19 research outputs found
Charge fluctuations and boundary conditions of biological ion channels : effect on the ionic transition rate
No full textA self-consistent solution is derived for the Poisson-Nernst-Planck (PNP) equation, valid both inside a biological ion channel and in the adjacent bulk fluid. An iterative procedure is used to match the two solutions together at the channel mouth. Charge fluctuations at the mouth are modeled as shot noise flipping the height of the potential barrier at the selectivity site. The resultant estimates of the conductivity of the ion channel are in good agreement with Gramicidin experimental measurements and they reproduce the observed current saturation with increasing concentration
Stochastic dynamics of remote knock-on permeation in biological ion channels
No full textBrownian 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
Non-equilibrium stochastic dynamics of open ion channels
No full textWe 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
Self-organized enhancement of conductivity in biological ion channels
No full textWe 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
On selectivity and gating of ionic channels
No full textA 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
Self-consistent analytic solution for the current and access resistance in open ionic channels
No full textIonic motion in the bulk solution away from the mouth of a biological ion channel, and inside the channel, is analyzed using Poisson-Nernst-Planck (PNP) equation. The one-dimensional method allows us to connect in a self-consistent way ion dynamics in the bulk solution and inside the channel by taking into account access resistance to the channel. In order to glue the PNP solution in the bulk to that inside the channel, a continuity condition is used for the concentration and the current near the channel mouth at the surface of the hemisphere. The resulting one dimensional (1D) current-voltage characteristics are compared with the Kurnikova(16) results which are in good agreement with experimental measurement on the channel, by using a filling factor as the only fitting parameter. The filling factor compensates the fact that the radial charge distribution is non-uniform in a real channel as compared to the cylindrically symmetrical channel used in the 1D approximation
Charge fluctuations and their effect on conduction in biological ion channels.
No full textThe 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
Ion channels as electrostatic amplifiers of charge fluctuations
No full textElectrostatic 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
Resonant multi-ion conduction in a simple model of calcium channels
No full textThe 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 demon-trate 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 long-standing puzzle of how the L-type calcium channel exhibits, simultaneously, both high calcium selectivity and conduction at almost the rate of free diffusion
Multi-ion conduction bands in a simple model of calcium ion channels
No full textWe 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 Q(f) at the SF. With increasing Q(f), 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
