medigraphic.com

2006, Number 2

<< Back

Rev Mex Ing Biomed 2006; 27 (2)

Ionic Channel Modeling As Markov Processes

Ávila-Pozos R, González-Vélez V, Godínez-Fernández R

Language: Spanish
References: 29
Page: 106-116
PDF size: 628.10 Kb.


ABSTRACT

We review basic concepts of Markov processes as they are discrete state models with stochastic transitions. We emphasize how to calculate transition probabilities between states and their random variables. Through this paper we discuss how this concepts could be applied to support a mathematical modelling of ionic channels. Channels have several conformational states and they skip from one to another in a non-deterministic fashion, so these techniques may be useful to understand channel behavior.
Finally, we detail the mathematical analysis for a two-state model and include some simulations obtained from it. The unitary currents simulated are important since they can be added to obtain the whole-cell macroscopic current, found in excitable cells.


REFERENCES

  1. OP Hamill, Marty A, Neher E, Sackman B, Sigworth FJ. Improved patch-clamp techniques forhigh-resolution current recording from cells and cell-free membrane patches. Plfügers Archiv 1981; 391: 85-100.

  2. Sakmann B, Neher E. Single-Channel Recording. Plenum, London, first edition, 1985.

  3. Colquhoun D, Hawkes AG. On the stochastic properties of single ionchannels. Proc R Soc London [Biol.] 1981; 211: 205-235.

  4. Hille B. Ionic selectivity, saturation, and block in sodium channels. A four-barrrier model. J Gen Physiology 1975; 66: 535-560.

  5. Ochi R. Single-channel mechanism of b-adrenergic enhancement of cardiac L-type calcium current. Japanese Journal of Physiology 1993; 43: 571-584.

  6. Greenstein JL, Winslow RL. An integrative model of the cardiac ventricular myocyte in corporating local control of Ca2+ release. Biophysical Journal 2002; 83: 2918-2945.

  7. Rice JJ, Jafri S, Winslow RL. Modeling gain and gradedness of Ca2+ release in the functional unit of the cardiac dyadic space. Biophysical Journal 1999; 77: 1871-1884.

  8. Vandenberg CA, Bezanilla F. A sodium channel gating model based on single channel, macroscopic ionic, and gating currents in the squid giant axon. Biophysical Journal 1991; 60(6): 1511-1533.

  9. Zagotta WN, Hoshi T, Aldrich RW. Shaker potassium channel gating evaluation of kinetic models for activation (iii). Journal of General Physiology 1994; 103(2): 321-3623.

  10. Becker JD, Honerkamp J, Hirsch J, Fröbe U, Schlatter E, Gregor R. Analysing ion channels with hidden Markov models. Pflügers Archiv 1994; 426: 328-332.

  11. Sigworth FJ. Voltage gating of ion channels. Quarterly Review of Biophysics 1999; 27(1): 1-40.

  12. Brzezniak Z, Zastawniak T. Basic stochastic processes. First edition. Springer, London, 1999.

  13. Doob JL. Stochastic Processes. First edition, Wiley, New York, 1990.

  14. Hornand R, Vandenberg CA. Statistical properties of single sodium channels. Journal of General Physiology 1984; 84: 505-534.

  15. Tuckwell HC. Introduction to Theoretical Neurobiology: Vol. 2, Nonlinear and Stochastic Theories. Cambridge University Press, Cambridge, 1997.

  16. Johnston DS, Miao-Sin Wu. Foundations of cellular neurophysiology. First edition. MIT Press, London, 1997.

  17. Hirsch MW, Smale S, Devaney RL. Diferential equations, dynamical systems and an introduction to chaos. Second edition, Elsevier Academic Press, San Diego, 2004.

  18. Catterall WA. Structure and function of voltage-gated ion channels. Trends in Neurosciences 1993; 16: 500-506.

  19. Scott A. Neuroscience. A mathematical primer. First edition. Springer-Verlag, New York, 2002.

  20. Stefani E, Toro L, Perozo E, Bezanilla F. Gating of Shaker K+ channels: I. Ionic and gating currents. Biophysical Journal 1994; 66: 996-1010.

  21. Schwartz M. Information transmission, modulation, and noise. Third edition. McGraw Hill, New York, 1981.

  22. Brown AM, Camerer H, Kunze DL, Lux HD. Similarity of unitary Ca2+ currents in three different species. Nature 1982; 299: 156-158.

  23. Jafri S, Rice JJ, Winslow RL. Cardiac Ca2+ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load. Biophysical Journal 1998; 74: 1149-1168.

  24. Tanskanen AJ, Greenstein JL, O’Rourke B, Winslow RL. The role of stochastic and modal gating of cardiac L-type Ca2+ channels on early after-depolarizations. Biophysical Journal 2005; 88: 85-95.

  25. Smith GD. Modeling the stochastic gating of ion channels. In: Fall CP, Marland ES, Wagner JM, Tyson JJ, editors. Computational cell biology, interdisciplinary applied mathematics. Springer-Verlag, New York, 2002; 11: 285-316.

  26. Ávila-Pozos R, Godínez-Fernández JR. Modelación estocástica de las corrientes iónicas en células excitables. Contactos, ISSN 0186-4084 2003; 49: 46-53.

  27. González-Vélez V, González-Vélez H. A grid-based stochastic simulation of unitary and membrane Ca2+ currents in spherical cells. Proc 18 th IEEE CBMS Symposium 2005; 1: 171-175.

  28. Lipscombe D. L-Type calcium channels: Highs and new lows. Circulation Research 2002; 90: 933-935.

  29. Hille B. Ionic channels of excitable membranes. Second edition. Sinauer Associates, Inc, Sunderland, 1992.




2020     |     www.medigraphic.com