I. Kh. Kaufman

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.

Noise‐enhanced optical heterodyning in an all‐optical bistable system

A new form of frequency‐selective all‐optical heterodyning at the difference frequency of two modulated laser beams, related to stochastic resonance, is reported. A noise‐induced enhancement of the heterodyne signal and of the signal‐to‐noise ratio has been predicted and observed in an all‐optical bistable system for the beams at different wavelengths.

High-frequency stochastic resonance in SQUIDs

Abstract It is shown theoretically and by analogue electronic experiment that stochastic resonance (SR), in which a weak periodic signal can be optimally enhanced by the addition of noise of appropriate intensity, is to be anticipated in underdamped SQUIDs (superconducting quantum interference devices). It manifests under conditions quite unlike those needed for classical SR, which is restricted to low frequencies and confined to systems that are both overdamped and bistable. The zero-dispersion SR reported here can be expected over a vastly wider, tunable, range of high frequencies in highly underdamped SQUIDs that need not necessarily be bistable.

Coulomb blockade oscillations in biological ion channels

The conduction and selectivity of calcium/sodium ion channels are described in terms of ionic Coulomb blockade, a phenomenon based on charge discreteness, an electrostatic exclusion principle, and stochastic ion motion through the channel. This novel approach provides a unified explanation of numerous observed and modelled conductance and selectivity phenomena, including the anomalous mole fraction effect and discrete conduction bands. Ionic Coulomb blockade and resonant conduction are similar to electronic Coulomb blockade and resonant tunnelling in quantum dots. The model is equally applicable to other 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.

Zero-Dispersion Stochastic Resonance in Underdamped SQUIDS

Zero-dispersion stochastic resonance (ZDSR) in underdamped SQUIDs (superconducting quantum interference devices) has been investigated theoretically and by analogue electronic experiment. It is shown that, in common with the standard form of stochastic resonance (SR) that occurs at low frequencies in overdamped bistable systems, ZDSR can result in large noise-induced enhancements of the signal/noise ratio for a weak periodic signal. Unlike standard SR, however, ZDSR is to be anticipated over a vastly wider and tunable range of high frequencies in highly underdamped SQUIDs that need not necessarily be bistable.

Relation between selectivity and conductivity in narrow ion channels

To establish the general statistical mechanical properties of highly conductive but selective nano-filters we develop an equilibrium statistical-mechanical theory of the KcsA filter, find the probabilities for the filter to bind ions from the mixed intra- and extra-cellular solutions, and evaluate the conductivity of the filter in its linear response regime. The results provide first principles analytical resolution of the long-standing paradox - how can narrow filter conduct potassium ions at nearly the rate of free diffusion while strongly selecting them over sodium ions - and are applicable to a wide range of biological and artificial channels.

Effect of local binding on stochastic transport in ion channels

Ionic Coulomb blockade is an electrostatic phenomenon recently discovered in low-capacitance ion channels/ nanopores. Depending on the fixed charge that is present, Coulomb blockade strongly and selectively influences the ease with which a given type of ion can permeate the pore. The phenomenon arises from the discreteness of the charge-carriers and it manifests itself strongly for divalent ions (e.g. Ca2+). Ionic Coulomb blockade is closely analogous to electronic Coulomb blockade in quantum dots. In addition to the non-local 1D Coulomb interaction considered in the standard Coulomb blockade model, we now propose a correction to take account of the singular part of the attraction to the binding site (i.e. local site binding) and of the local ion-ion repulsion. We show that this correction leads to a geometry-dependent shift of the single-ion barrier-less resonant conduction points M0. We also show that local repulsion accounts for a splitting of Ca2+ profiles observed earlier in Brownian dynamics simulations.

Fluctuations, stochastic resonance and noise-protected heterodyning in bistable optical systems

SummaryStatistical distributions, power spectra and susceptibilities of an all-optical bistable system subject to noise are considered. In the presence of an additional small periodic signal, a stochastic-resonance phenomenon for additive noise is found to occur, and has been investigated theoretically and experimentally. A new form of optical heterodyning related to stochastic resonance, in which two high-frequency signals (an input signal and a reference one) are applied to an all-optical bistable system, is reported. A noise-induced enhancement of the heterodyne signal has been investigated theoretically, by means of analogue electronic simulation and in experiments in which a optical system was driven by two modulated laser beams at different wavelengths.

Kinetic model of selectivity and conductivity of the KcsA filter

We introduce a self-consistent multi-species kinetic theory based on the structure of the narrow voltage-gated potassium channel. Transition rates depend on a complete energy spectrum with contributions including the dehydration amongst species, interaction with the dipolar charge of the filter and, bulk solution properties. It displays high selectivity between species coexisting with fast conductivity, and Coulomb blockade phenomena, and it fits well to data.