Coulomb blockade model of permeation and selectivity in biological ion channels

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 Ca 2+ conduction versus the fixed charge Q f 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.

Ionic Coulomb blockade and anomalous mole fraction effect in the NaChBac bacterial ion channel and its charge-varied mutants

“…It appears to be closely similar to its electronic counterpart in quantum dots [20]. As we have demonstrated earlier [12], strong ICB appears for Ca 2+ ions in model biological channels and manifests itself as an oscillation of the conductance as a function of Q f , divalent blockade, and the anomalous mole fraction effect (AMFE) well-known for calcium channels [21].…”

“…The ICB phenomenon manifests itself as multi-ion oscillations (alternating conduction bands and stop bands) in the Ca 2+ conductance and channel occupancy as functions of Q f [10,12]. Figure 2 presents the results of Brownian dynamics simulation of Ca 2+ conduction and occupancy over an extended range of Q f (0 À 10e).…”

“…Conduction and selectivity in calcium/sodium ion channels have recently been described [10][11][12] in terms of ionic Coulomb blockade (ICB) [13,14], a fundamental electrostatic phenomenon based on charge discreteness, an electrostatic exclusion principle, and single-file stochastic ion motion through the channel. Earlier, Von Kitzing had revealed the staircase-like shape of the occupancy vs. site affinity for the charged ion channel [15] (following discussions and suggestions in [16]), and comparable low-barrier ion-exchange transitions had been discovered analytically [17].…”

“…Site-directed mutagenesis and patch clamp measurements were used to investigate changes in the ion transport properties of the mutants caused by alterations in Q f . Increasing the value of Q f was expected to lead to stronger divalent blockade following the Langmuir isotherm and to a resonant variation of the divalent current with Q f [12].…”

“…Of course, our reduced model represents a significant simplification of the actual electrostatics and dynamics of ions and water molecules within the narrow selectivity filter due to, for example: the application of continuum electrostatics; the use of the implicit solvent model; and the assumption of 1D (i.e., single-file) movement of ions inside the selectivity filter. The validity and range of applicability of this kind of model have been discussed in detail elsewhere [11,12,24].…”