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Statistical mechanics and molecular dynamics in evaluating thermodynamic properties of biomolecular recognition

Published online by Cambridge University Press:  15 November 2011

Jeff Wereszczynski  and
J. Andrew McCammon
Jeff Wereszczynski*
Affiliation:
Department of Chemistry and Biochemistry, University of California, San Diego, CA, USA
J. Andrew McCammon
Affiliation:
Department of Chemistry and Biochemistry, Department of Pharmacology, Howard Hughes Medical Institute, Chevy Chase, MD, USA
*
*Author for correspondence: J. Wereszczynski, Department of Chemistry and Biochemistry, University of California, San Diego, CA, USA. Tel.: 858.822.0169; Fax: 858.534.4974; Email: [email protected]
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Abstract

Molecular recognition plays a central role in biochemical processes. Although well studied, understanding the mechanisms of recognition is inherently difficult due to the range of potential interactions, the molecular rearrangement associated with binding, and the time and length scales involved. Computational methods have the potential for not only complementing experiments that have been performed, but also in guiding future ones through their predictive abilities. In this review, we discuss how molecular dynamics (MD) simulations may be used in advancing our understanding of the thermodynamics that drive biomolecular recognition. We begin with a brief review of the statistical mechanics that form a basis for these methods. This is followed by a description of some of the most commonly used methods: thermodynamic pathways employing alchemical transformations and potential of mean force calculations, along with end-point calculations for free energy differences, and harmonic and quasi-harmonic analysis for entropic calculations. Finally, a few of the fundamental findings that have resulted from these methods are discussed, such as the role of configurational entropy and solvent in intermolecular interactions, along with selected results of the model system T4 lysozyme to illustrate potential and current limitations of these methods.

Type
Review Article
Information
Quarterly Reviews of Biophysics , Volume 45 , Issue 1 , February 2012 , pp. 1 - 25
Copyright
Copyright © Cambridge University Press 2011

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References

7. References

Abel, R., Wang, L. L., Friesner, R. A. & Berne, B. J. (2010). A displaced-solvent functional analysis of model hydrophobic enclosures. Journal of Chemical Theory and Computation 6, 2924–2934.CrossRefGoogle ScholarPubMed
Abel, R., Young, T., Farid, R., Berne, B. J. & Friesner, R. A. (2008). Role of the active-site solvent in the thermodynamics of factor Xa ligand binding. Journal of the American Chemical Society 130, 2817–2831.CrossRefGoogle ScholarPubMed
Adcock, S. A. & McCammon, J. A. (2006). Molecular dynamics: survey of methods for simulating the activity of proteins. Chemical Reviews 106, 1589–1615.CrossRefGoogle ScholarPubMed
Andricioaei, I. & Karplus, M. (2001). On the calculation of entropy from covariance matrices of the atomic fluctuations. Journal of Chemical Physics 115, 6289–6292.CrossRefGoogle Scholar
Baron, R., Hunenberger, P. H. & McCammon, J. A. (2009). Absolute single-molecule entropies from quasi-harmonic analysis of microsecond molecular dynamics: correction terms and convergence properties. Journal of Chemical Theory and Computation 5, 3150–3160.CrossRefGoogle ScholarPubMed
Baron, R. & McCammon, J. A. (2008). (Thermo)dynamic role of receptor flexibility, entropy, and motional correlation in protein-ligand binding. ChemPhysChem 9, 983–988.CrossRefGoogle ScholarPubMed
Baron, R., Setny, P. & McCammon, J. A. (2010). Water in cavity-ligand recognition. Journal of the American Chemical Society 132, 12091–12097.CrossRefGoogle ScholarPubMed
Baron, R., van Gunsteren, W. F. & Hunenberger, P. H. (2006). Estimating the configurational entropy from molecular dynamics simulations: anharmonicity and correlation corrections to the quasi-harmonic approximation. Trends in Physical Chemistry 11, 87–122.Google Scholar
Barril, X., Gelpi, J. L., Lopez, J. M., Orozco, M. & Luque, F. J. (2001). How accurate can molecular dynamics/linear response and Poisson–Boltzmann/solvent accessible surface calculations be for predicting relative binding affinities? Acetylcholinesterase huprine inhibitors as a test case. Theoretical Chemistry Accounts 106, 2–9.CrossRefGoogle Scholar
Best, R. B., Buchete, N. V. & Hummer, G. (2008). Are current molecular dynamics force fields too helical? Biophysical Journal 95, L7–L9.CrossRefGoogle ScholarPubMed
Beuming, T., Farid, R. & Sherman, W. (2009). High-energy water sites determine peptide binding affinity and specificity of PDZ domains. Protein Science 18, 1609–1619.CrossRefGoogle ScholarPubMed
Beutler, T. C. & van Gunsteren, W. F. (1994). Molecular-dynamics free-energy calculation in 4 dimensions. Journal of Chemical Physics 101, 1417–1422.CrossRefGoogle Scholar
Beutler, T. C., Mark, A. E., Vanschaik, R. C., Gerber, P. R. & van Gunsteren, W. F. (1994). Avoiding singularities and numerical instabilities in free-energy calculations based on molecular simulations. Chemical Physics Letters 222, 529–539.CrossRefGoogle Scholar
Boresch, S., Tettinger, F., Leitgeb, M. & Karplus, M. (2003). Absolute binding free energies: a quantitative approach for their calculation. Journal of Physical Chemistry B 107, 9535–9551.CrossRefGoogle Scholar
Boyce, S. E., Mobley, D. L., Rocklin, G. J., Graves, A. P., Dill, K. A. & Shoichet, B. K. (2009). Predicting ligand binding affinity with alchemical free energy methods in a polar model binding site. Journal of Molecular Biology 394, 747–763.CrossRefGoogle Scholar
Brooijmans, N. & Kuntz, I. D. (2003). Molecular recognition and docking algorithms. Annual Review of Biophysics and Biomolecular Structure 32, 335–373.CrossRefGoogle ScholarPubMed
Brooks, B. & Karplus, M. (1983). Harmonic dynamics of proteins-normal-modes and fluctuations in bovine pancreatic trypsin-inhibitor. Proceedings of the National Academy of Sciences of the United States of America 80, 6571–6575.CrossRefGoogle ScholarPubMed
Brooks, B. R., Janezic, D. & Karplus, M. (1995). Harmonic-analysis of large systems. 1. Methodology. Journal of Computational Chemistry 16, 1522–1542.CrossRefGoogle Scholar
Carlsson, J. & Åqvist, J. (2005). Absolute and relative entropies from computer simulation with applications to ligand binding. Journal of Physical Chemistry B 109, 6448–6456.CrossRefGoogle ScholarPubMed
Carlsson, J. & Åqvist, J. (2006). Calculations of solute and solvent entropies from molecular dynamics simulations. Physical Chemistry Chemical Physics 8, 5385–5395.CrossRefGoogle ScholarPubMed
Chandler, D. (1987). Introduction to Modern Statistical Mechanics. New York: Oxford University.Google Scholar
Chang, C. E. & Gilson, M. K. (2004). Free energy, entropy, and induced fit in host-guest recognition: calculations with the second-generation mining minima algorithm. Journal of the American Chemical Society 126, 13156–13164.CrossRefGoogle ScholarPubMed
Chang, C. E., Chen, W. & Gilson, M. K. (2005). Evaluating the accuracy of the quasiharmonic approximation. Journal of Chemical Theory and Computation 1, 1017–1028.CrossRefGoogle ScholarPubMed
Chang, C. E. A., McLaughlin, W. A., Baron, R., Wang, W. & McCammon, J. A. (2008). Entropic contributions and the influence of the hydrophobic environment in promiscuous protein-protein association. Proceedings of the National Academy of Sciences of the United States of America 105, 7456–7461.Google Scholar
Chen, W., Chang, C. E. & Gilson, M. K. (2004). Calculation of cyclodextrin binding affinities: energy, entropy, and implications for drug design. Biophysical Journal 87, 3035–3049.CrossRefGoogle ScholarPubMed
Chen, W., Gilson, M. K., Webb, S. P. & Potter, M. J. (2010). Modeling protein-ligand binding by mining minima. Journal of Chemical Theory and Computation 6, 3540–3557.CrossRefGoogle ScholarPubMed
Chipot, C. & Pohorille, A. (2007). Free Energy Calculations. Berlin: Springer.CrossRefGoogle Scholar
Christ, C. D. & van Gunsteren, W. F. (2007). Enveloping distribution sampling: a method to calculate free energy differences from a single simulation. Journal of Chemical Physics 126, 184110.CrossRefGoogle ScholarPubMed
Christ, C. D. & van Gunsteren, W. F. (2008). Multiple free energies from a single simulation: extending enveloping distribution sampling to nonoverlapping phase-space distributions. Journal of Chemical Physics 128, 174112.CrossRefGoogle ScholarPubMed
Colledge, M. & Scott, J. D. (1999). AKAPs: from structure to function. Trends in Cell Biology 9, 216–221.CrossRefGoogle ScholarPubMed
Darve, E., Rodriguez-Gomez, D. & Pohorille, A. (2008). Adaptive biasing force method for scalar and vector free energy calculations. Journal of Chemical Physics 128, 144120.Google Scholar
de Groot, B. L., Hayward, S., van Aalten, D. M. F., Amadei, A. & Berendsen, H. J. C. (1998). Domain motions in bacteriophage T4 lysozyme: a comparison between molecular dynamics and crystallographic data. Proteins-Structure Function and Genetics 31, 116–127.3.0.CO;2-K>CrossRefGoogle ScholarPubMed
Deng, Y. Q. & Roux, B. (2006). Calculation of standard binding free energies: aromatic molecules in the T4 lysozyme L99A mutant. Journal of Chemical Theory and Computation 2, 1255–1273.CrossRefGoogle ScholarPubMed
Durrant, J. D. & McCammon, J. A. (2010). Computer-aided drug-discovery techniques that account for receptor flexibility. Current Opinion In Pharmacology 10, 770–774.CrossRefGoogle ScholarPubMed
Eriksson, A. E., Baase, W. A., Wozniak, J. A. & Matthews, B. W. (1992). A cavity-containing mutant of T4 lysozyme is stabilized by buried benzene. Nature 355, 371–373.CrossRefGoogle ScholarPubMed
Fajer, M., Hamelberg, D. & McCammon, J. A. (2008). Replica-exchange accelerated molecular dynamics (REXAMD) applied to thermodynamic integration. Journal of Chemical Theory and Computation 4, 1565–1569.CrossRefGoogle ScholarPubMed
Fayos, R., Melacini, G., Newlon, M. G., Burns, L., Scott, J. D. & Jennings, P. A. (2003). Induction of flexibility through protein–protein interactions. Journal of Biological Chemistry 278, 18581–18587.CrossRefGoogle ScholarPubMed
Fuentes, G., Dastidar, S. G., Madhumalar, A. & Verma, C. S. (2011). Role of protein flexibility in the discovery of new drugs. Drug Development Research 72, 26–35.CrossRefGoogle Scholar
Gallicchio, E., Kubo, M. M. & Levy, R. M. (1998). Entropy-enthalpy compensation in solvation and ligand binding revisited. Journal of the American Chemical Society 120, 4526–4527.Google Scholar
Gallicchio, E., Kubo, M. M. & Levy, R. M. (2000). Enthalpy-entropy and cavity decomposition of alkane hydration free energies: numerical results and implications for theories of hydrophobic solvation. Journal of Physical Chemistry B 104, 6271–6285.CrossRefGoogle Scholar
Gellman, S. H. (1997). Molecular recognition. Chemical Reviews 97, 1231–1734.CrossRefGoogle ScholarPubMed
Gilson, M. K. & Honig, B. (1988). Calculation of the total electrostatic energy of a macromolecular system: solvation energies, binding energies, and conformational analysis. Proteins: Structure Function and Bioinformatics 4, 7–18.CrossRefGoogle ScholarPubMed
Gilson, M. K. & Zhou, H. X. (2007). Calculation of protein-ligand binding affinities. Annual Review of Biophysics and Biomolecular Structure 36, 21–42.CrossRefGoogle ScholarPubMed
Gilson, M. K., Given, J. A., Bush, B. L. & McCammon, J. A. (1997a). The statistical-thermodynamic basis for computation of binding affinities: a critical review. Biophysical Journal 72, 1047–1069.CrossRefGoogle ScholarPubMed
Gilson, M. K., Given, J. A. & Head, M. S. (1997b). A new class of models for computing receptor-ligand binding affinities. Chemistry and Biology 4, 87–92.CrossRefGoogle ScholarPubMed
Graves, A. P., Brenk, R. & Shoichet, B. K. (2005). Decoys for docking. Journal of Medicinal Chemistry 48, 3714–3728.CrossRefGoogle ScholarPubMed
Graves, A. P., Shivakumar, D. M., Boyce, S. E., Jacobson, M. P., Case, D. A. & Shoichet, B. K. (2008). Rescoring docking hit lists for model cavity sites: predictions and experimental testing. Journal of Molecular Biology 377, 914–934.CrossRefGoogle ScholarPubMed
Guimaraes, C. R. W. & Cardozo, M. (2008). MM-GB/SA rescoring of docking poses in structure-based lead optimization. Journal of Chemical Information and Modeling 48, 958–970.CrossRefGoogle ScholarPubMed
Guimãraes, C. R. W. & Mathiowetz, A. M. (2010). Addressing limitations with the MMGB/SA scoring procedure using the water map method and free energy perturbation calculations. Journal of Chemical Information and Modeling 50, 547–559.Google Scholar
Guvench, O. & MacKerell, A. D. (2009). Computational evaluation of protein-small molecule binding. Current Opinion in Structural Biology 19, 56–61.CrossRefGoogle ScholarPubMed
Halperin, I., Ma, B. Y., Wolfson, H. & Nussinov, R. (2002). Principles of docking: an overview of search algorithms and a guide to scoring functions. Proteins: Structure Function and Genetics 47, 409–443.CrossRefGoogle Scholar
Hamelberg, D. & McCammon, J. A. (2004). Standard free energy of releasing a localized water molecule from the binding pockets of proteins: double-decoupling method. Journal of the American Chemical Society 126, 7683–7689.CrossRefGoogle ScholarPubMed
Hamelberg, D., Mongan, J. & McCammon, J. A. (2004). Accelerated molecular dynamics: a promising and efficient simulation method for biomolecules. Journal of Chemical Physics 120, 11919–11929.CrossRefGoogle ScholarPubMed
Harris, S. A., Gavathiotis, E., Searle, M. S., Orozco, M. & Laughton, C. A. (2001). Cooperativity in drug-DNA recognition: a molecular dynamics study. Journal of the American Chemical Society 123, 12658–12663.CrossRefGoogle ScholarPubMed
Hayward, S. & Berendsen, H. J. C. (1998). Systematic analysis of domain motions in proteins from conformational change: new results on citrate synthase and T4 lysozyme. Proteins: Structure Function And Genetics 30, 144–154.Google Scholar
Hermans, J. & Wang, L. (1997). 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. Journal of the American Chemical Society 119, 2707–2714.CrossRefGoogle Scholar
Hummer, G. (2010). Molecular binding under water's influence. Nature Chemistry 2, 906–907.CrossRefGoogle ScholarPubMed
Jiang, W. & Roux, B. (2010). Free energy perturbation Hamiltonian replica-exchange molecular dynamics (FEP/H-REMD) for absolute ligand binding free energy calculations. Journal of Chemical Theory and Computation 6, 2559–2565.Google Scholar
Jorge, M., Garrido, N. M., Queimada, A. J., Economou, I. G. & Macedo, E. A. (2010). Effect of the integration method on the accuracy and computational efficiency of free energy calculations using thermodynamic integration. Journal of Chemical Theory and Computation 6, 1018–1027.Google Scholar
Karplus, M. & Kushick, J. N. (1981). Method for estimating the configurational entropy of macromolecules. Macromolecules 14, 325–332.CrossRefGoogle Scholar
Kirkwood, J. G. (1935). Statistical mechanics of fluid mixtures. Journal of Chemical Physics 3, 300–313.CrossRefGoogle Scholar
Kitchen, D. B., Decornez, H., Furr, J. R. & Bajorath, J. (2004). Docking and scoring in virtual screening for drug discovery: methods and applications. Nature Reviews Drug Discovery 3, 935–949.Google Scholar
Klebe, G. (2006). Virtual ligand screening: strategies, perspectives and limitations. Drug Discovery Today 11, 580–594.Google Scholar
Knight, J. L. & Brooks, C. L. (2009). λ-dynamics free energy simulation methods. Journal of Computational Chemistry 30, 1692–1700.CrossRefGoogle ScholarPubMed
Kollman, P. A., Massova, I., Reyes, C., Kuhn, B., Huo, S. H., Chong, L., Lee, M., Lee, T., Duan, Y., Wang, W., Donini, O., Cieplak, P., Srinivasan, J., Case, D. A. & Cheatham, T. E. (2000). Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models. Accounts of Chemical Research 33, 889–897.CrossRefGoogle ScholarPubMed
Kong, X. J. & Brooks, C. L. (1996). λ-dynamics: a new approach to free energy calculations. Journal of Chemical Physics 105, 2414–2423.Google Scholar
Kumar, S., Bouzida, D., Swendsen, R. H., Kollman, P. A. & Rosenberg, J. M. (1992). The weighted histogram analysis method for free-energy calculations on biomolecules .1. The method. Journal of Computational Chemistry 13, 1011–1021.Google Scholar
Ladbury, J. E. & Chowdhry, B. Z. (1996). Sensing the heat: the application of isothermal titration calorimetry to thermodynamic studies of biomolecular interactions. Chemical Biology 3, 791–801.CrossRefGoogle ScholarPubMed
Laio, A. & Parrinello, M. (2002). Escaping free-energy minima. Proceedings of the National Academy of Sciences of the United States of America 99, 12562–12566.CrossRefGoogle ScholarPubMed
Lawrenz, M., Baron, R. & McCammon, J. A. (2009). Independent-trajectories thermodynamic-integration free-energy changes for biomolecular systems: determinants of H5N1 avian influenza virus neuraminidase inhibition by peramivir. Journal of Chemical Theory and Computation 5, 1106–1116.Google Scholar
Lee, M. R. & Sun, Y. X. (2007). Improving docking accuracy through molecular mechanics generalized born optimization and scoring. Journal of Chemical Theory and Computation 3, 1106–1119.CrossRefGoogle ScholarPubMed
Levy, R. M. & Gallicchio, E. (1998). Computer simulations with explicit solvent: recent progress in the thermodynamic decomposition of free energies and in modeling electrostatic effects. Annual Review of Physical Chemistry 49, 531–567.CrossRefGoogle ScholarPubMed
Levy, R. M., Karplus, M., Kushick, J. & Perahia, D. (1984). Evaluation of the configurational entropy for proteins: application to molecular-dynamics simulations of an α-helix. Macromolecules 17, 1370–1374.Google Scholar
Lumry, R. & Rajender, S. (1970). Enthalpy-entropy compensation phenomena in water solutions of proteins and small molecules: a ubiquitous property of water. Biopolymers 9, 1125–1227.Google Scholar
Lyne, P. D., Lamb, M. L. & Saeh, J. C. (2006). Accurate prediction of the relative potencies of members of a series of kinase inhibitors using molecular docking and MM-GBSA scoring. Journal of Medicinal Chemistry 49, 4805–4808.CrossRefGoogle ScholarPubMed
Mackerell, A. D. (2004). Empirical force fields for biological macromolecules: overview and issues. Journal of Computational Chemistry 25, 1584–1604.Google Scholar
Mann, G. & Hermans, J. (2000). Modeling protein-small molecule interactions: structure and thermodynamics of noble gases binding in a cavity in mutant phage T4 lysozyme L99A. Journal of Molecular Biology 302, 979–989.CrossRefGoogle Scholar
McCammon, J. A. (1998). Theory of biomolecular recognition. Current Opinion in Structural Biology 8, 245–249.Google Scholar
Michel, J., Tirado-Rives, J. & Jorgensen, W. L. (2009a). Prediction of the water content in protein binding sites. Journal of Physical Chemistry B 113, 13337–13346.CrossRefGoogle ScholarPubMed
Michel, J., Tirado-Rives, J. & Jorgensen, W. L. (2009b). Energetics of displacing water molecules from protein binding sites: consequences for ligand optimization. Journal of the American Chemical Society 131, 15403–15411.CrossRefGoogle ScholarPubMed
Mobley, D. L., Chodera, J. D. & Dill, K. A. (2007a). Confine-and-release method: obtaining correct binding free energies in the presence of protein conformational change. Journal of Chemical Theory and Computation 3, 1231–1235.CrossRefGoogle ScholarPubMed
Mobley, D. L., Graves, A. P., Chodera, J. D., McReynolds, A. C., Shoichet, B. K. & Dill, K. A. (2007b). Predicting absolute ligand binding free energies to a simple model site. Journal of Molecular Biology 371, 1118–1134.CrossRefGoogle ScholarPubMed
Morton, A. & Matthews, B. W. (1995). Specificity of ligand-binding in a buried nonpolar cavity of T4 lysozyme-linkage of dynamics and structural plasticity. Biochemistry 34, 8576–8588.CrossRefGoogle Scholar
Morton, A., Baase, W. A. & Matthews, B. W. (1995). Energetic origins of specificity of ligand-binding in an interior nonpolar cavity of T4 lysozyme. Biochemistry 34, 8564–8575.Google Scholar
Olsson, T. S. G., Williams, M. A., Pitt, W. R. & Ladbury, J. E. (2008). The thermodynamics of protein-ligand interaction and solvation: insights for ligand design. Journal of Molecular Biology 384, 1002–1017.Google Scholar
Oostenbrink, C. & van Gunsteren, W. F. (2003). Single-step perturbations to calculate free energy differences from unphysical reference states: limits on size, flexibility, and character. Journal of Computational Chemistry 24, 1730–1739.Google Scholar
Oostenbrink, C. & van Gunsteren, W. F. (2005). Free energies of ligand binding for structurally diverse compounds. Proceedings of the National Academy of Sciences of the United States of America 102, 6750–6754.Google Scholar
Pearlstein, R. A., Hu, Q. Y., Zhou, J., Yowe, D., Levell, J., Dale, B., Kaushik, V. K., Daniels, D., Hanrahan, S., Sherman, W. & Abel, R. (2010). New hypotheses about the structure-function of proprotein convertase subtilisin/kexin type 9: analysis of the epidermal growth factor-like repeat a docking site using WaterMap. Proteins: Structure Function and Bioinformatics 78, 2571–2586.CrossRefGoogle ScholarPubMed
Petsko, G. A. & Ringe, D. (1984). Fluctuations in protein-structure from X-ray-diffraction. Annual Review of Biophysics and Bioengineering 13, 331–371.CrossRefGoogle ScholarPubMed
Rodinger, T., Howell, P. L. & Pomes, R. (2005). Absolute free energy calculations by thermodynamic integration in four spatial dimensions. Journal of Chemical Physics 123, 034104.CrossRefGoogle ScholarPubMed
Roux, B. (1995). The calculation of the potential of mean force using computer-simulations. Computer Physics Communications 91, 275–282.CrossRefGoogle Scholar
Roy, J. & Laughton, C. A. (2010). Long-timescale molecular-dynamics simulations of the major urinary protein provide atomistic interpretations of the unusual thermodynamics of ligand binding. Biophysical Journal 99, 218–226.Google Scholar
Samsonov, S., Teyra, J. & Pisabarro, T. (2008). A molecular dynamics approach to study the importance of solvent in protein interactions. Proteins: Structure Function and Bioinformatics 73, 515–525.Google Scholar
Setny, P., Baron, R. & McCammon, J. A. (2010). How can hydrophobic association be enthalpy driven? Journal of Chemical Theory and Computation 6, 2866–2871.Google Scholar
Shaw, D. E., Deneroff, M. M., Dror, R. O., Kuskin, J. S., Larson, R. H., Salmon, J. K., Young, C., Batson, B., Bowers, K. J., Chao, J. C., Eastwood, M. P., Gagliardo, J., Grossman, J. P., Ho, C. R., Ierardi, D. J., Kolossváry, I., Klepeis, J. L., Layman, T., McLeavey, C., Moraes, M. A., Mueller, R., Priest, E. C., Shan, Y., Spengler, J., Theobald, M., Towles, B. & Wang, S. C. (2008). Anton, a special-purpose machine for molecular dynamics simulation. Communications of the ACM 51, 91–97.CrossRefGoogle Scholar
Shirts, M. R. & Chodera, J. D. (2008). Statistically optimal analysis of samples from multiple equilibrium states. Journal of Chemical Physics 129, 124105.Google Scholar
Shirts, M. R. & Pande, V. S. (2005). Comparison of efficiency and bias of free energies computed by exponential averaging, the Bennett acceptance ratio, and thermodynamic integration. Journal of Chemical Physics 122, 144107.Google Scholar
Shirts, M. R., Bair, E., Hooker, G. & Pande, V. S. (2003). Equilibrium free energies from nonequilibrium measurements using maximum-likelihood methods. Physical Review Letters 91, 140601.CrossRefGoogle ScholarPubMed
Shirts, M. R., Mobley, D. L. & Chodera, J. D. (2007). Alchemical free energy calculations: ready for prime time? Annual Reports in Computational Chemistry 3, 41–59.Google Scholar
Sitkoff, D., Sharp, K. & Honig, B. (1994). Accurate calculation of hydration free energies using macroscopic solvent models. Journal of Physical Chemistry 98, 1978–1988.Google Scholar
Srinivasan, J., Cheatham, T. E., Cieplak, P., Kollman, P. A. & Case, D. A. (1998). Continuum solvent studies of the stability of DNA, RNA, and phosphoramidate-DNA helices. Journal of the American Chemical Society 120, 9401–9409.CrossRefGoogle Scholar
Still, W. C., Tempczyk, A., Hawley, R. C. & Hendrickson, T. (1990). Semianalytical treatment of solvation for molecular mechanics and dynamics. Journal of the American Chemical Society 112, 6127–6129.Google Scholar
Stone, J. E., Phillips, J. C., Freddolino, P. L., Hardy, D. J., Trabuco, L. G. & Schulten, K. (2007). Accelerating molecular modeling applications with graphics processors. Journal of Computational Chemistry 28, 2618–2640.Google Scholar
Stone, M. J. (2001). NMR relaxation studies of the role of conformational entropy in protein stability and ligand binding. Accounts of Chemical Research 34, 379–388.CrossRefGoogle ScholarPubMed
Straatsma, T. P. & McCammon, J. A. (1991). Multiconfiguration thermodynamic integration. Journal of Chemical Physics 95, 1175–1188.CrossRefGoogle Scholar
Straatsma, T. P. & McCammon, J. A. (1992). Computational alchemy. Annual Review of Physical Chemistry 43, 407–435.Google Scholar
Swanson, J. M. J., Henchman, R. H. & McCammon, J. A. (2004). Revisiting free energy calculations: a theoretical connection to MM/PBSA and direct calculation of the association free energy. Biophysical Journal 86, 67–74.Google Scholar
Thomas, A. S. & Elcock, A. H. (2006). Direct observation of salt effects on molecular interactions through explicit-solvent molecular dynamics simulations: differential effects on electrostatic and hydrophobic interactions and comparisons to Poisson-Boltzmann theory. Journal of the American Chemical Society 128, 7796–7806.CrossRefGoogle ScholarPubMed
Toda, M., Kubo, R. & Saitô, (1992). Statistical Physics I. Berlin: Springer.Google Scholar
Torrie, G. M. & Valleau, J. P. (1977). Non-physical sampling distributions in Monte-Carlo free-energy estimation – umbrella sampling. Journal of Computational Physics 23, 187–199.Google Scholar
Wang, J. M., Morin, P., Wang, W. & Kollman, P. A. (2001). Use of MM-PBSA in reproducing the binding free energies to HIV-1 RT of TIBO derivatives and predicting the binding mode to HIV-1 RT of efavirenz by docking and MM-PBSA. Journal of the American Chemical Society 123, 5221–5230.CrossRefGoogle ScholarPubMed
Wang, J. Y., Deng, Y. Q. & Roux, B. (2006). Absolute binding free energy calculations using molecular dynamics simulations with restraining potentials. Biophysical Journal 91, 2798–2814.Google Scholar
Wei, B. Q. Q., Baase, W. A., Weaver, L. H., Matthews, B. W. & Shoichet, B. K. (2002). A model binding site for testing scoring functions in molecular docking. Journal of Molecular Biology 322, 339–355.CrossRefGoogle Scholar
Weis, A., Katebzadeh, K., Soderhjelm, P., Nilsson, I. & Ryde, U. (2006). Ligand affinities predicted with the MM/PBSA method: dependence on the simulation method and the force field. Journal of Medicinal Chemistry 49, 6596–6606.CrossRefGoogle ScholarPubMed
Wereszczynski, J. & McCammon, J. A. (2010). Using selectively applied accelerated molecular dynamics to enhance free energy calculations. Journal of Chemical Theory and Computation 6, 3285–3293.CrossRefGoogle ScholarPubMed
Wilson, E. B., Decius, J. C. & Cross, P. C. (1955). Molecular Vibrations. New York: McGraw-Hill.Google Scholar
Woods, C. J., Essex, J. W. & King, M. A. (2003). The development of replica-exchange based free-energy methods. Journal of Physical Chemistry B 107, 13703–13710.Google Scholar
Young, T., Abel, R., Kim, B., Berne, B. J. & Friesner, R. A. (2007). Motifs for molecular recognition exploiting hydrophobic enclosure in protein-ligand binding. Proceedings of the National Academy of Sciences of the United States of America 104, 808–813.Google Scholar
Zacharias, M., Straatsma, T. P. & McCammon, J. A. (1994). Separation-shifted scaling, a new scaling method for Lennard–Jones interactions in thermodynamic integration. Journal of Chemical Physics 100, 9025–9031.Google Scholar
Zhou, H. X. & Gilson, M. K. (2009). Theory of free energy and entropy in noncovalent binding. Chemical Reviews 109, 4092–4107.Google Scholar
Zidek, L., Novotny, M. V. & Stone, M. J. (1999). Increased protein backbone conformational entropy upon hydrophobic ligand binding. Nature Structural Biology 6, 1118–1121.Google Scholar
Zwanzig, R. W. (1954). High-temperature equation of state by a perturbation method .1. Nonpolar gases. Journal of Chemical Physics 22, 1420–1426.CrossRefGoogle Scholar