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Image Charge Method for Reaction Fields in a Hybrid Ion-Channel Model

Published online by Cambridge University Press:  20 August 2015

Zhenli Xu ,
Wei Cai  and
Xiaolin Cheng
Zhenli Xu*
Affiliation:
Department of Mathematics and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
Wei Cai*
Affiliation:
Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA Beijing International Center for Mathematical Research, Beijing 100871, China
Xiaolin Cheng*
Affiliation:
Center for Molecular Biophysics, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
*
Corresponding author.Email:xuzl@sjtu.edu.cn
Email:wcai@uncc.edu
Email:chengx@ornl.gov
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Abstract

A multiple-image method is proposed to approximate the reaction-field potential of a source charge inside a finite length cylinder due to the electric polarization of the surrounding membrane and bulk water. When applied to a hybrid ion-channel model, this method allows a fast and accurate treatment of the electrostatic interactions of protein with membrane and solvent. To treat the channel/membrane interface boundary conditions of the electric potential, an optimization approach is used to derive image charges by fitting the reaction-field potential expressed in terms of cylindric harmonics. Meanwhile, additional image charges are introduced to satisfy the boundary conditions at the planar membrane interfaces. In the end, we convert the electrostatic interaction problem in a complex inhomogeneous system of ion channel/membrane/water into one in a homogeneous free space embedded with discrete charges (the source charge and image charges). The accuracy of this method is then validated numerically in calculating the solvation self-energy of a point charge.

Keywords

31B0592C0565Z05Ion channelsimage chargescylindrical harmonicselectrostatic interactions
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 4 , April 2011 , pp. 1056 - 1070
Copyright
Copyright © Global Science Press Limited 2011

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References

[1]Abagyan, R., and Totrov, M., Biased probability Monte Carlo conformational searches and electrostatic calculations for peptides and proteins, J. Mol. Biol., 235 (1994), 983–1002.CrossRefGoogle ScholarPubMed
[2]Abramowitz, M., and Stegun, I. A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1964.Google Scholar
[3]Beglov, D., and Roux, B., Finite representation of an infinite bulk system-Solvent boundary potential for computer simulations, J. Chem. Phys., 100 (1994), 9050–9063.Google Scholar
[4]Cai, W., Deng, S., and Jacobs, D., Extending the fast multipole method to charges inside or outside a dielectric sphere, J. Comput. Phys., 223 (2007), 846–864.CrossRefGoogle Scholar
[5]Cheng, H., Greengard, L., and Rokhlin, V., A fast adaptive multipole algorithm in three dimensions, J. Comput. Phys., 155 (1999), 468–498.Google Scholar
[6]Cui, S. T., Electrostatic potential in cylindrical dielectric media using the image charge method, Mol. Phys., 104 (2006), 2993–3001.CrossRefGoogle Scholar
[7]Darden, T. A., York, D. M., and Pedersen, L. G., Particle mesh Ewald: an Nlog(N) method for Ewald sums in large systems, J. Chem. Phys., 98 (1993), 10089–10092.CrossRefGoogle Scholar
[8]Deng, S., and Cai, W., Discrete image approximations of ionic solvent induced reaction field to charges, Commun. Comput. Phys., 2 (2007), 1007–1026.Google Scholar
[9]Duan, Z. H., and Krasny, R., An Ewald summation based multipole method, J. Chem. Phys., 113 (2000), 3492–3495.Google Scholar
[10]Eisenberg, B., Ionic channels in biological membranes: natural nanotubes, Acc. Chem. Res., 31 (1998), 117–123.Google Scholar
[11]Fogolari, F., Brigo, A., and Molinari, H., The Poisson-Boltzmann equation for biomolecular electrostatics: a tool for structural biology, J. Mol. Biol., 15 (2002), 377–392.Google Scholar
[12]Friedman, H. L., Image approximation to the reaction field, Mol. Phys., 29 (1975), 1533–1543.Google Scholar
[13]Greengard, L., and Rokhlin, V., A fast algorithm for particle simulations, J. Comput. Phys., 73 (1987), 325–348.CrossRefGoogle Scholar
[14]Hille, B., Ionic Channels of Excitable Membranes, Sinauer Associates, Inc., Sunderland, MA, 1992.Google Scholar
[15]Honig, B., and Nicholls, A., Classical electrostatics in biology and chemistry, Science., 268 (1995), 1144–1149.Google Scholar
[16]Im, W., Beglov, D., and Roux, B., Continuum solvation model: computation of electrostatic forces from numerical solutions to the Poisson-Boltzmann equation, Comput. Phys. Commun., 111 (1998), 59–75.Google Scholar
[17]Im, W., Feig, M., and Brooks, C. L. III, An implicit membrane generalized Born theory for the study of structure, stability, and interactions of membrane proteins, Biophys. J., 85 (2003), 2900–2918.Google Scholar
[18]Jackson, J. D., Classical Electrodynamics (3rd Edition), John Wiley & Sons, New York, 2001.Google Scholar
[19]Lazaridis, T., Implicit solvent simulations of peptide interactions with anionic lipid membranes, Proteins., 58 (2005), 518–527.Google Scholar
[20]Levitt, D. G., Modeling of ion channels, J. Gen. Physiol., 113 (1999), 789–794.CrossRefGoogle ScholarPubMed
[21]Lin, Y., Baumketner, A., Deng, S., Xu, Z., Jacobs, D., and Cai, W., An image-based reaction field method for electrostatic interactions in molecular dynamics simulations of aqueous solutions, J. Chem. Phys., 131 (2009), 154103.Google Scholar
[22]Lindell, I. V., Electrostatic image theory for the dielectric sphere, Radio. Sci., 27 (1992), 1–8.Google Scholar
[23]Lindell, I. V., The Review of Radio Science, (1990-1992), Chap. Application of the image concept in electromagnetism, Oxford University Press, Oxford, 1993, 107–126.Google Scholar
[24]Lu, B., Cheng, X., Huang, J., and McCammon, J. A., Order N algorithm for computation of electrostatic interactions in biomolecular systems, Proc. Natl. Acad. Sci. USA, 103 (2006), 19314–19319.Google Scholar
[25]Lu, B. Z., Zhou, Y. C., Holst, M. J., and McCammon, J. A., Recent progress in numerical methods for the Poisson-Boltzmann equation in biophysical applications, Commun. Comput. Phys., 3 (2008), 973–1009.Google Scholar
[26]Luty, B. A., Davis, M. E., Tironi, I. G., and Van Gunsteren, W. F., A comparison of particle-particle, particle-mesh and Ewald methods for calculating electrostatic interactions in periodic molecular systems, Mol. Simul., 14 (1994), 11–20.Google Scholar
[27]Neumann, C., Hydrodynamische untersuchungen: Nebst einem anhange uber die probleme der elektrostatik und der magnetischen induktion, Teubner,, Leipzig (1883), 279-282.Google Scholar
[28]Okur, A., and Simmerling, C., Hybrid explicit/implicit solvation methods, Annu. Rep. Comput. Chem., 2 (2006), 97–109.CrossRefGoogle Scholar
[29]Qin, P., Xu, Z., Cai, W., and Jacobs, D., Image charge methods for a three-dielectric-layer hybrid solvation model of biomolecules, Commun. Comput. Phys., 6 (2009), 955–977.Google Scholar
[30]Roux, B., Allen, T., Berneche, S., and Im, W., Theoretical and computational models of biological ion channels, Quart. Rev. Biophys., 37 (2004), 15–103.Google Scholar
[31]Smythe, W., Static and Dynamic Electricity, Taylor and Francis, 1989.Google Scholar
[32]Spassov, V. Z., Yan, L., and Szalma, S., Introducing an implicit membrane in generalized Born/solvent accessibility continuum solvent models, J. Phys. Chem. B., 106 (2002), 8726–8738.Google Scholar
[33]Tieleman, D. P., Biggin, P. C., Smith, G. R., and Sansom, M. S. P., Simulation approaches to ion channel structure-function relationships, Quart. Rev. Biophys., 34 (2001), 473–561.Google Scholar
[34]Ulmschneider, M. B., Ulmschneider, J. P., Sansom, M. S. P., and Di Nola, A., A generalized Born implicit-membrane representation compared to experimental insertion free energies, Biophys. J., 92 (2007), 2338–2349.Google Scholar
[35]Wang, J., Tan, C., Tan, Y. H., Lu, Q., and Luo, R., Poisson-Boltzmann solvents in molecular dynamics simulations, Commun. Comput. Phys., 3 (2008) 1010–1031.Google Scholar
[36]Wang, L., and Hermans, J., Reaction field molecular dynamics simulation with Friedman’s image method, J. Phys. Chem., 99 (1995), 12001–12007.Google Scholar
[37]Wolfram, S., Mathematica, version 5.0, Wolfram Research, Inc., 2003.Google Scholar
[38]Xu, Z., and Cai, W., Fast analytical methods for macroscopic electrostatic models in biomolec-ular simulations, SIAM Rev., to appear, available at http://math.uncc.edu/~wcai/fastRe viewFinal.pdf.Google Scholar
[39]Xu, Z., Deng, S., and Cai, W., Image charge approximations of reaction fields in solvents with arbitrary ionic strength, J. Comput. Phys., 228 (2009), 2092–2099.Google Scholar
[40]Yang, P. K., Liaw, S. H., and Lim, C., Representing an infinite solvent system with a rectangular finite system using image charges, J. Phys. Chem. B., 106 (2002), 2973–2982.CrossRefGoogle Scholar
[41]Ying, L., Biros, G., and Zorin, D., A kernel-independent adaptive fast multipole algorithm in two and three dimensions, J. Comput. Phys., 196 (2004), 591–626.Google Scholar
[42]Yossel, Y. Y., On the generalization of the reflection law for a point charge with respect to a sphere (in Russian), Elektrichestvo., 12 (1971), 79–81.Google Scholar