The Community for Technology Leaders
RSS Icon
Issue No.01 - January-February (2011 vol.8)
pp: 273-281
Vikram Krishnamurthy , University of British Columbia, Vancouver
Kai Yiu Luk , University of British Columbia, Vancouver
Constructing accurate computational models that explain how ions permeate through a biological ion channel is an important problem in biophysics and drug design. Brownian dynamics simulations are large-scale interacting particle computer simulations for modeling ion channel permeation but can be computationally prohibitive. In this paper, we show the somewhat surprising result that a small-dimensional semi-Markov model can generate events (such as conduction events and dwell times at binding sites in the protein) that are statistically indistinguishable from Brownian dynamics computer simulation. This approach enables the use of extrapolation techniques to predict channel conduction when performing the actual Brownian dynamics simulation that is computationally intractable. Numerical studies on the simulation of gramicidin A ion channels are presented.
Ion channel permeation, semi-Markov model, Brownian dynamics, binding sites, gramicidin.
Vikram Krishnamurthy, Kai Yiu Luk, "Semi-Markov Models for Brownian Dynamics Permeation in Biological Ion Channels", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.8, no. 1, pp. 273-281, January-February 2011, doi:10.1109/TCBB.2008.136
[1] B. Hille, Ionic Channels of Excitable Membranes, third ed. Sinauer Assoc., Inc., 2001.
[2] Biological Membrane Ion Channels: Dynamics, Structure and Applications, S. Chung, O. Andersen, and V. Krishnamurthy, eds. Springer-Verlag, 2007.
[3] R. Dutzler, E. Campbell, M. Cadene, B. Chait, and R. MacKinnon, "X-Ray Structure of a ClC Chloride Channel at 3.0 Å Reveals the Molecular Basis of Anion Selectivity," Nature, vol. 415, pp. 287-294, 2002.
[4] IEEE Trans. Nanobioscience, special issue Ion channels: bio nanotubes, V. Krishnamurthy, S. Chung, and G. Dumont, eds., vol. 4, no. 1, Mar. 2005.
[5] V. Krishnamurthy and S. Chung, "Large-Scale Dynamical Models and Estimation for Permeation in Biological Membrane Ion Channels," Proc. IEEE, vol. 95, no. 5, pp. 853-880, May 2007.
[6] D. Boda, W. Nonner, M. Valisk, D. Henderson, B. Eisenberg, and D. Gillespie, "Steric Selectivity in Na Channels Arising from Protein Polarization and Mobile Side Chains," Biophysical J., vol. 93, pp. 1960-1980, 2007.
[7] R. Coalson and M. Kurnikova, "Poisson-Nernst-Planck Theory Approach to the Calculation of Current Through Biological Ion Channels," IEEE Trans. Nanobioscience, vol. 4, pp. 263-277, 2005.
[8] R. Eisenberg, "Computing the Field in Proteins and Channels," J. Membrane Biology, vol. 150, pp. 1-25, 1996.
[9] R. Eisenberg, "From Structure to Function in Open Ionic Channels," J. Membrane Biology, vol. 171, pp. 1-24, 1999.
[10] A. Singer, D. Gillespie, J. Norbury, and R. Eisenberg, "Singular Perturbation Analysis of the Steady State Poisson-Nernst-Planck System: Applications to Ion Channels," European J. Applied Math., vol. 19, pp. 541-560, 2008.
[11] E. Barkai, R. Eisenberg, and Z. Schuss, "Bidirectional Shot Noise in a Singly Occupied Channel," Physical Rev. E, vol. 54, pp. 1161-1175, 1996.
[12] S. Edwards, B. Corry, S. Kuyucak, and S. Chung, "Continuum Electrostatics Fails to Describe Ion Permeation in the Gramicidin Channel," Biophysical J., vol. 83, pp. 1348-1360, Sept. 2002.
[13] T.W. Allen, O.S. Andersen, and B. Roux, "Energetics of Ion Conduction through the Gramicidin Channel," Proc. Nat'l Academy of Sciences USA, vol. 101, pp. 117-122, 2004.
[14] U. Hollerbach, D. Chen, and R. Eisenberg, "Two- and Three-Dimensional Poisson-Nernst-Planck Simulations of Current Flow through Gramicidin A," J. Scientific Computing, vol. 16, no. 4, pp. 373-409, Dec. 2001.
[15] V. Krishnamurthy, M. Hoyles, R. Saab, and S. Chung, "Permeation in Gramicidin Ion Channels by Directly Estimating the Potential of Mean Force Using Brownian Dynamics Simulation," J. Computational and Theoretical Nanoscience, vol. 3, pp. 702-711, 2006.
[16] G.A. Olah, H.W. Huang, W.H. Liu, and Y.L. Wu, "Location of Ion-Binding Sites in the Gramicidin Channel by X-Ray Diffraction," J. Molecular Biology, vol. 218, pp. 847-858, 1991.
[17] S.C. Choi and R. Wette, "Maximum Likelihood Estimation of the Parameters of the Gamma Distribution and Their Bias," Technometrics, vol. 11, no. 4, pp. 683-690, 1969.
[18] M. Hoyles, V. Krishnamurthy, M. Siksik, and S. Chung, "Brownian Dynamics Theory for Predicting Internal and External Blockages of Tetraethylammonium in the KcsA Potassium Channel," Biophysical J., vol. 94, pp. 366-378, Jan. 2008.
29 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool