Fractal, Chaotic, and Self-Organizing Critical System: Descriptions of the Kinetics of Cell Membrane Ion Channels
Channels are proteins in the cell membrane that spontaneously fluctuate between conformational shapes that are closed or open to the passage of ions. The kinetics of these changes in conformational state can be described in different ways, that suggest different physical properties for the ion channel protein. We describe kinetic models based on: 1) random switching between a few independent states, 2) random switching between many states that are cooperatively linked together, 3) deterministic, chaotic, nonlinear oscillations, amplifying themselves until the channel switches states, and 4) deterministic local interactions that self-organize the fluctuations in channel structure near a phase transition, switching it between different states.
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- Bak, P., Chao, T., and Wiesenfeld, K., 1988, Scale invariant spatial and temporal fluctuations in complex systems, in “Random Fluctuations and Pattern Growth: Experiments and Models,” H. E. Stanley and N. Ostrowsky, eds., Kluwer, Boston.Google Scholar
- Gleick, J., 1987, “Chaos, Making a New Science,” Viking, New York.Google Scholar
- Liebovitch, L. S. and Czegledy, F. P., 1990, A model of ion channel kinetics based on deterministic chaotic motion in a potential with two local minima, submitted to Ann. Biomed. Engr. Google Scholar
- Liebovitch, L. S. and Toth, T. I., 1990a, Fractal activity in cell membrane ion channels, in “Mathematical Approaches to Cardiac Arryhthmias,” J. Jalife, ed., Ann. New York, Acad. Sci., 591:375–391.Google Scholar
- Liebovitch, L. S. and Töth, T. I., 1990b, Distributions of activation energy barriers that produce stretched exponential probability distributions for the time spent in each state of the two state reaction A⇋B, Bull. Math. Biol., in press.Google Scholar
- Liebovitch, L. S. and Toth, T. I., 1990c, A model of ion channel kinetics using deterministic rather than stochastic processes, J. Theor. Biol., in press.Google Scholar
- Moon, F. C., 1987, “Chaotic Vibrations,” Wiley, New York.Google Scholar
- Sakmann, B. and Neher, E., eds., 1983, “Single-Channel Recording,” Plenum, New York.Google Scholar
- Scanlan, R. H. and Vellozzi, J. W., 1980, Catastrophic and annoying responses of long-span bridges to wind action, in “Long-Span Bridges,” E. Cohen and B. Birdsall, eds., Ann. New York, Acad. Sci., 352:247–263.Google Scholar
- Welch, G. R., ed., 1986, “The Fluctuating Enzyme,” Wiley, New York.Google Scholar