Ionic Coulomb blockade

Ionic Coulomb blockade (ICB)[1][2] is an electrostatic phenomenon predicted by M. Krems and Massimiliano Di Ventra (UC San Diego)[1] that appears in ionic transport through mesoscopic electro-diffusive systems (artificial nanopores[1][3] and biological ion channels[2]) and manifests itself as oscillatory dependences of the conductance on the fixed charge

ICB represents an ion-related counterpart of the better-known electronic Coulomb blockade (ECB) that is observed in quantum dots.

[4][5] Both ICB and ECB arise from quantisation of the electric charge and from an electrostatic exclusion principle and they share in common a number of effects and underlying physical mechanisms.

ICB provides some specific effects related to the existence of ions of different charge

In such cases there is strong quantisation of the energy spectrum inside the pore, and the system may either be “blockaded” against the transportation of ions or, in the opposite extreme, it may show resonant barrier-less conduction,[6][2] depending on the free energy bias coming from

Some effects, now recognised as belonging to ICB, were discovered and considered earlier in precursor papers on electrostatics-governed conduction mechanisms in channels and nanopores.

[2] ICB predictions have also been confirmed by a mutation study of divalent blockade in the NaChBac bacterial channel.

[13] ICB effects may be derived on the basis of a simplified electrostatics/Brownian dynamics model of a nanopore or of the selectivity filter of an ion channel.

[8] The model represents the channel/pore as a charged hole through a water-filled protein hub embedded in the membrane.

The model represents the water and protein as continuous media with dielectric constants

The model is applicable to both cationic[9] and anionic[14] biological ion channels and to artificial nanopores.

The model allows one to derive the pore and ion parameters satisfying the barrier-less permeation conditions, and to do so from basic electrostatics taking account of charge quantisation.

Thermodynamics and statistical mechanics describe systems that have variable numbers of particles via the chemical potential

In thermal and particle equilibrium with bulk reservoirs, the entire system has a common value of chemical potential

[16] The free energy needed for the entry of a new ion to the channel is defined by the excess chemical potential

defines the ionic energy level separation (Coulomb gap) and gives rise to most of the observed ICB effects.

exhibit multi-ion conduction bands - strong Coulomb blockade oscillations between minima

The ICB oscillations in conductance correspond to a Coulomb staircase in the pore occupancy

The saturated FD statistics of occupancy is equivalent to the Langmuir isotherm[19] or to Michaelis–Menten kinetics.

The more important of these shifts (excess potentials) are: Following its prediction based on analytic theory[1][2] and molecular dynamics simulations, experimental evidence for ICB emerged from experiments[3] on monolayer

Highly non-Ohmic conduction was observed between aqueous ionic solutions on either side of the membrane.

In particular, for low voltages across the membrane, the current remained close to zero, but it rose abruptly when a threshold of about

This was interpreted as complete ionic Coulomb blockade of current in the (uncharged) nanopore due to the large potential barrier at low voltages.

But the application of larger voltages pulled the barrier down, producing accessible states into which transitions could occur, thus leading to conduction.

The realisation that ICB could occur in biological ion channels[2] accounted for several experimentally observed features of selectivity, including: Valence selectivity is the channel's ability to discriminate between ions of different valence

[24] Valence selectivity has been attributed variously to pure electrostatics,[11] or to a charge space competition mechanism,[25] or to a snug fit of the ion to ligands,[26] or to quantised dehydration.

ions in a pure sodium solution pass unimpeded through a calcium channel, but are blocked by tiny (nM) extracellular concentrations of

Nonetheless, there are important distinctions between ICB and ECB: their similarities and differences are summarised in Table 1. anions (

negative (-1, -2...) Coulomb blockade can also appear in superconductors; in such a case the free charge carriers are Cooper pairs (

Despite appearing in completely classical systems, ICB exhibits some phenomena reminiscent of quantum-mechanics (QM).

Fig. 1. Generic electrostatic and Brownian dynamics model of a channel or nanopore
Fig.2. Resonant barrier-less conduction of ions, with energies plotted vertically. (a) Plot of as a function of fixed charge and position in the channel. At the "resonant" value of the transition is almost barrier-less (red cross-section). (b) Plots of (blue curve) and (dashed-green) and their sum (red) against for , showing that barrier-less conduction originates in a near-cancellation between and .
Fig.3. Ionic Coulomb blockade illustrated by BD-simulations of Ca conduction, as the fixed charge is varied: (a) Ca conduction bands; (b) Ca occupancy, forming a Coulomb staircase; and (c) Ground state energy (red)