Modeling electrostatic effects in proteins.

Electrostatic energies provide what is perhaps the most effective tool for structure-function correlation of biological molecules. This review considers the current state of simulations of electrostatic energies in macromolecules as well as the early developments of this field. We focus on the relationship between microscopic and macroscopic models, considering the convergence problems of the microscopic models and the fact that the dielectric 'constants' in semimacroscopic models depend on the definition and the specific treatment. The advances and the challenges in the field are illustrated considering a wide range of functional properties including pK(a)'s, redox potentials, ion and proton channels, enzyme catalysis, ligand binding and protein stability. We conclude by pointing out that, despite the current problems and the significant misunderstandings in the field, there is an overall progress that should lead eventually to quantitative descriptions of electrostatic effects in proteins and thus to quantitative descriptions of the function of proteins.

[1]  Alan M. Ferrenberg,et al.  Optimized Monte Carlo data analysis. , 1989, Physical Review Letters.

[2]  Nathan A. Baker,et al.  Electrostatics of nanosystems: Application to microtubules and the ribosome , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[3]  B. Honig,et al.  ELECTROSTATIC POTENTIALS IN RHODOPSEUDOMONAS VIRIDIS REACTION CENTERS : IMPLICATIONS FOR THE DRIVING FORCE AND DIRECTIONALITY OF ELECTRON TRANSFER , 1996 .

[4]  Arieh Warshel,et al.  A local reaction field method for fast evaluation of long‐range electrostatic interactions in molecular simulations , 1992 .

[5]  K. Sharp,et al.  Macroscopic models of aqueous solutions : biological and chemical applications , 1993 .

[6]  Helmut Grubmüller,et al.  The dynamics and energetics of water permeation and proton exclusion in aquaporins. , 2005, Current opinion in structural biology.

[7]  S. Creighton,et al.  Role of arginine-38 in regulation of the cytochrome c oxidation-reduction equilibrium. , 1989, Biochemistry.

[8]  A. Warshel Electrostatic basis of structure-function correlation in proteins , 1981 .

[9]  M. Gilson,et al.  The statistical-thermodynamic basis for computation of binding affinities: a critical review. , 1997, Biophysical journal.

[10]  Arieh Warshel,et al.  Exploring the origin of the ion selectivity of the KcsA potassium channel , 2003, Proteins.

[11]  S. Hammes‐Schiffer Quantum-classical simulation methods for hydrogen transfer in enzymes: a case study of dihydrofolate reductase. , 2004, Current opinion in structural biology.

[12]  Charles L. Brooks,et al.  Thermodynamics of aqueous solvation: Solution properties of alcohols and alkanes , 1987 .

[13]  V. Pande,et al.  Electric Fields at the Active Site of an Enzyme: Direct Comparison of Experiment with Theory , 2006, Science.

[14]  M. Karplus,et al.  Ion transport in the gramicidin channel: free energy of the solvated right-handed dimer in a model membrane , 1993 .

[15]  Peter C. Jordan,et al.  Water and ion permeation in bAQP1 and GlpF channels: a kinetic Monte Carlo study. , 2004, Biophysical journal.

[16]  D. Chandler,et al.  Diabatic surfaces and the pathway for primary electron transfer in a photosynthetic reaction center , 1993 .

[17]  R. Friesner,et al.  Generalized Born Model Based on a Surface Integral Formulation , 1998 .

[18]  K. Sharp,et al.  Electrostatic interactions in macromolecules: theory and applications. , 1990, Annual review of biophysics and biophysical chemistry.

[19]  A. Warshel,et al.  What are the dielectric “constants” of proteins and how to validate electrostatic models? , 2001, Proteins.

[20]  K. Schulten,et al.  Electrostatic tuning of permeation and selectivity in aquaporin water channels. , 2003, Biophysical journal.

[21]  M. Karplus,et al.  Stochastic boundary conditions for molecular dynamics simulations of ST2 water , 1984 .

[22]  R. Nussinov,et al.  Conservation of polar residues as hot spots at protein interfaces , 2000, Proteins.

[23]  R. Fox,et al.  Classical Electrodynamics, 3rd ed. , 1999 .

[24]  Paul Beroza,et al.  Calculation of amino acid pKaS in a protein from a continuum electrostatic model: Method and sensitivity analysis , 1996, J. Comput. Chem..

[25]  S C Harvey,et al.  Dielectric relaxation spectra of water adsorbed on lysozyme. , 1972, The Journal of physical chemistry.

[26]  T. L. Hill The Electrostatic Contribution to Hindered Rotation in Certain Ions and Dipolar Ions in Solution. I , 1943 .

[27]  Arieh Warshel,et al.  Computer Simulation Studies of the Catalytic Mechanism of Human Aldose Reductase , 2000 .

[28]  M. Michel-beyerle The reaction center of photosynthetic bacteria : structure and dynamics , 1996 .

[29]  A. Warshel,et al.  EFFECT OF SOLVENT DISCRETENESS ON SOLVATION , 1998 .

[30]  Johannes Buchner,et al.  Protein folding handbook , 2005 .

[31]  Michael Nilges,et al.  The impact of protein flexibility on protein–protein docking , 2004, Proteins.

[32]  A. Warshel,et al.  Electrostatic effects in macromolecules: fundamental concepts and practical modeling. , 1998, Current opinion in structural biology.

[33]  A. Warshel,et al.  Control of the redox potential of cytochrome c and microscopic dielectric effects in proteins. , 1986, Biochemistry.

[34]  E. Kosower An introduction to physical organic chemistry , 1968 .

[35]  Arieh Warshel,et al.  Converting conformational changes to electrostatic energy in molecular motors: The energetics of ATP synthase , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[36]  Daniel Herschlag,et al.  Testing Electrostatic Complementarity in Enzyme Catalysis: Hydrogen Bonding in the Ketosteroid Isomerase Oxyanion Hole , 2006, PLoS biology.

[37]  A. Warshel,et al.  Structure-energy analysis of the role of metal ions in phosphodiester bond hydrolysis by DNA polymerase I , 1995 .

[38]  N. Oppenheimer,et al.  Structure and mechanism , 1989 .

[39]  K. Schulten,et al.  The mechanism of proton exclusion in aquaporin channels , 2004, Proteins.

[40]  Vernon Ca The mechanisms of hydrolysis of glycosides and their revelance to enzyme-catalysed reactions. , 1967 .

[41]  Arieh Warshel,et al.  Consistent Calculations of pKa's of Ionizable Residues in Proteins: Semi-microscopic and Microscopic Approaches , 1997 .

[42]  M. Karplus,et al.  Evaluation of the configurational entropy for proteins: application to molecular dynamics simulations of an α-helix , 1984 .

[43]  Martin Almlöf,et al.  Free energy calculations and ligand binding. , 2003, Advances in protein chemistry.

[44]  J. McDouall,et al.  Assessment of the Langevin dipoles solvation model for Hartree-Fock wavefunctions , 1996 .

[45]  Heinz Rüterjans,et al.  Continuum electrostatic analysis of irregular ionization and proton allocation in proteins , 2002, Proteins.

[46]  Manfred Eigen,et al.  Proton Transfer, Acid-Base Catalysis, and Enzymatic Hydrolysis. Part I: ELEMENTARY PROCESSES†‡ , 1964 .

[47]  M. B. Pinto,et al.  Optimized δ expansion for relativistic nuclear models , 1997, nucl-th/9709049.

[48]  A. Warshel Charge stabilization mechanism in the visual and purple membrane pigments. , 1978, Proceedings of the National Academy of Sciences of the United States of America.

[49]  M. Karplus,et al.  Self-guided enhanced sampling methods for thermodynamic averages , 2003 .

[50]  M. Dewar,et al.  Alternative view of enzyme reactions. , 1985, Proceedings of the National Academy of Sciences of the United States of America.

[51]  A. Warshel,et al.  Calculations of antibody-antigen interactions: microscopic and semi-microscopic evaluation of the free energies of binding of phosphorylcholine analogs to McPC603. , 1992, Protein engineering.

[52]  J. Wendoloski,et al.  Molecular dynamics effects on protein electrostatics , 1989, Proteins.

[53]  A. Warshel,et al.  Why does the Ras switch “break” by oncogenic mutations? , 2004, Proteins.

[54]  H. Berendsen,et al.  The α-helix dipole and the properties of proteins , 1978, Nature.

[55]  D. Baker,et al.  A simple physical model for binding energy hot spots in protein–protein complexes , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[56]  G. Moore,et al.  Control of metalloprotein redox potentials: what does site-directed mutagenesis of hemoproteins tell us? , 1997, JBIC Journal of Biological Inorganic Chemistry.

[57]  Matthias Rarey,et al.  Small Molecule Docking and Scoring , 2001 .

[58]  J. V. van Beek,et al.  The contribution of electrostatic and van der Waals interactions to the stereospecificity of the reaction catalyzed by lactate dehydrogenase. , 1997, Biophysical journal.

[59]  Martin Almlöf,et al.  Probing the effect of point mutations at protein-protein interfaces with free energy calculations. , 2006, Biophysical journal.

[60]  Arieh Warshel,et al.  A surface constrained all‐atom solvent model for effective simulations of polar solutions , 1989 .

[61]  A. Warshel,et al.  Computer simulation studies of the fidelity of DNA polymerases , 2003, Biopolymers.

[62]  P A Kollman,et al.  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 , 1992, Protein science : a publication of the Protein Society.

[63]  R. Kassner,et al.  Effects of nonpolar environments on the redox potentials of heme complexes. , 1972, Proceedings of the National Academy of Sciences of the United States of America.

[64]  A. Warshel Calculations of enzymatic reactions: calculations of pKa, proton transfer reactions, and general acid catalysis reactions in enzymes. , 1981, Biochemistry.

[65]  E. Lattman,et al.  Experimental measurement of the effective dielectric in the hydrophobic core of a protein. , 1997, Biophysical chemistry.

[66]  A. Warshel,et al.  Reorganization energy of the initial electron-transfer step in photosynthetic bacterial reaction centers. , 1998, Biophysical journal.

[67]  Kenji Morihashi,et al.  MNDO-effective charge model study of solvent effect on the potential energy surface of the SN2 reaction , 1989 .

[68]  J. Deisenhofer,et al.  The Photosynthetic Reaction Center , 1993 .

[69]  A T Brünger,et al.  Microscopic theory of the dielectric properties of proteins. , 1991, Biophysical journal.

[70]  Eaton E Lattman,et al.  Experimental pK(a) values of buried residues: analysis with continuum methods and role of water penetration. , 2002, Biophysical journal.

[71]  A. Warshel What about protein polarity? , 1987, Nature.

[72]  D. Truhlar,et al.  Quantum Mechanical Dynamical Effects in an Enzyme-Catalyzed Proton Transfer Reaction , 1999 .

[73]  B. Honig,et al.  On the calculation of electrostatic interactions in proteins. , 1985, Journal of molecular biology.

[74]  R. H. Ritchie,et al.  Dielectric effects in biopolymers: The theory of ionic saturation revisited , 1985 .

[75]  David A. Case,et al.  Effective Born radii in the generalized Born approximation: The importance of being perfect , 2002, J. Comput. Chem..

[76]  L. R. Scott,et al.  Electrostatics and diffusion of molecules in solution: simulations with the University of Houston Brownian dynamics program , 1995 .

[77]  A. Warshel,et al.  How important are entropic contributions to enzyme catalysis? , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[78]  B. Honig,et al.  New Model for Calculation of Solvation Free Energies: Correction of Self-Consistent Reaction Field Continuum Dielectric Theory for Short-Range Hydrogen-Bonding Effects , 1996 .

[79]  J. Pfeilschifter,et al.  Physiology and pathophysiology of sphingolipid metabolism and signaling. , 2000, Biochimica et biophysica acta.

[80]  E. Lattman,et al.  High apparent dielectric constants in the interior of a protein reflect water penetration. , 2000, Biophysical journal.

[81]  M. Perutz,et al.  Identification of residues contributing to the Bohr effect of human haemoglobin. , 1980, Journal of molecular biology.

[82]  Arieh Warshel,et al.  Langevin Dipoles Model for ab Initio Calculations of Chemical Processes in Solution: Parametrization and Application to Hydration Free Energies of Neutral and Ionic Solutes and Conformational Analysis in Aqueous Solution , 1997 .

[83]  M. Levitt,et al.  Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. , 1976, Journal of molecular biology.

[84]  K. Dill Dominant forces in protein folding. , 1990, Biochemistry.

[85]  R. Nussinov,et al.  Relationship between ion pair geometries and electrostatic strengths in proteins. , 2002, Biophysical journal.

[86]  E. Alexov,et al.  A pragmatic approach to structure based calculation of coupled proton and electron transfer in proteins. , 2000, Biochimica et biophysica acta.

[87]  Marcos A. Villarreal,et al.  On the Ewald Artifacts in Computer Simulations. The Test-Case of the Octaalanine Peptide With Charged Termini , 2005, Journal of biomolecular structure & dynamics.

[88]  M. Tachiya Relation between the electron-transfer rate and the free energy change of reaction , 1989 .

[89]  K. Schulten,et al.  Control of the Selectivity of the Aquaporin Water Channel Family by Global Orientational Tuning , 2002, Science.

[90]  D. Minor,et al.  The Pore Helix Dipole Has a Minor Role in Inward Rectifier Channel Function , 2005, Neuron.

[91]  Ronald M. Levy,et al.  Dielectric and thermodynamic response of a generalized reaction field model for liquid state simulations , 1993 .

[92]  B. Honig,et al.  A rapid finite difference algorithm, utilizing successive over‐relaxation to solve the Poisson–Boltzmann equation , 1991 .

[93]  A. Warshel,et al.  How does GAP catalyze the GTPase reaction of Ras? A computer simulation study. , 2000, Biochemistry.

[94]  A. Warshel,et al.  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. , 2005, The journal of physical chemistry. B.

[95]  Pengyu Y. Ren,et al.  Consistent treatment of inter‐ and intramolecular polarization in molecular mechanics calculations , 2002, J. Comput. Chem..

[96]  Arieh Warshel,et al.  Computational Approaches to Biochemical Reactivity , 2002 .

[97]  R. Constanciel,et al.  Self consistent field theory of solvent effects representation by continuum models: Introduction of desolvation contribution , 1984, Theoretica chimica acta.

[98]  Methods of time-resolved study , 1988, Nature.

[99]  C. Tanford,et al.  Theory of Protein Titration Curves. I. General Equations for Impenetrable Spheres , 1957 .

[100]  B. Rabenstein,et al.  Energetics of electron-transfer and protonation reactions of the quinones in the photosynthetic reaction center of Rhodopseudomonas viridis. , 1998, Biochemistry.

[101]  Sergio Martí,et al.  Theoretical modeling of enzyme catalytic power: analysis of "cratic" and electrostatic factors in catechol O-methyltransferase. , 2003, Journal of the American Chemical Society.

[102]  Arieh Warshel,et al.  Calculations of chemical processes in solutions , 1979 .

[103]  Wilfred F. van Gunsteren,et al.  Absolute entropies from molecular dynamics simulation trajectories , 2000 .

[104]  A. Warshel,et al.  Energetics of ion permeation through membrane channels. Solvation of Na+ by gramicidin A. , 1989, Biophysical journal.

[105]  B. L. de Groot,et al.  The mechanism of proton exclusion in the aquaporin-1 water channel. , 2003, Journal of molecular biology.

[106]  Arieh Warshel,et al.  Computer Modeling of Chemical Reactions in Enzymes and Solutions , 1991 .

[107]  Martin J. Field,et al.  Simulating enzyme reactions: Challenges and perspectives , 2002, J. Comput. Chem..

[108]  C. A. Vernon The mechanisms of hydrolysis of glycosides and their revelance to enzyme-catalysed reactions , 1967, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[109]  Hirokazu Tsukaya,et al.  Probing Protein Electrostatics with a Synthetic Fluorescent Amino Acid , 2002 .

[110]  Arieh Warshel,et al.  The surface constraint all atom model provides size independent results in calculations of hydration free energies , 1998 .

[111]  A. Warshel,et al.  Dynamics of biochemical and biophysical reactions: insight from computer simulations , 2001, Quarterly Reviews of Biophysics.

[112]  A. Warshel,et al.  Electrostatics of Proteins: Principles, Models and Applications , 2008 .

[113]  Daniel Borgis,et al.  Electrostatics on particles: Phenomenological and orientational density functional theory approach , 2002 .

[114]  MartynC.R. Symons,et al.  Book reviewsThe chemical physics of solvation : Part B. Spectroscopy of solvation. R.R. Dogonadze, E. Kálmán, A.A. Kornyshev and J. Ulstmp (Editors). Elsevier, Amsterdam, 1986, ISBN 0-444-42674-4, XXVI + 560 pp., US$124.00, Dfl.335.00 , 1988 .

[115]  A. Warshel,et al.  Calculations of Solvation Free Energies in Chemistry and Biology. , 1995 .

[116]  A. Warshel,et al.  Energetics of enzyme catalysis. , 1978, Proceedings of the National Academy of Sciences of the United States of America.

[117]  Kenji Morihashi,et al.  An MNDO-effective charge model study of the solvent effect: The internal rotation about partial double bonds and the nitrogen inversion in amine , 1988 .

[118]  Malcolm E. Davis,et al.  Electrostatics in biomolecular structure and dynamics , 1990 .

[119]  Alan E. Mark,et al.  Dielectric properties of trypsin inhibitor and lysozyme calculated from molecular dynamics simulations , 1993 .

[120]  A. Wittinghofer,et al.  The 2.2 Å crystal structure of the Ras-binding domain of the serine/threonine kinase c-Raf1 in complex with RaplA and a GTP analogue , 1995, Nature.

[121]  V. Helms,et al.  Protein-protein docking of electron transfer complexes: Cytochromecoxidase and cytochromec: Docking of Electron Transfer Complexes , 2002 .

[122]  Sharon Hammes-Schiffer,et al.  Impact of distal mutations on the network of coupled motions correlated to hydride transfer in dihydrofolate reductase. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[123]  W G Hol,et al.  On the role of the active site helix in papain, an ab initio molecular orbital study. , 1979, Biophysical chemistry.

[124]  Gregory D. Hawkins,et al.  Parametrized Models of Aqueous Free Energies of Solvation Based on Pairwise Descreening of Solute Atomic Charges from a Dielectric Medium , 1996 .

[125]  J. Onuchic,et al.  Toward an outline of the topography of a realistic protein-folding funnel. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[126]  S. Marqusee,et al.  Structural distribution of stability in a thermophilic enzyme. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[127]  Arieh Warshel,et al.  CONTINUUM AND DIPOLE-LATTICE MODELS OF SOLVATION , 1997 .

[128]  A. Warshel,et al.  Calculations of electrostatic interactions in biological systems and in solutions , 1984, Quarterly Reviews of Biophysics.

[129]  B. Tidor,et al.  Do salt bridges stabilize proteins? A continuum electrostatic analysis , 1994, Protein science : a publication of the Protein Society.

[130]  K. Houk,et al.  A proficient enzyme revisited: the predicted mechanism for orotidine monophosphate decarboxylase. , 1997, Science.

[131]  B. Honig,et al.  Classical electrostatics in biology and chemistry. , 1995, Science.

[132]  J. Warwicker,et al.  Calculation of the electric potential in the active site cleft due to alpha-helix dipoles. , 1982, Journal of molecular biology.

[133]  G. Cymes,et al.  Probing ion-channel pores one proton at a time , 2005, Nature.

[134]  Arieh Warshel,et al.  Realistic simulations of proton transport along the gramicidin channel: demonstrating the importance of solvation effects. , 2005, The journal of physical chemistry. B.

[135]  C. Jarzynski Nonequilibrium Equality for Free Energy Differences , 1996, cond-mat/9610209.

[136]  G. Besra,et al.  Ion permeation mechanism of the potassium channel , 2022 .

[137]  Peter A. Kollman,et al.  Conformational and energetic effects of truncating nonbonded interactions in an aqueous protein dynamics simulation , 1993, J. Comput. Chem..

[138]  V. Luzhkov,et al.  K(+)/Na(+) selectivity of the KcsA potassium channel from microscopic free energy perturbation calculations. , 2001, Biochimica et biophysica acta.

[139]  M. Perutz Electrostatic effects in proteins. , 1978, Science.

[140]  Efthimios Kaxiras,et al.  A QM/MM Implementation of the Self-Consistent Charge Density Functional Tight Binding (SCC-DFTB) Method , 2001 .

[141]  J. Pitera,et al.  Dielectric properties of proteins from simulation: the effects of solvent, ligands, pH, and temperature. , 2001, Biophysical journal.

[142]  Ronald M. Levy,et al.  On Finite-Size Corrections to the Free Energy of Ionic Hydration , 1997 .

[143]  C. Pace,et al.  Buried, charged, non-ion-paired aspartic acid 76 contributes favorably to the conformational stability of ribonuclease T1. , 1999, Biochemistry.

[144]  M. Gilson,et al.  Prediction of pH-dependent properties of proteins. , 1994, Journal of molecular biology.

[145]  Vijay S. Pande,et al.  Screen Savers of the World Unite! , 2000, Science.

[146]  D. Pérahia,et al.  Internal and interfacial dielectric properties of cytochrome c from molecular dynamics in aqueous solution. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[147]  Huan-Xiang Zhou,et al.  Electrostatic contributions to T4 lysozyme stability: solvent-exposed charges versus semi-buried salt bridges. , 2002, Biophysical journal.

[148]  A. Fersht Structure and mechanism in protein science , 1998 .

[149]  R. Constanciel,et al.  Self consistent field theory of solvent effects representation by continuum models: Introduction of desolvation contribution , 1984 .

[150]  E. Alexov,et al.  Combining conformational flexibility and continuum electrostatics for calculating pK(a)s in proteins. , 2002, Biophysical journal.

[151]  D. Case,et al.  Generalized Born Models of Macromolecular Solvation Effects , 2001 .

[152]  Yury N. Vorobjev,et al.  A Critical Analysis of Methods of Calculation of a Potential in Simulated Polar Liquids: Strong Arguments in Favor of “Molecule-Based” Summation and of Vacuum Boundary Conditions in Ewald Summation , 1999 .

[153]  Arieh Warshel,et al.  The extended Ewald method: A general treatment of long‐range electrostatic interactions in microscopic simulations , 1988 .

[154]  Charles L. Brooks,et al.  CHARGE SCREENING AND THE DIELECTRIC CONSTANT OF PROTEINS : INSIGHTS FROM MOLECULAR DYNAMICS , 1996 .

[155]  H. Li,et al.  Remarkable stabilization of zwitterionic intermediates may account for a billion-fold rate acceleration by thiamin diphosphate-dependent decarboxylases. , 1999, Biochemistry.

[156]  W. H. Orttung Polarizability density of inert gas atom pairs. 1 , 1985 .

[157]  Amanda Yarnell BLOCKADE IN THE CELL'S WATERWAY , 2004 .

[158]  A. Liwo,et al.  Kinetic studies of folding of the B-domain of staphylococcal protein A with molecular dynamics and a united-residue (UNRES) model of polypeptide chains. , 2006, Journal of molecular biology.

[159]  E. Knapp,et al.  Tuning Heme Redox Potentials in the Cytochrome c Subunit of Photosynthetic Reaction Centers* , 2003, Journal of Biological Chemistry.

[160]  S. Benkovic,et al.  Solvation, Reorganization Energy, and Biological Catalysis* , 1998, The Journal of Biological Chemistry.

[161]  Peter C. Jordan Microscopic approaches to ion transport through transmembrane channels: the model system gramicidin , 1987 .

[162]  M K Gilson,et al.  Energetics of charge–charge interactions in proteins , 1988, Proteins.

[163]  B Honig,et al.  Free energy balance in protein folding. , 1995, Advances in protein chemistry.

[164]  M. Marchi,et al.  Simulation and modeling of the Rhodobacter sphaeroides bacterial reaction center II: Primary charge separation , 2003 .

[165]  H. Dufner,et al.  Ewald summation versus direct summation of shifted‐force potentials for the calculation of electrostatic interactions in solids: A quantitative study , 1997 .

[166]  E. Knapp,et al.  Electrostatic models for computing protonation and redox equilibria in proteins , 1999, European Biophysics Journal.

[167]  B. Honig,et al.  Calculation of the total electrostatic energy of a macromolecular system: Solvation energies, binding energies, and conformational analysis , 1988, Proteins.

[168]  Kevin L. Shaw,et al.  Increasing protein stability by altering long‐range coulombic interactions , 1999, Protein science : a publication of the Protein Society.

[169]  Ronald M. Welch,et al.  Climatic Impact of Tropical Lowland Deforestation on Nearby Montane Cloud Forests , 2001, Science.

[170]  A. Godzik,et al.  Simulations of the folding pathway of triose phosphate isomerase-type alpha/beta barrel proteins. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[171]  Emil Alexov,et al.  Comparative study of generalized born models: Born radii and peptide folding. , 2005, The journal of physical chemistry. B.

[172]  A. Warshel,et al.  Examining methods for calculations of binding free energies: LRA, LIE, PDLD‐LRA, and PDLD/S‐LRA calculations of ligands binding to an HIV protease , 2000, Proteins.

[173]  Klaus Schulten,et al.  Molecular Dynamics Simulation of the Primary Processes in the Photosynthetic Reaction Center of Rhodopseudomonas Viridis , 1988 .

[174]  C. Soares,et al.  Studies of the reduction and protonation behavior of tetraheme cytochromes using atomic detail , 2001, JBIC Journal of Biological Inorganic Chemistry.

[175]  A. Liwo,et al.  Ab initio simulations of protein-folding pathways by molecular dynamics with the united-residue model of polypeptide chains. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[176]  V. Luzhkov,et al.  Ions and blockers in potassium channels: insights from free energy simulations. , 2005, Biochimica et biophysica acta.

[177]  R. Kassner,et al.  A theoretical model for the effects of local nonpolar heme environments on the redox potentials in cytochromes. , 1973, Journal of the American Chemical Society.

[178]  M. M. Marino,et al.  Ab initio study of hydrogen adsorption on Be (0001) , 1991 .

[179]  Mika A. Kastenholz,et al.  Computation of methodology-independent ionic solvation free energies from molecular simulations. I. The electrostatic potential in molecular liquids. , 2006, The Journal of chemical physics.

[180]  A. Warshel,et al.  Remarkable rate enhancement of orotidine 5'-monophosphate decarboxylase is due to transition-state stabilization rather than to ground-state destabilization. , 2000, Biochemistry.

[181]  J. Bertrán,et al.  Transition structure selectivity in enzyme catalysis: a QM/MM study of chorismate mutase , 2001 .

[182]  Ian H. Williams,et al.  Theoretical modelling of enzyme catalytic power: Analysis of "cratic" and electrostatic factors in catechol O-methyl transferase , 2004 .

[183]  Huan‐Xiang Zhou,et al.  Microscopic formulation of Marcus’ theory of electron transfer , 1995 .

[184]  M K Gilson,et al.  The dielectric constant of a folded protein , 1986, Biopolymers.

[185]  A. Warshel Electrostatic Origin of the Catalytic Power of Enzymes and the Role of Preorganized Active Sites* , 1998, The Journal of Biological Chemistry.

[186]  J. Deisenhofer,et al.  Electrostatic Control of Electron Transfer in the Photosynthetic Reaction Center of Rhodopseudomonas viridis , 1988 .

[187]  Tony J. You,et al.  Conformation and hydrogen ion titration of proteins: a continuum electrostatic model with conformational flexibility. , 1995, Biophysical journal.

[188]  Calculations of the electrostatic free energy contributions to the binding free energy of sulfonamides to carbonic anhydrase , 1996 .

[189]  B. Roux The calculation of the potential of mean force using computer simulations , 1995 .

[190]  A. Warshel,et al.  The effect of protein relaxation on charge-charge interactions and dielectric constants of proteins. , 1998, Biophysical journal.

[191]  Barry Honig,et al.  Comparative study of generalized Born models: protein dynamics. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[192]  S. Creighton,et al.  Simulating the dynamics of the primary charge separation process in bacterial photosynthesis , 1988 .

[193]  M. Gilson,et al.  Simulation of charge-mutant acetylcholinesterases. , 1995, Biochemistry.

[194]  H Luecke,et al.  Dipoles localized at helix termini of proteins stabilize charges. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[195]  M. Simon,et al.  Crystal structures of CheY from Thermotoga maritima do not support conventional explanations for the structural basis of enhanced thermostability , 1998, Protein science : a publication of the Protein Society.

[196]  Arieh Warshel,et al.  Microscopic simulations of macroscopic dielectric constants of solvated proteins , 1991 .

[197]  Ting Wang,et al.  How optimal are the binding energetics of barnase and barstar? , 2004, Biophysical journal.

[198]  I. Shrivastava,et al.  Simulations of ion permeation through a potassium channel: molecular dynamics of KcsA in a phospholipid bilayer. , 2000, Biophysical journal.

[199]  G. Moore,et al.  On the energetics of conformational changes and pH dependent redox behaviour of electron transfer proteins , 1988, FEBS letters.

[200]  Linus Pauling,et al.  THE INTER-IONIC ATTRACTION THEORY OF IONIZED SOLUTES. IV. THE INFLUENCE OF VARIATION OF DIELECTRIC CONSTANT ON THE LIMITING LAW FOR SMALL CONCENTRATIONS , 1925 .

[201]  J. Åqvist,et al.  The catalytic power of ketosteroid isomerase investigated by computer simulation. , 2002, Biochemistry.

[202]  M Karplus,et al.  Improving the accuracy of protein pKa calculations: Conformational averaging versus the average structure , 1998, Proteins.

[203]  K. Sharp,et al.  Calculating the electrostatic potential of molecules in solution: Method and error assessment , 1988 .

[204]  A. Warshel,et al.  Simulations of ion current in realistic models of ion channels: The KcsA potassium channel , 2002, Proteins.

[205]  M. Karplus,et al.  A Comprehensive Analytical Treatment of Continuum Electrostatics , 1996 .

[206]  Huan-Xiang Zhou,et al.  Control of reduction potential by protein matrix: lesson from a spherical protein model , 1997, JBIC Journal of Biological Inorganic Chemistry.

[207]  Rob D. Coalson,et al.  Statistical Mechanics of a Multipolar Gas: A Lattice Field Theory Approach , 1996 .

[208]  S. Boxer,et al.  High yield of M-side electron transfer in mutants of Rhodobacter capsulatus reaction centers lacking the L-side bacteriopheophytin. , 2006, Biochemistry.

[209]  A. Warshel,et al.  How do serine proteases really work? , 1989, Biochemistry.

[210]  Arieh Warshel,et al.  Dynamics of reactions in polar solvents. Semiclassical trajectory studies of electron-transfer and proton-transfer reactions , 1982 .

[211]  W. W. Parson,et al.  Electrostatic interactions in an integral membrane protein. , 2002, Biochemistry.

[212]  W G Hol,et al.  The alpha-helix dipole and the properties of proteins. , 1978, Nature.

[213]  F. J. Luque,et al.  Generalized linear response approximation in discrete methods , 1997 .

[214]  F Guarnieri,et al.  A self-consistent, microenvironment modulated screened coulomb potential approximation to calculate pH-dependent electrostatic effects in proteins. , 1999, Biophysical journal.

[215]  E. Lippert N. Mataga und T. Kubota: Molecular Interactions and Electronic Spectra. Marcel Dekker, Inc., New York 1970, 504 Seiten. Preis: $28.50 , 1971 .

[216]  A. Warshel,et al.  Calculations of electrostatic energies in proteins. The energetics of ionized groups in bovine pancreatic trypsin inhibitor. , 1985, Journal of molecular biology.

[217]  Michael R. Shirts,et al.  COMPUTING: Screen Savers of the World Unite! , 2000, Science.

[218]  W. Person,et al.  Molecular Interactions and Electronic Spectra , 1970 .

[219]  O. Alvarez,et al.  Structure and function of channels and channelogs as studied by computational chemistry , 2005, The Journal of Membrane Biology.

[220]  T. Webb THE FREE ENERGY OF HYDRATION OF IONS AND THE ELECTROSTRICTION OF THE SOLVENT , 1926 .

[221]  Yi Liu,et al.  The static dielectric constant of the soft sticky dipole model of liquid water: Monte Carlo simulation , 1996 .

[222]  J. Schlitter Estimation of absolute and relative entropies of macromolecules using the covariance matrix , 1993 .

[223]  A. Warshel,et al.  On the origin of the electrostatic barrier for proton transport in aquaporin , 2004, FEBS letters.

[224]  T. Ichiye,et al.  Solvation Free Energy Reaction Curves for Electron Transfer in Aqueous Solution: Theory and Simulation , 1997 .

[225]  V. Helms,et al.  Protein--protein docking of electron transfer complexes: cytochrome c oxidase and cytochrome c. , 2002 .

[226]  A. Warshel,et al.  Simulating proton translocations in proteins: Probing proton transfer pathways in the Rhodobacter sphaeroides reaction center , 1999, Proteins.

[227]  R. Levy,et al.  Computer simulations with explicit solvent: recent progress in the thermodynamic decomposition of free energies and in modeling electrostatic effects. , 1998, Annual review of physical chemistry.

[228]  Peter Agre,et al.  Aquaporin water channels: molecular mechanisms for human diseases1 , 2003, FEBS letters.

[229]  Bong-Gyoon Han,et al.  Structural basis of water-specific transport through the AQP1 water channel , 2001, Nature.

[230]  Wilfred F van Gunsteren,et al.  Characterization of the denaturation of human α‐lactalbumin in urea by molecular dynamics simulations , 2004, Proteins.

[231]  Thomas Simonson,et al.  Electrostatics and dynamics of proteins , 2003 .

[232]  Tiqing Liu,et al.  Insights into properties and energetics of iron-sulfur proteins from simple clusters to nitrogenase. , 2002, Current opinion in chemical biology.

[233]  Bruno L. Victor,et al.  Docking and electron transfer studies between rubredoxin and rubredoxin:oxygen oxidoreductase , 2003, JBIC Journal of Biological Inorganic Chemistry.

[234]  Kenneth M. Merz,et al.  Dynamic Force Field Models: Molecular Dynamics Simulations of Human Carbonic Anhydrase II Using a Quantum Mechanical/Molecular Mechanical Coupled Potential , 1995 .

[235]  N. Go Theoretical studies of protein folding. , 1983, Annual review of biophysics and bioengineering.

[236]  J. Aqvist,et al.  A new method for predicting binding affinity in computer-aided drug design. , 1994, Protein engineering.

[237]  X. Daura,et al.  Entropy calculations on a reversibly folding peptide: Changes in solute free energy cannot explain folding behavior , 2001, Proteins.

[238]  M. Marahiel,et al.  Characterization of cspB, a Bacillus subtilis inducible cold shock gene affecting cell viability at low temperatures , 1992, Journal of bacteriology.

[239]  Arieh Warshel,et al.  Using simplified protein representation as a reference potential for all-atom calculations of folding free energy , 1999 .

[240]  A. Warshel,et al.  Electrostatic basis for enzyme catalysis. , 2006, Chemical reviews.

[241]  N. Agmon,et al.  The Grotthuss mechanism , 1995 .

[242]  J. Åqvist Analysis of Electrostatic Potential Truncation Schemes in Simulations of Polar Solvents , 1998 .

[243]  Emil Alexov,et al.  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 , 2002, J. Comput. Chem..

[244]  A. Warshel,et al.  Calculations of Electrostatic Energies in Proteins Using Microscopic, Semimicroscopic and Macroscopic Models and Free-Energy Perturbation Approaches , 2008 .

[245]  R. G. Alden,et al.  Calculations of Electrostatic Energies in Photosynthetic Reaction Centers , 1995 .

[246]  Ronald M. Levy,et al.  On finite‐size effects in computer simulations using the Ewald potential , 1995 .

[247]  A. Warshel,et al.  What are the roles of substrate-assisted catalysis and proximity effects in peptide bond formation by the ribosome? , 2005, Biochemistry.

[248]  A. Warshel,et al.  The low barrier hydrogen bond (LBHB) proposal revisited: The case of the Asp ··· His pair in serine proteases , 2004, Proteins.

[249]  Gerhard Hummer,et al.  Free Energy of Ionic Hydration , 1996 .

[250]  G Klebe,et al.  Improving macromolecular electrostatics calculations. , 1999, Protein engineering.

[251]  Arieh Warshel,et al.  Calculations of Activation Entropies of Chemical Reactions in Solution , 2000 .

[252]  W. C. Still,et al.  Semianalytical treatment of solvation for molecular mechanics and dynamics , 1990 .

[253]  L. Serrano,et al.  Predicting changes in the stability of proteins and protein complexes: a study of more than 1000 mutations. , 2002, Journal of molecular biology.

[254]  A. Warshel,et al.  Microscopic and semimacroscopic redox calculations: what can and cannot be learned from continuum models , 1997, JBIC Journal of Biological Inorganic Chemistry.

[255]  B. Berne,et al.  Combined fluctuating charge and polarizable dipole models: Application to a five-site water potential function , 2001 .

[256]  K. Sharp,et al.  On the calculation of absolute macromolecular binding free energies , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[257]  Arieh Warshel,et al.  Protein Control of Redox Potentials of Iron‐Sulfur Proteins , 1997 .

[258]  M Karplus,et al.  Computer simulation and analysis of the reaction pathway of triosephosphate isomerase. , 1991, Biochemistry.

[259]  Ian F. Thorpe,et al.  Conformational substates modulate hydride transfer in dihydrofolate reductase. , 2005, Journal of the American Chemical Society.

[260]  Barry Honig,et al.  Extending the Applicability of the Nonlinear Poisson−Boltzmann Equation: Multiple Dielectric Constants and Multivalent Ions† , 2001 .

[261]  A. Warshel,et al.  CONVERSION OF LIGHT ENERGY TO ELECTROSTATIC ENERGY IN THE PROTON PUMP OF HALOBACTERIUM HALOBIUM , 1979, Photochemistry and photobiology.

[262]  Lu Wang,et al.  Inclusion of Loss of Translational and Rotational Freedom in Theoretical Estimates of Free Energies of Binding. Application to a Complex of Benzene and Mutant T4 Lysozyme , 1997 .

[263]  M. Levitt,et al.  Computer simulation of protein folding , 1975, Nature.

[264]  Arieh Warshel,et al.  The barrier for proton transport in aquaporins as a challenge for electrostatic models: The role of protein relaxation in mutational calculations , 2006, Proteins.

[265]  Hervé Minoux,et al.  An electrostatic basis for the stability of thermophilic proteins , 2004, Proteins.

[266]  S. Chung,et al.  Molecular dynamics study of the KcsA potassium channel. , 1999, Biophysical journal.

[267]  Jinrang Kim,et al.  Are acidic and basic groups in buried proteins predicted to be ionized? , 2005, Journal of molecular biology.

[268]  G. Grant,et al.  Computer modelling of enzyme catalysed reaction mechanisms. , 1993, Protein engineering.

[269]  A. Warshel,et al.  Electrostatic control of GTP and GDP binding in the oncoprotein p21ras. , 1996, Structure.

[270]  J. Tomasi,et al.  Quantum Mechanical Models for Reactions in Solution , 2002 .

[271]  Roderick MacKinnon,et al.  Energetic optimization of ion conduction rate by the K+ selectivity filter , 2001, Nature.

[272]  R. Staden,et al.  Protein disk of tobacco mosaic virus at 2.8 Å resolution showing the interactions within and between subunits , 1978, Nature.

[273]  A. Warshel,et al.  What really prevents proton transport through aquaporin? Charge self-energy versus proton wire proposals. , 2003, Biophysical journal.

[274]  A. Warshel,et al.  Free energy of charges in solvated proteins: microscopic calculations using a reversible charging process. , 1986, Biochemistry.

[275]  F. Richards,et al.  Electrostatic orientation during electron transfer between flavodoxin and cytochrome c , 1983, Nature.

[276]  Nicolas Levy,et al.  Computing the electrostatic free-energy of complex molecules: The variational Coulomb field approximation , 2003 .

[277]  E. Alexov,et al.  Calculated protein and proton motions coupled to electron transfer: electron transfer from QA- to QB in bacterial photosynthetic reaction centers. , 1999, Biochemistry.

[278]  Ronald M. Levy,et al.  AGBNP: An analytic implicit solvent model suitable for molecular dynamics simulations and high‐resolution modeling , 2004, J. Comput. Chem..

[279]  Jose M. Sanchez-Ruiz,et al.  Genetic Algorithm to Design Stabilizing Surface-Charge Distributions in Proteins , 2002 .

[280]  R. G. Alden,et al.  Macroscopic and Microscopic Estimates of the Energetics of Charge Separation in Bacterial Reaction Centers , 1996 .

[281]  R. D. Gilliom Introduction to physical organic chemistry , 1970 .

[282]  Arieh Warshel,et al.  On the action of cytochrome c: correlating geometry changes upon oxidation with activation energies of electron transfer , 1983 .

[283]  J. Kirkwood,et al.  Theory of Solutions of Molecules Containing Widely Separated Charges with Special Application to Zwitterions , 1934 .

[284]  A. Warshel,et al.  Energetics of heme-protein interactions in hemoglobin , 1981 .

[285]  Huan‐Xiang Zhou,et al.  Modeling of protein conformational fluctuations in pKa predictions. , 1997, Journal of molecular biology.

[286]  T. Hansson,et al.  On the Validity of Electrostatic Linear Response in Polar Solvents , 1996 .

[287]  E. Alexov,et al.  Incorporating protein conformational flexibility into the calculation of pH-dependent protein properties. , 1997, Biophysical journal.

[288]  B. L. de Groot,et al.  Water Permeation Across Biological Membranes: Mechanism and Dynamics of Aquaporin-1 and GlpF , 2001, Science.

[289]  P. Kollman,et al.  Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models. , 2000, Accounts of chemical research.

[290]  A. Warshel,et al.  Why ion pair reversal by protein engineering is unlikely to succeed , 1988, Nature.

[291]  V. Pande,et al.  Absolute comparison of simulated and experimental protein-folding dynamics , 2002, Nature.

[292]  B. Hille Ionic channels of excitable membranes , 2001 .

[293]  J. Åqvist,et al.  Computer Simulation of the Triosephosphate Isomerase Catalyzed Reaction (*) , 1996, The Journal of Biological Chemistry.

[294]  Arieh Warshel,et al.  Studies of proton translocations in biological systems: simulating proton transport in carbonic anhydrase by EVB-based models. , 2004, Biophysical journal.

[295]  U. Singh,et al.  A combined ab initio quantum mechanical and molecular mechanical method for carrying out simulations on complex molecular systems: Applications to the CH3Cl + Cl− exchange reaction and gas phase protonation of polyethers , 1986 .

[296]  G. Náray‐Szabó Electrostatic modulation of electron transfer in the active site of heme peroxidases , 1997, JBIC Journal of Biological Inorganic Chemistry.

[297]  W. C. Still,et al.  The GB/SA Continuum Model for Solvation. A Fast Analytical Method for the Calculation of Approximate Born Radii , 1997 .

[298]  M. Karplus,et al.  Method for estimating the configurational entropy of macromolecules , 1981 .

[299]  D. A. Dunnett Classical Electrodynamics , 2020, Nature.

[300]  P. Lazzeretti LONGITUDINAL VECTOR POTENTIALS FOR MOLECULAR MAGNETIC PROPERTIES , 1995 .

[301]  M. Born Volumen und Hydratationswärme der Ionen , 1920 .

[302]  G. C.,et al.  Electricity and Magnetism , 1888, Nature.

[303]  K. Sharp,et al.  On the calculation of pKas in proteins , 1993, Proteins.

[304]  B. Zagrovic,et al.  Comparing atomistic simulation data with the NMR experiment: How much can NOEs actually tell us? , 2006, Proteins.

[305]  A. Warshel,et al.  Macroscopic models for studies of electrostatic interactions in proteins: limitations and applicability. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[306]  T. Ichiye,et al.  Structural origins of redox potentials in Fe-S proteins: electrostatic potentials of crystal structures. , 1996, Biophysical journal.

[307]  Arieh Warshel,et al.  Protein Control of Redox Potentials of Iron−Sulfur Proteins , 1996 .

[308]  A. Verméglio,et al.  The Photosynthetic Bacterial Reaction Center II , 1992, Nato ASI Series.

[309]  O. Schueler‐Furman,et al.  Progress in Modeling of Protein Structures and Interactions , 2005, Science.

[310]  Benoît Roux,et al.  Structural determinants of proton blockage in aquaporins. , 2004, Journal of molecular biology.

[311]  C. Cramer,et al.  General parameterized SCF model for free energies of solvation in aqueous solution , 1991 .

[312]  H. Nakamura,et al.  Roles of electrostatic interaction in proteins , 1996, Quarterly Reviews of Biophysics.

[313]  A. Warshel,et al.  Using a charging coordinate in studies of ionization induced partial unfolding. , 2006, The journal of physical chemistry. B.

[314]  B Pullman,et al.  New Paths in the Molecular Orbital Approach to Solvation of Biological Molecules , 1974, Quarterly Reviews of Biophysics.

[315]  Johan Aaqvist,et al.  Comment on "Transferability of Ion Models" , 1994 .

[316]  Minoru Saito,et al.  Molecular dynamics/free energy study of a protein in solution with all degrees of freedom and long-range Coulomb interactions , 1995 .

[317]  Bruno L. Victor,et al.  On the use of different dielectric constants for computing individual and pairwise terms in poisson-boltzmann studies of protein ionization equilibrium. , 2005, The journal of physical chemistry. B.

[318]  A. Warshel,et al.  Origin of the catalytic power of acetylcholinesterase: Computer simulation studies , 1998 .

[319]  T. Hansson,et al.  Analysis of Electrostatic Potential Truncation Schemes in Simulations of Polar Solvents , 1998 .

[320]  A. Warshel Computer simulations of enzyme catalysis: methods, progress, and insights. , 2003, Annual review of biophysics and biomolecular structure.

[321]  A. Warshel,et al.  Electrostatic control of charge separation in bacterial photosynthesis. , 1990, Biochimica et biophysica acta.

[322]  F. J. Luque,et al.  Salt bridge interactions: Stability of the ionic and neutral complexes in the gas phase, in solution, and in proteins , 1998, Proteins.

[323]  B Honig,et al.  Electrostatic contributions to the stability of hyperthermophilic proteins. , 1999, Journal of molecular biology.

[324]  Barry Honig,et al.  Calculating total electrostatic energies with the nonlinear Poisson-Boltzmann equation , 1990 .

[325]  F. Armstrong Evaluations of reduction potential data in relation to coupling, kinetics and function , 1997, JBIC Journal of Biological Inorganic Chemistry.

[326]  A. Leslie,et al.  Structure of Bovine Mitochondrial F1-ATPase with Nucleotide Bound to All Three Catalytic Sites Implications for the Mechanism of Rotary Catalysis , 2001, Cell.

[327]  T. DeCoursey Voltage-gated proton channels and other proton transfer pathways. , 2003, Physiological reviews.

[328]  R. Levy,et al.  Intrinsic pKas of ionizable residues in proteins: An explicit solvent calculation for lysozyme , 1994, Proteins.

[329]  P. Beroza,et al.  Computational, pulse‐radiolytic, and structural investigations of lysine‐136 and its role in the electrostatic triad of human C u,Z n superoxide dismutase , 1997, Proteins.

[330]  O. Schueler‐Furman,et al.  Improved side‐chain modeling for protein–protein docking , 2005, Protein science : a publication of the Protein Society.

[331]  R. MacKinnon,et al.  The cavity and pore helices in the KcsA K+ channel: electrostatic stabilization of monovalent cations. , 1999, Science.

[332]  Arieh Warshel,et al.  Microscopic and semimicroscopic calculations of electrostatic energies in proteins by the POLARIS and ENZYMIX programs , 1993, J. Comput. Chem..

[333]  S. Adelman Chemical Reaction Dynamics in Liquid Solution , 2007 .

[334]  Arieh Warshel,et al.  Frozen density functional free energy simulations of redox proteins: computational studies of the reduction potential of plastocyanin and rusticyanin. , 2003, Journal of the American Chemical Society.

[335]  Andreas Engel,et al.  Structural determinants of water permeation through aquaporin-1 , 2000, Nature.

[336]  W. Im,et al.  Ion channels, permeation, and electrostatics: insight into the function of KcsA. , 2000, Biochemistry.

[337]  Wilfred F van Gunsteren,et al.  Simulations of apo and holo-fatty acid binding protein: structure and dynamics of protein, ligand and internal water. , 2002, Journal of molecular biology.

[338]  A. Roitberg,et al.  All-atom structure prediction and folding simulations of a stable protein. , 2002, Journal of the American Chemical Society.

[339]  B. Honig,et al.  Calculated coupling of electron and proton transfer in the photosynthetic reaction center of Rhodopseudomonas viridis. , 1996, Biophysical journal.

[340]  Arieh Warshel,et al.  The Reorganization Energy of Cytochrome c Revisited , 1997 .

[341]  A. Warshel,et al.  Energy storage and reaction pathways in the first step of the vision process , 1982 .

[342]  G. Eichele,et al.  Electrostatic effects in water-accessible regions of proteins , 1984 .

[343]  Richard Horn,et al.  Ionic selectivity revisited: The role of kinetic and equilibrium processes in ion permeation through channels , 2005, The Journal of Membrane Biology.

[344]  John Karanicolas,et al.  The structural basis for biphasic kinetics in the folding of the WW domain from a formin-binding protein: Lessons for protein design? , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[345]  Peter A. Kollman,et al.  FREE ENERGY CALCULATIONS : APPLICATIONS TO CHEMICAL AND BIOCHEMICAL PHENOMENA , 1993 .

[346]  J. Åqvist,et al.  Ion-water interaction potentials derived from free energy perturbation simulations , 1990 .

[347]  V. Luzhkov,et al.  A computational study of ion binding and protonation states in the KcsA potassium channel. , 2000, Biochimica et biophysica acta.

[348]  V. Helms,et al.  Protein–protein docking of electron transfer complexes: Cytochrome c oxidase and cytochrome c , 2002, Proteins.

[349]  C. Luchinat,et al.  Are unit charges always negligible? , 1997, JBIC Journal of Biological Inorganic Chemistry.

[350]  A. Warshel,et al.  Simulating the effect of DNA polymerase mutations on transition-state energetics and fidelity: evaluating amino acid group contribution and allosteric coupling for ionized residues in human pol beta. , 2006, Biochemistry.

[351]  G. Lienhard,et al.  Mechanisms of thiamine-catalyzed reactions. Decarboxylation of 2-(1-carboxy-1-hydroxyethyl)-3,4-dimethylthiazolium chloride. , 1970, Journal of the American Chemical Society.

[352]  A. Warshel,et al.  Electrostatic energy and macromolecular function. , 1991, Annual review of biophysics and biophysical chemistry.

[353]  W. L. Jorgensen,et al.  Chemical consequences of orbital interactions. 14. Ab initio molecular orbital study of the geometries, properties, and protonation of simple organofluorides , 1978 .

[354]  J. Knowles,et al.  Direct evidence for the exploitation of an alpha-helix in the catalytic mechanism of triosephosphate isomerase. , 1993, Biochemistry.

[355]  Jens Carlsson,et al.  Absolute and relative entropies from computer simulation with applications to ligand binding. , 2005, The journal of physical chemistry. B.

[356]  J. Warwicker,et al.  Electrostatic Models for Calcium Binding Proteins , 1998 .

[357]  N. K. Rogers,et al.  The modelling of electrostatic interactions in the function of globular proteins. , 1986, Progress in biophysics and molecular biology.