Independent-Trajectory Thermodynamic Integration: A Practical Guide to Protein-Drug Binding Free Energy Calculations Using Distributed Computing

  • Morgan Lawrenz
  • Riccardo Baron
  • Yi Wang
  • J. Andrew McCammon
Part of the Methods in Molecular Biology book series (MIMB, volume 819)


The Independent-Trajectory Thermodynamic Integration (IT-TI) approach for free energy calculation with distributed computing is described. IT-TI utilizes diverse conformational sampling obtained from multiple, independent simulations to obtain more reliable free energy estimates compared to single TI predictions. The latter may significantly under- or over-estimate the binding free energy due to finite sampling. We exemplify the advantages of the IT-TI approach using two distinct cases of protein–ligand binding. In both cases, IT-TI yields distributions of absolute binding free energy estimates that are remarkably centered on the target experimental values. Alternative protocols for the practical and general application of IT-TI calculations are investigated. We highlight a protocol that maximizes predictive power and computational efficiency.

Key words

Neuraminidase dTDP-6-deoxy-D-xylo-4-hexopyranosid-4-ulose-3,5-epimerase Oseltamivir Independent-Trajectory Thermodynamic Integration Molecular dynamics Convergence Solvent effects 



The authors thank the members of the McCammon group for useful discussions. This work was supported, in part, by the National Institutes of Health, the National Science Foundation, the National Biomedical Computational Resource, and the Howard Hughes Medical Institute. We thank the Center for Theoretical Biological Physics (NSF Grant PHY-0822283), and the Texas Advanced Computer Center (grant TG-MCA93S013) for distributed computing resources. We also thank Dr. Ross C. Walker at the San Diego Supercomputing Center for additional computational resources.


  1. 1.
    Kirkwood, J. G. (1935) Statistical mechanics of fluid mixtures. J. Chem. Phys. 3, 300–313.CrossRefGoogle Scholar
  2. 2.
    Tembe, B., and McCammon, J. (1984) Ligand Receptor Interactions. J. Comput. Chem. 8, 281–283.CrossRefGoogle Scholar
  3. 3.
    Beveridge, D., and DiCapua, F. (1989) Free Energy Via Molecular Simulation: Application to Chemical and Biomolecular Systems. Annu. Rev. Biophys. Chem. 18, 431–492.CrossRefGoogle Scholar
  4. 4.
    Kollman, P. (1993) Free energy calculations: applications to chemical and biochemical phenomena. Chem. Rev. 2395–2417.Google Scholar
  5. 5.
    van Gunsteren, W. F., Beutler, T. C., Fraternali, F., King, P. M., Mark, A. E., and Smith, P. E. Computation of Free Energy in Practice: Choice of Approximations and Accuracy Limiting Factors; ESCOM Science Publishers: Leiden, 1993; Vol. 2.Google Scholar
  6. 6.
    Gilson, M. K., Given, J. A., Bush, B. L., and McCammon, J. A. (1997) The statistical-thermodynamic basis for computation of binding affinities: a critical review. Biophys. J. 72, 1047–1069.PubMedCrossRefGoogle Scholar
  7. 7.
    Jorgensen, W. (2004) The many roles of computation in drug discovery. Science 303, 1813–1818.PubMedCrossRefGoogle Scholar
  8. 8.
    Gilson, M. K., and Zhou, H.-X. (2007) Calculation of protein-ligand binding affinities. Annu. Rev. Biophys. Biomol. Struct. 36, 21–42.PubMedCrossRefGoogle Scholar
  9. 9.
    Pohorille, A., Jarzynski, C., and Chipot, C. (2010) Good Practices in Free-Energy Calculations. J. Phys. Chem. 10235–10253.Google Scholar
  10. 10.
    Christ, C. D., Mark, A. E., and Gunsteren, W. F. V. (2010) Basic ingredients of free energy calculations: a review. J. Comput. Chem. 31, 1569–1582.PubMedGoogle Scholar
  11. 11.
    Fujitani, H., Tanida, Y., Ito, M., Jayachandran, G., Snow, C. D., Shirts, M. R., Sorin, E. J., and Pande, V. S. (2005) Direct calculation of the binding free energies of FKBP ligands. J. Chem. Phys. 123, 084108.PubMedCrossRefGoogle Scholar
  12. 12.
    Zagrovic, B., and van Gunsteren, W. (2007) Computational Analysis of the Mechanism and Thermodynamics of Inhibition of Phosphodiesterase 5A by Synthetic Ligands. J. Chem. Theory Comput. 3, 301–311.CrossRefGoogle Scholar
  13. 13.
    Lawrenz, M., Baron, R., and McCammon, J. (2009) Independent-Trajectories Thermodynamic-Integration Free-Energy Changes for Biomolecular Systems: Determinants of H5N1 Avian Influenza Virus Neuraminidase Inhibition by Peramivir. J. Chem. Theory Comput. 5, 1106–1116.PubMedCrossRefGoogle Scholar
  14. 14.
    Lawrenz, M., Baron, R., Wang, Y., and McCammon, J. (2011) Effects of Biomolecular Flexibility on Alchemical Calculations of Absolute Binding Free Energies. J. Chem. Theory Comput. 7, 2224–2232.Google Scholar
  15. 15.
    Russell, R. J., Haire, L. F., Stevens, D. J., Collins, P. J., Lin, Y. P., Blackburn, G. M., Hay, A. J., Gamblin, S. J., and Skehel, J. J. (2006) The structure of H5N1 avian influenza neuraminidase suggests new opportunities for drug design. Nature 443, 45–49.PubMedCrossRefGoogle Scholar
  16. 16.
    Amaro, R. E., Minh, D. D. L., Cheng, L. S., Lindstrom, W. M., Olson, A. J., Lin, J.-H., Li, W. W., and McCammon, J. A. (2007) Remarkable loop flexibility in avian influenza N1 and its implications for antiviral drug design. J. Am. Chem. Soc. 129, 7764–7765.PubMedCrossRefGoogle Scholar
  17. 17.
    Sivendran, S., Jones, V., Sun, D., Wang, Y., Grzegorzewicz, A. E., Scherman, M. S., Napper, A. D., McCammon, J. A., Lee, R. E., Diamond, S. L., and McNeil, M. (2010) Identification of triazinoindol-benzimidazolones as nanomolar inhibitors of the Mycobacterium tuberculosis enzyme TDP-6-deoxy-d-xylo-4-hexopyranosid-4-ulose 3,5-epimerase (RmlC). Bioorg. Med. Chem. 18, 896–908.PubMedCrossRefGoogle Scholar
  18. 18.
    Hornak, V., Abel, R., Okur, A., Strockbine, B., Roitberg, A., and Simmerling, C. (2006) Comparison of multiple Amber force fields and development of improved protein backbone parameters. Proteins 65, 712–725.PubMedCrossRefGoogle Scholar
  19. 19.
    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.CrossRefGoogle Scholar
  20. 20.
    Åqvist, J. (1990) Ion-water interaction potentials derived from free energy perturbation simulations. J. Phys. Chem. 94, 8021–8024.CrossRefGoogle Scholar
  21. 21.
    Lawrenz, M., Wereszczynski, J., Amaro, R., Walker, R., Roitberg, A., and McCammon, J. A. (2010) Impact of calcium on N1 influenza neuraminidase dynamics and binding free energy. Proteins: Struct., Funct., Bioinf. 78, 2523–2532.Google Scholar
  22. 22.
    Wang, J., Wolf, R. M., Caldwell, J. W., and Case, P. A. K. D. A. (2004) Development and testing of a general amber force field. J. Comp. Chem. 25, 1157–1174.CrossRefGoogle Scholar
  23. 23.
    Cornell, W. D., Cieplak, P., Bayly, C. I., Gould, I. R., Merz, K. M., Ferguson, D. M., Spellmeyer, D. C., Fox, T., Caldwell, J. W., and Kollman, P. A. (1995) A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules. J. Am. Chem. Soc. 117, 5179–5197.CrossRefGoogle Scholar
  24. 24.
    Frisch, M. et al. Gaussian 03, Revision C.02, 2003, Gaussian, Inc., Wallingford, CT, 2004.Google Scholar
  25. 25.
    Phillips, J. C., Braun, R., Wang, W., Gumbart, J., Tajkhorshid, E., Villa, E., Chipot, C., Skeel, R. D., Kalé, L., and Schulten, K. (2005) Scalable molecular dynamics with NAMD. J. Comput. Chem. 26, 1781–1802.PubMedCrossRefGoogle Scholar
  26. 26.
    Andersen, H. (1983) Rattle: A “velocity” version of the shake algorithm for molecular dynamics calculations. J. Comput. Phys. 52, 24–34.CrossRefGoogle Scholar
  27. 27.
    Shuichi, M., and Peter, A. (1992) SETTLE: an analytical version of the SHAKE and RATTLE algorithm for rigid water models. J. Comput. Chem. 13, 952–962, 148324.CrossRefGoogle Scholar
  28. 28.
    Darden, T., York, D., and Pedersen, L. (1993) Particle mesh Ewald: An N [center-dot] log(N) method for Ewald sums in large systems. J. Chem. Phys. 98, 10089–10092.CrossRefGoogle Scholar
  29. 29.
    Feller, S., Zhang, Y., Pastor, R., and Brooks, B. (1995) Constant pressure molecular dynamics simulation: The Langevin piston method. J. Chem. Phys. 103, 4613–4621.CrossRefGoogle Scholar
  30. 30.
    Boresch, S., Tettinger, F., Leitgeb, M., and Karplus, M. (2003) Absolute binding free energies: A quantitative approach for their calculation. J. Phys. Chem. B 107, 9535–9551.CrossRefGoogle Scholar
  31. 31.
    General, I. J. (2010) A Note on the Standard State’s Binding Free Energy. J. Chem. Theory Comput. 6, 2520–2524.CrossRefGoogle Scholar
  32. 32.
    Hamelberg, D., and McCammon, J. A. (2004) Standard free energy of releasing a localized water molecule from the binding pockets of proteins: double-decoupling method. J. Am. Chem. Soc. 126, 7683–7689.PubMedCrossRefGoogle Scholar
  33. 33.
    García, A. E. (1992) Large-amplitude nonlinear motions in proteins. Phys. Rev. Lett. 68, 2696–2699.PubMedCrossRefGoogle Scholar
  34. 34.
    Amadei, A., Linssen, A. B. M., and Berendsen, H. J. C. (1993) Essential dynamics of proteins. Proteins: Struct., Funct., Bioinf. 17, 412–425.CrossRefGoogle Scholar
  35. 35.
    Hess, B., Kutzner, C., van der Spoel, D., and Lindahl, E. (2008) GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory Comput. 4, 435–447.CrossRefGoogle Scholar
  36. 36.
    Humphrey, W., Dalke, A., and Schulten, K. (1996) VMD: visual molecular dynamics. J. Mol. Graphics 14, 33–38, 27–28.CrossRefGoogle Scholar
  37. 37.
    Zacharias, M., Straatsma, T. P., and McCammon, J. A. (1994) Separation-shifted scaling, a new scaling method for Lennard-Jones interactions in thermodynamic integration. J. Chem. Phys. 100, 9025–9031.CrossRefGoogle Scholar
  38. 38.
    Jorge, M., Garrido, N., Queimada, A., Economou, I., and Macedo, E. (2010) Effect of the Integration Method on the Accuracy and Computational Efficiency of Free Energy Calculations Using Thermodynamic Integration. J. Chem. Theory Comput. 6, 1018–1027.CrossRefGoogle Scholar
  39. 39.
    Yang, W., Bitetti-Putzer, R., and Karplus, M. (2004) Free energy simulations: use of reverse cumulative averaging to determine the equilibrated region and the time required for convergence. J. Chem. Phys. 120, 2618–28.PubMedCrossRefGoogle Scholar
  40. 40.
    Mobley, D. L., Chodera, J. D., and Dill, K. A. (2006) On the use of orientational restraints and symmetry corrections in alchemical free energy calculations. J. Chem. Phys. 125, 084902.PubMedCrossRefGoogle Scholar
  41. 41.
    Wang, J., Deng, Y., and Roux, B. (2006) Absolute Binding Free Energy Calculations Using Molecular Dynamics Simulations with Restraining Potentials. Biophys. J. 91, 2798–2814.PubMedCrossRefGoogle Scholar
  42. 42.
    Cheng, Y., and Prusoff, W. H. (1973) Relationship between the inhibition constant (K1) and the concentration of inhibitor which causes 50 per cent inhibition (I50) of an enzymatic reaction. Biochem. Pharmacol. 22, 3099–108.PubMedCrossRefGoogle Scholar
  43. 43.
    Kati, W. M., Montgomery, D., Carrick, R., Gubareva, L., Maring, C., McDaniel, K., Steffy, K., Molla, A., Hayden, F., Kempf, D., and Kohlbrenner, W. (2002) In vitro characterization of A-315675, a highly potent inhibitor of A and B strain influenza virus neuraminidases and influenza virus replication. Antimicrob. Agents Chemother. 46, 1014–1021.PubMedCrossRefGoogle Scholar
  44. 44.
    Allen, M. P., and Tildesley, D. J. Computer Simulation of Liquids; Oxford University Press: Oxford, 1987.Google Scholar
  45. 45.
    Chodera, J., Swope, W., Pitera, J., Seok, C., and Dill, K. (2007) Use of the Weighted Histogram Analysis Method for the Analysis of Simulated and Parallel Tempering Simulations. J. Chem. Theory Comput. 3, 26–41, doi: 10.1021/ct0502864.CrossRefGoogle Scholar
  46. 46.
    Carlstein, E. (1986) The use of subseries values for estimating the variance of a general static from a stationary sequence. Annals of Statistics 14, 1171–1179.CrossRefGoogle Scholar
  47. 47.
    Åqvist, J., and Hansson, T. (1996) On the Validity of Electrostatic Linear Response in Polar Solvents. J. Phys. Chem. 100, 9512–9521.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Chemistry and Biochemistry, Center for Theoretical Biological PhysicsUniversity of California, San DiegoLa JollaUSA
  2. 2.Department of Medicinal Chemistry, College of Pharmacy, The Henry Eyring Center for Theoretical ChemistryUniversity of UtahSalt Lake CityUSA
  3. 3.Howard Hughes Medical Institute, Departments of Chemistry and Biochemistry and Pharmacology, Center for Theoretical Biological PhysicsUniversity of California, San DiegoLa JollaUSA

Personalised recommendations