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Outline

Prototype acetylcholine channel geometry

2004, Mathematical and Computer Modelling

https://doi.org/10.12732/IJPAM.V120I2.2

Abstract

Permeation of sodium (Na +) and potassium (K +) ions through the Acetylcholine (ACh) channel is fundamental to the initiation of action potential within excitible membranes. Using molecular dynamics, we trace the trajectories of sodium and potassium ions as they permeate the ACh receptor channel for the given geometry: the hyperboloid of one sheet. We estimate the formidable energy barrier that a sodium or potassium ion traversing the ACh channel encounters. The potential profile obtained from the simulations reveals a number of salient features of the ACh channel.

References (26)

  1. S.-H. Chung, T.W. Allen, S. Kuyucak, Modeling diverse range of potassium channels with Brownian Dynamics, Biophysical Journal 83 (2002) 263277.
  2. S. Aboud, D. Marreiro, M. Saraniti, R. Eisenberg, A Poisson P 3 MForce field scheme for particle-based simulations of ionic liquids, Journal of Computational Electronics 3 (2004) 117133.
  3. D. Chen, Fractional Poisson-Nerst-Planck model for ion channels I: Basic formulations and algorithms, Bulletin of Mathematical Biology 79 (2007) 2697-2726.
  4. D. Desai, G. Green, R. Mahurin, 2005, Simulation of charged particles in neutron decay correlation experiment, J. of Res. of Nat. Inst. of Stand. Technol. 110 (1982) 433 -449.
  5. E. Jacobsson, S. Chiu, Stochastic theory of ion movement in channels with single ion occupancy, Biophys. J. 52 (1987) 33 -45.
  6. D. Ermak, 1975A computer simulation of charged particles in solution II: polyion diffusion coefficient, J. of Chem Phys 62 (1975) 4197 -4203.
  7. D.G Levitt, Interpretation of biological ion channel flux data -reaction rate versus con- tinuum theory, Ann. Review of Biophysics and Biophysical Chemistry 15 (1986) 29 - 57.
  8. S.C Li, M. Hoyles, M. Kuyucak, S. Chung, Brownian dynamics study of ion transport in the vestibule of membrane channels, Biophys. J. 74 (1998) 37-47.
  9. S. Kuyucak, M. Hoyles, S.H. Chung, Analytical solutions of Poissons equation for realistic geometrical shapes of membrane ion channels, Biophys. J., 74 (1998) 22-36.
  10. A.Y. Aidoo, Effect of channel geometry on the electrostatic potential in acetylcholine channels, Math. Biosci. 186 (2003) 175-189.
  11. A.Y. Aidoo, Prototype acetylcholine channel geometry, Mathematical and Computer Modelling, 40 (2004) 271-283.
  12. A.T. Brunger, J. Kurijan, J., M. Karplus, Science 235 (1987) 458-460.
  13. L.E. Baum, T. Petrie, G. Soules, and Norman Weiss, A maximization technique occurring in the statistical analysis of probabilistic functions of markov Chains, Ann. of Math. Stat. 41 (1970), 164-171.
  14. G.A. Churchill, Stochastic models fo heterogeneous DNA sequences, Bull. of Math. Biol. 51 (1989) 79-94.
  15. D. Colquhoun, A. G. Hawkes, On the stochastic properties of single ion channels, Philo- sophical Transactions of the Royal Society London B (1982) 300, 1-59.
  16. A. Krogh, B. Larsson, G. von Heijne, Predicting transmembrane protein topology with a hidden Markov model: Application to complete genomes, J. of Molec. Biol. 305 (2001) 567-580.
  17. S.H. Chung, T. W. Allen, M. Hoyles, S. Kuyucak, Permeation of ions across the potassium channel: Brownian dynamics studies, Biophys. J. 77 (1999) 2517-2533.
  18. G. Moy, B. Corry, S. Kuyucak, S. Chung, Tests of continuum theories as models of ion channels. 1. Poisson-Boltzmann theory versus Brownian dynamics, Biophys. J. 78 (2000) 2349 -2363.
  19. B. Roux, T. Allen, S. Berneche, W. Im, Theoretical and computational models of bio- logical ion channels, Quarterly Reviews of Biophysics, 37 (2004) 15103.
  20. M. Hoyles, S. Kuyucak, S. Chung, Energy barrier presented to ions by vestibule of biological membrane channel, Biophysical Journal 70 (1996) 1628-1642.
  21. S-H. Chung, T.W. Allen, S. Kuyucak, Modeling diverse range of potassium channels with Brownian dynamics, Biophys. J. 83 (2002) 263-277.
  22. M. Patra, M. Karttunen, Systematic comparison of force fields for microscopic simulations of NaCl in aqueous solutions: Diffusion and structural properties, Journal of Comput. Chem. 25 (2004) 678.
  23. L. Greencard, V. Rokhlin, A fast algorithm for particle simulations, J. of Comput. Phys. 73 (1987) 315-348.
  24. T. Sauer, Computational solution of stochastic differential equations, Comput. Stat. 5 (2013) 362-371.
  25. C. E. Dangerfield, D. Kay, K. Burrage, Modeling ion channel dynamics through reflected stochastic differential equations, Phys. Rev. E 85 (2012) 051907.
  26. D.F. Anderson, B. Ermentrout, P.J. Thomas, Stochastic representations of ion Channel kinetics and exact stochastic simulation of neuronal dynamics, J. Comput. Neurosci. 38 (2015) 67.