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 Qf at its selectivity filter. We are thus able to reconcile the discrete calcium conduction bands recently revealed in our BD simulations, M0 (Qf = 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 Qf for the sodium-calcium channels family. An increase of Qf 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 Qf (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 Ca2+/Na+ valence selectivity of calcium and sodium ion channels. The model and results could be also applicable to biomimetic nanopores with charged walls

Stochastic dynamics of remote knock-on permeation in biological ion channels

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

Solution of the boundary value problem for nonlinear flows and maps

Fluctuational escape via an unstable limit cycle is investigated in stochastic flows and maps. A new topological method is suggested for analysis of the corresponding boundary value problems when the action functional has multiple local minima along the escape trajectories and the search for the global minimum is otherwise impossible. The method is applied to the analysis of the escape problem in the inverted Van der Pol oscillator and in the Henon map. An application of this technique to solution of the escape problem in chaotic maps with fractal boundaries, and in maps with chaotic saddles embedded within the basin of attraction, is discussed

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

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 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

Observation of "remote knock-on", a new permeation-enhancement mechanism in ion channels

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

Non-equilibrium stochastic dynamics of open ion channels

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

Bayesian characterisation of vertical-cavity surface-emitting lasers

A new method is introduced for characterising vertical-cavity surface-emitting lasers. This approach relies on the direct application of Bayes' theorem from classical probability theory on time-series data of polarisation measurements. The technique is shown to work for the simplified one-dimensional dynamics of the laser as an overdamped particle in a double-well potential driven by fluctuations, as well as for the most complicated case of fluctuational motion on the Poincaré sphere about one of the linearly-polarised states

Discrete conductance levels in calcium channel models:multiband calcium selective conduction

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 con-duction states had different selectivity, one resembling L-type CaV1 and the other RyR channels. We speculate that thermally acti-vated switching between conductance values could produce some types of spon-taneous gating. Below is calcium current J as a function of permanent charge Qf and calcium concentration