A model of sodium channels

Conservation of the voltage-sensitive sodium channel protein within the Insecta

The voltage-sensitive sodium channel (VSSC) is essential for the generation and propagation of action potentials. VSSC kinetics can be modified by producing different splice variants. The functionality of VSSC depends on features such as the voltage sensors, the selectivity filter and the inactivation loop. Mutations in Vssc conferring resistance to pyrethroid insecticides are known as knockdown resistance (kdr). We analysed the conservation of VSSC in both a broad scope and a narrow scope by three approaches: (1) we compared conservation of sequences and of differential exon use across orders of the Insecta; (2) we determined which kdr mutations were possible with a single nucleotide mutation in nine populations of Aedes aegypti; and (3) we examined the individual VSSC variation that exists within a population of Drosophila melanogaster. There is an increasing amount of transcript diversity possible from Diplura towards Diptera. The residues of the voltage sensors, selectivity filter and inactivation loop are highly conserved. The majority of exon sequences were >88.6% similar. Strain-specific differences in codon constraints exist for kdr mutations in nine strains of A. aegypti. Three Vssc mutations were found in one population of D. melanogaster. This study shows that, overall, Vssc is highly conserved across Insecta and within a population of an insect, but that important differences do exist.

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.

Computational methods of studying the binding of toxins from venomous animals to biological ion channels: theory and applications

The discovery of new drugs that selectively block or modulate ion channels has great potential to provide new treatments for a host of conditions. One promising avenue revolves around modifying or mimicking certain naturally occurring ion channel modulator toxins. This strategy appears to offer the prospect of designing drugs that are both potent and specific. The use of computational modeling is crucial to this endeavor, as it has the potential to provide lower cost alternatives for exploring the effects of new compounds on ion channels. In addition, computational modeling can provide structural information and theoretical understanding that is not easily derivable from experimental results. In this review, we look at the theory and computational methods that are applicable to the study of ion channel modulators. The first section provides an introduction to various theoretical concepts, including force-fields and the statistical mechanics of binding. We then look at various computational techniques available to the researcher, including molecular dynamics, brownian dynamics, and molecular docking systems. The latter section of the review explores applications of these techniques, concentrating on pore blocker and gating modifier toxins of potassium and sodium channels. After first discussing the structural features of these channels, and their modes of block, we provide an in-depth review of past computational work that has been carried out. Finally, we discuss prospects for future developments in the field.

Na(+)/Ca(2+) selectivity in the bacterial voltage-gated sodium channel NavAb

The recent publication of a number of high resolution bacterial voltage-gated sodium channel structures has opened the door for the mechanisms employed by these channels to distinguish between ions to be elucidated. The way these channels select between Na⁺ and K⁺ has been investigated in computational studies, but the selectivity for Na⁺ over Ca²⁺ has not yet been studied in this way. Here we use molecular dynamics simulations to calculate the energetics of Na⁺ and Ca²⁺ transport through the channel. Single ion profiles show that Ca²⁺ experiences a large barrier midway through the selectivity filter that is not seen by Na⁺. This barrier is caused by the need for Ca²⁺ to partly dehydrate to pass through this region and the lack of compensating interactions with the protein. Multi-ion profiles show that ions can pass each other in the channel, which is why the presence of Ca²⁺ does not block Na⁺ conduction despite binding more strongly in the pore.

Current and selectivity in a model sodium channel under physiological conditions: Dynamic Monte Carlo simulations

A reduced model of a sodium channel is analyzed using Dynamic Monte Carlo simulations. These include the first simulations of ionic current under approximately physiological ionic conditions through a model sodium channel and an analysis of how mutations of the sodium channel's DEKA selectivity filter motif transform the channel from being Na(+) selective to being Ca(2+) selective. Even though the model of the pore, amino acids, and permeant ions is simplified, the model reproduces the fundamental properties of a sodium channel (e.g., 10 to 1 Na(+) over K(+) selectivity, Ca(2+) exclusion, and Ca(2+) selectivity after several point mutations). In this model pore, ions move through the pore one at a time by simple diffusion and Na(+) versus K(+) selectivity is due to both the larger K(+) not fitting well into the selectivity filter that contains amino acid terminal groups and K(+) moving more slowly (compared to Na(+)) when it is in the selectivity filter.

A method for treating the passage of a charged hard sphere ion as it passes through a sharp dielectric boundary

In the implicit solvent models of electrolytes (such as the primitive model (PM)), the ions are modeled as point charges in the centers of spheres (hard spheres in the case of the PM). The surfaces of the spheres are not polarizable which makes these models appropriate to use in computer simulations of electrolyte systems where these ions do not leave their host dielectrics. The same assumption makes them inappropriate in simulations where these ions cross dielectric boundaries because the interaction energy of the point charge with the polarization charge induced on the dielectric boundary diverges. In this paper, we propose a procedure to treat the passage of such ions through dielectric interfaces with an interpolation method. Inspired by the "bubble ion" model (in which the ion's surface is polarizable), we define a space-dependent effective dielectric coefficient, ε(eff)(r), for the ion that overlaps with the dielectric boundary. Then, we replace the "bubble ion" with a point charge that has an effective charge q/ε(eff)(r) and remove the portion of the dielectric boundary where the ion overlaps with it. We implement the interpolation procedure using the induced charge computation method [D. Boda, D. Gillespie, W. Nonner, D. Henderson, and B. Eisenberg, Phys. Rev. E 69, 046702 (2004)]. We analyze the various energy terms using a spherical ion passing through an infinite flat dielectric boundary as an example.

Superstatistics analysis of the ion current distribution function: Met3PbCl influence study

A novel analysis of ion current time series is proposed. It is shown that higher (second, third and fourth) statistical moments of the ion current probability distribution function (PDF) can yield new information about ion channel properties. The method is illustrated on a two-state model where the PDF of the compound states are given by normal distributions. The proposed method was applied to the analysis of the SV cation channels of vacuolar membrane of Beta vulgaris and the influence of trimethyllead chloride (Met(3)PbCl) on the ion current probability distribution. Ion currents were measured by patch-clamp technique. It was shown that Met(3)PbCl influences the variance of the open-state ion current but does not alter the PDF of the closed-state ion current. Incorporation of higher statistical moments into the standard investigation of ion channel properties is proposed.

Intracellular calcium modulation of voltage-gated sodium channels in ventricular myocytes

AIMS

Cardiac voltage-gated sodium channels control action potential (AP) upstroke and cell excitability. Intracellular calcium (Ca(i)(2+)) regulates AP properties by modulating various ion channels. Whether Ca(i)(2+) modulates sodium channels in ventricular myocytes is unresolved. We studied whether Ca(i)(2+) modulates sodium channels in ventricular myocytes at Ca(i)(2+) concentrations ([Ca(i)(2+)]) present during the cardiac AP (0-500 nM), and how this modulation affects sodium channel properties in heart failure (HF), a condition in which Ca(i)(2+) homeostasis is disturbed.

METHODS AND RESULTS

Sodium current (I(Na)) and maximal AP upstroke velocity (dV/dt(max)), a measure of I(Na), were studied at 20 and 37 degrees C, respectively, in freshly isolated left ventricular myocytes of control and HF rabbits, using whole-cell patch-clamp methodology. [Ca(i)(2+)] was varied using different pipette solutions, the Ca(i)(2+) buffer BAPTA, and caffeine administration. Elevated [Ca(i)(2+)] reduced I(Na) density and dV/dt(max), but caused no I(Na) gating changes. Reductions in I(Na) density occurred simultaneously with increase in [Ca(i)(2+)], suggesting that these effects were due to permeation block. Accordingly, unitary sodium current amplitudes were reduced at higher [Ca(i)(2+)]. While I(Na) density and gating at fixed [Ca(i)(2+)] were not different between HF and control, reductions in dV/dt(max) upon increases in stimulation rate were larger in HF than in control; these differences were abolished by BAPTA.

CONCLUSION

Ca(i)(2+) exerts acute modulation of I(Na) density in ventricular myocytes, but does not modify I(Na) gating. These effects, occurring rapidly and in the [Ca(i)(2+)] range observed physiologically, may contribute to beat-to-beat regulation of cardiac excitability in health and disease.

Estimating the dielectric constant of the channel protein and pore

When modelling biological ion channels using Brownian dynamics (BD) or Poisson-Nernst-Planck theory, the force encountered by permeant ions is calculated by solving Poisson's equation. Two free parameters needed to solve this equation are the dielectric constant of water in the pore and the dielectric constant of the protein forming the channel. Although these values can in theory be deduced by various methods, they do not give a reliable answer when applied to channel-like geometries that contain charged particles. To determine the appropriate values of the dielectric constants, here we solve the inverse problem. Given the structure of the MthK channel, we attempt to determine the values of the protein and pore dielectric constants that minimize the discrepancies between the experimentally-determined current-voltage curve and the curve obtained from BD simulations. Two different methods have been applied to determine these values. First, we use all possible pairs of the pore dielectric constant of water, ranging from 20 to 80 in steps of 10, and the protein dielectric constant of 2-10 in steps of 2, and compare the simulated results with the experimental values. We find that the best agreement is obtained with experiment when a protein dielectric constant of 2 and a pore water dielectric constant of 60 is used. Second, we employ a learning-based stochastic optimization algorithm to pick out the optimum combination of the two dielectric constants. From the algorithm we obtain an optimum value of 2 for the protein dielectric constant and 64 for the pore dielectric constant.

Steric selectivity in Na channels arising from protein polarization and mobile side chains

Monte Carlo simulations of equilibrium selectivity of Na channels with a DEKA locus are performed over a range of radius R and protein dielectric coefficient epsilon(p). Selectivity arises from the balance of electrostatic forces and steric repulsion by excluded volume of ions and side chains of the channel protein in the highly concentrated and charged (approximately 30 M) selectivity filter resembling an ionic liquid. Ions and structural side chains are described as mobile charged hard spheres that assume positions of minimal free energy. Water is a dielectric continuum. Size selectivity (ratio of Na+ occupancy to K+ occupancy) and charge selectivity (Na+ to Ca2+) are computed in concentrations as low as 10(-5) M Ca2+. In general, small R reduces ion occupancy and favors Na+ over K+ because of steric repulsion. Small epsilon(p) increases occupancy and favors Na+ over Ca2+ because protein polarization amplifies the pore's net charge. Size selectivity depends on R and is independent of epsilon(p); charge selectivity depends on both R and epsilon(p). Thus, small R and epsilon(p) make an efficient Na channel that excludes K+ and Ca2+ while maximizing Na+ occupancy. Selectivity properties depend on interactions that cannot be described by qualitative or verbal models or by quantitative models with a fixed free energy landscape.

Role of a novel maintained low-voltage-activated inward current permeable to sodium and calcium in pacemaking of insect neurosecretory neurons

Among ionic currents underlying neuronal pacemaker activity, low-threshold-activated calcium currents contribute to setting the threshold for spike firing. In the insect central nervous system, dorsal unpaired median (DUM) neurons are capable of generating spontaneous electrical activity. It has previously been shown that two distinct (transient and maintained) low-voltage-activated (LVA) calcium currents are responsible for the generation of the pacemaker potential. Whole-cell recordings in voltage- and current-clamp mode were obtained from short-term cultured DUM neurons. Using 100 mM sodium and 2 mM calcium as charge carrier in the external solution as well as conditions that eliminate calcium currents (0.5 mM CdCl2), voltage-clamp experiments showed that a hitherto unanticipated LVA maintained inward current, activated at around -60 mV, was present. The current amplitude was strongly dependent on internal ATP concentration. Sodium-free solution reduced by 80% the current amplitude. Increasing (5 mM) or decreasing (calcium-free) external calcium concentrations enhanced or reduced, respectively, the maximum conductance without any effect on the voltage dependence. This novel ion channel was permeable to barium but manipulating internal or external magnesium concentrations was without effect on current amplitude or reversal potential. Based on IC50 values, the maintained current was 50-fold less sensitive to TTX than the classical transient voltage-dependent sodium current. Furthermore, it was insensitive to ethosuximide and halothane. Voltage-dependent inactivation analysis revealed an unexpected calcium-sensitive process that involved calcineurin. From these results it appears that, besides the two LVA calcium currents previously described, another LVA maintained inward current permeable to both sodium and calcium was also involved in the generation of the predepolarization. Based on these findings, we propose that a novel calcium-dependent mechanism is involved in the regulation of the pacemaker activity.

Electrostatic basis of valence selectivity in cationic channels

We examine how a variety of cationic channels discriminate between ions of differing charge. We construct models of the KcsA potassium channel, voltage gated sodium channel and L-type calcium channel, and show that they all conduct monovalent cations, but that only the calcium channel conducts divalent cations. In the KcsA and sodium channels divalent ions block the channel and prevent any further conduction. We demonstrate that in each case, this discrimination and some of the more complex conductance properties of the channels is a consequence of the electrostatic interaction of the ions with the charges in the channel protein. The KcsA and sodium channels bind divalent ions strongly enough that they cannot be displaced by other ions and thereby block the channel. On the other hand, the calcium channel binds them less strongly such that they can be destabilized by the repulsion of another incoming divalent ion, but not by the lesser repulsion from monovalent ions.