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Searching for self-similarity in switching time and turbulent cascades in ion transport through a biochannel. A time delay asymmetry
The process of ion transport through a locust potassium channel is described
by means of the Fokker-Planck equation (FPE). The deterministic and stochastic
components of the process of switching between various conducting states of the
channel are expressed by two coefficients, and , a drift and
a diffusion coefficient, respectively. The FPE leads to a Langevin equation.
This analysis reveals beside the well known deterministic aspects a turbulent,
cascade type of action. The (noisy-like) switching between different conducting
states prevents the channel from staying in one, closed or open state. The
similarity between the hydrodynamic flow in the turbulent regime and
hierarchical switching between conducting states of this biochannel is
discussed. A non-trivial character of and coefficients is
shown, which points to different processes governing the channel's action,
asymetrically depending on the history of the previously conducting states.
Moreover, the Fokker-Planck and Langevin equations provide information on
whether and how the statistics of the channel action change over various time
scales.Comment: submitted to physica A text : 12 pages + 8 figure
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