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Applications of Free Energy Calculations

  • Chapter
Molecular Dynamics

Abstract

One of the most exciting developments in the field of computer simulation has come from techniques which allow estimates of free energies (Beveridge and Dicapua, 1989a, b; van Gunsteren, 1989). Most previous simulations of macromolecules have only involved calculation of the average potential energy of the system. As it is the free energy which controls the equilibrium behaviour of a system of particles, this is an important development which has opened up a range of new applications which are relevant to designing rational strategies for the development of new drugs and for protein engineering experiments.

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References

  • Anderson, A. G. and Hermans, J. (1988) Microfolding: conformational probability for alanine dipeptide in water from molecular dynamics simulations. Proteins, 3, 262–265

    Article  CAS  PubMed  Google Scholar 

  • Bash, P. A., Singh, U. C., Brown, F. K., Langridge, R. and Kollman, P. A. (1987a). Calculation of relative change in binding free energy of a protein-inhibitor complex. Science, 235, 574–575

    Article  CAS  PubMed  Google Scholar 

  • Bash, P. A., Singh, U. C., Langridge, R. and Kollman, P. A. (1987b). Free energy calculations by computer simulation. Science, 236, 564–565

    Article  CAS  PubMed  Google Scholar 

  • Bennett, C. H. (1976). Efficient estimation of free energy differences from Monte Carlo data. J. Comput. Phys., 22, 245–268

    Article  Google Scholar 

  • Berendsen, H. J. C., Postma, J. P. M., van Gunsteren, W. F. and Hermans, J. (1981). Interaction models for water in relation to protein hydration. In Pullman, B. (Ed.), Intermolecular Forces. Reidel, Dordrecht, pp. 331–342

    Chapter  Google Scholar 

  • Berendsen, H. J. C., Postma, J. P. M. and van Gunsteren, W. F. (1985). In Hermans, J. (Ed.), Molecular Dynamics and Protein Structure. Polycrystal Book Service, Illinois, pp. 43–46

    Google Scholar 

  • Beveridge, D. L. and Dicapua, F. M. (1989a). Free energy via molecular simulation: a primer. In van Gunsteren, W. F. and Weiner, P. (Eds.), Computer Simulation of Biomolecular Systems. ESCOM, Leiden, pp. 1–26

    Google Scholar 

  • Beveridge, D. L. and Dicapua, F. M. (1989b). Free energy via molecular simulation: applications to chemical and biomolecular systems. Annu. Rev. Biophys. Biophys. Chem., 18, 431–492

    Article  CAS  PubMed  Google Scholar 

  • Brooks, B. R., Bruccoleri, R. E., Olafson, B. D., States, D. J., Swaminathan, S. and Karplus, M. (1983). CHARMM: a program for macromolecular energy minimization and dynamics calculations. J. Comput. Chem., 4, 187–217

    Article  CAS  Google Scholar 

  • Brooks, C. L. (1989). Thermodynamic calculations on biological molecules. In van Gunsteren, W. F. and Weiner, P. (Eds.), Computer Simulation of Biomolecular Systems. ESCOM, Leiden, pp. 73–88

    Google Scholar 

  • Chandrasekar, J., Smith, S. F. and Jorgensen, W. L. (1984). Sn2 reaction profiles in gas phase and aqueous solution. J. Am. Chem. Soc., 106, 3049–3050.

    Article  Google Scholar 

  • Cieplak, P. and Kollman, P. A. (1988). Calculation of the free energy of association of nucleic acid bases in vacuo and water solution. J. Am. Chem. Soc., 110, 3734–3739

    Article  CAS  Google Scholar 

  • Conley, J. D. and Kohn, H. (1987). Functionalised DL-amino acid derivatives: potent new agents for the treatment of epilepsy. J. Med. Chem., 30, 567–574

    Article  CAS  PubMed  Google Scholar 

  • Creighton, S., Hwang, J., Warshel, A., Parson, W. W. and Norris, J. (1988). Simulating the dynamics of the primary charge separation process in bacterial photosynthesis. Biochemistry, 27, 774–781

    Article  CAS  Google Scholar 

  • Essex, J. W., Reynolds, C. A. and Richards, W. G. (1989). Relative partition coefficients from partition functions: a theoretical approach to drug transport. J. Chem. Soc., Chem. Commun., 1152–1154

    Google Scholar 

  • Gilson, M. K. and Honig, B. H. (1987). Calculation of electrostatic potentials in an enzyme active site. Nature, 330, 84–86

    Article  CAS  PubMed  Google Scholar 

  • Goodfellow, J. M., Saqi, M. A. S., Thanki, N., Baum, J. O. and Finney, J. L. (1989). Monte Carlo calculations on proteins: hydration and electron transfer processes. In Beveridge, D. L. and Lavery, R. (Eds.), Theoretical Chemistry and Molecular Biophysics. Adenine Press, New York

    Google Scholar 

  • van Gunsteren, W. F. (1989) Methods for calculations of free energies and binding constants: successes and problems. In van Gunsteren, W. F. and Weiner, P. (Eds.), Computer Simulation of Biomolecular Systems. ESCOM, Leiden, pp. 27–59

    Google Scholar 

  • Hagler, A. T., Stern, P. S., Sharon, R., Becker, J. M. and Naider, F. (1979). Computer simulation of the conformational properties of oligopeptides. J. Am. Chem. Soc., 101, 6842–6852

    Article  CAS  Google Scholar 

  • Hermans, J., Berendsen, H. J. C., van Gunsteren, W. F. and Postma, J. P. M. (1984). A consistent empirical potential for water protein interactions. Biopolymers, 23, 1513–1518

    Article  CAS  Google Scholar 

  • Hirono, S. and Kollman, P. A. (1990). Calculation of the relative binding free energy of 2′GMP and 2′AMP to ribonuclease T, using molecular dynamics/free energy perturbation approaches. J. Mol. Biol., 212, 197–209

    Article  CAS  PubMed  Google Scholar 

  • Hol, W. G. J. (1986). Protein crystallography and computer graphics—towards rational drug design. Angew. Chem., Int. Edn. Engl, 25, 767–778

    Article  Google Scholar 

  • Huang, K. (1969). Statistical Mechanics. Wiley, New York

    Google Scholar 

  • Hwang, J.-K. and Warshel, A. (1987). Semiquantitative calculations of catalytic free energies in genetically modified enzymes. Biochemistry, 26, 2669–2673

    Article  CAS  PubMed  Google Scholar 

  • Jayaram, B., Mezei, M. and Beveridge, D. L. (1988a). Conformational stability of dimethyl phosphate anion in water: liquid state free energy simulations. J. Am. Chem. Soc., 110, 1691–1694

    Article  CAS  Google Scholar 

  • Jayaram, B., Ravishkanker, G. and Beveridge, D. L. (1988b). Conformational preferences of phosphodiester torsional angles in dimethylphosphate anion in free space. J. Phys. Chem., 92, 1032–1034

    Article  CAS  Google Scholar 

  • Jorgensen, W. L. and Gao, J. (1988). Cis-trans energy difference for the peptide bond in the gas phase and in aqueous solution. J. Am. Chem. Soc., 110, 4212–4216

    Article  CAS  Google Scholar 

  • Jorgensen, W. L. and Ravimohan, C. (1985). Monte Carlo simulation of differences in free energies of hydration. J. Chem. Phys., 83, 3050–3054

    Article  CAS  Google Scholar 

  • Jorgensen, W. L. and Tirado-Rives, J. (1988). The OPLS potential functions for proteins. J. Am. Chem. Soc., 110, 1657–1666

    Article  CAS  Google Scholar 

  • Jorgensen, W. L., Chandrasekhar, J., Madura, J. D., Impey, R. W. and Klein, M. L. (1983). Comparison of simple potential functions for simulating liquid water. J. Chem. Phys., 79, 926–935

    Article  CAS  Google Scholar 

  • Jorgensen, W. L., Briggs, J. M. and Gao, J. (1987). A priori calculations of pkas for organic compounds in water. J. Am. Chem. Soc., 109, 6857–6858

    Article  CAS  Google Scholar 

  • Kauzmann, W. (1967). Thermodynamics and Statistics: with Applications to Gases. Benjamin, Menlo park, CA

    Google Scholar 

  • Lybrand, T. P., Ghosh, I. and McCammon, J. A. (1985). Hydration of chloride and bromide anions: determination of relative free energy by computer simulation. J. Am. Chem. Soc., 107, 7793–7794

    Article  CAS  Google Scholar 

  • Madison, V. and Kopple, K. D. (1980). Solvent-dependent conformational distributions of some dipeptides. J. Am. Chem. Soc., 102, 4855–4863

    Article  CAS  Google Scholar 

  • Martin, Y. C. (1978). Quantitative Drug Design: 1, Dekker, New York

    Google Scholar 

  • McCammon, J. A. (1987). Computer-aided molecular design. Science, 238, 486–491

    Article  CAS  PubMed  Google Scholar 

  • McCammon, J. A. and Harvey, S. (1987). Dynamics of Proteins and Nucleic Acids. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Mehrotra, P. K., Mezei, M. and Beveridge, D. L. (1984). Monte Carlo determination of the internal energies for the alanine dipeptide in the C7, C5, ±R and PII conformations. Int. J. Quantum Chem., Quantum Biol. Symp., II, 301–308

    Article  Google Scholar 

  • Meirovitch, H., Vasquez, M. and Scheraga, H. A. (1987). Stability of polypeptide conformational states as determined by computer simulation of the free energy. Biopolymers, 26, 651

    Article  CAS  PubMed  Google Scholar 

  • Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953). Equation of state calculations by fast computing machines. J. Chem. Phys., 21, 1087–1092

    Article  CAS  Google Scholar 

  • Mezei, M. (1982). Comparisons of free energy of different water models computed by Monte Carlo methods. Mol. Phys., 47, 1307–1315

    Article  CAS  Google Scholar 

  • Mezei, M. and Beveridge, D. L. (1986). Free energy simulations. Ann. N.Y. Acad. Sci., 482, 1–12

    Article  CAS  PubMed  Google Scholar 

  • Mezei, M., Mehrotra, P. K. and Beveridge, D. L. (1985). Monte Carlo determination of the free energy and internal energy of hydration for the alanine dipeptide at 25°C. J. Am. Chem. Soc., 107, 2239–2245

    Article  CAS  Google Scholar 

  • Paine, G. H. and Scheraga, H. A. (1987). Prediction of the native conformation of a polypeptide by a statistical-mechanical procedure. Biopolymers, 26, 1125–1162

    Article  CAS  PubMed  Google Scholar 

  • Pangali, C., Rao, M. and Berne, B. J. (1979). Monte Carlo simulation of the hydrophobic interaction. J. Chem. Phys., 71, 2975–2981

    Article  CAS  Google Scholar 

  • Pearlman, D. and Kollman, P. A. (1989). A new method for carrying out free energy perturbation calculations: dynamically modified windows. J. Chem. Phys., 90, 2460–2470

    Article  CAS  Google Scholar 

  • Pettitt, B. M. (1989). Successes, failures and curiosities in free energy calculations. In van Gunsteren, W. F. and Weiner, P. (Eds.), Computer Simulation of Biomolecular Systems. ESCOM, Leiden, pp. 94–100

    Google Scholar 

  • Quirke, N. (1980). In Proceedings of NATO Summer School on Superionic Conductors, Odense. Plenum, New York

    Google Scholar 

  • Rao, S. N., Singh, U. C., Bash, P. A. and Kollman, P. A. (1987). Free energy perturbation calculations on binding and catalysis on mutating Asn 155 in subtilisin. Nature, 328, 551–554

    Article  CAS  PubMed  Google Scholar 

  • Reif, F. (1965). Fundamentals of Statistical and Thermal Physics. McGraw-Hill, New York

    Google Scholar 

  • Reynolds, C. A., King, P. M. and Richards, W. G. (1988). Computed redox potentials and the design of bioreductive agents. Nature, 334, 80–82

    Article  CAS  PubMed  Google Scholar 

  • Ripoli, D. R. and Scheraga, H. A. (1988). On the multiple-minima problem in conformational analysis of polypeptides. Biopolymers, 27, 1283–1303

    Article  Google Scholar 

  • Russell, A. J. and Fersht, A. R. (1987). Rational modification of enzyme catalysis by engineering surface charge. Nature, 328, 496–500

    Article  CAS  PubMed  Google Scholar 

  • Saito, M. and Nakamura, H. (1990). Hydration free energy calculations by the acceptance ratio method. J. Comput. Chem., in press

    Google Scholar 

  • Saqi, M. A. S. and Goodfellow, J. M. (1990). Free energy changes associated with amino acid substitution in proteins. Protein Eng., in press

    Google Scholar 

  • Scheraga, H. A. (1971). Theoretical and experimental studies of conformations of polypeptides. Chem. Rev., 71, 195–217

    Article  CAS  PubMed  Google Scholar 

  • Scheraga, H. A. and Li, Z. (1988). Structure and free energy of complex thermodynamic systems. J. Mol. Struct. (Theochem.), 179, 333–352

    Article  Google Scholar 

  • Sharp, K., Fine, R. and Honig, B. (1987). Computer simulations of diffusion of a substrate to an active site of an enzyme. Science, 236, 1460–1463

    Article  CAS  PubMed  Google Scholar 

  • Singh, U. C., Brown, F. K., Bash, P. A. and Kollman, P. A. (1987). An approach to the application of free energy perturbation methods using molecular dynamics. J. Am. Chem. Soc., 109, 1607–1614

    Article  CAS  Google Scholar 

  • Sternberg, M. J. E., Hayes, F. R. F., Russell, A. J., Thomas, P. G. and Fersht, A. R. (1987) Prediction of electrostatic effects of engineering of protein charges. Nature, 330, 86–88

    Article  CAS  PubMed  Google Scholar 

  • Straatsma, T. P. (1987). Free energy evaluation by molecular dynamics simulations. Ph.D. Thesis, University of Groningen

    Google Scholar 

  • Straatsma, T. P. and Berendsen, H. J. C. (1988). Free energy of ionic hydration: analysis of a thermodynamic integration technique to evaluate free energy differences by molecular dynamics simulations. J. Chem. Phys., 89, 5876–5886

    Article  CAS  Google Scholar 

  • Straatsma, T. P., Berendsen, H. J. C. and Postma, J. P. M. (1986). Free energy of hydrophobic hydration: a molecular dynamics study of noble gases in water. J. Chem. Phys., 85, 6720–6727

    Article  CAS  Google Scholar 

  • Sussman, F., Goodfellow, J. M., Barnes, P. and Finney, J. L. (1985). Calculation of free energy differences for water from computer simulation. Chem. Phys. Lett., 113, 372

    Article  CAS  Google Scholar 

  • Tembe, B. L. and McCammon, A. J. (1984). Ligand-receptor interactions. Comput. Chem., 8, 281–283

    Article  CAS  Google Scholar 

  • Torrie, G. M. and Valleau, J. P. (1977). Non-physical sampling distributions in Monte Carlo free energy estimation: umbrella sampling. J. Comput. Phys., 23, 187–199

    Article  Google Scholar 

  • Warshel, A., Sussman, F. and Hwang, J. K. (1988). Evaluation of catalytic free energies in genetically modified proteins. J. Mol. Biol., 201, 139–159

    Article  CAS  PubMed  Google Scholar 

  • Weiner, P. K. and Kollman, P. A. (1981). Quantum and molecular mechanical studies on alanyl dipeptide. J. Comput. Chem., 2, 287

    Article  CAS  Google Scholar 

  • Weiner, S. J., Kollman, P. A., Case, D. A., Singh, U. C., Ghio, C., Alagona, G., Profeta, S. and Weiner, P. (1984). A new force field for molecular mechanical simulation of nucleic acids and proteins. J. Am. Chem. Soc., 106, 765–784

    Article  CAS  Google Scholar 

  • Wong, C. F. and McCammon, J. A. (1986). Dynamics and design of enzymes and inhibitors. J. Am. Chem. Soc., 108, 3830–3832

    Article  CAS  Google Scholar 

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© 1991 Macmillan Publishers Limited

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Williams, M.A., Saqi, M.A.S., Goodfellow, J.M. (1991). Applications of Free Energy Calculations. In: Goodfellow, J.M. (eds) Molecular Dynamics. Topics in Molecular and Structural Biology. Palgrave, London. https://doi.org/10.1007/978-1-349-11044-5_6

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  • DOI: https://doi.org/10.1007/978-1-349-11044-5_6

  • Publisher Name: Palgrave, London

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