Abstract
The highly selective permeation of ions through biological ion channels is an unsolved problem of noise and fluctuations. In this paper, we motivate and introduce a non-equilibrium and self-consistent multi-species kinetic model, with the express aims of comparing with experimental recordings of current versus voltage and concentration and extracting important permeation parameters. For self-consistency, the behavior of the model at the two-state, i.e., selective limit in linear response, must agree with recent results derived from an equilibrium statistical theory. The kinetic model provides a good fit to data, including the key result of an anomalous mole fraction effect.
Highlights
Biological ion channels passively transport ions through the impermeable cell membrane, but precisely how they do it is a long-standing problem [1,2,3]
To extend the theory far from equilibrium, we introduce a set of master equations describing transitions within our state space
The transition rates must be constrained by the condition of detailed balance; and the probabilities will reduce to the form given by equilibrium statistical physics [29, 30, 35]
Summary
Biological ion channels passively (and stochastically) transport ions through the impermeable cell membrane, but precisely how they do it is a long-standing problem [1,2,3]. One generally assumes that the pore can be represented by a series of energy wells and barriers, and that occupancies (or states) can be described by a set of master equations from which the net °ux can be calculated These reproduce saturation of current versus concentration, as observed experimentally [15,16,17], and more interesting properties such as: the importance of volume exclusion [18], the role of selectivity and interactions between ions [16, 19, 20] and the consequence of mutagenisis [21]. I and c are the electro-chemical and chemical potentials in the pore
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