Searching for self-similarity in switching time and turbulent cascades in ion transport through a biochannel. A time delay asymmetry

TL;DR

This paper models ion transport in a biochannel using Fokker-Planck and Langevin equations, revealing turbulent cascade-like behavior and asymmetries in switching dynamics that depend on past states.

Contribution

It introduces a novel analysis linking turbulent cascade phenomena to ion channel switching, highlighting asymmetries and complex stochastic dynamics.

Findings

Identification of turbulent, cascade-like behavior in ion channel switching

Asymmetry in drift and diffusion coefficients depending on history

Insights into multi-scale statistical properties of channel dynamics

Abstract

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, $D^{(1)}$ and $D^{(2)}$, 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 $D^{(1)}$ and $D^{(2)}$ 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.