Exploring optimization strategies for improving explicit water models: Rigid n-point model and polarizable model based on Drude oscillator

Autoři: Yeyue Xiong aff001;  Alexey V. Onufriev aff002
Působiště autorů: Department of Biomedical Engineering and Mechanics, Virginia Tech, Blacksburg, VA, United States of America aff001;  Department of Physics, Virginia Tech, Blacksburg, VA, United States of America aff002;  Department of Computer Science, Virginia Tech, Blacksburg, VA, United States of America aff003;  Center for Soft Matter and Biological Physics, Virginia Tech, Blacksburg, VA, United States of America aff004
Vyšlo v časopise: PLoS ONE 14(11)
Kategorie: Research Article
doi: 10.1371/journal.pone.0224991


Rigid n-point water models are widely used in atomistic simulations, but have known accuracy drawbacks. Increasing the number of point charges, as well as adding electronic polarizability, are two common strategies for accuracy improvements. Both strategies come at considerable computational cost, which weighs heavily against modest possible accuracy improvements in practical simulations. In an effort to provide guidance for model development, here we have explored the limiting accuracy of “electrostatically globally optimal” n-point water models in terms of their ability to reproduce properties of water dimer—a mimic of the condensed state of water. For a given n, each model is built upon a set of reference multipole moments (e.g. ab initio) and then optimized to reproduce water dimer total dipole moment. The models are then evaluated with respect to the accuracy of reproducing the geometry of the water dimer. We find that global optimization of the charge distribution alone can deliver high accuracy of the water model: for n = 4 or n = 5, the geometry of the resulting water dimer can be almost within 50 of the ab initio reference, which is half that of the experimental error margin. Thus, global optimization of the charge distribution of classical n-point water models can lead to high accuracy models. We also find that while the accuracy improvement in going from n = 3 to n = 4 is substantial, the additional accuracy increase in going from n = 4 to n = 5 is marginal. Next, we have explored accuracy limitations of the standard practice of adding electronic polarizability (via a Drude particle) to a “rigid base”—pre-optimization rigid n-point water model. The resulting model (n = 3) shows a relatively small improvement in accuracy, suggesting that the strategy of merely adding the polarizability to an inferior accuracy water model used as the base cannot fix the defects of the latter. An alternative strategy in which the parameters of the rigid base model are globally optimized along with the polarizability parameter is much more promising: the resulting 3-point polarizable model out-performs even the 5-point optimal rigid model by a large margin. We suggest that future development efforts consider 3- and 4-point polarizable models where global optimization of the “rigid base” is coupled to optimization of the polarizability to deliver globally optimal solutions.

Klíčová slova:

Biochemical simulations – Dimers – Dipole moments – Electrostatics – Hydrogen bonding – Monomers – Oxygen – Simulation and modeling


1. Hasted JB. In: Franks F, editor. Liquid Water: Dielectric Properties. Boston, MA: Springer New York; 1972. p. 255–309. Available from: https://doi.org/10.1007/978-1-4684-8334-5_7.

2. Finney JL. The water molecule and its interactions: the interaction between theory, modelling, and experiment. Journal of Molecular Liquids. 2001;90(1):303–312. https://doi.org/10.1016/S0167-7322(01)00134-9

3. Brodsky A. Is there predictive value in water computer simulations? Chemical Physics Letters. 1996;261(4):563–568. https://doi.org/10.1016/0009-2614(96)00997-9

4. Rahman A, Stillinger FH. Molecular Dynamics Study of Liquid Water. The Journal of Chemical Physics. 1971;55(7):3336–3359. doi: 10.1063/1.1676585

5. Brini E, Fennell CJ, Fernandez-Serra M, Hribar-Lee B, Luksic M, Dill KA. How Water’s Properties Are Encoded in Its Molecular Structure and Energies. Chem Rev. 2017;117(19):12385–12414. doi: 10.1021/acs.chemrev.7b00259 28949513

6. Zhong D, Pal SK, Zewail AH. Biological water: A critique. Chemical Physics Letters. 2011;503(1):1–11. https://doi.org/10.1016/j.cplett.2010.12.077

7. Onufriev AV, Saeed I. Water models for biomolecular simulations. Wiley Interdisciplinary Reviews: Computational Molecular Science. 2018;8(2):e1347.

8. Jorgensen WL, Chandrasekhar J, Madura JD, Impey RW, Klein ML. Comparison of simple potential functions for simulating liquid water. The Journal of Chemical Physics. 1983;79(2):926–935. doi: 10.1063/1.445869

9. Jorgensen WL, Madura JD. Temperature and size dependence for Monte Carlo simulations of TIP4P water. Molecular Physics. 1985;56(6):1381–1392. doi: 10.1080/00268978500103111

10. Abascal JLF, Vega C. A general purpose model for the condensed phases of water: TIP4P/2005. The Journal of Chemical Physics. 2005;123(23):234505. doi: 10.1063/1.2121687 16392929

11. Mahoney MW, Jorgensen WL. A five-site model for liquid water and the reproduction of the density anomaly by rigid, nonpolarizable potential functions. The Journal of Chemical Physics. 2000;112(20):8910–8922. doi: 10.1063/1.481505

12. Berendsen HJC, Grigera JR, Straatsma TP. The missing term in effective pair potentials. The Journal of Physical Chemistry. 1987;91(24):6269–6271. doi: 10.1021/j100308a038

13. Ouyang JF, Bettens RPA. Modelling Water: A Lifetime Enigma. CHIMIA International Journal for Chemistry. 2015;69(3):104–111. doi: 10.2533/chimia.2015.104

14. Guillot B. A reappraisal of what we have learnt during three decades of computer simulations on water. Journal of Molecular Liquids. 2002;101(1):219–260. https://doi.org/10.1016/S0167-7322(02)00094-6

15. Pi HL, Aragones JL, Vega C, Noya EG, Abascal JLF, Gonzalez MA, et al. Anomalies in water as obtained from computer simulations of the TIP4P/2005 model: density maxima, and density, isothermal compressibility and heat capacity minima. Molecular Physics. 2009;107(4-6):365–374. doi: 10.1080/00268970902784926

16. Vega C. Water: one molecule, two surfaces, one mistake. Molecular Physics. 2015;113(9-10):1145–1163. doi: 10.1080/00268976.2015.1005191

17. Florová P, Sklenovský P, Banáš P, Otyepka M. Explicit Water Models Affect the Specific Solvation and Dynamics of Unfolded Peptides While the Conformational Behavior and Flexibility of Folded Peptides Remain Intact. Journal of Chemical Theory and Computation. 2010;6(11):3569–3579. doi: 10.1021/ct1003687

18. Humphrey W, Dalke A, Schulten K. VMD—Visual Molecular Dynamics. Journal of Molecular Graphics. 1996;14:33–38. doi: 10.1016/0263-7855(96)00018-5 8744570

19. Izadi S, Anandakrishnan R, Onufriev AV. Building Water Models: A Different Approach. The Journal of Physical Chemistry Letters. 2014;5(21):3863–3871. doi: 10.1021/jz501780a 25400877

20. Akin-Ojo O, Wang F. The quest for the best nonpolarizable water model from the adaptive force matching method. Journal of Computational Chemistry. 2011;32(3):453–462. doi: 10.1002/jcc.21634 20730778

21. Wang LP, Martinez TJ, Pande VS. Building Force Fields: An Automatic, Systematic, and Reproducible Approach. J Phys Chem Lett. 2014;5(11):1885–1891. doi: 10.1021/jz500737m 26273869

22. Rick SW. A reoptimization of the five-site water potential (TIP5P) for use with Ewald sums. The Journal of Chemical Physics. 2004;120(13):6085–6093. doi: 10.1063/1.1652434 15267492

23. Tu Y, Laaksonen A. The electronic properties of water molecules in water clusters and liquid water. Chemical Physics Letters. 2000;329(3):283–288. https://doi.org/10.1016/S0009-2614(00)01026-5

24. Ren P, Ponder JW. Polarizable Atomic Multipole Water Model for Molecular Mechanics Simulation. J Phys Chem B. 2003;107(24):5933–5947. doi: 10.1021/jp027815+

25. Caldwell J, Dang LX, Kollman PA. Implementation of nonadditive intermolecular potentials by use of molecular dynamics: development of a water-water potential and water-ion cluster interactions. Journal of the American Chemical Society. 1990;112(25):9144–9147. doi: 10.1021/ja00181a017

26. Dang LX. The nonadditive intermolecular potential for water revised. The Journal of Chemical Physics. 1992;97(4):2659–2660. doi: 10.1063/1.463054

27. Wang J, Cieplak P, Cai Q, Hsieh MJ, Wang J, Duan Y, et al. Development of Polarizable Models for Molecular Mechanical Calculations. 3. Polarizable Water Models Conforming to Thole Polarization Screening Schemes. The Journal of Physical Chemistry B. 2012;116(28):7999–8008. doi: 10.1021/jp212117d 22712654

28. Lemkul JA, Huang J, Roux B, MacKerell AD. An Empirical Polarizable Force Field Based on the Classical Drude Oscillator Model: Development History and Recent Applications. Chemical Reviews. 2016;116(9):4983–5013. doi: 10.1021/acs.chemrev.5b00505 26815602

29. Laury ML, Wang LP, Pande VS, Head-Gordon T, Ponder JW. Revised Parameters for the AMOEBA Polarizable Atomic Multipole Water Model. The Journal of Physical Chemistry B. 2015;119(29):9423–9437. doi: 10.1021/jp510896n 25683601

30. Wang LP, Head-Gordon T, Ponder JW, Ren P, Chodera JD, Eastman PK, et al. Systematic Improvement of a Classical Molecular Model of Water. The Journal of Physical Chemistry B. 2013;117(34):9956–9972. doi: 10.1021/jp403802c 23750713

31. Liu C, Piquemal JP, Ren P. AMOEBA+ Classical Potential for Modeling Molecular Interactions. Journal of Chemical Theory and Computation. 2019;15(7):4122–4139. doi: 10.1021/acs.jctc.9b00261 31136175

32. Huang J, Lopes PEM, Roux B, MacKerell AD. Recent Advances in Polarizable Force Fields for Macromolecules: Microsecond Simulations of Proteins Using the Classical Drude Oscillator Model. The Journal of Physical Chemistry Letters. 2014;5(18):3144–3150. doi: 10.1021/jz501315h 25247054

33. Jing Z, Liu C, Cheng SY, Qi R, Walker BD, Piquemal JP, et al. Polarizable Force Fields for Biomolecular Simulations: Recent Advances and Applications. Annual Review of Biophysics. 2019;48(1):371–394. doi: 10.1146/annurev-biophys-070317-033349 30916997

34. Vega C, Abascal JLF. Simulating water with rigid non-polarizable models: a general perspective. Phys Chem Chem Phys. 2011;13:19663–19688. doi: 10.1039/c1cp22168j 21927736

35. Mukhopadhyay A, Cole WTS, Saykally RJ. The water dimer I: Experimental characterization. Chemical Physics Letters. 2015;633:13–26. https://doi.org/10.1016/j.cplett.2015.04.016

36. Mukhopadhyay A, Xantheas SS, Saykally RJ. The water dimer II: Theoretical investigations. Chemical Physics Letters. 2018;700:163–175. https://doi.org/10.1016/j.cplett.2018.03.057

37. Anandakrishnan R, Baker C, Izadi S, Onufriev AV. Point Charges Optimally Placed to Represent the Multipole Expansion of Charge Distributions. PLOS ONE. 2013;8(7):e67715. doi: 10.1371/journal.pone.0067715 23861790

38. Yu H, Gunsteren WFv. Charge-on-spring polarizable water models revisited: From water clusters to liquid water to ice. The Journal of Chemical Physics. 2004;121(19):9549–9564. doi: 10.1063/1.1805516 15538877

39. Klopper W, van Duijneveldt-van de Rijdt JGCM, van Duijneveldt FB. Computational determination of equilibrium geometry and dissociation energy of the water dimer. Physical Chemistry Chemical Physics. 2000;2(10):2227–2234. doi: 10.1039/a910312k

40. Anandakrishnan R, Izadi S, Onufriev AV. Why Computed Protein Folding Landscapes Are Sensitive to the Water Model. Journal of Chemical Theory and Computation. 2019;15(1):625–636. doi: 10.1021/acs.jctc.8b00485 30514080

41. Dharmawardhana CC, Ichiye T. Building better water models using the shape of the charge distribution of a water molecule. The Journal of Chemical Physics. 2017;147(19):194103. doi: 10.1063/1.4986070 29166096

42. Rodgers JM, Ichiye T. Multipole moments of water molecules and the aqueous solvation of monovalent ions. Journal of Molecular Liquids. 2017;228:54–62. https://doi.org/10.1016/j.molliq.2016.10.007

43. Tan ML, Lucan L, Ichiye T. Study of multipole contributions to the structure of water around ions in solution using the soft sticky dipole-quadrupole-octupole (SSDQO) model of water. The Journal of Chemical Physics. 2006;124(17):174505. doi: 10.1063/1.2177240 16689581

44. Gongadze E, Velikonja A, Slivnik T, Kralj-Iglič V, Iglič A. The quadrupole moment of water molecules and the permittivity of water near a charged surface. Electrochimica Acta. 2013;109:656–662. https://doi.org/10.1016/j.electacta.2013.07.126

45. Case DA, Ben-Shalom IY, Brozell SR, Cerutti DS, Cheatham TE, III VWDC, et al. AMBER 2019. AMBER 2019, University of California, San Francisco. 2019;.

46. Clough SA, Beers Y, Klein GP, Rothman LS. Dipole moment of water from Stark measurements of H2O, HDO, and D2O. The Journal of Chemical Physics. 1973;59(5):2254–2259. doi: 10.1063/1.1680328

47. Niu S, Tan ML, Ichiye T. The large quadrupole of water molecules. The Journal of Chemical Physics. 2011;134(13):134501. doi: 10.1063/1.3569563 21476758

48. Drude P. Zur Elektronentheorie der Metalle. Annalen der Physik. 1900;306(3):566–613. doi: 10.1002/andp.19003060312

49. Sprik M, Klein ML. A polarizable model for water using distributed charge sites. The Journal of Chemical Physics. 1988;89(12):7556–7560. doi: 10.1063/1.455722

50. Jiang W, Hardy DJ, Phillips JC, MacKerell AD, Schulten K, Roux B. High-Performance Scalable Molecular Dynamics Simulations of a Polarizable Force Field Based on Classical Drude Oscillators in NAMD. The Journal of Physical Chemistry Letters. 2011;2(2):87–92. doi: 10.1021/jz101461d 21572567

51. Lamoureux G, M AD Jr, Roux B. A simple polarizable model of water based on classical Drude oscillators. The Journal of Chemical Physics. 2003;119(10):5185–5197. doi: 10.1063/1.1598191

52. Lamoureux G, Roux B. Modeling induced polarization with classical Drude oscillators: Theory and molecular dynamics simulation algorithm. The Journal of Chemical Physics. 2003;119(6):3025–3039. doi: 10.1063/1.1589749

53. Lemkul JA, Roux B, van der Spoel D, MacKerell AD Jr. Implementation of extended Lagrangian dynamics in GROMACS for polarizable simulations using the classical Drude oscillator model. Journal of Computational Chemistry. 2015;36(19):1473–1479. doi: 10.1002/jcc.23937 25962472

54. Huang J, Lemkul JA, Eastman PK, MacKerell AD Jr. Molecular dynamics simulations using the drude polarizable force field on GPUs with OpenMM: Implementation, validation, and benchmarks. Journal of Computational Chemistry. 2018;39(21):1682–1689. doi: 10.1002/jcc.25339 29727037

55. Lamoureux G, Harder E, Vorobyov IV, Roux B, MacKerell AD. A polarizable model of water for molecular dynamics simulations of biomolecules. Chemical Physics Letters. 2006;418(1):245–249. https://doi.org/10.1016/j.cplett.2005.10.135

56. Ludwig R. Water: From Clusters to the Bulk. Angewandte Chemie International Edition. 2001;40(10):1808–1827. doi: 10.1002/1521-3773(20010518)40:10%3C1808::AID-ANIE1808%3E3.0.CO;2-1 11385651

57. Nguyen M, Rick SW. The influence of polarizability and charge transfer on specific ion effects in the dynamics of aqueous salt solutions. The Journal of Chemical Physics. 2018;148(22):222803. doi: 10.1063/1.5012682 29907071

58. Kumar R, Wang FF, Jenness GR, Jordan KD. A second generation distributed point polarizable water model. The Journal of Chemical Physics. 2010;132(1):014309. doi: 10.1063/1.3276460 20078163

59. Kuwajima S, Warshel A. Incorporating electric polarizabilities in water-water interaction potentials. The Journal of Physical Chemistry. 1990;94(1):460–466. doi: 10.1021/j100364a080

60. Bachmann SJ, Gunsteren WFv. An improved simple polarisable water model for use in biomolecular simulation. The Journal of Chemical Physics. 2014;141(22):22D515. doi: 10.1063/1.4897976 25494786

61. Masia M, Probst M, Rey R. On the performance of molecular polarization methods. I. Water and carbon tetrachloride close to a point charge. The Journal of Chemical Physics. 2004;121(15):7362–7378. doi: 10.1063/1.1791637 15473807

62. Tröster P, Lorenzen K, Tavan P. Polarizable Six-Point Water Models from Computational and Empirical Optimization. The Journal of Physical Chemistry B. 2014;118(6):1589–1602. doi: 10.1021/jp4125765

63. Soetens JC, Millot C. Effect of distributing multipoles and polarizabilities on molecular dynamics simulations of water. Chemical Physics Letters. 1995;235(1):22–30. https://doi.org/10.1016/0009-2614(95)00090-Q

64. Vega C, Sanz E, Abascal JLF. The melting temperature of the most common models of water. The Journal of Chemical Physics. 2005;122(11):114507. doi: 10.1063/1.1862245 15836229

Článek vyšel v časopise


2019 Číslo 11