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2015 | 3 | 1 |
Tytuł artykułu

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundaryintegral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood’s classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson–Boltzmann equation. The eigenfunctionexpansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pHdependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online.
Słowa kluczowe
Wydawca
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2014-08-24
zaakceptowano
2014-12-11
online
2015-01-14
Twórcy
  • Dept. of Mechanical and Industrial Engineering, Northeastern University,
    Boston MA 02115
  • Computation Institute, University of Chicago, Chicago IL 60637
autor
  • Google Inc., Mountain View CA 94041
Bibliografia
  • [1] B. Roux and T. Simonson. Implicit solvent models. Biophys. Chem., 78:1–20, 1999.[Crossref]
  • [2] C. Azuara, H. Orland, M. Bon, P. Koehl, and M. Delarue. Incorporating dipolar solvents with variable density in Poisson–Boltzmann electrostatics. Biophys. J., 95:5587–5605, 2008.[Crossref]
  • [3] P. Koehl and M. Delarue. AQUASOL: an eflcient solver for the dipolar Poisson–Boltzmann–Langevin equation. J. Chem.Phys., 132:064101, 2010.
  • [4] J. G. Kirkwood. Theory of solutions ofmolecules containingwidely separated chargeswith special application to zwitterions.J. Chem. Phys., 2:351, 1934.
  • [5] J. D. Jackson. Classical Electrodynamics. Wiley, 3rd edition, 1998.
  • [6] J. J. Havranek and P. B. Harbury. Tanford–Kirkwood electrostatics for protein modeling. Proc. Natl. Acad. Sci. USA,96(20):11145–11150, 1999.[Crossref]
  • [7] H.-X. Zhou. Control of reduction potential by protein matrix: lesson from a spherical protein model. Journal of BiologicalInorganic Chemistry, 2:109–113, 1997.
  • [8] E. Kangas and B. Tidor. Optimizing electrostatic aflnity in ligand–receptor binding: Theory, computation, and ligand properties.J. Chem. Phys., 109:7522–7545, 1998.
  • [9] G. Sigalov, P. Scheffel, and A. Onufriev. Incorporating variable dielectric environments into the generalized Born model. J.Chem. Phys., 122:094511, 2005.
  • [10] I. M. Mladenov. Kirkwood’s formula revisited. Europhysics Letters, 33:577–581, 1996.[Crossref]
  • [11] K. E. Atkinson. The Numerical Solution of Integral Equations of the Second Kind. Cambridge University Press, 1997.
  • [12] J. J. Bowman, T. B. A. Senior, and P. L. E. Uslenghi. Electromagnetic and acoustic scattering by simple shapes. North-Holland,Amsterdam, 1969.
  • [13] R. E. Kleinman, R. Kress, and E. Martensen, editors. The spectrum of the electrostatic integral operator for an ellipsoid,Frankfurt/Bern, 1995. Lang.
  • [14] R. R. Dogonadze and A. A. Kornyshev. Polar solvent structure in the theory of ionic solvation. J. Chem. Soc. Faraday Trans.2, 70:1121–1132, 1974.[Crossref]
  • [15] A. A. Kornyshev, A. I. Rubinshtein, and M. A. Vorotyntsev. Model nonlocal electrostatics: I. Journal of Physics C: Solid StatePhysics, 11:3307, Dec 1978.
  • [16] M. V. Basilevsky and D. F. Parsons. An advanced continuum medium model for treating solvation effects: Nonlocal electrostaticswith a cavity. J. Chem. Phys., 105(9):3734, Aug 1996.
  • [17] A. Hildebrandt, R. Blossey, S. Rjasanow, O. Kohlbacher, and H.-P. Lenhof. Novel formulation of nonlocal electrostatics. Phys.Rev. Lett., 93:108104, 2004.[Crossref]
  • [18] A. Rubinstein and S. Sherman. Influence of the solvent structure on the electrostatic interactions in proteins. Biophys. J.,87(3):1544–1557, Sep 2004.[Crossref]
  • [19] P. Attard, D. Wei, and G. N. Patey. Critical comments on the nonlocal dielectric function employed in recent theories of thehydration force. Chemical Physics Letters, 172:69–72, 1990.
  • [20] M. V. Basilevsky and D. F. Parsons. Nonlocal continuum solvation model with exponential susceptibility kernels. J. Chem.Phys., 108:9107–9113, 1998.
  • [21] S. Weggler. Correlation induced electrostatic effects in biomolecular systems. PhD thesis, Universität des Saarlandes, 2010.
  • [22] A. Rubinstein and S. Sherman. Evaluation of the influence of the internal aqueous solvent structure on electrostatic interactionsat the protein-solvent interface by nonlocal continuum electrostatic approach. Biopolymers, 87(2-3):149–164, Oct2007.[Crossref]
  • [23] A. Rubinstein, R. Sabirianov, W. Mei, F. Namavar, and A. Khoynezhad. Effect of the ordered interfacial water layer in proteincomplex formation: A nonlocal electrostatic approach. Phys. Rev. E, 82(2):021915, Aug 2010.[Crossref]
  • [24] M. A. Vorotyntsev. Model nonlocal electrostatics. II. spherical interface. Journal of Physics C: Solid State Physics, 11:3323–3331, 1978.
  • [25] A. Hildebrandt. Biomolecules in a structured solvent: A novel formulation of nonlocal electrostatics and its numerical solution.PhD thesis, Universität des Saarlandes, 2005.
  • [26] A. Hildebrandt, R. Blossey, S. Rjasanow, O. Kohlbacher, and H.-P. Lenhof. Electrostatic potentials of proteins in water: astructured continuum approach. Bioinformatics, 23(2):e99–e103, Jan 2007.[Crossref]
  • [27] S. Weggler, V. Rutka, and A. Hildebrandt. A new numerical method for nonlocal electrostatics in biomolecular simulations.J. Comput. Phys., 229(11):4059–4074, Jun 2010.
  • [28] R. L. Ochs Jr. and G. Kristensson. Using local differential operators to model dispersion in dielectric media. Journal of theoptical society of America A, 15:2208–2215, 1998.
  • [29] R. A. B. Engelen, M. G. D. Geers, and F. P. T. Baaijens. Nonlocal implicit gradient-enhanced elasto-plasticity for the modellingof softening behavior. International Journal of Plasticity, 19:403–433, 2003.[Crossref]
  • [30] J. P. Bardhan. Gradient models inmolecular biophysics: progress, challenges, opportunities. Journal of Mechanical Behaviorof Materials, 22:169–184, 2013.
  • [31] C. Fasel, S. Rjasanow, and O. Steinbach. A boundary integral formulation for nonlocal electrostatics. In Karl Kunisch,GüntherOf, andOlaf Steinbach, editors, NumericalMathematics and Advanced Applications, pages 117–124. Springer BerlinHeidelberg, 2008.
  • [32] N. A. Baker, D. Sept, M. J. Holst, and J. A. McCammon. Electrostatics of nanoysystems: Application to microtubules and theribosome. Proc. Natl. Acad. Sci. USA, 98:10037–10041, 2001.[Crossref]
  • [33] A. H. Boschitsch, M. O. Fenley, and H.-X. Zhou. Fast boundary element method for the linear Poisson–Boltzmann equation.J. Phys. Chem. B, 106(10):2741–54, 2002.[Crossref]
  • [34] B. Z. Lu, X. L. Cheng, J. Huang, and J. A. McCammon. Order N algorithm for computation of electrostatic interactions inbiomolecular systems. Proc. Natl. Acad. Sci. USA, 103(51):19314–19319, 2006.[Crossref]
  • [35] M. D. Altman, J. P. Bardhan, J. K. White, and B. Tidor. Accurate solution of multi-region continuum electrostatic problemsusing the linearized Poisson–Boltzmann equation and curved boundary elements. J. Comput. Chem., 30:132–153, 2009.[Crossref]
  • [36] J. P. Bardhan and A. Hildebrandt. A fast solver for nonlocal electrostatic theory in biomolecular science and engineering. InIEEE/ACM Design Automation Conference (DAC), 2011.
  • [37] J. Warwicker and H. C. Watson. Calculation of the electric potential in the active site cleft due to alpha-helix dipoles. J. Mol.Biol., 157:671–679, 1982.
  • [38] D. Xie, Y. Jiang, and L. R. Scott. Eflcient algorithms for a nonlocal dielectric model for protein in ionic solvent. SIAM Journalof Scientific and Statistical Computing, 35:B1267–B1284, 2013.
  • [39] A. H. Juffer, E. F. F. Botta, B. A. M. van Keulen, A. van der Ploeg, and H. J. C. Berendsen. The electric potential of a macromoleculein a solvent: A fundamental approach. J. Comput. Phys., 97(1):144–171, 1991.[Crossref]
  • [40] B. J. Yoon and A. M. Lenhoff. A boundary element method for molecular electrostatics with electrolyte effects. J. Comput.Chem., 11(9):1080–1086, 1990.[Crossref]
  • [41] S. S. Kuo, M. D. Altman, J. P. Bardhan, B. Tidor, and J. K. White. Fast methods for simulation of biomolecule electrostatics.In International Conference on Computer Aided Design (ICCAD), 2002.
  • [42] M. D. Altman, J. P. Bardhan, B. Tidor, and J. K. White. FFTSVD: A fast multiscale boundary-element method solver suitablefor BioMEMS and biomolecule simulation. IEEE T. Comput.-Aid. D., 25:274–284, 2006.
  • [43] G. C. Hsiao and R. E. Kleinman. Error analysis in numerical solution of acoustic integral equations. International Journal forNumerical Methods in Engineering, 37:2921–2933, 1994.
  • [44] J. P. Bardhan, M. G. Knepley, and P. Brune. Public mercurial repository containing all source code in supplementarymaterial.https://bitbucket.org/jbardhan/matlab-analytical-nonlocal-sphere.
  • [45] L. W. Cai. On the computation of spherical Bessel functions of complex arguments. Comp. Phys. Comm., 182:663–668,2011.
  • [46] J. Van Bladel. Electromagnetic Fields. John Wiley & Sons, Hoboken, NJ, second edition, 2007.
  • [47] M. V. Fedorov and A. A. Kornyshev. Unravelling the solvent response to neutral and charged solutes. Molecular Physics,105:1–16, 2007.[Crossref]
  • [48] A. A. Kornyshev and J. Ulstrup. Polar solvent structural parameters from protonation equilibria of aliphatic and alicyclicdiamines and from absorption bands of mixed-valence transition-metal complexes. Chemical Physics Letters, 126, 1986.
  • [49] D. Xie, Y. Jiang, P. Brune, and L. R. Scott. A fast solver for a nonlocal dielectric continuum model. SIAM Journal of ScientificComputing, 34:B107–B126, 2012.[Crossref]
  • [50] M. Nina, W. Im, and B. Roux. Optimized atomic radii for protein continuum electrostatics solvation forces. Biophys. Chem.,78:89–96, 1999.[Crossref]
  • [51] J. P. Bardhan, P. Jungwirth, and L. Makowski. Aflne-response model of molecular solvation of ions: Accurate predictions ofasymmetric charging free energies. J. Chem. Phys., 137:124101, 2012.
  • [52] Henry S. Ashbaugh. Convergence of molecular and macroscopic continuum descriptions of ion hydration. The Journal ofPhysical Chemistry B, 104(31):7235–7238, 2000.[Crossref]
  • [53] A. A. Rashin and B. Honig. Reevaluation of the Born model of ion hydration. J. Phys. Chem., 89:5588–5593, 1985.[Crossref]
  • [54] I. S. Joung and T. E. Cheatham III. Determination of alkali and halide monovalent ion parameters for use in explicitly solvatedbiomolecular simulations. J. Phys. Chem. B, 112:9020–9041, 2008.[Crossref]
  • [55] W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein. Comparison of simple potential functions forsimulating liquid water. J. Chem. Phys., 79:926–935, 1983.
  • [56] H. J. C. Berendsen, J. R. Grigera, and T. P. Straatsma. The missing term in effective pair potentials. The Journal of PhysicalChemistry, 91(24):6269–6271, 1987.[Crossref]
  • [57] H. Gong, G. Hocky, and K. F. Freed. Influence of nonlinear electrostatics on transfer energies between liquid phases: Chargeburial is far less expensive than Born model. Proc. Natl. Acad. Sci. USA, 105:11146–11151, 2008.[Crossref]
  • [58] A. Mukhopadhyay, A. T. Fenley, I. S. Tolokh, and A. V. Onufriev. Charge hydration asymmetry: the basic principle and howto use it to test and improve water models. J. Phys. Chem. B, 116:9776–9783, 2012.[Crossref]
  • [59] S. Rajamani, T. Ghosh, and S. Garde. Size dependent ion hydration, its asymmetry, and convergence to macroscopic behavior.J. Chem. Phys., 120:4457, 2004.
  • [60] D. L. Mobley, K. A. Dill, and J. D. Chodera. Treating entropy and conformational changes in implicit solvent simulations ofsmall molecules. J. Phys. Chem. B, 112:938–946, 2008.[Crossref]
  • [61] Y. Y. Sham, I.Muegge, and A.Warshel. The effect of protein relaxation on charge-charge interactions and dielectric constantsof proteins. Biophys. J., 74(4):1744–1753, 1998.[Crossref]
  • [62] C. N. Schutz and A.Warshel. What are the dielectric constants of proteins and howto validate electrostatic models? Proteins,44:400–417, 2001.[Crossref]
  • [63] M. Gilson and B. Honig. The dielectric constant of a folded protein. Biopolymers, 25:2097–2119, 1986.[Crossref]
  • [64] E. Demchuk and R. C.Wade. Improving the continuumdielectric approach to calculating pKas of ionizable groups in proteins.J. Phys. Chem., 100:17373–17387, 1996.[Crossref]
  • [65] J. P. Bardhan. Nonlocal continuum electrostatic theory predicts surprisingly small energetic penalties for charge burial inproteins. J. Chem. Phys., 135:104113, 2011.
  • [66] J. P. Bardhan and M. G. Knepley. Mathematical analysis of the boundary-integral based electrostatics estimation approximationfor molecular solvation: Exact results for spherical inclusions. J. Chem. Phys., 135:124107, 2011.
  • [67] J. Liang and S. Subramaniam. Computation of molecular electrostatics with boundary element methods. Biophys. J.,73(4):1830–1841, 1997.[Crossref]
  • [68] G. Sigalov, A. Fenley, and A. Onufriev. Analytical electrostatics for biomolecules: Beyond the generalized Born approximation.J. Chem. Phys., 124(124902), 2006.
  • [69] J. F. Ahner and R. F. Arenstorf. On the eigenvalues of the electrostatic integral operator. Journal of Mathematical Analysisand Applications, 117:187–197, 1986.
  • [70] J. F. Ahner, V. V. Dyakin, V. Ya. Raevskii, and St. Ritter. Spectral properties of operators of the theory of harmonic potential.Mathematical Notes, 59(1):3–11, 1996.[Crossref]
  • [71] J. P. Bardhan and M. G. Knepley. Computational science and re-discovery: open-source implementation of ellipsoidal harmonicsfor problems in potential theory. Computational Science and Discovery, 5:014006, 2012.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_mlbmb-2015-0001
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