Rodrigue Tindjong

Multi-ion conduction bands in a simple model of calcium ion channels

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 models 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.

Energetics of discrete selectivity bands and mutation-induced transitions in the calcium-sodium ion channels family

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.

NONEQUILIBRIUM RATE THEORY FOR CONDUCTION IN OPEN ION CHANNELS

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.

Ion channels as electrostatic amplifiers of charge fluctuations

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.

Charge fluctuations and their effect on conduction in biological ion channels

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.

Resonant multi-ion conduction in a simple model of calcium channels

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 simulations of ionic current through an open channel

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.

Effect of charge fluctuations on the permeation of ions through biological ion channels

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.

On selectivity and gating of ionic channels

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.

Ionic current through an open channel: a low-dimensional model of coupling with vibrations of the wall

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