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Journal of Computer-Aided Molecular Design

, Volume 30, Issue 11, pp 989–1006 | Cite as

Calculating distribution coefficients based on multi-scale free energy simulations: an evaluation of MM and QM/MM explicit solvent simulations of water-cyclohexane transfer in the SAMPL5 challenge

  • Gerhard König
  • Frank C. Pickard IV
  • Jing Huang
  • Andrew C. Simmonett
  • Florentina Tofoleanu
  • Juyong Lee
  • Pavlo O. Dral
  • Samarjeet Prasad
  • Michael Jones
  • Yihan Shao
  • Walter Thiel
  • Bernard R. Brooks
Article

Abstract

One of the central aspects of biomolecular recognition is the hydrophobic effect, which is experimentally evaluated by measuring the distribution coefficients of compounds between polar and apolar phases. We use our predictions of the distribution coefficients between water and cyclohexane from the SAMPL5 challenge to estimate the hydrophobicity of different explicit solvent simulation techniques. Based on molecular dynamics trajectories with the CHARMM General Force Field, we compare pure molecular mechanics (MM) with quantum-mechanical (QM) calculations based on QM/MM schemes that treat the solvent at the MM level. We perform QM/MM with both density functional theory (BLYP) and semi-empirical methods (OM1, OM2, OM3, PM3). The calculations also serve to test the sensitivity of partition coefficients to solute polarizability as well as the interplay of the quantum-mechanical region with the fixed-charge molecular mechanics environment. Our results indicate that QM/MM with both BLYP and OM2 outperforms pure MM. However, this observation is limited to a subset of cases where convergence of the free energy can be achieved.

Keywords

Distribution coefficient Partition coefficient Water Cyclohexane Multi-scale free energy simulations Explicit solvent 

Notes

Acknowledgments

The authors would like to thank Tim Miller, Richard Venable and John Legato for technical assistance. We would also like to thank Richard Pastor and Richard Venable for very helpful discussions concerning the nature of the apolar phase, especially in octanol. This work was partially supported by the intramural research program of the National Heart, Lung and Blood Institute of the National Institutes of Health and utilized the high-performance computational capabilities of the LoBoS and Biowulf Linux clusters at the National Institutes of Health. (http://www.lobos.nih.gov and http://hpc.nih.gov). The research leading to these results has also received funding from the European Research Council within an ERC Advanced Grant (OMSQC).

References

  1. 1.
    Kah M, Brown CD (2008) LogD: lipophilicity for ionisable compounds. Chemosphere 72(10):1401–1408. doi: 10.1016/j.chemosphere.2008.04.074 CrossRefGoogle Scholar
  2. 2.
    Lee J, Miller BT, Brooks BR (2016) Computational scheme for pH-dependent binding free energy calculation with explicit solvent. Protein Sci 25(1, SI):231–243 10.1002/pro.2755CrossRefGoogle Scholar
  3. 3.
    Ryde U, Söderhjelm P (2016) Ligand-binding affinity estimates supported by quantum-mechanical methods. Chem Rev 116(9, SI):5520–5566. doi: 10.1021/acs.chemrev.5b00630 CrossRefGoogle Scholar
  4. 4.
    Stanton RV, Hartsough DS, Merz KM (1993) Calculation of solvation free energies using a density functional/molecular dynamics coupled potential. J Phys Chem 97:11868–11870CrossRefGoogle Scholar
  5. 5.
    Reddy MR, Singh UC, Erion MD (2004) Development of a quantum mechanics-based free-energy perturbation method: use in the calculation of relative solvation free energies. J Am Chem Soc 126:6224–6225CrossRefGoogle Scholar
  6. 6.
    Reddy MR, Singh UC, Erion MD (2007) Ab initio quantum mechanics-based free energy perturbation method for calculating relative solvation free energies. J Comput Chem 28:491–494CrossRefGoogle Scholar
  7. 7.
    Riccardi D, Schaefer P, Yang Y, Yu H, Ghosh N, Prat-Resina X, König P, Li G, Xu D, Guo H, Elstner M, Cui Q (2006) Development of effective quantum mechanical/molecular mechanical (QM/MM) methods for complex biological processes. J Phys Chem B 110:6458–6469CrossRefGoogle Scholar
  8. 8.
    Yang W, Cui Q, Min D, Li H (2010) Chapter 4-QM/MM alchemical free energy simulations: challenges and recent developments. Annu Rep Comput Chem 6:651–662. doi: 10.1016/S1574-1400(10)06004-4 Google Scholar
  9. 9.
    Yang W, Bitetti-Putzer R, Karplus M (2004) Chaperoned alchemical free energy simulations: a general method for QM, MM, and QM/MM potentials. J Chem Phys 120:9450–9453CrossRefGoogle Scholar
  10. 10.
    Min D, Chen M, Zheng L, Jin Y, Schwartz MA, Sang Q-XA, Yang W (2011) Enhancing QM/MM molecular dynamics sampling in explicit environments via an orthogonal-space-random-walk-based strategy. J Phys Chem B 115:3924–3935CrossRefGoogle Scholar
  11. 11.
    Min D, Zheng L, Harris W, Chen M, Lv C, Yang W (2010) Practically efficient QM/MM alchemical free energy simulations: the orthogonal space random walk strategy. J Chem Theory Comput 6:2253–2266CrossRefGoogle Scholar
  12. 12.
    Kästner J, Senn H, Thiel S, Otte N, Thiel W (2006) QM/MM free-energy perturbation compared to thermodynamic integration and umbrella sampling: Application to an enzymatic reaction. J Chem Theory Comput 2(2):452–461. doi: 10.1021/ct050252w CrossRefGoogle Scholar
  13. 13.
    Polyak I, Benighaus T, Boulanger E, Thiel W (2013) Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation. J Chem Phys 139:064105–064116CrossRefGoogle Scholar
  14. 14.
    Senn HM, Thiel W (2009) QM/MM methods for biomolecular systems. Ang Chem Int Ed 48:1198–1229CrossRefGoogle Scholar
  15. 15.
    Nam K, Gao J, York DM (2005) An efficient linear-scaling Ewald method for long-range electrostatic interactions in combined QM/MM calculations. J Chem Theory Comput 1:2–13CrossRefGoogle Scholar
  16. 16.
    Štrajbl M, Hong G, Warshel A (2002) Ab initio QM/MM simulation with proper sampling: “first principle” calculations of the free energy of the autodissociation of water in aqueous solution. J Phys Chem B 106(51):13333–13343. doi: 10.1021/jp021625h CrossRefGoogle Scholar
  17. 17.
    Plotnikov NV, Kamerlin SCL, Warshel A (2011) Paradynamics: an effective and reliable model for ab initio QM/MM free-energy calculations and related tasks. J Phys Chem B 115(24):7950–7962. doi: 10.1021/jp201217b CrossRefGoogle Scholar
  18. 18.
    Rod TH, Ryde U (2005) Quantum mechanical free energy barrier for an enzymatic reaction. Phys Rev Lett 94(13):138302. doi: 10.1103/PhysRevLett.94.138302 CrossRefGoogle Scholar
  19. 19.
    Rod TH, Ryde U (2005) Accurate QM/MM free energy calculations of enzyme reactions: methylation by catechol O-methyltransferase. J Chem Theory Comput 1(6):1240–1251. doi: 10.1021/ct0501102 CrossRefGoogle Scholar
  20. 20.
    Beierlein FR, Michel J, Essex JW (2011) A simple QM/MM approach for capturing polarization effects in protein-ligand binding free energy calculations. J Phys Chem B 115(17):4911–4926. doi: 10.1021/jp109054j CrossRefGoogle Scholar
  21. 21.
    Fox SJ, Pittock C, Tautermann CS, Fox T, Christ C, Malcolm NOJ, Essex JW, Skylaris C-K (2013) Free energies of binding from large-scale first-principles quantum mechanical calculations: application to ligand hydration energies. J Phys Chem B 117(32):9478–9485. doi: 10.1021/jp404518r CrossRefGoogle Scholar
  22. 22.
    Mikulskis P, Cioloboc D, Andrejić M, Khare S, Brorsson J, Genheden S, Mata RA, Söderhjelm P, Ryde U (2014) Free-energy perturbation and quantum mechanical study of SAMPL4 octa-acid host-guest binding energies. J Comput Aided Mol Des 28(4, SI):375–400. doi: 10.1007/s10822-014-9739-x CrossRefGoogle Scholar
  23. 23.
    Genheden S, Ryde U, Söderhjelm P (2015) Binding affinities by alchemical perturbation using QM/MM with a large QM system and polarizable MM model. J Comput Chem 36(28):2114–2124. doi: 10.1002/jcc.24048 CrossRefGoogle Scholar
  24. 24.
    Sampson C, Fox T, Tautermann CS, Woods C, Skylaris C-K (2015) A “stepping stone” approach for obtaining quantum free energies of hydration. J Phys Chem B 119(23):7030–7040. doi: 10.1021/acs.jpcb.5b01625 CrossRefGoogle Scholar
  25. 25.
    König G, Brooks BR (2015) Correcting for the free energy costs of bond or angle constraints in molecular dynamics simulations, Biochim. Biophys Acta Gen Subj 1850(5, SI):932–943. doi: 10.1016/j.bbagen.2014.09.001 CrossRefGoogle Scholar
  26. 26.
    Cave-Ayland C, Skylaris CK, Essex JW (2015) Direct validation of the single step classical to quantum free energy perturbation. J Phys Chem B 119(3, SI):1017–1025. doi: 10.1021/jp506459v CrossRefGoogle Scholar
  27. 27.
    Ollson MA, Söderhjelm P, Ryde U (2016) Converging ligand-binding free energies obtained with free-energy perturbations at the quantum mechanical level. J Comput Chem. 37(17):1589–1600. doi: 10.1002/jcc.24375 CrossRefGoogle Scholar
  28. 28.
    Gao J, Xia X (1992) A priori evaluation of aqueous polarization effects through Monte Carlo QM-MM simulations. Science 258(5082):631–635CrossRefGoogle Scholar
  29. 29.
    Gao J, Luque FJ, Orozco M (1993) Induced dipole moment and atomic charges based on average electrostatic potentials in aqueous solution. J Chem Phys 98(4):2975. doi: 10.1063/1.464126 CrossRefGoogle Scholar
  30. 30.
    Luzhkov V, Warshel A (1992) Microscopic models for quantum mechanical calculations of chemical processes in solutions: LD/AMPAC and SCAAS/AMPAC calculations of solvation energies. J Comput Chem 13(2):199–213. doi: 10.1002/jcc.540130212 CrossRefGoogle Scholar
  31. 31.
    Wesolowski T, Warshel A (1994) Ab initio free energy perturbation calculations of solvation free energy using the frozen density functional approach. J Phys Chem 98(20):5183–5187. doi: 10.1021/j100071a003 CrossRefGoogle Scholar
  32. 32.
    Gao J, Freindorf M (1997) Hybrid ab initio QM/MM Simulation of N-methylacetamide in aqueous solution. J Phys Chem A 101(17):3182–3188. doi: 10.1021/jp970041q CrossRefGoogle Scholar
  33. 33.
    Kollman P (1993) Free energy calculations: applications to chemical and biochemical phenomena. Chem Rev 93(7):2395–2417. doi: 10.1021/cr00023a004 CrossRefGoogle Scholar
  34. 34.
    Li H, Yang W (2007) Sampling enhancement for the quantum mechanical potential based molecular dynamics simulations: A general algorithm and its extension for free energy calculation on rugged energy surface. J Chem Phys 126(11):114104. doi: 10.1063/1.2710790 CrossRefGoogle Scholar
  35. 35.
    Woods CJ, Manby FR, Mulholland AJ (2008) An efficient method for the calculation of quantum mechanics/molecular mechanics free energies. J Chem Phys 128(1):014109. doi: 10.1063/1.2805379 CrossRefGoogle Scholar
  36. 36.
    Heimdal J, Ryde U (2012) Convergence of QM/MM free-energy perturbations based on molecular-mechanics or semiempirical simulations. Phys Chem Chem Phys 14:1259212604. doi: 10.1039/c2cp41005b CrossRefGoogle Scholar
  37. 37.
    Hu H, Lu Z, Yang W (2007) QM/MM minimum free energy path: methodology and application to triosephosphate isomerase. J Chem Theory Comput 3(2):390–406. doi: 10.1021/ct600240y CrossRefGoogle Scholar
  38. 38.
    Zeng X, Hu H, Hu X, Cohen AJ, Yang W (2008) Ab initio quantum mechanical/molecular mechanical simulation of electron transfer process: fractional electron approach. J Chem Phys 128(12):124510. doi: 10.1063/1.2832946 CrossRefGoogle Scholar
  39. 39.
    Hu H, Lu Z, Parks JM, Burger SK, Yang W (2008) Quantum mechanics/molecular mechanics minimum free-energy path for accurate reaction energetics in solution and enzymes: sequential sampling and optimization on the potential of mean force surface. J Chem Phys 128(3):034105. doi: 10.1063/1.2816557 CrossRefGoogle Scholar
  40. 40.
    Hu H, Yang W (2010) Elucidating solvent contributions to solution reactions with ab initio QM/MM methods. J Phys Chem B 114(8):2755–2759. doi: 10.1021/jp905886q CrossRefGoogle Scholar
  41. 41.
    König G, Pickard FC, Mei Y, Brooks BR (2014) Predicting hydration free energies with a hybrid QM/MM approach: an evaluation of implicit and explicit solvation models in SAMPL4. J Comput Aided Mol Des 28(3, SI):245–257. doi: 10.1007/s10822-014-9708-4 CrossRefGoogle Scholar
  42. 42.
    König G, Hudson PS, Boresch S, Woodcock HL (2014) Multiscale free energy simulations: an efficient method for connecting classical MD simulations to QM or QM/MM free energies using non-Boltzmann Bennett reweighting schemes. J Chem Theory Comput 10(4):1406–1419. doi: 10.1021/ct401118k CrossRefGoogle Scholar
  43. 43.
    Hudson PS, Woodcock HL, Boresch S (2015) Use of nonequilibrium work methods to compute free energy differences between molecular mechanical and quantum mechanical representations of molecular systems. J Phys Chem Lett 6(23):4850–4856. doi: 10.1021/acs.jpclett.5b02164 CrossRefGoogle Scholar
  44. 44.
    Hudson PS, White JK, Kearns FL, Hodošček M, Boresch S, Woodcock HL (2015) Efficiently computing pathway free energies: new approaches based on chain-of-replica and Non-Boltzmann Bennett reweighting schemes Biochim. Biophys Acta Gen Subj 1850(5, SI):944–953. doi: 10.1016/j.bbagen.2014.09.016 CrossRefGoogle Scholar
  45. 45.
    Tuttle T, Thiel W (2008) OMx-D: semiempirical methods with orthogonalization and dispersion corrections. implementation and biochemical application. Phys Chem Chem Phys 10:2159–2166. doi: 10.1039/B718795E CrossRefGoogle Scholar
  46. 46.
    Repasky MP, Chandrasekhar J, Jorgensen WL (2002) PDDG/PM3 and PDDG/MNDO: improved semiempirical methods. J Comput Chem 23:1601–1622CrossRefGoogle Scholar
  47. 47.
    Elstner M, Porezag D, Jungnickel G, Elsner J, Haugk M, Frauenheim T, Suhai S, Seifert G (1998) Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties. Phys Rev B 58(11):7260–7268. doi: 10.1103/PhysRevB.58.7260 CrossRefGoogle Scholar
  48. 48.
    Dral PO, Wu X, Spörkel L, Koslowski A, Weber W, Steiger R, Scholten M, Thiel W (2016) Semiempirical quantum-chemical orthogonalization-corrected methods: theory, implementation, and parameters. J Chem Theory Comput 12(3):1082–1096. doi: 10.1021/acs.jctc.5b01046 CrossRefGoogle Scholar
  49. 49.
    Simmonett AC, Pickard FC, Schaefer HF III, Brooks BR (2014) An efficient algorithm for multipole energies and derivatives based on spherical harmonics and extensions to particle mesh Ewald. J Chem Phys 140(18):184101. doi: 10.1063/1.4873920 CrossRefGoogle Scholar
  50. 50.
    Simmonett AC, Pickard FC, Shao Y, Cheatham TE III, Brooks BR (2015) Efficient treatment of induced dipoles. J Chem Phys 143(7):074115. doi: 10.1063/1.4928530 CrossRefGoogle Scholar
  51. 51.
    Rustenburg AS, Dancer J, Lin B, Ortwine DF, Mobley DL, Chodera JD (in press) Measuring experimental cyclohexane/water distribution coefficients for the SAMPL5 challenge. J Comput Aided Mol DesGoogle Scholar
  52. 52.
    König G, Mei Y, Pickard FC, Simmonett AC, Miller BT, Herbert JM, Woodcock HL, Brooks BR, Shao Y (2016) Computation of hydration free energies using the multiple environment single system quantum mechanical/molecular mechanical method. J Chem Theory Comput 12(1):332–344. doi: 10.1021/acs.jctc.5b00874 CrossRefGoogle Scholar
  53. 53.
    Kolb M, Thiel W (1993) Beyond the MNDO model: methodical considerations and numerical results. J Comput Chem 14(7):775–789. doi: 10.1002/jcc.540140704 CrossRefGoogle Scholar
  54. 54.
    Weber W, Thiel W (2000) Orthogonalization corrections for semiempirical methods. Theor Chem Acc 103(6):495–506. doi: 10.1007/s002149900083 CrossRefGoogle Scholar
  55. 55.
    Scholten M (2003) Semiempirische Verfahren mit Orthogonalisierungskorrekturen: Die OM3 methode. Ph.D. thesis, Heinrich-Heine-Universität DüsseldorfGoogle Scholar
  56. 56.
    Stewart J (1989) Optimization of parameters for semiempirical methods I. Method. J Comput Chem 10(2):209–220. doi: 10.1002/jcc.540100208 CrossRefGoogle Scholar
  57. 57.
    Shaw KE, Woods CJ, Mulholland AJ (2010) Compatibility of quantum chemical methods and empirical (MM) water models in quantum mechanics/molecular mechanics liquid water simulations. J Phys Chem Lett 1(1):219–223. doi: 10.1021/jz900096p CrossRefGoogle Scholar
  58. 58.
    Dewar M, Zoebisch E, Healy E, Stewart J (1985) AM1—a new general purpose quantum mechanical molecular model. J Am Chem Soc 107(13):3902–3909. doi: 10.1021/ja00299a024 CrossRefGoogle Scholar
  59. 59.
    Dewar M, Thiel W (1977) Ground states of molecules. 38. The MNDO method. Approximations and parameters. J Am Chem Soc 99(15):4899–4907. doi: 10.1021/ja00457a004 CrossRefGoogle Scholar
  60. 60.
    Thiel W, Voityuk A (1996) Extension of MNDO to d orbitals: parameters and results for the second-row elements and for the zinc group. J Phys Chem 100(2):616–626. doi: 10.1021/jp952148o CrossRefGoogle Scholar
  61. 61.
    Thiel W (1981) The MNDOC method, a correlated version of the MNDO model. J Am Chem Soc 103(6):1413–1420. doi: 10.1021/ja00396a021 CrossRefGoogle Scholar
  62. 62.
    Grimme S, Antony J, Ehrlich S, Krieg H (2010) A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J Chem Phys 132(15):154104. doi: 10.1063/1.3382344 CrossRefGoogle Scholar
  63. 63.
    Pickard FC, König G, Tofoleanu F, Lee J, Simmonett AC, Shao Y, Ponder JW, Brooks BR (2016) Blind prediction of distribution in the SAMPL5 challenge with QM based protomer and pKa corrections. J Comput Aided Mol Des. doi: 10.1007/s10822-016-9955-7 Google Scholar
  64. 64.
    Nicholls A, Mobley DL, Guthrie JP, Chodera JD, Bayly CI, Cooper MD, Pande VS (2008) Predicting small-molecule solvation free energies: an informal blind test for computational chemistry. J Med Chem 51(4):769–779. doi: 10.1021/jm070549+ CrossRefGoogle Scholar
  65. 65.
    Guthrie JP (2009) A blind challenge for computational solvation free energies: introduction and overview. J Phys Chem B 113(14):4501–4507. doi: 10.1021/jp806724u CrossRefGoogle Scholar
  66. 66.
    Marenich AV, Cramer CJ, Truhlar DG (2009) Performance of SM6, SM8, and SMD on the SAMPL1 test set for the prediction of small-molecule solvation free energies. J Phys Chem B 113(14):4538–4543CrossRefGoogle Scholar
  67. 67.
    Geballe MT, Skillman AG, Nicholls A, Guthrie JP, Taylor PJ (2010) The SAMPL2 blind prediction challenge: introduction and overview. J Comput Aided Mol Des 24(4, SI):259–279. doi: 10.1007/s10822-010-9350-8 CrossRefGoogle Scholar
  68. 68.
    Klimovich PV, Mobley DL (2010) Predicting hydration free energies using all-atom molecular dynamics simulations and multiple starting conformations. J Comput Aided Mol Des 24(4, SI):307–316. doi: 10.1007/s10822-010-9343-7 CrossRefGoogle Scholar
  69. 69.
    Klamt A, Diedenhofen M (2010) Blind prediction test of free energies of hydration with COSMO-RS. J Comput Aided Mol Des 24(4, SI):357–360. doi: 10.1007/s10822-010-9354-4 CrossRefGoogle Scholar
  70. 70.
    Ribeiro R, Marenich A, Cramer C, Truhlar D (2010) Prediction of sampl2 aqueous solvation free energies and tautomeric ratios using the sm8, sm8ad, and smd solvation models. J Comput Aided Mol Des 24(4):317–333CrossRefGoogle Scholar
  71. 71.
    Muddana HS, Varnado CD, Bielawski CW, Urbach AR, Isaacs L, Geballe MT, Gilson MK (2012) Blind prediction of host-guest binding affinities: a new SAMPL3 challenge. J Comput Aided Mol Des 26(5):475–487. doi: 10.1007/s10822-012-9554-1 CrossRefGoogle Scholar
  72. 72.
    König G, Brooks BR (2012) Predicting binding affinities of host-guest systems in the SAMPL3 blind challenge: the performance of relative free energy calculations. J Comput Aided Mol Des 26(5):543–550. doi: 10.1007/s10822-011-9525-y CrossRefGoogle Scholar
  73. 73.
    Gallicchio E, Levy RM (2012) Prediction of SAMPL3 host-guest affinities with the binding energy distribution analysis method (BEDAM). J Comput Aided Mol Des 26(5):505–516. doi: 10.1007/s10822-012-9552-3 CrossRefGoogle Scholar
  74. 74.
    Lawrenz M, Wereszczynski J, Ortiz-Sánchez JM, Nichols SE, McCammon JA (2012) Thermodynamic integration to predict host-guest binding affinities. J Comput Aided Mol Des 26(5):569–576. doi: 10.1007/s10822-012-9542-5 CrossRefGoogle Scholar
  75. 75.
    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. doi: 10.1007/s10822-011-9528-8 CrossRefGoogle Scholar
  76. 76.
    Geballe MT, Guthrie JP (2012) The SAMPL3 blind prediction challenge: transfer energy overview. J Comput Aided Mol Des 26(5, SI):489–496. doi: 10.1007/s10822-012-9568-8 CrossRefGoogle Scholar
  77. 77.
    Beckstein O, Iorga BI (2012) Prediction of hydration free energies for aliphatic and aromatic chloro derivatives using molecular dynamics simulations with the OPLS-AA force field. J Comput Aided Mol Des 26(5, SI):635–645. doi: 10.1007/s10822-011-9527-9 CrossRefGoogle Scholar
  78. 78.
    Reinisch J, Klamt A, Diedenhofen M (2012) Prediction of free energies of hydration with COSMO-RS on the SAMPL3 data set. J Comput Aided Mol Des 26(5, SI):669–673. doi: 10.1007/s10822-012-9576-8 CrossRefGoogle Scholar
  79. 79.
    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, SI):551–562. doi: 10.1007/s10822-011-9528-8 CrossRefGoogle Scholar
  80. 80.
    Kehoe CW, Fennell CJ, Dill KA (2012) Testing the semi-explicit assembly solvation model in the SAMPL3 community blind test. J Comput Aided Mol Des 26(5, SI):563–568. doi: 10.1007/s10822-011-9536-8 CrossRefGoogle Scholar
  81. 81.
    Guthrie JP (2014) SAMPL4 A blind challenge for computational solvation free energies: the compounds considered. J Comput Aided Mol Des 28(3):151–168CrossRefGoogle Scholar
  82. 82.
    Mobley DL, Wymer K, Lim NM (2014) Blind prediction of solvation free energies from the SAMPL4 challenge. J Comput Aided Mol Des 28(3):135–150CrossRefGoogle Scholar
  83. 83.
    Genheden S (2016) Predicting partition coefficients with a simple all-atom/coarse-grained hybrid model. J Chem Theory Comput 12(1):297–304. doi: 10.1021/acs.jctc.5b00963 CrossRefGoogle Scholar
  84. 84.
    Tembe BL, McCammon JA (1984) Ligand-receptor interactions. Comput Chem 8:281–283CrossRefGoogle Scholar
  85. 85.
    Villa A, Mark AE (2002) Calculation of the free energy of solvation for neutral analogs of amino acid side chains. J Comput Chem 23:548–553. doi: 10.1002/jcc.10052 CrossRefGoogle Scholar
  86. 86.
    MacCallum J, Tieleman D (2003) Calculation of the water-cyclohexane transfer free energies of neutral amino acid side-chain analogs using the OPLS all-atom force field. J Comput Chem 24(15):1930–1935. doi: 10.1002/jcc.10328 CrossRefGoogle Scholar
  87. 87.
    Michel J, Orsi M, Essex JW (2008) Prediction of partition coefficients by multiscale hybrid atomic-level/coarse-grain simulations. J Phys Chem B 112(3):657–660. doi: 10.1021/jp076142y CrossRefGoogle Scholar
  88. 88.
    Brooks B, Brooks C III, MacKerell A Jr, Nilsson L, Petrella R, Roux B, Won Y, Archontis G, Bartels C, Boresch S, Caflisch A, Caves L, Cui Q, Dinner A, Feig M, Fischer S, Gao J, Hodošček M, Im W, Kuczera K, Lazaridis T, Ma J, Ovchinnikov V, Paci E, Pastor R, Post C, Pu J, Schaefer M, Tidor B, Venable R, Woodcock H, Wu X, Yang W, York D, Karplus M (2009) CHARMM: the biomolecular simulation program. J Comput Chem 30(10):1545–1614. doi: 10.1002/jcc.21287 CrossRefGoogle Scholar
  89. 89.
    Brooks BR, Bruccoleri RE, Olafson BD, States DJ, Swaminathan S, Karplus M (1983) CHARMM: a program for macromolecular energy, minimization and dynamics calculations. J Comput Chem 4:187–217CrossRefGoogle Scholar
  90. 90.
    Vanommeslaeghe K, Hatcher E, Acharya C, Kundu S, Zhong S, Shim J, Darian E, Guvench O, Lopes P, Vorobyov I, MacKerell AD Jr (2010) CHARMM general force field: a force field for drug-like molecules compatible with the CHARMM All-atom additive biological force fields. J Comp Chem 31(4):671–690. doi: 10.1002/jcc.21367 Google Scholar
  91. 91.
    Bennett CH (1976) Efficient estimation of free energy differences from Monte Carlo data. J Comput Phys 22:245–268CrossRefGoogle Scholar
  92. 92.
    König G, Bruckner S, Boresch S (2009) Unorthodox uses of Bennett’s acceptance ratio method. J Comput Chem 30(11):1712–1718. doi: 10.1002/jcc.21255 CrossRefGoogle Scholar
  93. 93.
    König G, Boresch S (2011) Non-Boltzmann sampling and Bennett’s acceptance ratio method: how to profit from bending the rules. J Comput Chem 32(6):1082–1090. doi: 10.1002/jcc.21687 CrossRefGoogle Scholar
  94. 94.
    Jorgensen WL, Chandrasekhar H, Madura JD, Impey RW, Klein ML (1983) Comparison of simple potential functions for simulating liquid water. J Chem Phys 79:926CrossRefGoogle Scholar
  95. 95.
    Neria E, Fischer S, Karplus M (1996) Simulation of activation free energies in molecular systems. J Chem Phys 105:1902CrossRefGoogle Scholar
  96. 96.
    Darden T, York D, Pedersen L (1993) Particle mesh Ewald—an N. Log(N) method for Ewald sums in large systems. J Chem Phys 98:10089–10092CrossRefGoogle Scholar
  97. 97.
    Van Gunsteren WF, Berendsen HJC (1977) Algorithms for macromolecular dynamics and costraint dynamics. Mol Phys 34:1311–1327CrossRefGoogle Scholar
  98. 98.
    Sugita Y, Kitao A, Okamoto Y (2000) Multidimensional replica-exchange method for free-energy calculations. J Chem Phys 113:6042CrossRefGoogle Scholar
  99. 99.
    Zacharias M, Straatsma TP, McCammon JA (1994) Separation-shifted scaling, a new scaling method for Lennard-Jones interactions in thermodynamic integration. J Chem Phys 100:9025CrossRefGoogle Scholar
  100. 100.
    Shao Y, Molnar LF, Jung Y, Kussmann J, Ochsenfeld C, Brown ST, Gilbert ATB, Slipchenko LV, Levchenko SV, O’Neill DP, DiStasio RA Jr, Lochan RC, Wang T, Beran GJO, Besley NA, Herbert JM, Lin CY, Van Voorhis T, Chien SH, Sodt A, Steele RP, Rassolov VA, Maslen PE, Korambath PP, Adamson RD, Austin B, Baker J, Byrd EFC, Dachsel H, Doerksen RJ, Dreuw A, Dunietz BD, Dutoi AD, Furlani TR, Gwaltney SR, Heyden A, Hirata S, Hsu C-P, Kedziora G, Khalliulin RZ, Klunzinger P, Lee AM, Lee MS, Liang W, Lotan I, Nair N, Peters B, Proynov EI, Pieniazek PA, Rhee YM, Ritchie J, Rosta E, Sherrill CD, Simmonett AC, Subotnik JE, Woodcock HL III, Zhang W, Bell AT, Chakraborty AK, Chipman DM, Keil FJ, Warshel A, Hehre WJ, Schaefer HF III, Kong J, Krylov AI, Gill PMW, Head-Gordon M (2006) Advances in methods and algorithms in a modern quantum chemistry program package. Phys Chem Chem Phys 8(27):3172–3191. doi: 10.1039/b517914a CrossRefGoogle Scholar
  101. 101.
    Woodcock HL III, Hodošček M, Gilbert ATB, Gill PMW, Schaefer HF III, Brooks BR (2007) Interfacing Q-Chem and CHARMM to perform QM/MM reaction path calculations. J Comput Chem 28(9):1485–1502. doi: 10.1002/jcc.20587 CrossRefGoogle Scholar
  102. 102.
    Thiel W (2006) MNDO2005, version 7.1, Max-Planck-Institut für Kohlenforschung: Mülheim an der Ruhr, GermanyGoogle Scholar
  103. 103.
    Zwanzig RW (1954) High-temperature equation of state by a perturbation method. I. Nonpolar gases. J Chem Phys 22:1420CrossRefGoogle Scholar
  104. 104.
    Jia X, Wang M, Shao Y, König G, Brooks BR, Zhang JZH, Mei Y (2016) Calculations of solvation free energy through energy reweighting from molecular mechanics to quantum mechanics. J Chem Theory Comput 12(2):499–511. doi: 10.1021/acs.jctc.5b00920 CrossRefGoogle Scholar
  105. 105.
    Dybeck EC, König G, Brooks BR, Shirts MR (2016) A comparison of methods to reweight from classical molecular simulations to QM/MM potentials. J Chem Theory Comput 12(4):1466–1480. doi: 10.1021/acs.jctc.5b01188 CrossRefGoogle Scholar
  106. 106.
    Becke A (1988) Density-functional exchange-energy approximation with correct asymptotic behavior. Phys Rev A 38(6):3098–3100. doi: 10.1103/PhysRevA.38.3098 CrossRefGoogle Scholar
  107. 107.
    Lee C, Yang W, Parr R (1988) Development of the Colle–Salvetti correlation-energy formula into a functional of the electron density. Phys Rev B 37(2):785–789. doi: 10.1103/PhysRevB.37.785 CrossRefGoogle Scholar
  108. 108.
    Piana S, Donchev AG, Robustelli P, Shaw DE (2015) Water dispersion interactions strongly influence simulated structural properties of disordered protein states. J Phys Chem B 119(16):5113–5123. doi: 10.1021/jp508971m CrossRefGoogle Scholar
  109. 109.
    Bruckner S, Boresch S (2011) Efficiency of alchemical free energy simulations I: practical comparison of the exponential formula, thermodynamic integration and Bennett’s acceptance ratio method. J Comput Chem 32:1303–1319CrossRefGoogle Scholar
  110. 110.
    Wolfenden R, Radzicka A (1994) On the probability of finding a water molecule in a nonpolar cavity. Science 265(5174):936–937. doi: 10.1126/science.8052849 CrossRefGoogle Scholar
  111. 111.
    Dral PO, Wu X, Spörkel L, Koslowski A, Thiel W (2016) Semiempirical quantum-chemical orthogonalization-corrected methods: benchmarks for ground-state properties. J Chem Theory Comput 12(3):1097–1120. doi: 10.1021/acs.jctc.5b01047 CrossRefGoogle Scholar
  112. 112.
    Grimme S, Ehrlich S, Goerigk L (2011) Effect of the damping function in dispersion corrected density functional theory. J Comput Chem 32(7):1456–1465. doi: 10.1002/jcc.21759 CrossRefGoogle Scholar
  113. 113.
    Risthaus T, Grimme S (2013) Benchmarking of London dispersion-accounting density functional theory methods on very large molecular complexes. J Chem Theory Comput 9(3):1580–1591. doi: 10.1021/ct301081n CrossRefGoogle Scholar
  114. 114.
    König G, Boresch S (2009) Hydration free energies of amino acids: why side chain analog data are not enough. J Phys Chem B 113(26):8967–8974. doi: 10.1021/jp902638y CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland (outside the USA) 2016

Authors and Affiliations

  • Gerhard König
    • 1
    • 2
  • Frank C. Pickard IV
    • 1
  • Jing Huang
    • 1
  • Andrew C. Simmonett
    • 1
  • Florentina Tofoleanu
    • 1
  • Juyong Lee
    • 1
  • Pavlo O. Dral
    • 2
  • Samarjeet Prasad
    • 1
  • Michael Jones
    • 1
  • Yihan Shao
    • 1
  • Walter Thiel
    • 2
  • Bernard R. Brooks
    • 1
  1. 1.Laboratory of Computational BiologyNational Heart, Lung and Blood Institute, National Institutes of HealthBethesdaUSA
  2. 2.Max-Planck-Institut für KohlenforschungMülheim an der RuhrGermany

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