Regensburg 2004 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 23: Statistical Physics of RNA

DY 23.3: Vortrag

Dienstag, 9. März 2004, 12:15–12:30, H3

Fractional diffusion model of ion channel gating — •Igor Goychuk and Peter Hänggi — Institut für Physik, Universität Augsburg, Germany

We have put forward a fractional diffusion model of ion channel gating which is capable to explain the origin of non-exponential distributions of the residence time intervals as they are observed in several types of ion channels. The model presents a generalization of the discrete diffusion model by Millhauser, Salpeter and Oswald [Proc. Natl. Acad. Sci. USA 85, 1503 (1988)] to the case of continuous, anomalously slow conformational diffusion which is described within the mathematical framework of the fractional diffusion equation approach. Our model contains three parameters only: the mean residence time, the conformational diffusion time and the index of fractional diffusion 0<α≤ 1. A tractable analytical expression for the characteristic function of the residence time distribution is derived which in the normal diffusion case, α=1, reduces to our earlier result in [1]. Our new result captures a description of the residence time distributions that do exhibit a decaying power law in time with an (negative) exponent that differs from the normal diffusive behavior; i.e. a value for the exponent given by 3/2. It is shown that depending on the parameters of the studied model the residence time distribution may exhibit up to three characteristic time-regimes: initially a stretched exponential and then two different power laws.

[1] I. Goychuk and P. Hänggi, Proc. Natl. Acad. Sci. USA 99, 3552 (2002); Physica A 325, 9 (2003).