Ionic Coulomb blockade

Classical ionic conduction through an inorganic monolayer nanopore is analogous to the quantum-mechanical phenomenon of electronic Coulomb blockade in quantum dots

Coulomb blockade model of permeation and selectivity in biological ion channels

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

On Resolution of the Selectivity/Conductivity Paradox for the Potassium Ion Channel

The ability of the potassium channel to conduct K+ at almost the rate of free diffusion, while discriminating strongly against the (smaller) Na+ ion, is of enormous biological importance [1]. Yet its function remains at the center of a “many-voiced debate” [2,3]. In this presentation, a first-principles explanation is provided for the seemingly paradoxical coexistence of high conductivity with high selectivity between monovalent ions within the channel. It is shown that the conductivity of the selectivity filter is described by the generalized Einstein relation. A novel analytic approach to the analysis of the conductivity is proposed, based on the derivation of an effective grand canonical ensemble for ions within the filter. The conditions for barrier-less diffusion-limited conduction through the KcsA filter are introduced, and the relationships between system parameters required to satisfy these conditions are derived. It is shown that the Eisenman selectivity equation is one of these, and that it follows directly from the condition for barrier-less conduction. The proposed theory provides analytical insight into the “knock-on” [1] and Coulomb blockade [4] mechanisms of K+ conduction through the KcsA filter. It confirms and illuminates an earlier argument [3] that the “snug-fit" model cannot describe the fast diffusion-limited conduction seen in experiments. Numerical examples are provided illustrating agreement of the theory with experimentally-measured I-V curves. The results are not restricted to biological systems, but also carry implications for the design of artificial nanopores

Putative resolution of the EEEE selectivity paradox in L-type Ca2+ and bacterial Na+ biological ion channels

The highly selective permeation of ions through biological ion channels can be described and explained in terms of fluctuational dynamics under the influence of powerful electrostatic forces. Hence valence selectivity, e.g. between Ca2+ and Na+ in calcium and sodium channels, can be described in terms of ionic Coulomb blockade, which gives rise to distinct conduction bands and stop-bands as the fixed negative charge Qf at the selectivity filter of the channel is varied. This picture accounts successfully for a wide range of conduction phenomena in a diversity of ion channels. A disturbing anomaly, however, is that what appears to be the same electrostatic charge and structure (the so-called EEEE motif) seems to select Na+ conduction in bacterial channels but Ca2+ conduction in mammalian channels. As a possible resolution of this paradox it is hypothesised that an additional charged protein residue on the permeation path of the mammalian channel increases |Qf | by e, thereby altering the selectivity from Na+ to Ca2+. Experiments are proposed that will enable the hypothesis to be tested

Theory of Alike Selectivity in Biological Channels

We introduce a statistical mechanical model of the selectivity filter that accounts for the interaction between ions within the channel and derive Eisenman equation of the filter selectivity directly from the condition of barrier-less conduction

Ionic Coulomb blockade and the determinants of selectivity in the NaChBac bacterial sodium channel

Mutation-induced transformations of conductivity and selectivity in NaChBac bacterial channels are studied experimentally and interpreted within the framework of ionic Coulomb blockade (ICB), while also taking account of resonant quantised dehydration (QD) and site protonation. Site-directed mutagenesis and whole-cell patch-clamp experiments are used to investigate how the fixed charge Qf at the selectivity filter (SF) affects both valence selectivity and same-charge selectivity. The new ICB/QD model predicts that increasing |Qf | should lead to a shift in selectivity sequences towards larger ion sizes, in agreement with the present experiments and with earlier work. Comparison of the model with experimental data leads to the introduction of an effective charge Qf∗ at the SF, which was found to differ between Aspartate and Glutamate charged rings, and also to depend on position within the SF. It is suggested that protonation of the residues within the restricted space of the SF is important in significantly reducing the effective charge of the EEEE ring. Values of Qf∗ derived from experiments on divalent blockade agree well with expectations based on the ICB/QD model and have led to the first demonstration of ICB oscillations in Ca2+ conduction as a function of the fixed charge. Preliminary studies of the dependence of Ca2+ conduction on pH are qualitatively consistent with the predictions of the model