Abstract
Biological ion channels are protein nanotubes embedded in, and passing through, the bilipid membranes of cells. Physiologically, they are of crucial importance in that they allow ions to pass into and out of cells, fast and efficiently, though in a highly selective way. Here we show that the conduction and selectivity of calcium/sodium ion channels can be described in terms of ionic Coulomb blockade in a simplified electrostatic and Brownian dynamics model of the channel. The Coulomb blockade phenomenon arises from the discreteness of electrical charge, the strong electrostatic interaction, and an electrostatic exclusion principle. The model predicts a periodic pattern of Ca2+ conduction versus the fixed charge Qf at the selectivity filter (conduction bands) with a period equal to the ionic charge. It thus provides provisional explanations of some observed and modelled conduction and valence selectivity phenomena, including the anomalous mole fraction effect and the calcium conduction bands. Ionic Coulomb blockade and resonant conduction are similar to electronic Coulomb blockade and resonant tunnelling in quantum dots. The same considerations may also be applicable to other kinds of channel, as well as to charged artificial nanopores.
Highlights
Biological ion channels are natural nanopores providing fast and highly selective permeation of physiologically important ions through the bilipid membranes of biological cells [1,2,3]
Mutant studies of the DEKA sodium channel [22, 24, 26] have measured the dependence of anomalous mole fraction effect (AMFE) on the selectivity filter locus and its Qf, and it was shown that log(IC50) can successfully be fitted by a linear function of Qf, in agreement with the prediction (17) of the Coulomb blockade model, or
A parametric study [57] based on Brownian dynamics modelling has shown that, in accordance with (7), strong Coulomb blockade may be expected in channels of radii R = 0.25 − 0.35 nm for ions having z = 2, e.g. for Ca+ ions in calcium/sodium channels
Summary
Biological ion channels are natural nanopores providing fast and highly selective permeation of physiologically important ions (e.g. cations such as Na+, K+ and Ca2+) through the bilipid membranes of biological cells [1,2,3]. Self-consistent electrostatic and Brownian dynamics simulations [15, 30, 43,44,45] describe ionic motion as an electro-diffusion process, leading to fast and direct estimation of the currents under non-equilibrium conditions Such simulations have shown very clearly that the permeation and selectivity features of many channels are defined by just the basic electrostatics of narrow waterfilled channels, rather than by the details of the channel structures themselves. Our earlier simulations of a simple electrostatic model of calcium/sodium ion channels revealed a periodic set of Ca2+ conduction-bands and stop-bands as a function of the fixed charge Qf at the selectivity filter [57,58,59] similar to transitions [51].
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