueous solution. Gazz. chim. Ital. 108, 149151.
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, 635659.
Salem, L. (1982). Electrons in Chemical Reactions; First Principles, pp. 240242. New York: Wiley.
Salemme, F. R. (1977). Structure and function of cytochrome c. A. Rev. Biochem. 46, 299329.
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, 26062610.
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, 432436.
Scheiner, S. & Lipscomb, W. N. (1977). Molecular orbital studies of enzyme activity. IV. Hydrolysis of peptides by carboxypeptidase A. J. Am. chem. Soc. 99, 34663472.
Scheraga, H. A. (1979). Interactions in aqueous solution. Acct chem. Res. 12, 713.
Schultan, K. & Tavan, P. (1978). A mechanism for the light-driven proton pump of Halobacterium halobiwn. Nature, Lond. 272, 8586.
Sheridan, R. P. & Allen, L. C. (1980 a). The nature of hydrogen bonding in electron-transport proteins. Chem. Phys. Lett. 69, 600603.
Sheridan, R. P. & Allen, L. C. (1980 b). The electrostatic potential of the alpha helix. Biophys. Chem. II, 133136.
Sheridan, R. P. & Allen, L. C. (1981). The active site electrostatic potential of human carbonic anhydrase. J. Am. chem. Soc. 103, 15441550.
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, 50525057.
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, 13521358.
Stillinger, F. H. & Rahman, A. (1974). Improved simulation of liquid water by molecular dynamics. J. chem. Phys. 60, 15451557.
Stillinger, F. H. (1977). Theoretical approaches to the intermolecular nature of water. Phil. Trans. R. Soc. Lond. 278, 97110.
Stockmayer, W. H. (1941). Second virial coefficients of polar gases. J. chem. Phys. 9, 398402.
Stoeckenius, W., Lozier, R. H. & Bogomolni, R. A. (1979). Bacteriorhodopsin and the purple membrane of halobacteria. Biochim. biophys. Acta 505, 215278.
Suzuki, H., Komatsu, T. & Kitojima, H. (1974). Theory of the optical property of visual pigment. J. phys. Soc. Japan 37, 177185.
Tanford, C. & Kirkwood, J. G. (1957). Theory of protein titration curves. I. General equations for impenetrable spheres. J. Am. chem. Soc. 79, 53335339.
Tanford, C. & Roxby, R. (1972). Interpretation of protein titration curves. Application to lysozyme. Biochemistry II, 21922198.
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, 36243635.
Thoma, J. A. (1974). Separation of factors responsible for lysozyme catalysis. J. theor. Biol. 44, 305317.
Umeyama, H., Imamura, A., Nagata, C. & Hanano, M. (1973). A molecular orbital study on the enzymic reaction mechanism of chymotrypsin. J. theor. Biol. 41, 485502.
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. 137168. New York: Plenum.
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. 169194. New York: Plenum.
Van Der Zwan, G. & Hynes, J. T. (1983). Nonequilibrium solvation dynamics in solution reactions. J. chem. Phys. 78, 41744184.
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, 651671.
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, 273280.
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, 43154319.
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, 5870.
Wada, A. (1976). The α-helix as an electric macro-dipole. Adv. Biophys. 9, 163.
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, 261266.
Warshel, A. (1976). Bicycle-pedal model for the first step of the vision process. Nature, Lond. 260, 679683.
Warshel, A. (1977 a). The consistent force field and its quantum mechanical extension. In Modern Theoretical Chemistry, vol. 7 (ed. Segal, G. A.), pp. 133171. New York: Plenum Press.
Warshel, A. (1977 b). A microscopic dielectric model for reactions in water. Phil. Trans. R. Soc. Lond. 278, 111112.
Warshel, A. (1977 c). Interpretation of resonance Raman spectra of biological molecules. Ann. Rev. Biophys. Bioeng. 6, 273300.
Warshel, A. (1978 a). A macroscopic model for calculations of chemical processes in aqueous solutions. Chem. Phys. Lett. 55, 454458.
Warshel, A. (1978 b). Energetics of enzyme catalysis. Proc. natn. Acad. Sci. U.S.A. 75, 52505254.
Warshel, A. (1978 c). Charge stabilization mechanism in the visual and purple membrane pigments. Proc. natn. Acad. Sci. U.S.A. 75, 25582562.
Warshel, A. (1979 a). Calculations of chemical processes in solutions. J. phys. Chem. 83, 16401652.
Warshel, A. (1979 b). Conversion of light energy to electrostatic energy in the proton pump of Halobacterium halobium. Photochem. Photobiol. 30, 285290.
Warshel, A. (1981 a). Calculations of enzymic reactions: calculations of pKa, proton transfer reactions and general acid catalysis in enzymes. Biochemistry 20, 31673177.
Warshel, A. (1981 b). Energetic of light-induced charge separation across membranes. Israel J. Chem. 21, 341347.
Warshel, A. (1981 c). Electrostatic basis of structure-function correlation in proteins. Acc. Chem. Res. 14, 284290.
Warshel, A. (1982 a). Dynamics of reactions in polar solvents. Semiclassical trajectory studies of electron transfer and proton transfer reactions. J. phys. Chem. 86, 22182224.
Warshel, A. & Barboy, N. (1982 b). Energy storage and reaction pathways in the first step of the vision process. J. Am. chem. Soc. 104, 14691475.
Warshel, A. (1982 c). Optimal protein relaxation for electron transfer in bacterial photosynthesis. In Electron Transport and Oxygen Utilization (ed. Ho, Chien), pp. 112115. North Holland: Elsevier.
Warshel, A. (1984 a). Dynamics of enzymatic reactions. Proc. natn. Acad. Sci. 81, 444448.
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, 5881.
Warshel, A. & King, G. (1985). Electrostatic surface constraints in dynamical studies of polar solvents (in preparation).
Warshel, A. & Lappicirella, A. (1981). Calculations of ground and excited state potential surfaces for conjugated heteroatomic molecules. J. Am. chem. Soc. 103, 46644673.
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, 227249.
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, 582594.
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.)
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. 267273. Amsterdam: Elsevier.
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, 55645568.
Warshel, A. & Weiss, R. M. (1980). An empirical valence bond approach for comparing reactions in solutions and in enzymes. J. Am. chem. Soc. 102, 62186226.
Warshel, A. & Weiss, R. M. (1981 e). Energetics of heme-protein interactions in hemoglobin. J. Am. chem. Soc. 103, 446451.
Watts, R. O. (1974). Monte Carlo studies of liquid water. Molec. Phys. 28, 10691083.
Webb, T. J. (1920). The free energy of hydration of ions and the electrostriction of the solvent. J. Am. chem. Soc. 48, 25892603.
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.)
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, 98107.
Winstein, S., Clippinger, E., Fainberg, A. H. & Robinson, G. C. (1954). The nature and behavior of ion pairs in acetolysis. Chem. and Ind. 664665.
Wolfenden, R., Anderson, L., Cullis, P. M. & Southgate, C. C. B. (1981). Affinities of amino acid side chains for solvent water. Bio-chemistry 20, 849855.
Wüthrich, K. & Wagner, G. (1979). Nuclear magnetic resonance of labile protons in the basic pancreatic trypsin inhibitor. J. molec. Biol. 130, 118.
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Quarterly Reviews of Biophysics
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