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Investigating the Selectivity of KcsA Channel by an Image Charge Solvation Method (ICSM) in Molecular Dynamics Simulations

Part of: Physiological, cellular and medical topics Higher-dimensional theory

Published online by Cambridge University Press:  12 April 2016

Katherine Baker ,
Duan Chen  and
Wei Cai
Katherine Baker
Affiliation:
Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA
Duan Chen
Affiliation:
Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA
Wei Cai*
Affiliation:
Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA
*
*Corresponding author. Email addresses:[email protected] (K. Baker), [email protected] (D. Chen), [email protected] (W. Cai)
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Abstract

In this paper, we study the selectivity of the potassium channel KcsA by a recently developed image-charge solvation method (ICSM) combined with molecular dynamics simulations. The hybrid solvation model in the ICSM is able to demonstrate atomistically the function of the selectivity filter of the KcsA channel when potassium and sodium ions are considered and their distributions inside the filter are simulated. Our study also shows that the reaction field effect, explicitly accounted for through image charge approximation in the ICSM model, is necessary in reproducing the correct selectivity property of the potassium channels.

Keywords

Potassium ion channelselectivityimage charge solvation methodmolecular dynamics

MSC classification

Secondary: 31B05: Harmonic, subharmonic, superharmonic functions 92C05: Biophysics 65Z05: Applications to physics
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 4 , April 2016 , pp. 927 - 943
Copyright
Copyright © Global-Science Press 2016 

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References

[1]Baker, K., Baumketner, A., Lin, Y., Deng, S., Jacobs, D., and Cai, W.ICSM: An order n method for calculating electrostatic interactions added to TINKER. Comp. Phys. Comm., 184:19–26, 2013.CrossRefGoogle ScholarPubMed
[2]Berneche, S and Roux, B.Molecular dynamics of the kcsa k+ channel in a bilayer membrane. Biophysical Journal, 78:2900–2917, 2000.Google Scholar
[3]Biggin, P. C., Smith, G. R., Shrivastava, I., Choe, S., and Sansom, M.S. P. Potassium and sodium ions in a potassium channel studied by molecular dynamics simulations. Biochim. Biophys. Acta, 1510.CrossRefGoogle Scholar
[4]Burger, M., Eisenberg, R.S., and Heinz, E.Inverse Problems Related to Ion Channel Selectivity. SIAM J Applied Math, 67(4):960–989, 2007.Google Scholar
[5]Cai, W., Deng, S., and Jacobs, D.Extending the fast multipole method to charges inside or outside a dielectric sphere. J. Comput. Phys., 223:846–864, 2007.Google Scholar
[6]Cai, W., Deng, S., and Xu, Z.Image charge approximations of reaction fields in solvents with arbitrary ionic strength. Journal of Computational Physics, 228:2092–2099, 2009.Google Scholar
[7]Deng, S.Cai, W.Discrete image approximations of ionic solvent induced reaction field to charges. Commun. Comput. Phys., 2:1007–1026, 2007.Google Scholar
[8]Deng, S.Cai, W.Extending the fast multipole method for charges inside a dielectric sphere in an ionic solvent: High-order image approximations for reaction fields. J. Comput. Phys., 227, 2007.CrossRefGoogle Scholar
[9]Chen, D.P., Lear, J., and Eisenberg, B.Permeation through an open channel: Poisson-Nernst-Planck theory of a synthetic ionic channel. Biophys J., 72(1):97–116, 1997.CrossRefGoogle ScholarPubMed
[10]Chung, S.H. and Kuyucak, S.Recent advances in ion channel research. Biochimica et Biophysica Acta, 1565:267–286, 2002.CrossRefGoogle ScholarPubMed
[11]Coalson, R. D. and Kurnikova, M. G.Poisson-Nernst-Planck theory approach to the calculation of current through biological ion channels. IEEE Trans Nanobioscience, 4(1):81–93, 2005.Google Scholar
[12]Doyle, D.A., Cabral, J. M., Pfuetzner, R. A., Kuo, A., Gulbis, J. M., Cohen, S.L., Chait, B.T., and MacKinnon, R.The structure of the potassium channel: Molecular basis of K conduction and selectivity. Science, 280:69–77, 1998.Google Scholar
[13]Egwolf, B. and Roux, B.Ion selectivity of the kcsa channel: A perspective from multi-ion free energy landscapes. J. Chem. Phys., 401:831–842, 2010.Google Scholar
[14]Gautschi, W.Algorithm 726; ORTHPOL-a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules. ACM Trans. Math. Softw., 20:21–62, 1994.Google Scholar
[15]Gillespie, D., Nonner, W., and Eisenberg, R.S.Density functional theory of charged, hard-sphere fluids. Phys. Rev. E, 68:1–10, 2003.Google Scholar
[16]Hladky, S.B. and Haydon, D.A.Ion transfer across lipid membranes in the presence of gramicidin a. i. studies of the unit conductance channel. Biochim. Biophys. Acta, 274:294–312, 1972.Google Scholar
[17]Hodgkin, A.L. and Huxley, A.F.A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol., 117:500–544, 1952.CrossRefGoogle ScholarPubMed
[18]Hyon, Y., Eisenberg, B., and Liu, C.A mathematical model of the hard sphere repulsion in ionic solutions. Communications in Mathematical Sciences, 9:459–475, 2011.Google Scholar
[19]Jackson, J.D.Classical Electrodynamics. New York : John Wiley, 1999.Google Scholar
[20]Jordan, P.C.Fifty years of progress in ion channel research. IEEE TRANSACTIONS ON NANOBIOSCIENCE, 4:3–9, 2005.Google Scholar
[21]Jung, Y., Lu, B., and Mascagni, M.A computational study of ion conductance in the KcsA K+ channel using a Nernst-Planck model with explicit resident ions. J. Chem. Phys., page 215101, 2009.CrossRefGoogle ScholarPubMed
[22]Li, H. and Lu, B.An ionic concentration and size dependent dielectric permittivity Poisson-Boltzmann model for biomolecular solvation studies. J. Chem. Phys., 141:024115, 2014.Google Scholar
[23]Liang, Y., Xu, Z., and Xing, X.A multi-scale Monte Carlo method for electrolytes. New Journal of Physic, 17(8):083062, 2015.Google Scholar
[24]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.Google ScholarPubMed
[25]MacKerell, A. D. Jr., Bashford, D., Bellot, M., Dunbrack, R. L. Jr., Evanseck, J. D., Field, M. J., Fischer, S., Gao, J., Guo, H., Ha, S., Joseph-McCarthy, D., Kuchnir, L., Kuczera, K., Lau, F. T. K., Mattos, C., Michnick, S., Ngo, T., Nguyen, D. T., Prodhom, B., Reiher, W. E. III, Roux, B., Schlenkrich, M., Smith, J. C., Stote, R., Straub, J., Watanabe, M., Wiorkiewicz-Kuczera, J., Yin, D., and Karplus, M.All-atom empirical potential for molecular modeling and dynamics studies of proteins. Journal of Physical Chemistry B, 102(18):3586–3616, 1998.Google Scholar
[26]Roux, B.MacKinnon, R.The cavity and pore helices in the kcsa k+ channel: electrostatic stabilization of monovalent cations. Science, 285(5424):100–102, 1999.Google Scholar
[27] University of Illinois at Urbana-Champaign. Kcsa potassium channel. Online.Google Scholar
[28]Perlman, D.A., Case, D.A., Caldwell, J.W., Ross, W.S., Cheatham, T.E., Debolt, S., Ferguson, D., Seibel, G., and Kollman, P. Amber, a package of computer programs for applying molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations to simulate the structural and energetic properties of molecules. Comp. Phys. Commun., 91:1–41, 1995.Google Scholar
[29]Ponder, J. W. Tinker - software tools for molecular design. http://dasher.wustl.edu/ffe/downloads/guide.pdf, 2004.Google Scholar
[30]Shrivastava, I.H., Tieleman, D.P., Biggin, P. C., and Sansaom, M.S.P.K+ versus Na+ ions in a K channel selectivity filter: A simulation study. Biophysical Journal, 83:633–645, 2002.CrossRefGoogle Scholar
[31]Thompson, A., Kim, I., Panosian, T., Iverson, T., Allen, T., and Nimigean, C.Mechanism of potassium-channel selectivity revealed by na+ and li+ binding sites within the kcsa pore. Nature Structural and Molecular Biology, 16:1317–1324, 2009.Google Scholar
[32]Weiner, P. K. and Kollman, P. A. Amber: Assisted model-building with energy refinement.a general program for modeling molecules and their interactions. J. Comput. Chem., 2:287–303, 1981.Google Scholar
[33]Xie, D., Jiang, Y., and Scott, L.R.Efficient algorithms for solving a nonlocal dielectric model for protein in ionic solvent. SIAM Journal on Scientific Computing, 38:B1267–1284, 2013.Google Scholar
[34]Yang, L.J.New-generation amber united-atom force field. J. Phys.Chem. B, 110:13166–13176, 2006.Google Scholar
[35]Yu, L., Sun, C., Song, D., Shen, J., Xu, N., Gunasekera, A., Hajduk, P. J., and Olejniczak, E. T.Nuclear magnetic resonance structural studies of a potassium channel-charybdotoxin complex. Biochemistry, pages 15834–15841, 2005.Google Scholar
[36]Zhou, S., Wang, Z., and Li, B.Mean-field description of ionic size effects with non-uniform ionic sizes: A numerical approach. Phys. Rev. E, 84:021901, 2011.Google Scholar
[37]Zhou, Y., Morais-Cabra, J., Kaufman, A., and Mackinnon, R.Chemistry of ion coordination and hydration revealed by a K+ channel-Fab complex at 2.0 A resolution. Nature, 414:43–48, 2001.Google Scholar