✍ Scribed by Marcel Ausloos; Kristinka Ivanova; Zuzanna Siwy
No coin nor oath required. For personal study only.
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 coe cients, D (1) and D (2) , a drift and a di usion coe cient, 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 di erent conducting states prevents the channel from staying in one, closed or open state. The similarity between the hydrodynamic ow in the turbulent regime and hierarchical switching between conducting states of this biochannel is discussed. A non-trivial character of D (1) and D (2) coe cients is shown, which points to di erent 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.
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