Skip to main content
SpringerLink
Log in

Predicting hydration free energies with a hybrid QM/MM approach: an evaluation of implicit and explicit solvation models in SAMPL4

  • Published:
Journal of Computer-Aided Molecular Design Aims and scope Submit manuscript

Abstract

The correct representation of solute-water interactions is essential for the accurate simulation of most biological phenomena. Several highly accurate quantum methods are available to deal with solvation by using both implicit and explicit solvents. So far, however, most evaluations of those methods were based on a single conformation, which neglects solute entropy. Here, we present the first test of a novel approach to determine hydration free energies that uses molecular mechanics (MM) to sample phase space and quantum mechanics (QM) to evaluate the potential energies. Free energies are determined by using re-weighting with the Non-Boltzmann Bennett (NBB) method. In this context, the method is referred to as QM-NBB. Based on snapshots from MM sampling and accounting for their correct Boltzmann weight, it is possible to obtain hydration free energies that incorporate the effect of solute entropy. We evaluate the performance of several QM implicit solvent models, as well as explicit solvent QM/MM for the blind subset of the SAMPL4 hydration free energy challenge. While classical free energy simulations with molecular dynamics give root mean square deviations (RMSD) of 2.8 and 2.3 kcal/mol, the hybrid approach yields an improved RMSD of 1.6 kcal/mol. By selecting an appropriate functional and basis set, the RMSD can be reduced to 1 kcal/mol for calculations based on a single conformation. Results for a selected set of challenging molecules imply that this RMSD can be further reduced by using NBB to reweight MM trajectories with the SMD implicit solvent model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. 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 51:769–779

    Article  CAS  Google Scholar 

  2. 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

    Article  CAS  Google Scholar 

  3. Geballe MT, Skillman AG, Nicholls A, Guthrie JP, Taylor PJ (2010) The SAMPL2 blind prediction challenge: introduction and overview. J Comput Aid Mol Des 24(4, SI):259–279. doi:10.1007/s10822-010-9350-8

    Article  CAS  Google Scholar 

  4. 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 Aid Mol Des 26(5):475–487. doi:10.1007/s10822-012-9554-1

    Article  CAS  Google Scholar 

  5. 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. doi:10.1021/ct800409d

    Article  CAS  Google Scholar 

  6. Klimovich PV, Mobley DL (2010) Predicting hydration free energies using all-atom molecular dynamics simulations and multiple starting conformations. J Comput Aid Mol Des 24(4, SI):307–316. doi:10.1007/s10822-010-9343-7

    Article  CAS  Google Scholar 

  7. Mobley DL, Liu S, Cerutti DS, Swope WC, Rice JE (2012) Alchemical prediction of hydration free energies for SAMPL. J Comput Aid Mol Des 26(5, SI):551–562. doi:10.1007/s10822-011-9528-8

    Article  CAS  Google Scholar 

  8. Jambeck JPM, Mocci F, Lyubartsev AP, Laaksonen A (2013) Partial atomic charges and their impact on the free energy of solvation. J Comput Chem 34(3):187–197. doi:10.1002/jcc.23117

    Article  CAS  Google Scholar 

  9. 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):4538–4543

    Article  CAS  Google Scholar 

  10. 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 Aid Mol Des 24(4):317–333

    Article  CAS  Google Scholar 

  11. Klamt A, Diedenhofen M (2010) Blind prediction test of free energies of hydration with COSMO-RS. J Comput Aid Mol Des 24(4, SI):357–360. doi:10.1007/s10822-010-9354-4

    Article  CAS  Google Scholar 

  12. 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

    Article  CAS  Google Scholar 

  13. Fox SJ, Pittock C, Tautermann CS, Fox T, Christ C, Malcolm NOJ, Essex JW, Skylaris CK (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

    Article  CAS  Google Scholar 

  14. Rod TH, Ryde U (2005) Quantum mechanical free energy barrier for an enzymatic reaction. Phys Rev Lett 94(13):138–302. doi:10.1103/PhysRevLett.94.138302

    Article  CAS  Google Scholar 

  15. 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

    Article  CAS  Google Scholar 

  16. Heimdal J, Ryde U (2012) Convergence of QM/MM free-energy perturbations based on molecular-mechanics or semiempirical simulations. Phys Chem Chem Phys 14:12,592–12,604. doi:10.1039/c2cp41005b

    Article  CAS  Google Scholar 

  17. 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(8):2253–2266. doi:10.1021/ct100033s

    Article  CAS  Google Scholar 

  18. 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 6:51–62. doi:10.1016/S1574-1400(10)06004-4

    Article  CAS  Google Scholar 

  19. 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) doi:10.1063/1.2710790

  20. 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

    Article  CAS  Google Scholar 

  21. König G, Hudson P, 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 (in press)

  22. Bennett CH (1976) Efficient estimation of free energy differences from Monte Carlo data. J Comp Phys 22:245–268

    Article  Google Scholar 

  23. Mikulskis P, Cioloboc D, Andrejić M, Khare S, Brorsson J, Genheden S, Mata RA, Söderhjelm P, Ryde U (2014) Free energy pertrubation and quantum mechanical study of SAMPL4 octa-acid host-guest binding energies. J Comput Aided Mol Des (in press)

  24. Zwanzig RW (1954) High-temperature equation of state by a perturbation method. I. Nonpolar gases. J Chem Phys 22:1420

    Article  CAS  Google Scholar 

  25. Guthrie JP (2014) SAMPL4, a blind challenge for computational solvation free energies: the compounds considered. J Comput Aided Mol Des (in press)

  26. Mobley DL, Wymer KL, Lim NM, Guthrie JP (2014) Blind prediction of solvation free energies from the SAMPL4 challenge. J Comput Aided Mol Des. doi:10.1007/s10822-014-9718-2

  27. 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, Hodoscek 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, Sp. Iss. SI):1545–1614. doi:10.1002/jcc.21287

    Article  CAS  Google Scholar 

  28. 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 4:187–217

    Article  CAS  Google Scholar 

  29. Vanommeslaeghe K, Hatcher E, Acharya C, Kundu S, Zhong S, Shim J, Darian E, Guvench O, Lopes P, Vorobyov I, MacKerell Jr AD (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

  30. Sugita Y, Kitao A, Okamoto Y (2000) Multidimensional replica-exchange method for free-energy calculations. J Chem Phys 113:6042

    Article  CAS  Google Scholar 

  31. Darden T, York D, Pedersen L (1993) Particle mesh ewald—an n.log(n) method for ewald sums in large systems. J Chem Phys 98:10089–10092

    Article  CAS  Google Scholar 

  32. Lee MS, Feig M, Salsbury FR, Brooks CL III (2003) New analytic approximation to the standard molecular volume definition and its application to generalized born calculations. J Comput Chem 23:1348–1356

    Article  CAS  Google Scholar 

  33. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino, J, Zheng, G, Sonnenberg, JL, Hada, M, Ehara, M, Toyota, K, Fukuda, R, Hasegawa, J, Ishida, M, Nakajima, T, Honda, Y, Kitao, O, Nakai, H, Vreven, T, Montgomery Jr, JA, Peralta, JE, Ogliaro, F, Bearpark, M, Heyd, JJ, Brothers, E, Kudin, KN, Staroverov, VN, Keith, T, Kobayashi, R, Normand, J, Raghavachari, K, Rendell, A, Burant, JC, Iyengar, SS, Tomasi, J, Cossi, M, Rega, N, Millam, JM, Klene, M, Knox, JE, Cross, JB, Bakken, V, Adamo, C, Jaramillo, J, Gomperts, R, Stratmann, RE, Yazyev, O, Austin, AJ, Cammi, R, Pomelli, C, Ochterski, JW, Martin, RL, Morokuma, K, Zakrzewski, VG, Voth, GA, Salvador, P, Dannenberg, JJ, Dapprich, S, Daniels, AD, Farkas, O, Foresman, JB, Ortiz, JV, Cioslowski, J, Fox, DJ (2010) Gaussian 09, Revision B.01, Gaussian, Inc., Wallingford, CT

  34. Becke AD (1993) Density-functional thermochemistry. III. The role of exact exchange. J Chem Phys 98(7):5648–5652. doi:10.1063/1.464913

    Article  CAS  Google Scholar 

  35. Zhao Y, Truhlar DG (2007) The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other function. Theor Chem Acc 120:215–241

    Article  CAS  Google Scholar 

  36. Zhao Y, Truhlar DG (2008) Density functionals with broad applicability in chemistry. Acc Chem Res 41:157–167

    Article  CAS  Google Scholar 

  37. Hariharan PC, Pople JA (1974) Accuracy of ah n equilibrium geometries by single determinant molecular orbital theory. Mol Phys 27(1):209–214. doi:10.1080/00268977400100171

    Article  CAS  Google Scholar 

  38. Dunning TH Jr (1989) Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J Chem Phys 90(2):1007–1023

    Article  CAS  Google Scholar 

  39. Tomasi J, Mennucci B, Cammi R (2005) Quantum mechanical continuum solvation models. Chem Rev 105(8):2999–3094. doi:10.1021/cr9904009

    Article  CAS  Google Scholar 

  40. Marenich AV, Cramer CJ, Truhlar DG (2009) Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions. J Phys Chem B 113(18):6378–6396

    Article  CAS  Google Scholar 

  41. Liptak M, Shields G (2001) Accurate pK(a) calculations for carboxylic acids using complete basis set and gaussian-n models combined with CPCM continuum solvation methods. J Am Chem Soc 123(30):7314–7319. doi:10.1021/ja010534f

    Article  CAS  Google Scholar 

  42. Shao Y, Molnar LF, Jung Y, Kussmann J, Ochsenfeld C, Brown ST, Gilbert ATB, Slipchenko LV, Levchenko SV, O’Neill DP, DiStasio Jr RA, 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 CP, 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 III HL, Zhang W, Bell AT, Chakraborty AK, Chipman DM, Keil FJ, Warshel A, Hehre WJ, Schaefer III HF, 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

  43. Woodcock HL III, Hodoscek M, Gilbert ATB, Gill PMW, Schaefer HF III, Brooks BR (2007) Interfacing Q-chem and CHARMM to perform QM/MM reaction path calculations. J Comp Chem 28(9):1485–1502. doi:10.1002/jcc.20587

    Article  CAS  Google Scholar 

  44. Jorgensen WL, Chandrasekhar J, Madura JD, Impey RW, Klein ML (1983) Comparison of simple potential functions for simulating liquid water. J Chem Phys 79(2):926–935. doi:10.1063/1.445869

    Article  CAS  Google Scholar 

  45. 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+

    Article  CAS  Google Scholar 

  46. Geballe MT, Guthrie JP (2012) The SAMPL3 blind prediction challenge: transfer energy overview. J Comput Aid Mol Des 26(5, SI):489–496. doi:10.1007/s10822-012-9568-8

    Article  CAS  Google Scholar 

  47. 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 Aid Mol Des 26(5, SI):635–645. doi:10.1007/s10822-011-9527-9

    Article  CAS  Google Scholar 

  48. Reinisch J, Klamt A, Diedenhofen M (2012) Prediction of free energies of hydration with COSMO-RS on the SAMPL3 data set. J Comput Aid Mol Des 26(5, SI):669–673. doi:10.1007/s10822-012-9576-8

    Article  CAS  Google Scholar 

  49. Kehoe CW, Fennell CJ, Dill KA (2012) Testing the semi-explicit assembly solvation model in the SAMPL3 community blind test. J Comput Aid Mol Des 26(5, SI):563–568. doi:10.1007/s10822-011-9536-8

    Article  CAS  Google Scholar 

  50. König G, Bruckner S, Boresch S (2013) Absolute hydration free energies of blocked amino acids: implications for protein solvation and stability. Biophys J 104(2):453–462. doi:10.1016/j.bpj.2012.12.008

    Article  CAS  Google Scholar 

  51. 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

    Article  CAS  Google Scholar 

  52. 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 Aid Mol Des 26(5):543–550. doi:10.1007/s10822-011-9525-y

    Article  CAS  Google Scholar 

  53. Vanommeslaeghe K, Raman EP, MacKerell AD Jr (2012) Automation of the CHARMM General Force Field (CGenFF) II: assignment of bonded parameters and partial atomic charges. J Chem Inf Model 52(12):3155–3168. doi:10.1021/ci3003649

    Article  CAS  Google Scholar 

Download references

Acknowledgments

The authors would like to thank Tim Miller, Richard Venable and John Legato for technical assistance with the parallelization of the QM/MM calculations. The support by Yihan Shao was invaluable during the setup of the Q-Chem scripts and we also would like to thank Florentina Tofoleanu, Tim Miller and Juyong Lee for carefully reading and commenting on the manuscript as well as Stefan Boresch and Lee Woodcock for fruitful discussions on the optimal performance of NBB. This work was 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://biowulf.nih.gov).

Author information

Authors and Affiliations

  1. Laboratory of Computational Biology, National Institutes of Health, National Heart, Lung and Blood Institute, 5635 Fishers Lane, T-900 Suite, Rockville, MD, 20852, USA

    Gerhard König, Frank C. Pickard IV, Ye Mei & Bernard R. Brooks

  2. State Key Laboratory of Precision Spectroscopy, Institute of Theoretical and Computational Science, East China Normal University, Shanghai, 200062, China

    Ye Mei

Authors
  1. Gerhard König
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Frank C. Pickard IV
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ye Mei
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Bernard R. Brooks
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gerhard König.

Electronic supplementary material

Below is the link to the electronic supplementary material.

PDF (40 KB)

Rights and permissions

Reprints and permissions

About this article

Cite this article

König, G., Pickard, F.C., Mei, Y. et al. 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, 245–257 (2014). https://doi.org/10.1007/s10822-014-9708-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10822-014-9708-4

Keywords

Search

Navigation