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Lead optimization mapper: automating free energy calculations for lead optimization

Abstract

Alchemical free energy calculations hold increasing promise as an aid to drug discovery efforts. However, applications of these techniques in discovery projects have been relatively few, partly because of the difficulty of planning and setting up calculations. Here, we introduce lead optimization mapper, LOMAP, an automated algorithm to plan efficient relative free energy calculations between potential ligands within a substantial library of perhaps hundreds of compounds. In this approach, ligands are first grouped by structural similarity primarily based on the size of a (loosely defined) maximal common substructure, and then calculations are planned within and between sets of structurally related compounds. An emphasis is placed on ensuring that relative free energies can be obtained between any pair of compounds without combining the results of too many different relative free energy calculations (to avoid accumulation of error) and by providing some redundancy to allow for the possibility of error and consistency checking and provide some insight into when results can be expected to be unreliable. The algorithm is discussed in detail and a Python implementation, based on both Schrödinger’s and OpenEye’s APIs, has been made available freely under the BSD license.

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Notes

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    assuming N del  = 0; if it is not, the threshold is adjusted slightly.

References

  1. 1.

    Beutler T, Mark AE, van Schaik RC, Gerber PR, van Gunsteren WF (1994) Avoiding singularities and numerical instabilities in free energy calculations based on molecular simulations. Chem Phys Lett 222(6):529–539

    Article  CAS  Google Scholar 

  2. 2.

    Bondy A, Murty U (2008) Graph theory. Springer, New York

    Book  Google Scholar 

  3. 3.

    Boresch S, Bruckner S (2011) Avoiding the van der Waals endpoint problem using serial atomic insertion. J Comput Chem 32(11):2449–2458

    Article  CAS  Google Scholar 

  4. 4.

    Boresch S, Karplus M (1999) The role of bonded terms in free energy simulations 2 calculation of their influence on free energy differences of solvation. J Phys Chem A 103(1):119–136. doi:10.1021/jp981629f

    Article  CAS  Google Scholar 

  5. 5.

    Boresch S, Karplus M (1999) The role of bonded terms in free energy simulations: 1. theoretical analysis. J Phys Chem A 103(1):103–118. doi:10.1021/jp981628n

    Article  CAS  Google Scholar 

  6. 6.

    van den Bosch M, Swart M, Snijders J, Berendsen H, Mark AE, Oostenbrink C, van Gunsteren W, Canters G (2005) Calculation of the redox potential of the protein azurin and some mutants. Chem Bio Chem 6(4):738–746

    Article  Google Scholar 

  7. 7.

    Bowers KJ, Chow E, Xu H, Dror RO, Eastwood MP, Gregersen BA, Klepeis JL, Kolossváry I, Moraes MA, Sacerdoti FD, Salmon JK, Shan Y, Shaw DE (2006) Scalable algorithms for molecular dynamics simulations on commodity clusters. In: Proceedings of the 2006 ACM/IEEE Conference on supercomputing, 84. Tampa, FL

  8. 8.

    Boyce SE, Mobley DL, Rocklin GJ, Graves AP, Dill KA, Shoichet BK (2009) Predicting ligand binding affinity with alchemical free energy methods in a polar model binding site. J Mol Biol 394(4):747–763

    Article  CAS  Google Scholar 

  9. 9.

    Chipot C (2006) Free energy calculations in biological systems. How useful are they in practice? In: Leimkuhler B, Chipot C, Elber R, Laaksonen A, Mark A, Schlick T, Schütte C, Skeel Rr (eds) New algorithms for macromolecular simulation, Lecture Notes in Comput Sci Eng 49:185–211. Springer, Berlin, Heidelberg. doi:10.1007/3-540-31618-3_12

  10. 10.

    Chipot C, Rozanska X, Dixit SB (2005) Can free energy calculations be fast and accurate at the same time? Binding of low-affinity, non-peptide inhibitors to the SH2 domain of the src protein. J Comput Aided Mol Des 19(11):765–770

    Article  CAS  Google Scholar 

  11. 11.

    Chodera JD, Mobley DL, Shirts MR, Dixon RW, Branson K, Pande VS (2011) Alchemical free energy methods for drug discovery: progress and challenges. Curr Opin Struct Biol 21(2):150–160

    Article  CAS  Google Scholar 

  12. 12.

    Christ CD, Mark AE, van Gunsteren W (2010) Basic ingredients of free energy calculations: a review. J Comput Chem 31(8):1569–1582

    CAS  Google Scholar 

  13. 13.

    Deng Y, Roux B (2009) Computations of standard binding free energies with molecular dynamics simulations. J Phys Chem B 113(8):2234–2246

    Article  CAS  Google Scholar 

  14. 14.

    Dolenc J, Oostenbrink C, Koller J, van Gunsteren W (2005) Molecular dynamics simulations and free energy calculations of netropsin and distamycin binding to an AAAAA DNA binding site. Nucleic Acids Res 33(2):725

    Article  CAS  Google Scholar 

  15. 15.

    Ellson J, Gansner E, Koutsofios E, North S, Woodhull G (2003) Graphviz and dynagraph—static and dynamic graph drawing tools. In: Junger M, Mutzel P (eds.) Graph drawing software. Springer, New York, 127–148

  16. 16.

    Enyedy IJ, Egan WJ (2008) Can we use docking and scoring for hit-to-lead optimization? J Comp-Aided Mol Des 22:161–168

    Article  CAS  Google Scholar 

  17. 17.

    Erhardt PW, Proudfoot JR (2007) Drug discovery: historical perspective, current status, and outlook. Compr Med Chem II 1:29–96

    Google Scholar 

  18. 18.

    Gilson MK, Zhou HX (2007) Calculation of protein-ligand binding affinities. Ann Rev Biophys Biomol Struct 36:21–42

    Article  CAS  Google Scholar 

  19. 19.

    de Graaf C, Oostenbrink C, Keizers PHJ, van Vugt-Lussenburg BMA, Commandeur JNM, Vermeulen NPE (2007) Molecular modeling-guided site-directed mutagenesis of cytochrome P450 2D6. Curr Drug Metab 8(1):59–77

    Article  Google Scholar 

  20. 20.

    Hagberg AA, Schult DA, Swart PJ (2008) Exploring network structure, dynamics, and function using NetworkX. In: Proceedings of the 7th Python in Science Conference (SciPy2008), pp 11–15. Pasadena, CA USA

  21. 21.

    Hess B, Kutzner C, van der Spoel D, Lindahl E (2008) Gromacs 4: Algorithms for highly efficient, load-balanced, and scalable molecular simulation. J Chem Theory Comput 4(3):435–447. doi:10.1021/ct700301q

    Article  CAS  Google Scholar 

  22. 22.

    Homeyer N, Gohlke H (2013) FEW-A workflow tool for free energy calculations of ligand binding. J Comput Chem 34:965–973

    Article  CAS  Google Scholar 

  23. 23.

    Hünenberger P, McCammon JA (1999) Ewald artifacts in computer simulations of ionic solvation and ion–ion interaction: a continuum electrostatics study. J Chem Phys 110:1856

    Article  Google Scholar 

  24. 24.

    Hünenberger P, Reif M (2011) Single-ion solvation: experimental and theoretical approaches to elusive thermodynamic quantities. RSC theoretical and computational chemistry series, vol 0, Royal Soc Chem, Cambridge

  25. 25.

    Jarzynski C (2006) Rare events and the convergence of exponentially averaged work values. Phys Rev E 73(4):46,105

    Article  Google Scholar 

  26. 26.

    Kastenholz M, Hünenberger P (2006) Computation of methodology-independent ionic solvation free energies from molecular simulations. I. The electrostatic potential in molecular liquids. J Chem Phys 124:124,106

    CAS  Google Scholar 

  27. 27.

    Kastenholz M, Hünenberger P (2006) Computation of methodology-independent ionic solvation free energies from molecular simulations. II. The hydration free energy of the sodium cation. J Chem Phys 124:224,501

    Google Scholar 

  28. 28.

    Klimovich P, Mobley DL (2010) Predicting hydration free energies using all-atom molecular dynamics simulations and multiple starting conformations. J Comput Aided Mol Des 24(4):307–316

    Article  CAS  Google Scholar 

  29. 29.

    Lu N, Kofke DA, Woolf TB (2004) Improving the efficiency and reliability of free energy perturbation calculations using overlap sampling methods. J Comput Chem 25(1):28–40

    Article  CAS  Google Scholar 

  30. 30.

    Luccarelli J, Michel J, Tirado-Rives J, Jorgensen WL (2010) Effects of water placement on predictions of binding affinities for p38 MAP kinase inhibitors. J Chem Theory Comput 6(12):3850–3856

    Article  CAS  Google Scholar 

  31. 31.

    Manly C, Chandrasekhar J, Ochterski J, Hammer J, Warfield, B (2008): Strategies and tactics for optimizing the hit-to-lead process and beyond—A computational chemistry perspective. Drug Discov Today 13(3–4):99–109

    Article  CAS  Google Scholar 

  32. 32.

    Matter H, Defossa E, Heinelt U, Blohm PM, Schneider D, Müller A, Herok S, Schreuder H, Liesum A, Brachvogel V, Lönze P, Walser A, Al-Obeidi F, Wildgoose P (2002) Design and quantitative structureactivity relationship of 3-amidinobenzyl-1h-indole-2-carboxamides as potent, nonchiral, and selective inhibitors of blood coagulation factor xa. J Med Chem 45(13):2749–2769. doi:10.1021/jm0111346

    Article  CAS  Google Scholar 

  33. 33.

    Michel J, Essex JW (2010) Prediction of protein–ligand binding affinity by free energy simulations: assumptions, pitfalls and expectations. J Comput-Aided Mol Des 1–20

  34. 34.

    Michel J, Tirado-Rives J, Jorgensen W (2009) Prediction of the water content in protein binding sites. J Phys Chem B 113(40):13337–13346

    Article  CAS  Google Scholar 

  35. 35.

    Mobley DL, Bayly CI, Cooper MD, Shirts MR, Dill KA (2009) Small molecule hydration free energies in explicit solvent: an extensive test of fixed-charge atomistic simulations. J Chem Theory Comput 5(2):350–358

    Article  CAS  Google Scholar 

  36. 36.

    Mobley DL, Chodera JD, Dill KA (2007) Confine-and-release method: obtaining correct binding free energies in the presence of protein conformational change. J Chem Theory Comput 3(4):1231–1235

    Article  CAS  Google Scholar 

  37. 37.

    Mobley DL, Dill K, Chodera JD (2008) Treating entropy and conformational changes in implicit solvent simulations of small molecules. J Phys Chem B 112(3):938

    Article  CAS  Google Scholar 

  38. 38.

    Mobley DL, Dumont É, Chodera JD, Dill K (2007) Comparison of charge models for fixed-charge force fields: small-molecule hydration free energies in explicit solvent. J Phys Chem B 111(9):2242–2254

    Article  CAS  Google Scholar 

  39. 39.

    Mobley DL, Graves AP, Chodera JD, McReynolds A, Shoichet BK, Dill KA (2007) Predicting absolute ligand binding free energies to a simple model site. J Mol Biol 371:1118–1134

    Article  CAS  Google Scholar 

  40. 40.

    Mobley DL, Klimovich PV (2012) Perspective: alchemical free energy calculations for drug discovery. J Chem Phys 137(23):230,901

    Article  Google Scholar 

  41. 41.

    Mobley DL, Liu S, Cerutti DS, Swope WC, Rice JE (2012) Alchemical prediction of hydration free energies for SAMPL. J Comput Aided Mol Des 26(5):551–562

    Article  CAS  Google Scholar 

  42. 42.

    Newman J, Dolezal O, Fazio V, Caradoc-Davies T, Peat TS (2012) The DINGO dataset: a comprehensive set of data for the SAMPL challenge. J Comput Aided Mol Des 26(5):497–503

    Google Scholar 

  43. 43.

    OpenEye Scientific Software, Inc. Santa Fe, NM, USA: OpenEye unified python toolkit (2012). Version 2.0.0

  44. 44.

    Palma PN, Bonifácio MJ, Loureiro AI, Soares-da Silva P (2012) Computation of the binding affinities of catechol-O-methyltransferase inhibitors: multisubstate relative free energy calculations. J Comput Chem 33(9):970–986

    Article  CAS  Google Scholar 

  45. 45.

    Paton K (1969) An algorithm for finding a fundamental set of cycles of a graph. Commun ACM 12(9):514–518

    Article  Google Scholar 

  46. 46.

    Perola E, Walters WP, Charifson PS (2004) A detailed comparison of current docking and scoring methods on systems of pharmaceutical relevance. Proteins 56(2):235–249

    Article  CAS  Google Scholar 

  47. 47.

    Reynolds CH (2010) Computer-aided drug design: a practical guide to protein-structure-based modeling. In: Merz KM, Ringe D, Reynolds CH (eds) Drug design: structure- and ligand-based approaches. Cambridge University Press, Cambridge

    Google Scholar 

  48. 48.

    de Ruiter A, Oostenbrink C (2012) Efficient and accurate free energy calculations on trypsin inhibitors. J Chem Theory Comput 8(10):3686–3695

    Article  Google Scholar 

  49. 49.

    Schnecke V, Bostrom J (2006) Computational chemistry-driven decision making in lead generation. Drug Disc Today 11(12):43–50

    Article  CAS  Google Scholar 

  50. 50.

    Schrödinger (2012) LLC, New York, NY: Desmond, 3.4 (ed)

  51. 51.

    Schrödinger (2013) LLC, New York, NY: Canvas. Version 1.6

  52. 52.

    Shi Y, OConnor SP, Sitkoff D, Zhang J, Shi M, Bisaha SN, Wang Y, Li C, Ruan Z, Lawrence RM, Klei HE, Kish K, Liu ECK, Seiler SM, Schweizer L, Steinbacher TE, Schumacher WA, Robl JA, Macor JE, Atwal KS, Stein PD (2011) Arylsulfonamidopiperidone derivatives as a novel class of factor xa inhibitors. Bioorg Med Chem Lett 21(24):7516–7521. doi:10.1016/j.bmcl.2011.06.098

    Article  CAS  Google Scholar 

  53. 53.

    Shirts M, Mobley D (2013) An introduction to best practices in free energy calculations. In: Monticelli L, Salonen E (eds), Biomolecular simulations. Methods in molecular biology, vol. 924, pp 271–311. Humana Press. doi:10.1007/978-1-62703-017-5_11

  54. 54.

    Shirts M, Mobley D, Brown SP (2010) Free-energy calculations in structure-based drug design. Drug Des: structure- and ligand-based approaches

  55. 55.

    Shirts MR, Chodera JD (2008) Statistically optimal analysis of samples from multiple equilibrium states. J Chem Phys 129, 124,105. https://dx.doi.org/10.1063/1.2978177, See code at: http://simtk.org/home/pymbar

  56. 56.

    Shirts MR, Pande VS (2005) Solvation free energies of amino acid side chain analogs for common molecular mechanics water models. J Chem Phys 122:134,508

    Google Scholar 

  57. 57.

    Shirts MR, Pitera JW, Swope WC, Pande VS (2003) Extremely precise free energy calculations of amino acid side chain analogs: comparison of common molecular mechanics force fields for proteins. J Chem Phys 119(11):5740–5761

    Article  CAS  Google Scholar 

  58. 58.

    Steinbrecher T (2012) Free energy calculations in drug lead optimization. In: Gohlke H (eds) Protein-ligand interactions. Wiley, New Jersey

    Google Scholar 

  59. 59.

    Steinbrecher T, Labahn A (2010) Towards accurate free energy calculations in ligand protein-binding studies. Curr Med Chem 17(8):767–785

    Article  CAS  Google Scholar 

  60. 60.

    Steinbrecher T, Mobley DL, Case DA (2007) Nonlinear scaling schemes for Lennard-Jones interactions in free energy calculations. J Chem Phys 127(21):214,108

    Article  Google Scholar 

  61. 61.

    Villa A, Zangi R, Pieffet G, Mark AE (2003) Sampling and convergence in free energy calculations of protein–ligand interactions: the binding of triphenoxypyridine derivatives to factor Xa and trypsin. J Comput-Aided Mol Des 17:673–686

    Google Scholar 

  62. 62.

    Wang L, Berne BJ, Friesner RA (2012) On achieving high accuracy and reliability in the calculation of relative protein-ligand binding affinities. Proc Nat Acad Sci 109(6):1937–1942

    Article  CAS  Google Scholar 

  63. 63.

    Wang L, Deng Y, Knight JL, Wu Y, Kim B, Sherman W, Shelley JC, Lin T, Abel R (2013) Modeling local structural rearrangements using fep/rest: application to relative binding affinity predictions of cdk2 inhibitors. J Chem Theory Comput 9(2):1282–1293. doi:10.1021/ct300911a

    Article  CAS  Google Scholar 

  64. 64.

    Warren GL, Andrews CW, Capelli AM, Clarke B, Lalonde SJ, Lambert MH, Lindvall M, Nevins N, Semus SF, Senger S, Tedesco G, Wall ID, Woolven JM, Peishoff CE, Head MS (2006) A critical assessment of docking programs and scoring functions. J Med Chem 495:912–5931

    Google Scholar 

  65. 65.

    Yoshikawa K, Kobayashi S, Nakamoto Y, Haginoya N, Komoriya S, Yoshino T, Nagata T, Mochizuki A, Watanabe K, Suzuki M, Kanno H, Ohta T (2009) Design, synthesis, and sar of cis-1,2-diaminocyclohexane derivatives as potent factor xa inhibitors. Part ii: exploration of 66 fused rings as alternative s1 moieties. Bioorg Med Chem Lett 17(24):8221–8233. doi:10.1016/j.bmc.2009.10.024

    Article  CAS  Google Scholar 

  66. 66.

    Yoshikawa K, Yokomizo A, Naito H, Haginoya N, Kobayashi S, Yoshino T, Nagata T, Mochizuki A, Osanai K, Watanabe K, Kanno H, Ohta T (2009) Design, synthesis, and sar of cis-1,2-diaminocyclohexane derivatives as potent factor xa inhibitors. Part i: exploration of 56 fused rings as alternative s1 moieties. Bioorg Med Chem Lett 17(24):8206–8220. doi:10.1016/j.bmc.2009.10.023

    Article  CAS  Google Scholar 

  67. 67.

    Young RJ, Adams C, Blows M, Brown D, Burns-Kurtis CL, Chan C, Chaudry L, Convery MA, Davies DE, Exall AM, Foster G, Harling JD, Hortense E, Irvine S, Irving WR, Jackson S, Kleanthous S, Pateman AJ, Patikis AN, Roethka TJ, Senger S, Stelman GJ, Toomey JR, West RI, Whittaker C, Zhou P, Watson NS (2011) Structure and property based design of factor xa inhibitors: pyrrolidin-2-ones with aminoindane and phenylpyrrolidine p4 motifs. Bioorg Med Chem Lett 21(6):1582–1587. doi:10.1016/j.bmcl.2011.01.131

    Article  CAS  Google Scholar 

  68. 68.

    Zacharias M, Straatsma TP, McCammon JA (1994) Separation-shifted scaling, a new scaling method for Lennard-Jones interactions in thermodynamic integration. J Chem Phys 100(12):025–9031

    Article  Google Scholar 

  69. 69.

    Zagrovic B, van Gunsteren W (2007) Computational analysis of the mechanism and thermodynamics of inhibition of phosphodiesterase 5A by synthetic ligands. J Chem Theory Comput 3(1):301–311

    Article  CAS  Google Scholar 

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Acknowledgments

We are grateful to Michael Shirts (University of Virginia) and Pavel Klimovich (UCI) for helpful discussions, and to John Chodera (Memorial Sloan Kettering Cancer Center) for both useful input and an initial MCSS tool that helped motivate the work. We acknowledge the financial support of the National Institutes of Health (1R15GM096257-01A1), the National Science Foundation LA-SiGMA program (EPS-1003897), the Louisiana Board of Regents Research Competitiveness and Research Enhancement Subprograms, Children’s Hospital of New Orleans, and computer time from the UCI GreenPlanet cluster, supported in part by NSF CHE-0840513.

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Correspondence to David L. Mobley.

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Liu, S., Wu, Y., Lin, T. et al. Lead optimization mapper: automating free energy calculations for lead optimization. J Comput Aided Mol Des 27, 755–770 (2013). https://doi.org/10.1007/s10822-013-9678-y

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Keywords

  • Binding free energy
  • Alchemical
  • Planning
  • Molecular dynamics
  • Molecular simulations
  • Lead optimization