Conformational model for ion permeation in membrane channels: a comparison with multi-ion models and applications to calcium channel permeability

Voltage-gated calcium channels: Determinants of channel function and modulation by inorganic cations

Voltage-gated calcium channels (VGCCs) represent a key link between electrical signals and non-electrical processes, such as contraction, secretion and transcription. Evolved to achieve high rates of Ca(2+)-selective flux, they possess an elaborate mechanism for selection of Ca(2+) over foreign ions. It has been convincingly linked to competitive binding in the pore, but the fundamental question of how this is reconcilable with high rates of Ca(2+) transfer remains unanswered. By virtue of their similarity to Ca(2+), polyvalent cations can interfere with the function of VGCCs and have proven instrumental in probing the mechanisms underlying selective permeation. Recent emergence of crystallographic data on a set of Ca(2+)-selective model channels provides a structural framework for permeation in VGCCs, and warrants a reconsideration of their diverse modulation by polyvalent cations, which can be roughly separated into three general mechanisms: (I) long-range interactions with charged regions on the surface, affecting the local potential sensed by the channel or influencing voltage-sensor movement by repulsive forces (electrostatic effects), (II) short-range interactions with sites in the ion-conducting pathway, leading to physical obstruction of the channel (pore block), and in some cases (III) short-range interactions with extracellular binding sites, leading to non-electrostatic modifications of channel gating (allosteric effects). These effects, together with the underlying molecular modifications, provide valuable insights into the function of VGCCs, and have important physiological and pathophysiological implications. Allosteric suppression of some of the pore-forming Cavα1-subunits (Cav2.3, Cav3.2) by Zn(2+) and Cu(2+) may play a major role for the regulation of excitability by endogenous transition metal ions. The fact that these ions can often traverse VGCCs can contribute to the detrimental intracellular accumulation of metal ions following excessive release of endogenous Cu(2+) and Zn(2+) or exposure to non-physiological toxic metal ions.

Reinterpreting the anomalous mole fraction effect: the ryanodine receptor case study

The origin of the anomalous mole fraction effect (AMFE) in calcium channels is explored with a model of the ryanodine receptor. This model predicted and experiments verified new AMFEs in the cardiac isoform. In mole fraction experiments, conductance is measured in mixtures of ion species X and Y as their relative amounts (mole fractions) vary. This curve can have a minimum (an AMFE). The traditional interpretation of the AMFE is that multiple interacting ions move through the pore in a single file. Mole fraction curves without minima (no AMFEs) are generally interpreted as X displacing Y from the pore in a proportion larger than its bath mole fraction (preferential selectivity). We find that the AMFE is also caused by preferential selectivity of X over Y, if X and Y have similar conductances. This is a prediction applicable to any channel and provides a fundamentally different explanation of the AMFE that does not require single filing or multiple occupancy: preferential selectivity causes the resistances to current flow in the baths, channel vestibules, and selectivity filter to change differently with mole fraction, and produce the AMFE.

The anomalous mole fraction effect in calcium channels: a measure of preferential selectivity

The cause of the anomalous mole fraction effect (AMFE) in calcium-selective ion channels is studied. An AMFE occurs when the conductance through a channel is lower in a mixture of salts than in the pure salts at the same concentration. The textbook interpretation of the AMFE is that multiple ions move through the pore in coordinated, single-file motion. Instead of this, we find that at its most basic level an AMFE reflects a channel's preferential binding selectivity for one ion species over another. The AMFE is explained by considering the charged and uncharged regions of the pore as electrical resistors in series: the AMFE is produced by these regions of high and low ion concentration changing differently with mole fraction due to the preferential ion selectivity. This is demonstrated with simulations of a model L-type calcium channel and a mathematical analysis of a simplistic point-charge model. The particle simulations reproduce the experimental data of two L-type channel AMFEs. Conditions under which an AMFE may be found experimentally are discussed. The resistors-in-series model provides a fundamentally different explanation of the AMFE than the traditional theory and does not require single filing, multiple occupancy, or momentum-correlated ion motion.

Synthetic nanopores as a test case for ion channel theories: the anomalous mole fraction effect without single filing

The predictions of a theory for the anomalous mole fraction effect (AMFE) are tested experimentally with synthetic nanopores in plastic. The negatively charged synthetic nanopores under consideration are highly cation selective and 50 A in diameter at their smallest point. These pores exhibit an AMFE in mixtures of Ca(2+) and monovalent cations. An AMFE occurs when the conductance through a pore is lower in a mixture of salts than in the pure salts at the same concentration. For ion channels, the textbook interpretation of the AMFE is that multiple ions move through the pore in coordinated, single-file motion. However, because the synthetic nanopores are so wide, their AMFE shows that single filing is not necessary for the AMFE. It is shown that the AMFE in the synthetic nanopores is explained by a theory of preferential ion selectivity. The unique properties of the synthetic nanopores allow us to experimentally confirm several predictions of this theory. These same properties make synthetic nanopores an interesting new platform to test theories of ion channel permeation and selectivity in general.

Kinetic models for stochastically modified ionic channels

Ionic channels form pores in biomembranes. These pores are large macromolecular structures. Due to thermal fluctuations of countless degrees-of-freedom of the biomembrane material, the actual form of the pores is permanently subject to modification. Furthermore, the arrival of an ion at the binding site can change this form by repolarizing the surrounding aminoacids. In any case the variations of the pore structure are stochastic. In this paper, we discuss the effect of such modifications on the channel conductivity. Applying a simple kinetic description, we show that stochastic variations in channel properties can significantly alter the ionic current, even leading to its substantial increase or decrease for the specific matching of some time-scales of the system.

Approximate analytical time-dependent solutions to describe large-amplitude local calcium transients in the presence of buffers

Local Ca(2+) signaling controls many neuronal functions, which is often achieved through spatial localization of Ca(2+) signals. These nanodomains are formed due to combined effects of Ca(2+) diffusion and binding to the cytoplasmic buffers. In this article we derived simple analytical expressions to describe Ca(2+) diffusion in the presence of mobile and immobile buffers. A nonlinear character of the reaction-diffusion problem was circumvented by introducing a logarithmic approximation of the concentration term. The obtained formulas reproduce free Ca(2+) levels up to 50 microM and their changes in the millisecond range. Derived equations can be useful to predict spatiotemporal profiles of large-amplitude [Ca(2+)] transients, which participate in various physiological processes.

Block of CaV1.2 channels by Gd3+ reveals preopening transitions in the selectivity filter

Using the lanthanide gadolinium (Gd³⁺) as a Ca²⁺ replacing probe, we investigated the voltage dependence of pore blockage of Ca_V1.2 channels. Gd⁺³ reduces peak currents (tonic block) and accelerates decay of ionic current during depolarization (use-dependent block). Because diffusion of Gd³⁺ at concentrations used (<1 μM) is much slower than activation of the channel, the tonic effect is likely to be due to the blockage that occurred in closed channels before depolarization. We found that the dose–response curves for the two blocking effects of Gd³⁺ shifted in parallel for Ba²⁺, Sr²⁺, and Ca²⁺ currents through the wild-type channel, and for Ca²⁺ currents through the selectivity filter mutation EEQE that lowers the blocking potency of Gd³⁺. The correlation indicates that Gd³⁺ binding to the same site causes both tonic and use-dependent blocking effects. The apparent on-rate for the tonic block increases with the prepulse voltage in the range −60 to −45 mV, where significant gating current but no ionic current occurs. When plotted together against voltage, the on-rates of tonic block (−100 to −45 mV) and of use-dependent block (−40 to 40 mV) fall on a single sigmoid that parallels the voltage dependence of the gating charge. The on-rate of tonic block by Gd³⁺ decreases with concentration of Ba²⁺, indicating that the apparent affinity of the site to permeant ions is about 1 mM in closed channels. Therefore, we propose that at submicromolar concentrations, Gd³⁺ binds at the entry to the selectivity locus and that the affinity of the site for permeant ions decreases during preopening transitions of the channel.

Dynamical description of sinoatrial node pacemaking: improved mathematical model for primary pacemaker cell

We developed an improved mathematical model for a single primary pacemaker cell of the rabbit sinoatrial node. Original features of our model include 1) incorporation of the sustained inward current (I(st)) recently identified in primary pacemaker cells, 2) reformulation of voltage- and Ca(2+)-dependent inactivation of the L-type Ca(2+) channel current (I(Ca,L)), 3) new expressions for activation kinetics of the rapidly activating delayed rectifier K(+) channel current (I(Kr)), and 4) incorporation of the subsarcolemmal space as a diffusion barrier for Ca(2+). We compared the simulated dynamics of our model with those of previous models, as well as with experimental data, and examined whether the models could accurately simulate the effects of modulating sarcolemmal ionic currents or intracellular Ca(2+) dynamics on pacemaker activity. Our model represents significant improvements over the previous models, because it can 1) simulate whole cell voltage-clamp data for I(Ca,L), I(Kr), and I(st); 2) reproduce the waveshapes of spontaneous action potentials and ionic currents during action potential clamp recordings; and 3) mimic the effects of channel blockers or Ca(2+) buffers on pacemaker activity more accurately than the previous models.

Mechanisms of cation permeation in cardiac sodium channel: description by dynamic pore model

The selective permeability to monovalent metal cations, as well as the relationship between cation permeation and gating kinetics, was investigated for native tetrodotoxin-insensitive Na-channels in guinea pig ventricular myocytes using the whole-cell patch clamp technique. By the measurement of inward unidirectional currents and biionic reversal potentials, we demonstrate that the cardiac Na-channel is substantially permeable to all of the group Ia and IIIa cations tested, with the selectivity sequence Na(+) >/= Li(+) > Tl(+) > K(+) > Rb(+) > Cs(+). Current kinetics was little affected by the permeant cation species and concentrations tested (</=160 mM), suggesting that the permeation process is independent of the gating process in the Na-channel. The permeability ratios determined from biionic reversal potentials were concentration and orientation dependent: the selectivity to Na(+) increased with increasing internal [K(+)] or external [Tl(+)]. The dynamic pore model describing the conformational transition of the Na-channel pore between different selectivity states could account for all the experimental data, whereas conventional static pore models failed to fit the concentration-dependent permeability ratio data. We conclude that the dynamic pore mechanism, independent of the gating machinery, may play an important physiological role in regulating the selective permeability of native Na-channels.

L-type Ca2+ channels in inspiratory neurones of mice and their modulation by hypoxia

1. Whole-cell (ICa) and single Ca2+ channel currents were measured in inspiratory neurones of neonatal mice (4-12 days old). During whole-cell recordings, ICa slowly declined and disappeared within 10-20 min. The run-down was delayed during hypoxia, indicating ICa potentiation. 2. Ca2+ channels were recorded in cell-attached patches using pipettes which contained 110 mM Ba2+. L-type Ca2+ channels exhibited a non-ohmic I-V relationship. The slope conductance was 24 pS below and 50 pS above their null potential. The open probability of the channels increased during oxygen depletion, reaching a maximum 2 min after the onset of hypoxia. Restoration of the oxygen supply brought the channel activity back to initial levels. 3. The channel activity was enhanced by 3-30 microM S(-)Bay K 8644, an agonist of L-type Ca2+ channels. The open probability was increased about 3-fold and the activation curve was shifted by 20 mV in the hyperpolarizing direction. In the presence of the agonist, channel open time increased and long openings appeared. Agonist-modulated channels were also potentiated during oxygen depletion. The effect was due to an increase in open time and a decrease in closed time. The channels were inhibited by bath application of nifedipine (10 microM) and nitrendipine (20 microM). 4. Weak bases such as NH4Cl and TMA increased and weak acids such as sodium acetate and propionate decreased activity of the channels, indicating that they are modulated by intracellular pH. Bath application of 1 microM forskolin enhanced the channel activity, whereas 500 microM NaF suppressed it. 5. L-type Ca2+ channels were modulated by an agonist for mGluR1/5 receptors, (S)-3, 5-dihydrophenylglycine (DHPG, 5 microM). In its presence, the hypoxic facilitation of channels was abolished. 6. After blockade of L-type Ca2+ channels, the respiratory response to hypoxia was modified. The transient enhancement of the respiratory rhythm (augmentation) was no longer evident and the secondary depression occurred earlier. 7. We suggest that L-type Ca2+ channels contribute to the early hypoxic response of the respiratory centre. Glutamate release during hypoxia stimulates postsynaptic metabotropic glutamate receptors, which activate the Ca2+ channels.

Ion channel selectivity through stepwise changes in binding affinity

Voltage-gated Ca2+ channels select Ca2+ over competing, more abundant ions by means of a high affinity binding site in the pore. The maximum off rate from this site is approximately 1,000x slower than observed Ca2+ current. Various theories that explain how high Ca2+ current can pass through such a sticky pore all assume that flux occurs from a condition in which the pore's affinity for Ca2+ transiently decreases because of ion interactions. Here, we use rate theory calculations to demonstrate a different mechanism that requires no transient changes in affinity to quantitatively reproduce observed Ca2+ channel behavior. The model pore has a single high affinity Ca2+ binding site flanked by a low affinity site on either side; ions permeate in single file without repulsive interactions. The low affinity sites provide steps of potential energy that speed the exit of a Ca2+ ion off the selectivity site, just as potential energy steps accelerate other chemical reactions. The steps could be provided by weak binding in the nonselective vestibules that appear to be a general feature of ion channels, by specific protein structures in a long pore, or by stepwise rehydration of a permeating ion. The previous ion-interaction models and this stepwise permeation model demonstrate two general mechanisms, which might well work together, to simultaneously generate high flux and high selectivity in single file pores.

Cation permeability of a cloned rat epithelial amiloride-sensitive Na+ channel

1. Conductance of heterotrimeric rat epithelial Na+ channels (alpha, beta, gamma-rENaCs) for Li+ and Na+ in planar lipid bilayers was a non-linear function of ion concentration, with a maximum of 30.4 +/- 2.9 pS and 18.5 +/- 1.9 pS at 1 M Li+ and Na+, respectively. 2. The alpha, beta, gamma-rENaC conductance measured in symmetrical mixtures of Na(+)-Li+ (1 M) exhibited an anomalous mole fraction dependence, with a minimum at 4:1 Li+ to Na+ molar ratio. 3. Permeability ratios PK/PNa and PLi/PNa of the channel calculated from the bionic reversal potentials were dependent on ion concentration: PK/PNa was 0.11 +/- 0.01, and PLi/PNa was 1.6 +/- 0.3 at 50 mM; PK/PNa was 0.04 +/- 0.01 and PLi/PNa was 2.5 +/- 0.4 at 3 M, but differed from the ratios of single-channel conductances in symmetrical Li+, Na+ or K+ solutions. The permeability sequence determined by either method was Li+ > Na+ > K+ >> Rb+ Cs+. 4. Predictions of a model featuring two binding sites and three energy barriers (2S3B), and allowing double occupancy, developed on the basis of single ion current-voltage relationships, are in agreement with the observed conductance maximum in single ion experiments, conductance minimum in the mole fraction experiments, non-linearity of the current-voltage curves in bionic experiments, and the concentration dependence of permeability ratios. 5. Computer simulations using the 2S3B model recreate the ion concentration dependencies of single-channel conductance observed for the immunopurified bovine renal amiloride-sensitive Na+ channel, and short-circuit current in frog skin, thus supporting the hypothesis that ENaCs form a core conduction unit of epithelial Na+ channels.

Ca2+ and Na+ permeability of high-threshold Ca2+ channels and their voltage-dependent block by Mg2+ ions in chick sensory neurones

1. The Mg2+ block of Na+ and Ca2+ currents through high-voltage activated (HVA; L- and N-type) Ca2+ channels was studied in chick dorsal root ganglion neurones. 2. In low extracellular [Ca2+] (< 10(-8) M) and with Na+o and Cs+i as the main charge carriers (120 mM), HVA Na+ currents started to activate at -40 mV, reached inward peak values near 0 mV and reversed at about +40 mV. 3. Addition of 30-500 microM Mg2+ to the bath caused a strong depression of inward Na+ currents that was voltage and dose dependent (KD = 39 microM in 120 mM Na+ at -10 mV). The block was maximal at negative potentials (< -70 mV) and decreased with increasing positive potentials, suggesting that Mg2+ cannot escape to the cell interior. 4. Block of Ca2+ currents by Mg2+ was also voltage dependent, but by three orders of magnitude less potent than with Na+ currents (KD = 24 mM in 2 mM Ca2+ at -30 mV). The high concentration of Mg2+ caused a prominent voltage shift of channel gating kinetics induced by surface charge screening effects. To compensate for this, Mg2+ block of inward Ca2+ currents was estimated from the instantaneous I-V relationships on return from very positive potentials (+100 mV). 5. Inward Na+ and Ca2+ tail currents following depolarization to +90 mV were markedly depressed, suggesting that channels cleared of Mg2+ ions during strong depolarization are quickly re-blocked on return to negative potentials. The kinetics of re-block by Mg2+ was too fast (< 100 microseconds) to be resolved by our recording apparatus. This implies a rate of entry for Mg2+ > 1.45 x 10(8) M-1 S-1 when Na+ is the permeating ion and a rate approximately 3 orders of magnitude smaller for Ca2+. 6. Mg2+ unblock of HVA Na+ currents at +100 mV was independent of the size of outward currents, whether Na+, Cs+ or NMG+ were the main internal cations. 7. Consistent with the idea of a high-affinity binding site for Ca2+ inside the channel, micromolar amounts of Ca2+ caused a strong depression of Na+ currents between -40 and 0 mV, which was effectively relieved with more positive as well as with negative potentials (KD = 0.7 microM in 120 mM Na+ at -20 mV). In this case, the kinetics of re-block could be resolved and gave rates of entry and exit for Ca2+ of 1.4 x 10(8) M-1 S-1 and 2.95 x 10(2) s-1, respectively. 8. The strong voltage dependence and weak current dependence of HVA channel block by divalent cations and the markedly different KD values of Na+ and Ca2+ current block by Mg2+ can be well described by a previously proposed model for Ca2+ channel permeation based on interactions between the permeating ion and the negative charges forming the high-affinity binding site for Ca2+ inside the pore (Lux, Carbone & Zucker, 1990).

Structural model of a synthetic Ca2+ channel with bound Ca2+ ions and dihydropyridine ligand

Grove et al. have demonstrated L-type Ca2+ channel activity of a synthetic channel peptide (SCP) composed of four helices (sequence: DPWNVFDFLI10VIGSIIDVIL20SE) tethered by their C-termini to a nanopeptide template. We sought to obtain the optimal conformations of SCP and locate the binding sites for Ca2+ and for the dihydropyridine ligand nifedipine. Eight Ca2+ ions were added to neutralize the 16 acidic residues in the helices. Eight patterns of the salt bridges between Ca2+ ions and pairs of the acidic residues were calculated by the Monte Carlo-with-energy-minimization (MCM) protocol. In the energetically optimal conformation, two Ca2+ ions were bound to Asp-1 residues at the intracellular side of SCP, and six Ca2+ ions were arrayed in two files at the diametrically opposite sides of the pore, implying a Ca2+ relay mechanism. Nine modes of nifedipine binding to SCP were simulated by the MCM calculations. In the energetically optimal mode, the ligand fits snugly in the pore. The complex is stabilized by Ca2+ bound between two Asp-17 residues and hydrophilic groups of the ligand. The latter substitute water molecules adjacent to Ca2+ in the ligand-free pore and thus do not obstruct Ca2+ relay. The ligand-binding site is proximal to a hydrophobic bracelet of Ile-10 residues whose rotation is sterically hindered. In some conformations, the bracelet is narrow enough to block the permeation of the hydrated Ca2+ ions. The bracelet may thus act as a "gate" in SCP. Nifedipine and (R)-Bay K 8644, which act as blockers of the SCP, extend a side-chain hydrophobic moiety toward the Ile-10 residues. This would stabilize the pore-closing conformation of the gate. In contrast, the channel activator (S)-Bay K 8644 exposes a hydrophilic moiety toward the Ile-10 residues, thus destabilizing the pore-closing conformation of the gate.

Rectifying conductance substates in a large conductance Ca(2+)-activated K+ channel: evidence for a fluctuating barrier mechanism

In this study, we investigated the mechanism underlying the production of inwardly rectifying subconductance states induced in large conductance Ca(2+)-activated K+ channels (maxi K(Ca) channels) by the small, homologous proteins, bovine pancreatic trypsin inhibitor (BPTI) and dendrotoxin-I (DTX). Low-resolution bilayer recordings of BPTI-induced substates display excess noise that is well described by a beta-distribution characteristic of a filtered, two-state process. High-resolution patch recordings of maxi K(Ca) channels from vascular smooth muscle cells confirm that the BPTI-induced substate is actually comprised of rapid, voltage-dependent transitions between the open state and a nearly closed state. Patch recordings of DTX-induced substates also exhibit excess noise consistent with a similar two-state fluctuation process that occurs at rates faster than those measured for the BPTI-induced substate. The results indicate that these examples of ligand-induced substates originate by a fluctuating barrier mechanism that is similar to one class of models proposed by Dani, J.A., and J.A. Fox (1991. J. Theor. Biol. 153: 401-423) to explain subconductance behavior of ion channels. To assess the general impact of such rapid fluctuations on the practical measurement of unitary currents by amplitude histograms, we simulated single-channel records for a linear, three-state scheme of C (closed)-O(open)-S(substate). This simulation defines a range of transition rates relative to filter frequency where rapid fluctuations can lead to serious underestimation of actual unitary current levels. On the basis of these experiments and simulations, we conclude that fluctuating barrier processes and open channel noise may play an important physiological role in the modulation of ion permeation.

Monovalent amidiniums block calcium channels in chick sensory neurons

The effect of amidiniums on high-threshold Ca2+ channel currents (ICa) was studied in chick dorsal root ganglion neurons. Guanidinium reduced ICa in a dose-dependent fashion. The block was relieved by increasing the concentration of the permeant ions, Ba2+ or Ca2+, suggesting a competition for a common binding site within the channel. Formamidinium and methyl-guanidinium suppressed ICa with similar potencies, whereas L-arginine had no effect. A neutral amidine, urea, increased ICa. In Ca(2+)-free solutions guanidinium and Na+ permeated through the Ca2+ channel equally well. Structure-activity relationship obtained for blocking efficacies of different amidiniums are used to discuss possible configurations of the selectivity filter in the Ca2+ channel.