We report observation of a novel "remote knock-on" mechanism for enhancement of permeation in Brownian dynamics simulations of a simple model ion channel. Unlike conventional knock-on, which requires a second ion of the same species to enter the channel in order to knock forward and replace an ion already in the channel, the new mechanism does not require the instigating ion to enter the channel, nor that it be of the same species. The figure plots the conditional probability distribution as a function of the position x of the instigating ion at the instant of permeation when the ion initially trapped at x=0 escapes to the right. The curves are plotted for different solute concentrations CL. The most probable position of the instigating ion is clearly at the left mouth of the channel (x=-15Å). A 2nd small peak corresponding to conventional knock-on appears at x=0 for high enough CL.

characterized by chronic progressive weakness whose affected members harbor a novel Cav1.1 R1242G mutation affecting the third arginine in S4 of domain IV. Whole-cell patch clamp recordings of the R1242G mutant showed a strong hyperpolarized shift of steady-state inactivation in GLT mouse myotube expression system. The facilitated inactivation resulting in the reduction of channel availability may account for the chronic progressive weakness of the patients. In addition, we found an outward gating pore current through the mutant voltage sensor of R1242G which might induce a reduction in the amplitude and duration of the action potential and cause the failure of muscle fiber excitability.

We use Brownian dynamics (BD) simulations to study the ionic conduction and valence selectivity of a generic electrostatic model of a biological ion channel as functions of the fixed charge Q(f) at its selectivity filter. We are thus able to reconcile the discrete calcium conduction bands recently revealed in our BD simulations, M0 (Q(f)=1e), M1 (3e), M2 (5e), with a set of sodium conduction bands L0 (0.5e), L1 (1.5e), thereby obtaining a completed pattern of conduction and selectivity bands vs Q(f) for the sodium-calcium channels family. An increase of Q(f) leads to an increase of calcium selectivity: L0 (sodium-selective, nonblocking channel) → M0 (nonselective channel) → L1 (sodium-selective channel with divalent block) → M1 (calcium-selective channel exhibiting the anomalous mole fraction effect). We create a consistent identification scheme where the L0 band is putatively identified with the eukaryotic sodium channel The scheme created is able to account for the experimentally observed mutation-induced transformations between nonselective channels, sodium-selective channels, and calcium-selective channels, which we interpret as transitions between different rows of the identification table. By considering the potential energy changes during permeation, we show explicitly that the multi-ion conduction bands of calcium and sodium channels arise as the result of resonant barrierless conduction. The pattern of periodic conduction bands is explained on the basis of sequential neutralization taking account of self-energy, as Q(f)(z,i)=ze(1/2+i), where i is the order of the band and z is the valence of the ion. Our results confirm the crucial influence of electrostatic interactions on conduction and on the Ca(2+)/Na(+) valence selectivity of calcium and sodium ion channels. The model and results could be also applicable to biomimetic nanopores with charged walls.

We present and discuss a modified version of reaction rate theory (RRT) to describe the passage of a positive ion through a biological ion channel. It takes explicit account of the non-equilibrium nature of the permeation process. Unlike traditional RRT, it allows for the non-constant transition rates that arise naturally in an archetypal model of an ion channel. In particular, we allow for the fact that the average escape time of an ion trapped at the selectivity filter (SF) can be reduced substantially by the pair correlations between ions: the arrival of a second ion at the channel entrance significantly reduces the potential barrier impeding the escape of the ion from the SF. The effects of this rate modulation on the current- voltage and current-concentration characteristics of the channel are studied parametrically. Stochastic amplification of the channel conductivity by charge fluctuations is demonstrated and compared with the results of Brownian dynamics simulations.

The ionic permeation of a biological ion channel is a multi-particle, non-equilibrium, stochastic process. Brownian dynamics simulations for a simple electrostatic model of the calcium channel reveal regular structure in the conductance and selectivity as functions of the negative fixed charge Qf on the protein wall at the selectivity filter. This structure consists of distinct high conductance regions (conduction bands) separated by regions of near non-conductance (stop-bands). We report self-consistent electrostatic calculations of single-file, double-ion, stochastic optimal trajectories, and of the energy profiles along these trajectories, for different Qf. We show that the energy difference ΔE along the optimal path exhibits a pronounced minimum near Qf = 3e corresponding to an almost barrier-less (ΔE ~ kBT) resonance-like form of conduction. We demonstrate explicitly that the sharply-defined conduction/selectivity peak of the L-type calcium channel is attributable to the barrier-less knock-on motion of a pair of calcium ions that can occur when their mutual electrostatic repulsion balances their electrostatic attraction to the charge at the selectivity filter. The electrostatics calculations agree well with the results of Brownian dynamics simulations. These results clarify the longstanding puzzle of how the L-type calcium channel exhibits, simultaneously, both high calcium selectivity and conduction at almost the rate of free diffusion.

Brownian dynamics were simulated for the simple model of calcium channels introduced by Nonner and Eisenberg, computing electric forces from all charges. Permanent charge (of acidic side chains) was varied. Substantial conduction was found only at certain discrete values of permanent charge. Different conduction states had different selectivity, one resembling L-type CaV1 and the other RyR channels. We speculate that thermally activated switching between conductance values could produce some types of spontaneous gating. Below is calcium current J as a function of permanent charge Qf and calcium concentration. Details at arXiv.org 1209.2381

Brownian dynamics simulations provide evidence for a remote knock-on mechanism facilitating the permeation of a biological ion channel by an ion that is initially trapped at the selectivity filter (SF). Unlike the case of conventional direct knock-on, the second ion that instigates permeation does not need to enter the channel. Nor does it necessarily take the place of the permeating ion at the SF, and it can even be of a different ionic species. The study is based on the simultaneous, self-consistent, solution of the coupled Poisson and Langevin equations for a simple generic model, taking account of all the charges present. The new permeation mechanism involves electrostatic amplification attributable to the permittivity mismatch between water and protein: the arrival of the instigating ion at the channel entrance reduces the exit barrier for the ion trapped at the SF, facilitating escape.

We discuss an example of self-organization in a biological system. It arises from long-range ion–ion interactions, and it leads us to propose a new kind of enhanced conduction in ion channels. The underlying mechanism involves charge fluctuations near the channel mouth, amplified by the mismatch between the relative permittivities of water and the protein of the channel walls. We use Brownian dynamics simulations to show that, as in conventional ‘knock on’ permeation, these interactions can strongly enhance the channel current; but unlike the conventional mechanism, the enhancement occurs without the instigating bath ion entering the channel. The transition between these two mechanisms is clearly demonstrated, emphasizing their distinction. A simple model accurately reproduces the observed phenomena. We point out that electrolyte plus protein of low relative permittivity are universal in living systems, so that long-range ion–ion correlations of the kind considered must be common.

We report self-consistent Brownian dynamics simulations of a simple electrostatic model of the selectivity filters (SF) of calcium ion channels. They reveal regular structure in the conductance and selectivity as functions of the fixed negative charge Qf at the SF. With increasing Qf, there are distinct regions of high conductance (conduction bands) M0, M1, M2 separated by regions of almost zero-conductance (stop-bands). Two of these conduction bands, M1 and M2, are related to the saturated calcium occupancies of P = 1 and P = 2, respectively and demonstrate self-sustained conductivity. Despite the model's limitations, its M1 and M2 bands show high calcium selectivity and prominent anomalous mole fraction effects and can be identified with the L-type and RyR calcium channels. The non-selective band M0 can be identified with a non-selective cation channel, or with OmpF porin.

We present a nonequilibrium reaction rate model of the ionic transition through an open ion channel, taking account of the interaction between an ion at the entrance of the channel and an ion at the binding site in a self-consistent way. The electrostatic potential is calculated by solution of the Poisson equation for a channel modeled as a cylindrical tube. The transition rate, and the binding site occupancy as a function of the left bulk concentration are compared to 1D Brownian dynamics simulations. The analysis is performed for a single binding site of high-affinity, with the exit rate influenced by barrier fluctuations at the channel exit. The results are compared with experimental data for the permeation of the Na+ ion through the Gramicidin A channel, with which they are shown to be in good agreement.

We analyse the permeation of an open, single-site, ion channel by use of Brownian Dynamics (BD) simulations at different concentrations. We show for the first time by modelling that the ionic escape rate increases significantly with concentration due to electrostatic amplification of charge fluctuations at the channel mouth. We use the reduced model of an axis-symmetric water-filled channel whose protein wall has a single charged site. The channel length, radius and fixed charge are selected to match experimental data for Gramicidin A. The ion current, occupancy and escape rate are simulated by the 1D self-consistent BD technique with account taken of the electrostatic ion-ion interaction. The bath with non-zero ion concentration on one side of the channel is modelled via the Smoluchowski arrival rate. It is shown that: a) The occupancy saturates with Michaelis-Menten kinetics. b) The escape rate starts from the Kramers value at small concentrations and then increases with concentration due to the electrostatic amplification of charge fluctuations. The resulting dynamics of the current can be described by modified reaction rate theory accounting for ionic escape over the fluctuating barrier [1].

The problem of calculating the current and access resistance in open ion channels is considered. A self-consistent analytic solution is introduced for an arbitrary number of species within the Poisson-Nernst-Planck (PNP) equations formalism. The model considered is a cylindrical channel of radius a in the protein which allows ions to cross a membrane that is bathed by two solutions of different concentration on its left and right-hand sides. Electro-diffusion in this system is described by the Poisson equation combined with the continuity equations for the mobile ions. The PNP equations are solved in the bulk in the Boltzmann approximation in 3D, assuming spherical symmetry, and in the pore in a 1D approximation. The boundary conditions (BCs) for the potential and concentration are set at infinity. The internal BCs for the current and the gradient of the potential are set at the surfaces of two hemispheres of radius a. The two solutions are matched together at the internal BCs using an iterative procedure in a self-consistent way. The method allows for calculation of the currents for an arbitrary number of ions species that have different diffusion constants in the channel and in the bulk. The sizes of the ions are taken into account by introducing a "filling factor" as an additional fitting parameter. The method is applied to model experimental I-V characteristics of the Gramicidin A channel for various concentrations, yielding qualitative good agreement.

How open ion channels are able to conduct ions with a throughput comparable to free diffusion, and yet remain highly selective, is an unresolved scientific conundrum of long standing. To shed new light on this problem, the effect of charge fluctuations on the conduction of open ion channels is investigated theoretically. The model considered is a cylindrical channel across the membrane bathed by two solutions of different concentration. The charge fluctuations at the channel mouth are analyzed using Brownian Dynamics simulations and shown to have the form of trichotomous noise on the timescale of nanoseconds. The channel potential with a local minimum at the selectivity site due to the fixed wall charge is calculated by solution of the 3D Poisson equation for two configurations, with one ion moving along the channel axis in the presence or absence of the fluctuating charge at the channel mouth. It is shown that narrow channels act as electrostatic amplifiers of the modulation of the potential barriers at the selectivity site, due to charge fluctuations at the channel mouths. This modulation at the selectivity site was largely neglected in earlier research. It results in a leading order contribution to the transition rates of open ion channels. The proposed model of ion permeation takes into account the dynamical effect of the charge fluctuations through the resultant shot noise, which flips the electrostatic potential at the selectivity site, causing it to fluctuate between three values at a rate corresponding to the random arrivals of ions at the channel mouth. The model is applied to calculation of the current-voltage characteristics of Gramicidin A channel for different concentrations and is shown to be in good agreement with experimental results, including the effect of current saturation at high concentrations.

Electrostatic interactions between ions in an ionic channel and the charge fluctuations in the channel mouth are considered. It is shown that the charge fluctuations can be enhanced in channels of low dielectric constant, resulting in strong modulation of the potential barrier at the selectivity site. It is conjectured that similar effects can alter transition probabilities in other molecular dynamical systems.

The effect of fluctuations on the conductivity of ion channels is investigated. It is shown that modulation of the potential barrier at the selectivity site due to electrostatic amplification of charge fluctuations at the channel mouth exerts a leading-order effect on the channel conductivity. A Brownian dynamical model of ion motion in a channel is derived that takes into account both fluctuations at the channel mouth and vibrational modes of the wall. The charge fluctuations are modeled as a shot noise flipping the height of the potential barrier. The wall fluctuations are introduced as a slow vibrational mode of the protein motion that modulates ion conductance both stochastically and periodically. The model is used to estimate the contribution to the conductivity of ion channels coming from the electrostatic amplification of charge fluctuations.

A self-consistent analytic approach is introduced for the estimation of the access resistance and the current through an open ion channel for an arbitrary number of species. For an ion current flowing radially inward from infinity to the channel mouth, the Poisson-Boltzmann-Nernst-Planck equations are solved analytically in the bulk with spherical symmetry in three dimensions, by linearization. Within the channel, the Poisson-Nernst-Planck equation is solved analytically in a one-dimensional approximation. An iterative procedure is used to match the two solutions together at the channel mouth in a self-consistent way. It is shown that the current-voltage characteristics obtained are in good quantitative agreement with experimental measurements.

A novel conceptual model is introduced in which ion permeation is coupled to the protein wall vibration and the later in turn modulates exponentially strongly the permeation via radial oscillations of the potential of mean force. In the framework of this model of ion-wall-water interaction we discuss problems of selectivity between alike ions and coupling of ion permeation to gating.

The effect of charge fluctuations at the mouth of an open ion channel on its conduction mechanism is analyzed within the framework of self‐consistent Brownian dynamics simulations. It is shown that volume charge fluctuations at the channel mouth can be modelled as a generalized shot noise and result in strong modulation of the potential barrier for an ion at the selectivity site, on a sub‐nanosecond time scale.

Ionic motion through an open ion channel is analyzed within the framework of self‐consistent Brownian dynamics. A novel conceptual model in which the ions motion is coupled to the vibrations of the pore walls is introduced. The model allows to include into simulations an important additional mechanism of energy dissipation and the effects of self‐induced strong modulation of the channel conductivity.