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A model of ion channel kinetics based on deterministic, chaotic motion in a potential with two local minima

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Abstract

Models of the gating of ion channels have usually assumed that the switching between the open and closed states is a random process without a mechanistic basis. We explored the properties of a deterministic model of channel gating based on a chaotic dynamic system. The channel is modeled as a nonlinear oscillator, that has a potential function with two minima, which correspond to the stable open and closed states, and is driven by a periodic driving force. The properties of the model are like some properties of single channel data and unlike other properties. The model is like the data in that: the current switches between two well-defined states, this switching is nonperiodic, and there are subconductance states. These subconductance states are subharmonic resonances, due to the nonlinearities in the equation of the model, rather than stable conformational states due to local minima in the potential energy. The model is not like the data in that the current fluctuates too much within in each state and there are sometimes periodic fluctuations within a state. At the present time, the selection of the most appropriate channel model (Markov, chaotic, or other) is not possible, and in addition to chaotic models, other nonlinear models may be suitable.

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Authors and Affiliations

  1. Department of Ophthalmology College of Physicians & Surgeons, Columbia University, 630 West 168th Street, 10032, New York, NY

    Larry S. Liebovitch & Ferenc P. Czegledy

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  1. Larry S. Liebovitch
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  2. Ferenc P. Czegledy
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Liebovitch, L.S., Czegledy, F.P. A model of ion channel kinetics based on deterministic, chaotic motion in a potential with two local minima. Ann Biomed Eng 20, 517–531 (1992). https://doi.org/10.1007/BF02368171

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  • DOI: https://doi.org/10.1007/BF02368171

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