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Tolokh IS, Folescu DE, Onufriev AV. Inclusion of Water Multipoles into the Implicit Solvation Framework Leads to Accuracy Gains. J Phys Chem B 2024; 128:5855-5873. [PMID: 38860842 PMCID: PMC11194828 DOI: 10.1021/acs.jpcb.4c00254] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2024] [Revised: 05/28/2024] [Accepted: 05/29/2024] [Indexed: 06/12/2024]
Abstract
The current practical "workhorses" of the atomistic implicit solvation─the Poisson-Boltzmann (PB) and generalized Born (GB) models─face fundamental accuracy limitations. Here, we propose a computationally efficient implicit solvation framework, the Implicit Water Multipole GB (IWM-GB) model, that systematically incorporates the effects of multipole moments of water molecules in the first hydration shell of a solute, beyond the dipole water polarization already present at the PB/GB level. The framework explicitly accounts for coupling between polar and nonpolar contributions to the total solvation energy, which is missing from many implicit solvation models. An implementation of the framework, utilizing the GAFF force field and AM1-BCC atomic partial charges model, is parametrized and tested against the experimental hydration free energies of small molecules from the FreeSolv database. The resulting accuracy on the test set (RMSE ∼ 0.9 kcal/mol) is 12% better than that of the explicit solvation (TIP3P) treatment, which is orders of magnitude slower. We also find that the coupling between polar and nonpolar parts of the solvation free energy is essential to ensuring that several features of the IWM-GB model are physically meaningful, including the sign of the nonpolar contributions.
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Affiliation(s)
- Igor S. Tolokh
- Department
of Computer Science, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Dan E. Folescu
- Department
of Computer Science, Virginia Tech, Blacksburg, Virginia 24061, United States
- Department
of Mathematics, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Alexey V. Onufriev
- Department
of Computer Science, Virginia Tech, Blacksburg, Virginia 24061, United States
- Department
of Physics, Virginia Tech, Blacksburg, Virginia 24061, United States
- Center
for Soft Matter and Biological Physics, Virginia Tech, Blacksburg, Virginia 24061, United States
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2
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Mason PE, Tavagnacco L, Saboungi ML, Hansen T, Fischer HE, Neilson GW, Ichiye T, Brady JW. Molecular Dynamics and Neutron Scattering Studies of Potassium Chloride in Aqueous Solution. J Phys Chem B 2019; 123:10807-10813. [PMID: 31769976 DOI: 10.1021/acs.jpcb.9b08422] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
Neutron diffraction with isotopic substitution (NDIS) experiments were done on both natural abundance potassium and isotopically labeled 41KCl heavy water solutions to characterize the solvent structuring around the potassium ion in water. Preliminary measurements suggested that the literature value for the coherent neutron scattering length (2.69 fm) for 41K was significantly in error. This value was remeasured using a neutron powder diffractometer and found to be 2.40 fm. This revision increases significantly the contrast between the natural abundance K and 41K by about 30% (from 1.0 to 1.3 fm). The experimentally determined structure factor of the potassium ion was then compared to that calculated from molecular dynamics (MD) simulations. Previous neutron scattering measurements of potassium gave a solvation number of 5.5 (see below). In this study, the NDIS and MD results are in good agreement and allowed us to derive a coordination number of 6.1 for water molecules and 0.8 for chloride ions around each K+ ion in 4 molal aqueous KCl solution.
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Affiliation(s)
- Philip E Mason
- Institute of Organic Chemistry and Biochemistry , Academy of Sciences of the Czech Republic & Center for Biomolecules and Complex Molecular Systems , 16610 Prague 6 , Czech Republic
| | - Letizia Tavagnacco
- Department of Food Science , Cornell University , Ithaca , New York 14853 , United States
| | - Marie-Louise Saboungi
- Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie , UMR 7590 CNRS - Sorbonne Université, Campus Pierre et Marie Curie , 4, Place Jussieu , 75005 Paris , France
| | - Thomas Hansen
- Institut Laue-Langevin , 71 Avenue des Martyrs , 38042 Grenoble Cedex 9 , France
| | - Henry E Fischer
- Institut Laue-Langevin , 71 Avenue des Martyrs , 38042 Grenoble Cedex 9 , France
| | - George W Neilson
- H.H. Wills Physics Laboratory , University of Bristol , BS8 1TL Bristol , U.K
| | - Toshiko Ichiye
- Department of Chemistry , Georgetown University , Box 571227, Washington , DC 20057 , United States
| | - John W Brady
- Department of Food Science , Cornell University , Ithaca , New York 14853 , United States
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Onufriev AV, Izadi S. Water models for biomolecular simulations. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2017. [DOI: 10.1002/wcms.1347] [Citation(s) in RCA: 94] [Impact Index Per Article: 13.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Alexey V. Onufriev
- Department of Physics; Virginia Tech; Blacksburg VA USA
- Department of Computer Science; Virginia Tech; Blacksburg VA USA
- Center for Soft Matter and Biological Physics; Virginia Tech; Blacksburg VA USA
| | - Saeed Izadi
- Early Stage Pharmaceutical Development; Genentech Inc.; South San Francisco, CA USA
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Rodgers JM, Ichiye T. Multipole moments of water molecules and the aqueous solvation of monovalent ions. J Mol Liq 2017. [DOI: 10.1016/j.molliq.2016.10.007] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Izadi S, Onufriev AV. Accuracy limit of rigid 3-point water models. J Chem Phys 2016; 145:074501. [PMID: 27544113 PMCID: PMC4991989 DOI: 10.1063/1.4960175] [Citation(s) in RCA: 164] [Impact Index Per Article: 20.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2016] [Accepted: 07/19/2016] [Indexed: 11/14/2022] Open
Abstract
Classical 3-point rigid water models are most widely used due to their computational efficiency. Recently, we introduced a new approach to constructing classical rigid water models [S. Izadi et al., J. Phys. Chem. Lett. 5, 3863 (2014)], which permits a virtually exhaustive search for globally optimal model parameters in the sub-space that is most relevant to the electrostatic properties of the water molecule in liquid phase. Here we apply the approach to develop a 3-point Optimal Point Charge (OPC3) water model. OPC3 is significantly more accurate than the commonly used water models of same class (TIP3P and SPCE) in reproducing a comprehensive set of liquid bulk properties, over a wide range of temperatures. Beyond bulk properties, we show that OPC3 predicts the intrinsic charge hydration asymmetry (CHA) of water - a characteristic dependence of hydration free energy on the sign of the solute charge - in very close agreement with experiment. Two other recent 3-point rigid water models, TIP3PFB and H2ODC, each developed by its own, completely different optimization method, approach the global accuracy optimum represented by OPC3 in both the parameter space and accuracy of bulk properties. Thus, we argue that an accuracy limit of practical 3-point rigid non-polarizable models has effectively been reached; remaining accuracy issues are discussed.
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Affiliation(s)
- Saeed Izadi
- Department of Biomedical Engineering and Mechanics, Virginia Tech, Blacksburg, Virginia 24060, USA
| | - Alexey V Onufriev
- Departments of Computer Science and Physics, Center for Soft Matter and Biological Physics, Virginia Tech, Blacksburg, Virginia 24060, USA
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Mukhopadhyay A, Tolokh IS, Onufriev AV. Accurate evaluation of charge asymmetry in aqueous solvation. J Phys Chem B 2015; 119:6092-100. [PMID: 25830623 DOI: 10.1021/acs.jpcb.5b00602] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Charge hydration asymmetry (CHA)-a characteristic dependence of hydration free energy on the sign of the solute charge-quantifies the asymmetric response of water to electric field at microscopic level. Accurate estimates of CHA are critical for understanding hydration effects ubiquitous in chemistry and biology. However, measuring hydration energies of charged species is fraught with significant difficulties, which lead to unacceptably large (up to 300%) variation in the available estimates of the CHA effect. We circumvent these difficulties by developing a framework which allows us to extract and accurately estimate the intrinsic propensity of water to exhibit CHA from accurate experimental hydration free energies of neutral polar molecules. Specifically, from a set of 504 small molecules we identify two pairs that are analogous, with respect to CHA, to the K(+) /F(-) pair-a classical probe for the effect. We use these "CHA-conjugate" molecule pairs to quantify the intrinsic charge-asymmetric response of water to the microscopic charge perturbations: the asymmetry of the response is strong, ∼50% of the average hydration free energy of these molecules. The ability of widely used classical water models to predict hydration energies of small molecules correlates with their ability to predict CHA.
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Affiliation(s)
- Abhishek Mukhopadhyay
- †Department of Physics and ‡Department of Computer Science, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Igor S Tolokh
- †Department of Physics and ‡Department of Computer Science, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Alexey V Onufriev
- †Department of Physics and ‡Department of Computer Science, Virginia Tech, Blacksburg, Virginia 24061, United States
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Izadi S, Anandakrishnan R, Onufriev AV. Building Water Models: A Different Approach. J Phys Chem Lett 2014; 5:3863-3871. [PMID: 25400877 PMCID: PMC4226301 DOI: 10.1021/jz501780a] [Citation(s) in RCA: 577] [Impact Index Per Article: 57.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2014] [Accepted: 10/16/2014] [Indexed: 05/19/2023]
Abstract
Simplified classical water models are currently an indispensable component in practical atomistic simulations. Yet, despite several decades of intense research, these models are still far from perfect. Presented here is an alternative approach to constructing widely used point charge water models. In contrast to the conventional approach, we do not impose any geometry constraints on the model other than the symmetry. Instead, we optimize the distribution of point charges to best describe the "electrostatics" of the water molecule. The resulting "optimal" 3-charge, 4-point rigid water model (OPC) reproduces a comprehensive set of bulk properties significantly more accurately than commonly used rigid models: average error relative to experiment is 0.76%. Close agreement with experiment holds over a wide range of temperatures. The improvements in the proposed model extend beyond bulk properties: compared to common rigid models, predicted hydration free energies of small molecules using OPC are uniformly closer to experiment, with root-mean-square error <1 kcal/mol.
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Affiliation(s)
- Saeed Izadi
- Department of Biomedical Engineering and Mechanics, Department of Computer Science, and Departments of Computer
Science and Physics, Virginia Tech, Blacksburg, Virginia 24060, United States
| | - Ramu Anandakrishnan
- Department of Biomedical Engineering and Mechanics, Department of Computer Science, and Departments of Computer
Science and Physics, Virginia Tech, Blacksburg, Virginia 24060, United States
| | - Alexey V. Onufriev
- Department of Biomedical Engineering and Mechanics, Department of Computer Science, and Departments of Computer
Science and Physics, Virginia Tech, Blacksburg, Virginia 24060, United States
- E-mail:
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Fukuda I, Kamiya N, Nakamura H. The zero-multipole summation method for estimating electrostatic interactions in molecular dynamics: analysis of the accuracy and application to liquid systems. J Chem Phys 2014; 140:194307. [PMID: 24852538 DOI: 10.1063/1.4875693] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
In the preceding paper [I. Fukuda, J. Chem. Phys. 139, 174107 (2013)], the zero-multipole (ZM) summation method was proposed for efficiently evaluating the electrostatic Coulombic interactions of a classical point charge system. The summation takes a simple pairwise form, but prevents the electrically non-neutral multipole states that may artificially be generated by a simple cutoff truncation, which often causes large energetic noises and significant artifacts. The purpose of this paper is to judge the ability of the ZM method by investigating the accuracy, parameter dependencies, and stability in applications to liquid systems. To conduct this, first, the energy-functional error was divided into three terms and each term was analyzed by a theoretical error-bound estimation. This estimation gave us a clear basis of the discussions on the numerical investigations. It also gave a new viewpoint between the excess energy error and the damping effect by the damping parameter. Second, with the aid of these analyses, the ZM method was evaluated based on molecular dynamics (MD) simulations of two fundamental liquid systems, a molten sodium-chlorine ion system and a pure water molecule system. In the ion system, the energy accuracy, compared with the Ewald summation, was better for a larger value of multipole moment l currently induced until l ≲ 3 on average. This accuracy improvement with increasing l is due to the enhancement of the excess-energy accuracy. However, this improvement is wholly effective in the total accuracy if the theoretical moment l is smaller than or equal to a system intrinsic moment L. The simulation results thus indicate L ∼ 3 in this system, and we observed less accuracy in l = 4. We demonstrated the origins of parameter dependencies appearing in the crossing behavior and the oscillations of the energy error curves. With raising the moment l we observed, smaller values of the damping parameter provided more accurate results and smoother behaviors with respect to cutoff length were obtained. These features can be explained, on the basis of the theoretical error analyses, such that the excess energy accuracy is improved with increasing l and that the total accuracy improvement within l ⩽ L is facilitated by a small damping parameter. Although the accuracy was fundamentally similar to the ion system, the bulk water system exhibited distinguishable quantitative behaviors. A smaller damping parameter was effective in all the practical cutoff distance, and this fact can be interpreted by the reduction of the excess subset. A lower moment was advantageous in the energy accuracy, where l = 1 was slightly superior to l = 2 in this system. However, the method with l = 2 (viz., the zero-quadrupole sum) gave accurate results for the radial distribution function. We confirmed the stability in the numerical integration for MD simulations employing the ZM scheme. This result is supported by the sufficient smoothness of the energy function. Along with the smoothness, the pairwise feature and the allowance of the atom-based cutoff mode on the energy formula lead to the exact zero total-force, ensuring the total-momentum conservations for typical MD equations of motion.
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Affiliation(s)
- Ikuo Fukuda
- Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita, Osaka 565-0871, Japan
| | - Narutoshi Kamiya
- Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita, Osaka 565-0871, Japan
| | - Haruki Nakamura
- Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita, Osaka 565-0871, Japan
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Lamichhane M, Newman KE, Gezelter JD. Real space electrostatics for multipoles. II. Comparisons with the Ewald sum. J Chem Phys 2014; 141:134110. [DOI: 10.1063/1.4896628] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Affiliation(s)
- Madan Lamichhane
- Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - Kathie E. Newman
- Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - J. Daniel Gezelter
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, USA
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Lamichhane M, Gezelter JD, Newman KE. Real space electrostatics for multipoles. I. Development of methods. J Chem Phys 2014; 141:134109. [DOI: 10.1063/1.4896627] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Madan Lamichhane
- Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - J. Daniel Gezelter
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - Kathie E. Newman
- Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA
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Anandakrishnan R, Baker C, Izadi S, Onufriev AV. Point charges optimally placed to represent the multipole expansion of charge distributions. PLoS One 2013; 8:e67715. [PMID: 23861790 PMCID: PMC3701554 DOI: 10.1371/journal.pone.0067715] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2013] [Accepted: 05/21/2013] [Indexed: 11/18/2022] Open
Abstract
We propose an approach for approximating electrostatic charge distributions with a small number of point charges to optimally represent the original charge distribution. By construction, the proposed optimal point charge approximation (OPCA) retains many of the useful properties of point multipole expansion, including the same far-field asymptotic behavior of the approximate potential. A general framework for numerically computing OPCA, for any given number of approximating charges, is described. We then derive a 2-charge practical point charge approximation, PPCA, which approximates the 2-charge OPCA via closed form analytical expressions, and test the PPCA on a set of charge distributions relevant to biomolecular modeling. We measure the accuracy of the new approximations as the RMS error in the electrostatic potential relative to that produced by the original charge distribution, at a distance 2x the extent of the charge distribution--the mid-field. The error for the 2-charge PPCA is found to be on average 23% smaller than that of optimally placed point dipole approximation, and comparable to that of the point quadrupole approximation. The standard deviation in RMS error for the 2-charge PPCA is 53% lower than that of the optimal point dipole approximation, and comparable to that of the point quadrupole approximation. We also calculate the 3-charge OPCA for representing the gas phase quantum mechanical charge distribution of a water molecule. The electrostatic potential calculated by the 3-charge OPCA for water, in the mid-field (2.8 Å from the oxygen atom), is on average 33.3% more accurate than the potential due to the point multipole expansion up to the octupole order. Compared to a 3 point charge approximation in which the charges are placed on the atom centers, the 3-charge OPCA is seven times more accurate, by RMS error. The maximum error at the oxygen-Na distance (2.23 Å) is half that of the point multipole expansion up to the octupole order.
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Affiliation(s)
- Ramu Anandakrishnan
- Department of Computer Science, Virginia Tech, Blacksburg, Virginia, United States of America
| | - Charles Baker
- Graduate Program in Biophysics, Harvard University, Cambridge, Massachusetts, United States of America
| | - Saeed Izadi
- Department of Engineering Science and Mechanics, Virginia Tech, Blacksburg, Virginia, United States of America
| | - Alexey V. Onufriev
- Department of Computer Science, Virginia Tech, Blacksburg, Virginia, United States of America
- Department of Physics, Virginia Tech, Blacksburg, Virginia, United States of America
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Abstract
Many quantum mechanical calculations indicate water molecules in the gas and liquid phase have much larger quadrupole moments than any of the common site models of water for computer simulations. Here, comparisons of multipoles from quantum mechanical∕molecular mechanical (QM∕MM) calculations at the MP2∕aug-cc-pVQZ level on a B3LYP∕aug-cc-pVQZ level geometry of a waterlike cluster and from various site models show that the increased square planar quadrupole can be attributed to the p-orbital character perpendicular to the molecular plane of the highest occupied molecular orbital as well as a slight shift of negative charge toward the hydrogens. The common site models do not account for the p-orbital type electron density and fitting partial charges of TIP4P- or TIP5P-type models to the QM∕MM dipole and quadrupole give unreasonable higher moments. Furthermore, six partial charge sites are necessary to account reasonably for the large quadrupole, and polarizable site models will not remedy the problem unless they account for the p-orbital in the gas phase since the QM calculations show it is present there too. On the other hand, multipole models by definition can use the correct multipoles and the electrostatic potential from the QM∕MM multipoles is much closer than that from the site models to the potential from the QM∕MM electron density. Finally, Monte Carlo simulations show that increasing the quadrupole in the soft-sticky dipole-quadrupole-octupole multipole model gives radial distribution functions that are in good agreement with experiment.
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Affiliation(s)
- Shuqiang Niu
- Department of Chemistry, Georgetown University, Washington, DC 20057, USA
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