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Calculations of Electrostatic Energies in Proteins Using Microscopic, Semimicroscopic and Macroscopic Models and Free-Energy Perturbation Approaches

  • William W. Parson
  • Arieh Warshel
Part of the Advances in Photosynthesis and Respiration book series (AIPH, volume 26)

This chapter discusses computer models for evaluating electrostatic interactions in proteins, with emphasis on calculations of the free energies of electron-transfer states in photosynthetic bacterial reaction centers. We describe the microscopic Protein Dipoles Langevin Dipoles (PDLD) method, semimicroscopic approaches including the Poisson-Boltzmann, PDLD/S and Generalized Born models, a macroscopic model with a homogeneous dielectric medium, and microscopic free-energy-perturbation methods based on molecular dynamics simulations. We also describe the use of molecular dynamics simulations to obtain free energy surfaces of the reactant and product states as functions of the reaction coordinate for electron transfer.

Keywords

Chem Phys Solvation Free Energy Molecular Dynamic Trajectory Photosynthetic Reaction Center Generalize Bear 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Alagona G, Ghio C and Kollman P (1986) Monte Carlo simulation studies of the solvation of ions. 1. Acetate ion and methylammonium cation. J Am Chem Soc 108: 185-191Google Scholar
  2. Alden RG, Parson WW, Chu ZT and Warshel A (1995) Calculations of electrostatic energies in photosynthetic reaction centers. J Am Chem Soc 117: 12284-12298Google Scholar
  3. Alden RG, Parson WW, Chu ZT and Warshel A (1996) Macroscopic and microscopic estimates of the energetics of charge separation in bacterial reaction centers. In: Michel-Beyerle ME (ed) The Reaction Center of Photosynthetic Bacteria: Structure and Dynamics, pp 105-116. Springer Verlag, BerlinGoogle Scholar
  4. Alexov EG and Gunner M (1997) Incorporating protein conformational flexibility into the calculation of the pH-dependent protein properties. Biophys J 72: 2075-2093PubMedGoogle Scholar
  5. Alexov EG and Gunner M (1999) Calculated protein and proton to QB in bacterial photosynthetic reaction centers. Biochemistry 38: 8253-8270PubMedGoogle Scholar
  6. Alexov E, Miksovska J, Baciou L, Schiffer M, Hanson DK, Sebban P and Gunner MR (2000) Modeling the effects of mutations on the free energy of the first electron transfer from − to QB in photosynthetic reaction centers. Biochemistry 39: 5940-5952PubMedGoogle Scholar
  7. Allen MP and Tildesley DJ (1987) Computer Simulations of Lipids. Oxford University Press OxfordGoogle Scholar
  8. Antosiewicz J, McCammon JA and Gilson MK (1994) Prediction of pH-dependent properties of proteins. J Mol Biol 238: 415-436PubMedGoogle Scholar
  9. Åqvist J (1996) Calculation of absolute binding free energies for charged ligands and effects of long-range electrostatic interactions. J Comput Chem 17: 1587-1597Google Scholar
  10. Åqvist J and Hansson T (1996) On the validity of electrostatic linear response in polar solvents. J Phys Chem 100: 9512-9521Google Scholar
  11. Baker NA, Sept D, Simpson J, Holst MJ and McCammon JA (2001) Electrostatics of nanosystems: Application to microtubules and the ribosome. Proc Natl Acad Sci USA 98: 10037-10041PubMedGoogle Scholar
  12. Bashford D and Case DA (2000) Generalized Born models of macromolecular solvation effects. Annu Rev Phys Chem 51: 129-152PubMedGoogle Scholar
  13. Beck DA and Daggett V (2004) Methods for molecular dynamics simulations of protein folding/unfolding in solution. Methods 34: 112-120PubMedGoogle Scholar
  14. Beck DAC, Armen RS and Daggett V (2005) Cutoff size need not strongly influence molecular dynamics results for solvated polypeptides. Biochemistry 44: 609-616PubMedGoogle Scholar
  15. Belch AC, Berkowitz M and McCammon JA (1986) Solvation structure of a sodium chloride ion-pair in water. J Am Chem Soc 108: 1755-1761Google Scholar
  16. Beveridge DL and DiCapua FM (1989) Free energy via molecular simulation: Applications to chemical and biomolecular systems. Annu Rev Biophys Biophys Chem 18: 431-492PubMedGoogle Scholar
  17. Blomberg MRA, Siegbahn PEM and Babcock GT (1998) Modeling electron transfer in biochemistry: A quantum chemical study of charge separation in Rhodobacter sphaeroides and Photosystem II. J Am Chem Soc 120: 8812-8824Google Scholar
  18. Blumberger J and Sprik M (2006) Quantum versus classical electron transfer energy as reaction coordinate for the aqueous Ru2+/Ru3+ redox reaction. Theor Chem Acc 115: 113-126Google Scholar
  19. Bogusz S, Cheatham III TE and Brooks BR (1998) Removal of pressure and free energy artifacts in charged periodic systems via net charge corrections to the Ewald potential. J Chem Phys 108: 7070-7084Google Scholar
  20. Born M (1920) Volumen und Hydratationswärme der Ionen. Z Phys 1: 45-47Google Scholar
  21. Brooks III CL and Karplus M (1983) Deformable stochastic boundaries in molecular dynamics. J Chem Phys 79: 6312-6325Google Scholar
  22. Buono GS, Figueirido F and Levy RM (1994) Intrinsic pKa’s of ionizable residues in proteins: An explicit solvent calculation for lysozyme. Proteins Struct Funct Gen 20: 85-97Google Scholar
  23. Burkert U and Allinger NL (1982) Molecular Mechanics. American Chemical Society, Washington DCGoogle Scholar
  24. Ceccarelli M and Marchi M (2003a) Simulation and modeling of the Rhodobacter sphaeroides bacterial reaction center: Structure and interactions. J Phys Chem B 107: 1423-1431Google Scholar
  25. Ceccarelli M and Marchi M (2003b) Simulation and modeling of the Rhodobacter sphaeroides bacterial reaction center II: Primary charge separation. J Phys Chem B 107: 5630-5641Google Scholar
  26. Chandrasekhar J, Spellmeyer DC and Jorgensen WL (1984) Energy component analysis for dilute aqueous solutions of Li+, Na+, Fand Cl ions. J Am Chem Soc 106: 903-910Google Scholar
  27. Constanciel R and Contreras R (1984) Self-consistent field theory of solvent effects representation by continuum models: introduction of desolvation contribution. Theor Chim Acta 65: 1-11Google Scholar
  28. Creighton S, Hwang JK, Warshel A, Parson WW and Norris J (1988) Simulating the dynamics of the primary charge separation process in bacterial photosynthesis. Biochemistry 27: 774-781Google Scholar
  29. Darden T, York DM and Pedersen L (1993) Particle mesh Ewald: An N.log(N) method for Ewald sums in large systems. J Chem Phys 98: 10089-10092Google Scholar
  30. Darden T, Toukmaji A and Pedersen LG (1997) Long-range electrostatic effects in biomolecular simulations. J Chim Phys Physico-Chimie Biol 94: 1346-1364Google Scholar
  31. Darden T, Perera L, Li LP and Pedersen L (1999) New tricks for modelers from the crystallography toolkit: The particle mesh Ewald algorithm. Struct Fold & Design 7: R55-R60Google Scholar
  32. de Leeuw SW, Perram JW and Smith ER (1986) Computer simulation of the static dielectric constant of systems with permanent electric dipoles. Annu Rev Phys Chem 37: 245-270Google Scholar
  33. Essmann U, Perera L, Berkowitz ML, Darden T, Lee H and Pedersen L (1995) A smooth particle mesh Ewald method. J Chem Phys 103: 8577-8593Google Scholar
  34. Ewald PP (1921) Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann Phys 64: 253-287Google Scholar
  35. Fan H, Mark AE, Zhu J and Honig B (2005) Comparative study of generalized Born models: Protein dynamics. Proc Natl Acad Sci USA 102: 6760-6764PubMedGoogle Scholar
  36. Figueirido F, DelBuono GS and Levy RM (1997) On the finite size corrections to the free energy of ionic hydration. J Phys Chem B 101: 5622-5623Google Scholar
  37. Forsyth WR and Robertson AD (2000) Insensitivity of perturbed carboxyl pKa values in the ovomucoid third domain to charge replacement at a neighboring residue. Biochemistry 39: 8067-8072PubMedGoogle Scholar
  38. Gallicchio E and Levy RM (2004) AGBNP: An analytic implicit solvent model suitable for molecular dynamics simulations and high-resolution modeling. J Comput Chem 25: 479-499PubMedGoogle Scholar
  39. Georgescu RE, Alexov EG and Gunner M (2002) Combining conformational flexibility and continuum electrostatics for calculating pKas in proteins. Biophys J 1731-1748Google Scholar
  40. Ghosh A, Rapp CS and Friesner RA (1998) Generalized Born model based on a surface integral formulation. J Phys Chem B 102: 10983-10990Google Scholar
  41. Gilson M and Honig B (1988) Calculation of the total electrostatic energy of a macromolecular system. Solvation energies, binding energies and conformational analysis. Proteins Struct Funct Gen 4: 7-18Google Scholar
  42. Gilson M, Rashin A, Fine R and Honig B (1985) On the calculation of electrostatic interactions in proteins. J Mol Biol 503-516Google Scholar
  43. Gilson M, Sharp KA and Honig B (1987) Calculating the electrostatic potential of molecules in solution: method and error assessment. J Comput Chem 9: 327-335Google Scholar
  44. Guenot J and Kollman P (1992) Molecular dynamics studies of a DNA-binding protein. 2. An evaluation of implicit and explicit solvent models for the molecular-dynamics simulation of the Escherichia coli Trp repressor. Protein Sci 1: 1185-11205PubMedGoogle Scholar
  45. Guenot J and Kollman P (1993) Conformational and energetic effects of truncating nonbonded interactions in an aqueous protein dynamics simulation. J Comput Chem 14: 295-311Google Scholar
  46. Gunner M and Alexov EG (2000) A pragmatic approach to structure based calculation of coupled proton and electron transfer in proteins. Biochim Biophys Acta 1485: 63-87Google Scholar
  47. Gunner MR and Honig B (1991) Electrostatic control of midpoint potentials in the cytochrome subunit of the Rhodopseudomonas viridis reaction center. Proc Natl Acad Sci USA 88: 9151-9155PubMedGoogle Scholar
  48. Gunner M, Nicholls A and Honig B (1996) Electrostatic potentials in Rhodopseudomonas viridis reaction centers: Implications for the driving force and directionality of electron transfer. J Phys Chem 100: 4277-4291Google Scholar
  49. Gunner M, Alexov EG, Torres E and Lipovaca S (1997) The importance of the protein in controling the electrochemistry of heme metalloproteins: Methods of calculation and analysis. J Biol Inorg Chem 2: 126-134Google Scholar
  50. Haffa ALM, Lin S, Williams JC, Bowen BP, Taguchi AKW, Allen JP and Woodbury NW (2004) Controlling the pathway of photosynthetic charge separation in bacterial reaction centers. J Phys Chem B 108: 4-7Google Scholar
  51. Hasegawa J and Nakatsuji H (1998) Mechanism and unidirectionality of the electron transfer in the photosynthetic reaction center of Rhodopseudomonas viridis: SAC-CI theoretical study. J Phys Chem B 102: 10420-10430Google Scholar
  52. Hawkins GD, Cramer CJ and Truhlar DG (1996) Parametrized models of aqueous free energies of solvation based on pairwise descreening of solute atomic charges from a dielectric medium. J Phys Chem 100: 19824-19839Google Scholar
  53. Heinzinger K (1985) Computer simulations of aqueous electrolyte solutions. Physica B 131: 196-216Google Scholar
  54. Hendrickson JB (1961) Molecular geometry. I. Machine computation of the common rings. J Am Chem Soc 83: 4537-4547Google Scholar
  55. Hingerty BE, Richie RH, Ferrell TL and Turner JE (1985) Dielectric effects in biopolymers. The theory of ionic saturation revisited. Biopolymers 24: 427-439Google Scholar
  56. Honig B and Nicholls A (1995) Classical electrostatics in biology and chemistry. Science 268: 1144-1149PubMedGoogle Scholar
  57. Hughes JM, Hutter MC and Hush NS (2001) Modeling the bacterial photosynthetic reaction center. 4. The structural, electrochemical, and hydrogen-bonding properties of 22 mutants of Rhodobacter sphaeroides. J Am Chem Soc 123: 8550-8563PubMedGoogle Scholar
  58. Hummer G and Szabo A (1996) Calculation of free-energy differences from computer simulations of initial and final states. J Chem Phys 105: 2004-2010Google Scholar
  59. Hummer G, Pratt LR and Garcia AE (1996) Free energy of ionic hydration. J Phys Chem 100: 1206-1215Google Scholar
  60. Hummer G, Pratt LR, Garcia AE, Berne BJ and Rick SW (1997) Electrostatic potentials and free energies of solvation of polar and charged molecules. J Phys Chem B 101: 3017-3020Google Scholar
  61. Hunenberger PH and McCammon JA (1999) Ewald artifacts in computer simulations of ionic solvation and ion-ion interaction: A continuum electrostatics study. J Chem Phys 110: 1856-1872Google Scholar
  62. Hwang J-K and Warshel A (1987) Microscopic examination of free energy relationships for electron transfer in polar solvents. J Am Chem Soc 109: 715-720Google Scholar
  63. Hwang J-K, King G, Creighton S and Warshel A (1988) Simulation of free energy relationships and dynamics of SN2 reactions in aqueous solution. J Am Chem Soc 110: 5297-5311Google Scholar
  64. Impey RW, Madden PA and McDonald IR (1983) Hydration and mobility of ions in solution. J Phys Chem 87: 5071-5083Google Scholar
  65. Ivashin N, Källenbring B, Larsson S and Hansson Ö (1998) Charge separation in photosynthetic reaction centers. J Phys Chem B 102: 5017-5022Google Scholar
  66. Johnson ET and Parson WW (2002) Electrostatic interactions in an integral membrane protein. Biochemistry 41: 6483-6494PubMedGoogle Scholar
  67. Johnson ET, Müh F, Nabedryk E, Williams JC, Allen JP, Lubitz W, Breton J and Parson WW (2002) Electronic and vibronic coupling of the special pair of bacteriochlorophylls in photosynthetic reaction centers from wild-type and mutant strains of Rhodobacter sphaeroides. J Phys Chem B 106: 11859-11869Google Scholar
  68. Kastenholz MA and Hunenberger PH (2004) Influence of artificial periodicity and ionic strength in molecular dynamics simulations of charged biomolecules employing lattice-sum methods. J Phys Chem B 108: 774-788Google Scholar
  69. Katilius E, Babendure JL, Lin S and Woodbury NW (2004) Electron transfer dynamics in Rhodobacter sphaeroides reaction center mutants with a modified ligand for the monomer bacteriochlorophyll on the active side. Photosynth Res 81: 165-180Google Scholar
  70. Kato M and Warshel A (2005) Through the channel and around the channel: Validating and comparing microscopic approaches for the evaluation of free energy profiles for ion penetration through ion channels. J Phys Chem B 109: 19516-19522PubMedGoogle Scholar
  71. Kim J, Mao J and Gunner M (2005) Are acidic and basic groups in buried proteins predicted to be ionized? J Mol Biol 348: 1283-1298PubMedGoogle Scholar
  72. King G and Warshel A (1989) A surface constrained all-atom solvent model for effective simulations of polar solutions. J Chem Phys 91: 3647-3661Google Scholar
  73. King G and Warshel A (1990) Investigation of the free energy functions for electron transfer reactions. J Chem Phys 93: 8682-8692Google Scholar
  74. King G, Lee FS and Warshel A (1991) Microscopic simulations of macroscopic dielectric constants of solvated proteins. J Chem Phys 95: 4366-4377Google Scholar
  75. Kirmaier C, He C and Holten D (2001) Manipulating the direction of electron transfer in the bacterial reaction center by swapping Phe for Tyr near BChlM (L181) and Tyr for Phe near BChlL (M208). Biochem 40: 12132-12139Google Scholar
  76. Kirmaier C, Laible PD, Czarnecki K, Hata AN, Hanson DK, Bocian DF and Holten D (2002) Comparison of M-side electron transfer in Rb. sphaeroides and Rb. capsulatus reaction centers. J Phys Chem B 106: 1799-1808Google Scholar
  77. Kirmaier C, Laible PD, Hanson DK and Holten D (2004) B-side − in reaction centers from the F(L181)Y/Y(M208)F mutant of Rhodobacter capsulatus. J Phys Chem B 108: 11827-11832Google Scholar
  78. Klein BJ and Pack GR (1983) Calculations of the spatial distribution of charge density in the environment of DNA. Biopolymers 22: 2331-2352PubMedGoogle Scholar
  79. Kollman P (1993) Free energy calculations: Applications to chemical and biochemical phenomena. Chem Rev 93: 2395-2417Google Scholar
  80. Kollman P (2000) Calculating structures and free energies of complex molecules: Combining molecular mechanics and continuum models. Acc Chem Res 33: 889-897PubMedGoogle Scholar
  81. Kozaki T, Morihashi K and Kikuchi O (1988) An MNDO effective charge model study of the solvent effect. The internal rotation about partial double bonds and the nitrogen inversion in amine. J Mol Struct 168: 265-277Google Scholar
  82. Kozaki T, Morihashi K and Kikuchi O (1989) MNDO effective charge model study of solvent effect on the potential energy surface of the SN2 reaction. J Am Chem Soc 111: 1547-1552Google Scholar
  83. Kubo R, Toda M and Hashitsume N (1985) Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer-Verlag, BerlinGoogle Scholar
  84. Kuharski RA, Bader JS, Chandler D, Sprik M, Klein ML and Impey RW (1988) Molecular model for aqueous ferrous-ferric electron transfer. J Chem Phys 89: 3248-3257Google Scholar
  85. Kuwajima S and Warshel A (1988) The extended Ewald method: A general treatment of long-range electrostatic interactions in microscopic simulations. J Chem Phys 89: 3751-3759Google Scholar
  86. Lancaster CRD, Michel H, Honig B and Gunner M (1996) Calculated coupling of electron and protein transfer in the photosynthetic reaction center of Rhodopseudomonas viridis. Biophys J 70: 2469-2492PubMedGoogle Scholar
  87. Lee FS and Warshel A (1992) A local reaction field method for fast evaluation of long-range electrostatic interactions in molecular simulations. J Chem Phys 97: 31003-3107Google Scholar
  88. Lee FS, Chu ZT, Bolger MB and Warshel A (1992) Calculations of antibody-antigen interactions: microscopic and semi-microscopic evaluation of the free energies of binding of phosphorylcholine analogs to McPC603. Protein Eng 5: 215-228PubMedGoogle Scholar
  89. Lee FS, Chu ZT and Warshel A (1993) Microscopic and semimicroscopic calculations of electrostatic energies in proteins by the POLARIS and ENZYMIX programs. J Comput Chem 14: 161-185Google Scholar
  90. Levitt M and Lifson S (1969) Refinement of protein conformations using a macromolecular energy minimization procedure. J Mol Biol 46: 269-279PubMedGoogle Scholar
  91. Levitt M, Hirshberg M, Sharon R and Daggett V (1995) Potential-energy function and parameters for simulations of the molecular dynamics of proteins and nucleic acids in solution. Comput Phys Commun 91: 215-231Google Scholar
  92. Lifson S and Warshel A (1968) A consistent force field for calculation of conformations, vibrational spectra and enthalpies of cycloalkanes and n-alkane molecules. J Chem Phys 49: 5116-5129Google Scholar
  93. Lockhart DJ and Kim PS (1993) Electrostatic screening of charge and dipole interactions with the helix backbone. Science 260: 198-202PubMedGoogle Scholar
  94. Madura JD, Briggs JM, Wade RC, Davis ME, Luty BA and McCammon JA (1995) Electrostatics and diffusion of molecules in solution: Simulations with the University of Houston Brownian Dynamics Program. Comp Phys Commun 91: 57-95Google Scholar
  95. Marchi M and Procacci P (1998) Coordinates scaling and multiple time step algorithms for simulation of solvated proteins in the NPT ensemble. J Chem Phys 109: 5194-5202Google Scholar
  96. Marchi M, Gehlen JN, Chandler D and Newton M (1993) Diabatic surfaces and the pathway for primary electron transfer in a photosynthetic reaction center. J Am Chem Soc 115: 4178-4190Google Scholar
  97. McClesky EW (2000) Ion channel selectivity using an electric stew. Biophys J 79: 1691-1692Google Scholar
  98. Mehler EL and Eichele G (1984) Electrostatic effects in wateraccessible regions of proteins. Biochemistry 23: 3887-3891Google Scholar
  99. Mehler EL and Guarnieri F (1998) A self-consistent, microenvironment modulated screened Coulomb potential approximation to calculate pH-dependent electrostatic fields in proteins. Biophys J 77: 3-22Google Scholar
  100. Mezei M and Beveridge DL (1981) Monte Carlo studies of the structure of dilute aqueous solutions of Li+, Na+, K+, F and Cl. J Chem Phys 74: 6902-6910Google Scholar
  101. Miertus S, Scrocco E and Tomasi J (1981) Electrostatic interaction of a solute with a continuum. A direct utilization of ab initio molecular potentials for the provision of solvent effects. J Chem Phys 55: 117-129Google Scholar
  102. Muegge I, Apostolakis J, Ermler U, Fritzsch G, Lubitz W and Knapp EW (1996) Shift of the special pair redox properties: Electrostatic energy computations of mutants of the reaction center from Rhodobacter sphaeroides. Biochemistry 35: 8359-8370PubMedGoogle Scholar
  103. Nichols A and Honig B (1991) A rapid finite-difference algorithm utilizing successive over-relaxation to solve the PoissonBoltzmann equation. J Comput Chem 12: 435-445Google Scholar
  104. Nielsen JE, Andersen KV, Honig B, Hooft RV, Klebe G, Vriend G and Wade RC (1999) Improving macromolecular electrostatics calculations. Protein Eng 12: 657-662PubMedGoogle Scholar
  105. Onufriev A, Case DA and Bashford D (2002) The effective Born radii in the generalized Born approximation: The importance of being perfect. J Comput Chem 23: 1297-1304PubMedGoogle Scholar
  106. Parson WW, Chu ZT and Warshel A (1990) Electrostatic control of charge separation in bacterial photosynthesis. Biochim Biophys Acta 1017: 251-272PubMedGoogle Scholar
  107. Parson WW, Chu ZT and Warshel A (1998) Reorganization energy of the initial electron-transfer step in photosynthetic bacterial reaction centers. Biophys J 74: 182-191PubMedGoogle Scholar
  108. Qiu D, Shenkin PS, Hollinger FP and Still WC (1997) The GB/SA continuum model for solvation. A fast analytical method for the calculation of approximate Born radii. J Phys Chem 101: 3005-3014Google Scholar
  109. Rabenstein B, Ullmann GM and Knapp E (1998) Calculation of protonation patterns in proteins with structural relaxation and molecular ensembles: Application to the photosynthetic reaction center. Eur Biophys J Biophys Lett 27: 626-637Google Scholar
  110. Rees DC (1980) Experimental evaluation of the effective dielectric constant of proteins. J Mol Biol 141: 323-326PubMedGoogle Scholar
  111. Rocchia W, Alexov EG and Honig B (2001) Extending the applicability of the nonlinear Poisson-Boltzmann equation: Multiple dielectric constants and multivalent ions. J Phys Chem B 105: 6507-6514Google Scholar
  112. Rocchia W, Sridharan S, Nicholls A, Alexov EG, Chiabrera A and Honig B (2002) Rapid grid-based construction of the molecular surface and the use of induced surface charge to calculate reaction field energies: Applications to the molecular systems and geometric objects. J Comput Chem 23: 128-137PubMedGoogle Scholar
  113. Saito M (1992) Molecular dynamics simulations of proteins in water without the truncation of long-range Coulomb interactions. Mol Simul 8: 321-333Google Scholar
  114. Saito M (1994) Molecular dynamics simulations of proteins in solution: Artifacts caused by the cutoff approximation. J Chem Phys 101: 4055-4061Google Scholar
  115. Schaefer M and Karplus M (1996) A comprehensive analytical treatment of continuum electrostatics. J Phys Chem 100: 1578-1599Google Scholar
  116. Scherer POJ and Fischer SF (1989) Long-range electron transfer within the hexamer of the photosynthetic reaction center Rhodopseudomonas viridis. J Phys Chem 93: 1633-1637Google Scholar
  117. Scherer POJ, Scharnagl C and Fischer SF (1995) Symmetry breakage in electronic structure of the photosynthetic reaction center of Rhodopseudomonas viridis. Chem Phys 197: 333-341Google Scholar
  118. Schutz CN and Warshel A (2001) What are the dielectric ‘constants’ of proteins and how to validate electrostatic models. Proteins Struct Funct Gen 44: 400-417Google Scholar
  119. Sham YY and Warshel A (1998) The surface constrained all atom model provides size independent results in calculations of hydration free energies. J Chem Phys 109: 7940-7944Google Scholar
  120. Sham YY, Chu ZT and Warshel A (1997) Consistent calculations of pKa’s of ionizable residues in proteins: Semi-microscopic and macroscopic approaches. J Phys Chem B 101: 4458-4472Google Scholar
  121. Sham YY, Muegge I and Warshel A (1998) The effect of protein relaxation on charge-charge interactions and dielectric constants in proteins. Biophys J 74: 1744-1753PubMedGoogle Scholar
  122. Sharp KA and Honig B (1990a) Electrostatic interactions in macromolecules: Theory and applications. Ann Rev Biophys Biophys Chem 19: 301-332Google Scholar
  123. Sharp KA and Honig B (1990b) Calculating total electrostatic energies with the nonlinear Poisson-Boltzmann equation. J Phys Chem 94: 7684-7692Google Scholar
  124. Sitkoff D, Sharp KA and Honig B (1994) Accurate calculation of hydration free energies using macroscopic solvent models. J Phys Chem 98: 1978-1988Google Scholar
  125. Steinbach PJ and Brooks BR (1994) New spherical-cutoff methods for long-range forces in macromolecular simulation. J Comput Chem 15: 667-683Google Scholar
  126. Still WC, Tempczyk A, Hawley RC and Hendrickson T (1990) Semianalytical treatment of solvation for molecular mechanics and dynamics. J Am Chem Soc 112: 6127-6129Google Scholar
  127. Tachiya M (1989) Relation between the electron transfer rate and the free energy change of reaction. J Phys Chem 93: 7050-7052Google Scholar
  128. Tanford C and Kirkwood JG (1957) Theory of protein titration curves. I. General equations for impenetrable spheres. J Am Chem Soc 79: 5333-5339Google Scholar
  129. Thompson MA, Zerner MC and Fajer J (1991) A theoretical examination of the electronic structure and spectroscopy of the photosynthetic reaction center from Rhodopseudomonas viridis. J Am Chem Soc 113: 8210-8215Google Scholar
  130. Ullmann GM and Knapp E (1999) Electrostatic models for computing protonation and redox equilibria in proteins. Eur Biophys J Biophys Lett 28: 533-551Google Scholar
  131. Valleau JP and Torrie GM (1977) A guide to Monte Carlo for statistical mechanics. 2. Byways. In: Bern BJ (ed) Modern Theoretical Chemistry, Vol 5, pp 169-194. Plenum Press, New YorkGoogle Scholar
  132. Voigt P and Knapp E (2003) Tuning heme redox potentials in the cytochrome c subunit of photosynthetic reaction centers. J Biol Chem 278: 51993-52001PubMedGoogle Scholar
  133. Warshel A (1979) Calculations of chemical processes in solutions. J Phys Chem 83: 1640-1650Google Scholar
  134. Warshel A (1981) Calculations of enzymic reactions: calculations of pKa, proton transfer reactions, and general acid catalysis reactions in enzymes. Biochemistry 20: 3167-3177PubMedGoogle Scholar
  135. Warshel A (1982) Dynamics of reactions in polar solvents. Semiclassical trajectory studies of electron-transfer and protontransfer reactions. J Phys Chem 86: 2218-2224Google Scholar
  136. Warshel A (1987) What about protein polarity? Nature 333: 15-18Google Scholar
  137. Warshel A (1991) Computer Modeling of Chemical Reactions in Enzymes and Solutions. John Wiley & Sons, New YorkGoogle Scholar
  138. Warshel A and Lappicirella VA (1981) Calculations of ground and excited-state potential surfaces for conjugated heteroatomic molecules. J Am Chem Soc 103: 4664-4673Google Scholar
  139. Warshel A and Levitt M (1976) Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. J Mol Biol 103: 227-249PubMedGoogle Scholar
  140. Warshel A and Papazyan A (1998) Electrostatic effects in macromolecules: Fundamental concepts and practical modeling. Curr Opin Struct Biol 8: 211-217PubMedGoogle Scholar
  141. Warshel A and Parson WW (1991) Computer simulations of electron transfer reactions in solution and photosynthetic reaction centers. Annu Rev Phys Chem 42: 279-309PubMedGoogle Scholar
  142. Warshel A and Parson WW (2001) Dynamics of biochemical and biophysical reactions: Insight from computer simulations. Q Rev Biophys 34: 563-670PubMedGoogle Scholar
  143. Warshel A and Russell ST (1984) Calculations of electrostatic interactions in biological systems and in solutions. Q Rev Biophys 17: 283-421PubMedGoogle Scholar
  144. Warshel A, Russell ST and Churg AK (1984) Macroscopic models for studies of electrostatic interactions in proteins: limitations and applicability. Proc Natl Acad Sci USA 81: 4785-4789PubMedGoogle Scholar
  145. Warshel A, Naray-Szabo G, Sussman F and Hwang J-K (1989) How do serine proteases really work? Biochemistry 28: 3629-3673PubMedGoogle Scholar
  146. Warshel A, Chu ZT and Parson WW (1994) On the energetics of the primary electron-transfer process in bacterial reaction centers. J Photochem Photobiol A: Chem 82: 123-128Google Scholar
  147. Warshel A, Papazyan A and Muegge I (1997) Microscopic and semimacroscopic redox calculations: What can and cannot be learned from continuum models. J Biol Inorg Chem 2: 143-152Google Scholar
  148. Warwicker J and Watson HC (1982) Calculation of the electric potential in the active site cleft due to alpha-helix dipoles. J Mol Biol 157: 671-679PubMedGoogle Scholar
  149. Weber W, Hünenberger PH and McCammon JA (2000) Molecular dynamics simulations of a polyalanine octapeptide under Ewald boundary conditions: Influence of artificial periodicity on peptide conformation. J Phys Chem B 104: 3668-3675Google Scholar
  150. Wong CF and McCammon JA (1986) Dynamics and design of enzymes and inhibitors. J Am Chem Soc 108: 3830-3832Google Scholar
  151. York DM, Darden T and Pedersen LG (1993) The effect of long-range electrostatic interactions in simulations of macromolecular crystals. A comparison of the Ewald and truncated list methods. J Chem Phys 99: 8345-8348Google Scholar
  152. Zhou HX and Szabo A (1995) Microscopic formulation of the Marcus theory of electron transfer. J Chem Phys 103: 3481-3494Google Scholar
  153. Zhou Z and Swenson RP (1995) Electrostatic effects of surface acidic amino acid residues on oxidation-reduction potentials of the flavodoxin from Desulfovibrio vulgaris (Hildenborough). Biochemistry 34: 3183-3192PubMedGoogle Scholar
  154. Zhu J, Alexov EG and Honig B (2005) Comparative study of generalized Born models: Born radii and peptide folding. J Phys Chem B 109: 3008-3022PubMedGoogle Scholar
  155. Zwanzig RW (1954) High-temperature equation of state by a perturbation method. I. Nonpolar gases. J Chem Phys 22: 1420-1426Google Scholar

Copyright information

© Springer Science+Business Media B.V 2008

Authors and Affiliations

  • William W. Parson
    • 1
  • Arieh Warshel
    • 2
  1. 1.Department of BiochemistryUniversity of WashingtonSeattleUSA
  2. 2.Department of ChemistryUniversity of Southern CaliforniaLos AngelesUSA

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