Voltage-gated calcium channel α 2δ subunits: an assessment of proposed novel roles.

Voltage-gated calcium (CaV) channels are associated with ß and α2δ auxiliary subunits. This review will concentrate on the function of the α2δ protein family, which has four members. The canonical role for α2δ subunits is to convey a variety of properties on the CaV1 and CaV2 channels, increasing the density of these channels in the plasma membrane and also enhancing their function. More recently, a diverse spectrum of non-canonical interactions for α2δ proteins has been proposed, some of which involve competition with calcium channels for α2δ or increase α2δ trafficking and others which mediate roles completely unrelated to their calcium channel function. The novel roles for α2δ proteins which will be discussed here include association with low-density lipoprotein receptor-related protein 1 (LRP1), thrombospondins, α-neurexins, prion proteins, large conductance (big) potassium (BK) channels, and N-methyl-d-aspartate (NMDA) receptors.

Ca(2+)-activation kinetics modulate successive puff/spark amplitude, duration and inter-event-interval correlations in a Langevin model of stochastic Ca(2+) release.

Through theoretical analysis of the statistics of stochastic calcium (Ca(2+)) release (i.e., the amplitude, duration and inter-event interval of simulated Ca(2+) puffs and sparks), we show that a Langevin description of the collective gating of Ca(2+) channels may be a good approximation to the corresponding Markov chain model when the number of Ca(2+) channels per Ca(2+) release unit (CaRU) is in the physiological range. The Langevin description of stochastic Ca(2+) release facilitates our investigation of correlations between successive puff/spark amplitudes, durations and inter-spark intervals, and how such puff/spark statistics depend on the number of channels per release site and the kinetics of Ca(2+)-mediated inactivation of open channels. When Ca(2+) inactivation/de-inactivation rates are intermediate-i.e., the termination of Ca(2+) puff/sparks is caused by an increase in the number of inactivated channels-the correlation between successive puff/spark amplitudes is negative, while the correlations between puff/spark amplitudes and the duration of the preceding or subsequent inter-spark interval are positive. These correlations are significantly reduced or change signs when inactivation/de-inactivation rates are extreme (slow or fast) and puff/sparks terminate via stochastic attrition.

Transmitter release is evoked with low probability predominately by calcium flux through single channel openings at the frog neuromuscular junction.

The quantitative relationship between presynaptic calcium influx and transmitter release critically depends on the spatial coupling of presynaptic calcium channels to synaptic vesicles. When there is a close association between calcium channels and synaptic vesicles, the flux through a single open calcium channel may be sufficient to trigger transmitter release. With increasing spatial distance, however, a larger number of open calcium channels might be required to contribute sufficient calcium ions to trigger vesicle fusion. Here we used a combination of pharmacological calcium channel block, high-resolution calcium imaging, postsynaptic recording, and 3D Monte Carlo reaction-diffusion simulations in the adult frog neuromuscular junction, to show that release of individual synaptic vesicles is predominately triggered by calcium ions entering the nerve terminal through the nearest open calcium channel. Furthermore, calcium ion flux through this channel has a low probability of triggering synaptic vesicle fusion (∼6%), even when multiple channels open in a single active zone. These mechanisms work to control the rare triggering of vesicle fusion in the frog neuromuscular junction from each of the tens of thousands of individual release sites at this large model synapse.

Computer simulation of voltage sensitive calcium ion channels in a dendritic spine.

Membrane current through voltage-sensitive calcium ion channels at the postsynaptic density of a dendritic spine is investigated. To simulate the ion channels that carry such current and the resulting temporal and spatial distribution of concentration, current, and voltage within the dendritic spine, the immersed boundary method with electrodiffusion is applied. In this simulation method a spatially continuous chemical potential barrier is used to simulate the influence of the membrane on each species of ion. The amplitudes of these barriers can be regulated to simulate channel gating. Here we introduce this methodology in a one-dimensional setting. First, we study the current-voltage relationship obtained with fixed chemical potential barriers. Next, we simulate stochastic ion-channel gating in a calcium channel with multiple subunits, and observe the diffusive wave of calcium entry within the dendritic spine that follows channel opening. This work lays the foundation for future three-dimensional studies of electrodiffusion and advection electrodiffusion in dendritic spines.

Role of mixed ion channel effects in the cardiovascular safety assessment of the novel anti-MRSA fluoroquinolone JNJ-Q2.

BACKGROUND AND PURPOSE: JNJ-Q2, a novel broad-spectrum fluoroquinolone with anti-methicillin-resistant Staphylococcus aureus activity, was evaluated in a comprehensive set of non-clinical and clinical cardiovascular safety studies. The effect of JNJ-Q2 on different cardiovascular parameters was compared with that of moxifloxacin, sparfloxacin and ofloxacin. Through comparisons with these well-known fluoroquinolones, the importance of effects on compensatory ion channels to the cardiovascular safety of JNJ-Q2 was investigated. EXPERIMENTAL APPROACH: JNJ-Q2 and comparator fluoroquinolones were evaluated in the following models/test systems: hERG-transfected HEK293 cells sodium channel-transfected CHO cells, guinea pig right atria, arterially perfused rabbit left ventricular wedge preparations and in vivo studies in anaesthetized guinea pigs, anaesthetized and conscious telemetered dogs, and a thorough QT study in humans. KEY RESULTS: The trend for effects of JNJ-Q2 on Tp-Te, QT, QRS and PR intervals in the non-clinical models and the plateau in QTc with increasing plasma concentration in humans are consistent with offsetting sodium and calcium channel activities that were observed in the non-clinical studies. These mixed ion channel activities result in the less pronounced or comparable increase in QTc interval for JNJ-Q2 compared with moxifloxacin and sparfloxacin despite its greater in vitro inhibition of I(Kr). CONCLUSIONS AND IMPLICATIONS: Based on the non-clinical and clinical cardiovascular safety assessment, JNJ-Q2 has a safe cardiovascular profile for administration in humans with comparable or reduced potential to prolong QT intervals, compared with moxifloxacin. The results demonstrate the importance of compensatory sodium and calcium channel activity in offsetting potassium channel activity for compounds with a fluoroquinolone core.

Electrophysiological models of neural processing.

The brain is an amazing information processing system that allows organisms to adaptively monitor and control complex dynamic interactions with their environment across multiple spatial and temporal scales. Mathematical modeling and computer simulation techniques have become essential tools in understanding diverse aspects of neural processing ranging from sub-millisecond temporal coding in the sound localization circuity of barn owls to long-term memory storage and retrieval in humans that can span decades. The processing capabilities of individual neurons lie at the core of these models, with the emphasis shifting upward and downward across different levels of biological organization depending on the nature of the questions being addressed. This review provides an introduction to the techniques for constructing biophysically based models of individual neurons and local networks. Topics include Hodgkin-Huxley-type models of macroscopic membrane currents, Markov models of individual ion-channel currents, compartmental models of neuronal morphology, and network models involving synaptic interactions among multiple neurons.

Fast Kalman filtering on quasilinear dendritic trees.

Optimal filtering of noisy voltage signals on dendritic trees is a key problem in computational cellular neuroscience. However, the state variable in this problem-the vector of voltages at every compartment-is very high-dimensional: realistic multicompartmental models often have on the order of N = 10(4) compartments. Standard implementations of the Kalman filter require O(N (3)) time and O(N (2)) space, and are therefore impractical. Here we take advantage of three special features of the dendritic filtering problem to construct an efficient filter: (1) dendritic dynamics are governed by a cable equation on a tree, which may be solved using sparse matrix methods in O(N) time; and current methods for observing dendritic voltage (2) provide low SNR observations and (3) only image a relatively small number of compartments at a time. The idea is to approximate the Kalman equations in terms of a low-rank perturbation of the steady-state (zero-SNR) solution, which may be obtained in O(N) time using methods that exploit the sparse tree structure of dendritic dynamics. The resulting methods give a very good approximation to the exact Kalman solution, but only require O(N) time and space. We illustrate the method with applications to real and simulated dendritic branching structures, and describe how to extend the techniques to incorporate spatially subsampled, temporally filtered, and nonlinearly transformed observations.

Membrane signalling complexes: implications for development of functionally selective ligands modulating heptahelical receptor signalling.

Technological development has considerably changed the way in which we evaluate drug efficacy and has led to a conceptual revolution in pharmacological theory. In particular, molecular resolution assays have revealed that heptahelical receptors may adopt multiple active conformations with unique signalling properties. It is therefore becoming widely accepted that ligand ability to stabilize receptor conformations with distinct signalling profiles may allow to direct the stimulus generated by an activated receptor towards a specific signalling pathway. This capacity to induce only a subset of the ensemble of responses regulated by a given receptor has been termed "functional selectivity" (or "stimulus trafficking"), and provides the bases for a highly specific regulation of receptor signalling. Concomitant with these observations, heptahelical receptors have been shown to associate with G proteins and effectors to form multimeric arrays. These complexes are constitutively formed during protein synthesis and are targeted to the cell surface as integral signalling units. Herein we summarize evidence supporting the existence of such constitutive signalling arrays and analyze the possibility that they may constitute viable targets for developing ligands with "functional selectivity".

Simulation of Ca-calmodulin-dependent protein kinase II on rabbit ventricular myocyte ion currents and action potentials.

Ca-calmodulin-dependent protein kinase II (CaMKII) was recently shown to alter Na(+) channel gating and recapitulate a human Na(+) channel genetic mutation that causes an unusual combined arrhythmogenic phenotype in patients: simultaneous long QT syndrome and Brugada syndrome. CaMKII is upregulated in heart failure where arrhythmias are common, and CaMKII inhibition can reduce arrhythmias. Thus, CaMKII-dependent channel modulation may contribute to acquired arrhythmic disease. We developed a Markovian Na(+) channel model including CaMKII-dependent changes, and incorporated it into a comprehensive myocyte action potential (AP) model with Na(+) and Ca(2+) transport. CaMKII shifts Na(+) current (I(Na)) availability to more negative voltage, enhances intermediate inactivation, and slows recovery from inactivation (all loss-of-function effects), but also enhances late noninactivating I(Na) (gain of function). At slow heart rates, with long diastolic time for I(Na) recovery, late I(Na) is the predominant effect, leading to AP prolongation (long QT syndrome). At fast heart rates, where recovery time is limited and APs are shorter, there is little effect on AP duration, but reduced availability decreases I(Na), AP upstroke velocity, and conduction (Brugada syndrome). CaMKII also increases cardiac Ca(2+) and K(+) currents (I(Ca) and I(to)), complicating CaMKII-dependent AP changes. Incorporating I(Ca) and I(to) effects individually prolongs and shortens AP duration. Combining I(Na), I(Ca), and I(to) effects results in shortening of AP duration with CaMKII. With transmural heterogeneity of I(to) and I(to) downregulation in heart failure, CaMKII may accentuate dispersion of repolarization. This provides a useful initial framework to consider pathways by which CaMKII may contribute to arrhythmogenesis.

The effect of protein dielectric coefficient on the ionic selectivity of a calcium channel.

Calcium-selective ion channels are known to have carboxylate-rich selectivity filters, a common motif that is primarily responsible for their high Ca(2+) affinity. Different Ca(2+) affinities ranging from micromolar (the L-type Ca channel) to millimolar (the ryanodine receptor channel) are closely related to the different physiological functions of these channels. To understand the physical mechanism for this range of affinities given similar amino acids in their selectivity filters, we use grand canonical Monte Carlo simulations to assess the binding of monovalent and divalent ions in the selectivity filter of a model Ca channel. We use a reduced model where the electolyte is modeled by hard-sphere ions embedded in a continuum dielectric solvent, while the interior of protein surrounding the channel is allowed to have a dielectric coefficient different from that of the electrolyte. The induced charges that appear on the protein/lumen interface are calculated by the induced charge computation method [Boda et al., Phys. Rev. E 69, 046702 (2004)]. It is shown that decreasing the dielectric coefficient of the protein attracts more cations into the pore because the protein's carboxyl groups induce negative charges on the dielectric boundary. As the density of the hard-sphere ions increases in the filter, Ca(2+) is absorbed into the filter with higher probability than Na(+) because Ca(2+) provides twice the charge to neutralize the negative charge of the pore (both structural carboxylate oxygens and induced charges) than Na(+) while occupying about the same space (the charge/space competition mechanism). As a result, Ca(2+) affinity is improved an order of magnitude by decreasing the protein dielectric coefficient from 80 to 5. Our results indicate that adjusting the dielectric properties of the protein surrounding the permeation pathway is a possible way for evolution to regulate the Ca(2+) affinity of the common four-carboxylate motif.

Stochastic calcium oscillations.

While the oscillatory release of calcium from intracellular stores is comprised of fundamentally stochastic events, most models of calcium oscillations are deterministic. As a result, the transition to calcium oscillations as parameters, such as IP(3) concentration, are changed is not described correctly. The fundamental difficulty is that whole-cell models of calcium dynamics are based on the assumptions that the calcium concentration is spatially homogeneous, and that there are a sufficiently large number of release sites per unit volume so that the law of large numbers is applicable. For situations where these underlying assumptions are not applicable, a new modelling approach is needed. In this paper, we present a model and its analysis of calcium dynamics that incorporates the fundamental stochasticity of release events. The model is based on the assumptions that release events are rapid, while reactivation is slow. The model presented here is comprised of two parts. In the first, a stochastic version of the fire-diffuse-fire model is studied in order to understand the spark-to-wave transition and the probability of sparks resulting in abortive waves versus whole-cell calcium release. In the second, this information about the spark-to-wave transition is incorporated into a stochastic model (a Chapman-Kolmogorov equation) that tracks the number of activated and inactivated calcium release sites as a function of time. By solving this model numerically, information about the timing of whole-cell calcium release is obtained. The results of this analysis show a transition to oscillations that agrees well with data and with Monte Carlo simulations.

Brevity of the Ca2+ microdomain and active zone geometry prevent Ca2+-sensor saturation for neurotransmitter release.

The brief time course of the calcium (Ca2+) channel opening combined with the molecular-level colocalization of Ca2+ channels and synaptic vesicles in presynaptic terminals predict sub-millisecond calcium concentration ([Ca2+]) transients of > or = 100 microM in the immediate vicinity of the vesicle. This [Ca2+] is much higher than some of the recent estimates for the equilibrium dissociation constant of the Ca2+ sensor(s) that control neurotransmitter release, suggesting release should be close to saturation, yet it is well known that release is highly sensitive to changes in Ca2+ influx. We show that due to the brevity of the Ca2+ influx the binding kinetics of the Ca2+ sensor rather than its equilibrium affinity determine receptor occupancy. For physiologically relevant Ca2+ currents and forward Ca2+ binding rates, the effective affinity of the Ca2+ sensor can be several-fold lower than the equilibrium affinity. Using simple models, we show redundant copies of the binding sites increase effective affinity of the Ca2+ sensor for release. Our results predict that different levels of expression of Ca2+ binding sites could account for apparent differences in Ca2+ sensor affinities between synapses. Using Monte Carlo simulations of Ca2+ dynamics with nanometer resolution, we demonstrate that these kinetic constraints combined with vesicles acting as diffusion barriers can prevent saturation of the Ca2+-sensor(s) for neurotransmitter release. We further show the random positioning of the Ca2+-sensor molecules around the vesicle can result in the emergence of two distinct populations of the vesicles with low and high release probability. These considerations allow experimental evidence for the Ca2+ channel-vesicle colocalization to be reconciled with a high equilibrium affinity for the Ca2+ sensor of the release machinery.

The effect of residual Ca2+ on the stochastic gating of Ca2+-regulated Ca2+ channel models.

Single-channel models of intracellular Ca(2+) channels such as the inositol 1,4,5-trisphosphate receptor and ryanodine receptor often assume that Ca(2+)-dependent transitions are mediated by a constant background [Ca(2+)] as opposed to a dynamic [Ca(2+)] representing the formation and collapse of a localized Ca(2+) domain. This assumption neglects the fact that Ca(2+) released by open intracellular Ca(2+) channels may influence subsequent gating through the processes of Ca(2+)-activation or -inactivation. We study the effect of such "residual Ca(2+)" from previous channel opening on the stochastic gating of minimal and realistic single-channel models coupled to a restricted cytoplasmic compartment. Using Monte Carlo simulation as well as analytical and numerical solution of a system of advection-reaction equations for the probability density of the domain [Ca(2+)] conditioned on the state of the channel, we determine how the steady-state open probability (p(open)) of single-channel models of Ca(2+)-regulated Ca(2+) channels depends on the time constant for Ca(2+) domain formation and collapse. As expected, p(open) for a minimal model including Ca(2+) activation increases as the domain time constant becomes large compared to the open and closed dwell times of the channel, that is, on average the channel is activated by residual Ca(2+) from previous openings. Interestingly, p(open) for a channel model that is inactivated by Ca(2+) also increases as a function of the domain time constant when the maximum domain [Ca(2+)] is fixed, because slow formation of the Ca(2+) domain attenuates Ca(2+)-mediated inactivation. Conversely, when the source amplitude of the channel is fixed, increasing the domain time constant leads to elevated domain [Ca(2+)] and decreased open probability. Consistent with these observations, a realistic De Young-Keizer-like IP(3)R model responds to residual Ca(2+) with a steady-state open probability that is a monotonic function of the domain time constant, though minimal models that include both Ca(2+)-activation and -inactivation show more complex behavior. We show how the probability density approach described here can be generalized for arbitrarily complex channel models and for any value of the domain time constant. In addition, we present a comparatively simple numerical procedure for estimating p(open) for models of Ca(2+)-regulated Ca(2+) channels in the limit of a very fast or very slow Ca(2+) domain. When the ordinary differential equation for the [Ca(2+)] in a restricted cytoplasmic compartment is replaced by a partial differential equation for the buffered diffusion of intracellular Ca(2+) in a homogeneous isotropic cytosol, we find the dependence of p(open) on the buffer time constant is qualitatively similar to the above-mentioned results.

A stochastic automata network descriptor for Markov chain models of instantaneously coupled intracellular Ca2+ channels.

Although there is consensus that localized Ca(2+) elevations known as Ca(2+) puffs and sparks arise from the cooperative activity of intracellular Ca(2+) channels, the precise relationship between single-channel kinetics and the collective phenomena of stochastic Ca(2+) excitability is not well understood. Here we present a formalism by which mathematical models for Ca(2+)-regulated Ca(2+) release sites are derived from stochastic models of single-channel gating that include Ca(2+) activation, Ca(2+) inactivation, or both. Such models are stochastic automata networks (SANs) that involve a large number of functional transitions, that is, the transition probabilities of the infinitesimal generator matrix of one of the automata (i.e., an individual channel) may depend on the local [Ca(2+)] and thus the state of the other channels. Simulation and analysis of the SAN descriptors representing homogeneous clusters of intracellular Ca(2+) channels show that (1) release site density can modify both the steady-state open probability and stochastic excitability of Ca(2+) release sites, (2) Ca(2+) inactivation is not a requirement for Ca(2+) puffs or sparks, and (3) a single-channel model with a bell-shaped open probability curve does not lead to release site activity that is a biphasic function of release site density. These findings are obtained using iterative, memory-efficient methods (novel in this biophysical context and distinct from Monte Carlo simulation) that leverage the highly structured SAN descriptor to unambiguously calculate the steady-state probability of each release site configuration and puff statistics such as puff duration and inter-puff interval. The validity of a mean field approximation that neglects the spatial organization of Ca(2+) release sites is also discussed.

Consequences of molecular-level Ca2+ channel and synaptic vesicle colocalization for the Ca2+ microdomain and neurotransmitter exocytosis: a monte carlo study.

Morphological and biochemical studies indicate association between voltage-gated Ca2+ channels and the vesicle docking complex at vertebrate presynaptic active zones, which constrain the separation between some Ca2+ channels and vesicles to 20 nm or less. To address the effect of the precise geometrical relationship among the vesicles, the Ca2+ channel, and the proteins of the release machinery on neurotransmitter release, we developed a Monte Carlo simulation of Ca2+ diffusion and buffering with nanometer resolution. We find that the presence of a vesicle as a diffusion barrier alters the shape of the Ca2+ microdomain of a single Ca2+ channel around the vesicle. This effect is maximal in the vicinity of the vesicle and depends critically on the vesicle's distance from the plasmalemma. Ca2+-sensor(s) for release would be exposed to markedly different [Ca2+], varying by up to 13-fold, depending on their position around the vesicle. As a result, the precise position of Ca2+-sensor(s) with respect to the vesicle and the channel can be critical to determining the release probability. Variation in the position of Ca2+-sensor molecule(s) and their accessibility could be an important source of heterogeneity in vesicle release probability.

Effects of pyrethroids on voltage-sensitive calcium channels: a critical evaluation of strengths, weaknesses, data needs, and relationship to assessment of cumulative neurotoxicity.

The Food Quality Protection Act of 1996 requires that the U.S. Environmental Protection Agency conduct cumulative risk assessments for classes of pesticides that have a common mode or mechanism of action. For the pyrethroid insecticides, disruption of voltage-sensitive sodium channel function is generally accepted as the mechanism underlying acute neurotoxicity. However, data exist which suggest that voltage-sensitive calcium (Ca(2+)) channels (VSCC) may also be important targets of pyrethroid action. VSCC are important to neuronal function during development and for neurotransmitter release, gene expression, and electrical excitability in the nervous system. Disruption of these and other processes mediated by VSCC can result in neurotoxicity. If effects on VSCC are demonstrated to contribute to pyrethroid neurotoxicity, then such effects will have to be considered when making decisions regarding cumulative risk of exposure to this class of compounds. This document provides a critical review of the data related to the hypothesis that VSCC are important targets of pyrethroid effects. Data supporting effects of pyrethroids on VSCC have been generated by several different laboratories using different techniques and biological preparations. Thus, the many reports of effects on VSCC provide evidence that pyrethroids may interact with VSCC. However, evidence to support a role of VSCC in pyrethroid neurotoxicity is based entirely on in vitro observations, and numerous limitations exist in these data, including: (1) lack of defined concentration-response relationships, with some effects observed only at relatively high concentrations, (2) the use of indirect measures of VSCC function, (3) data from nonmammalian species, (4) data from studies that have not been peer-reviewed, (5) the need for replication of some effects, and (6) inconsistent or contradictory results from different laboratories/preparations. Thus, at the present time, it is premature to conclude that effects on VSCC play an important role in the acute neurotoxicity of pyrethroid insecticides in mammals. To demonstrate that VSCC are important targets of pyrethroid neurotoxicity in mammals, in vivo studies supporting a role for pyrethroid effects on VSCC are needed. Additional support could be provided by demonstration of direct effects of pyrethroid compounds on mammalian neuronal VSCC in vitro, including demonstration that concentration-response relationships are similar, or greater, in sensitivity to effects of pyrethroids on voltage-sensitive sodium channels. If such effects were to be demonstrated, the rationale for considering VSCC as targets of pyrethroid compounds when assessing cumulative risk would be strengthened. However, at the present time, the data available neither support nor refute conclusively the hypothesis that effects on VSCC are important to the acute neurotoxicity of pyrethroids.

Antibody probe study of Ca2+ channel regulation by interdomain interaction within the ryanodine receptor.

N-terminal and central domains of ryanodine receptor 1 (RyR1), where many reported malignant hyperthermia (MH) mutations are localized, represent putative channel regulatory domains. Recent domain peptide (DP) probe studies led us to the hypothesis that these domains interact to stabilize the closed state of channel (zipping), while weakening of domain-domain interactions (unzipping) by mutation de-stabilizes the channel, making it leaky to Ca2+ or sensitive to the agonists of RyR1. As shown previously, DP1 (N-terminal domain peptide) and DP4 (central domain peptide) produced MH-like channel activation/sensitization effects, presumably by peptide binding to sites critical to stabilizing domain-domain interactions and resultant loss of conformational constraints. Here we report that polyclonal anti-DP1 and anti-DP4 antibodies also produce MH-like channel activation and sensitization effects as evidenced by about 4-fold enhancement of high affinity [3H]ryanodine binding to RyR1 and by a significant left-shift of the concentration-dependence of activation of sarcoplasmic reticulum Ca2+ release by polylysine. Fluorescence quenching experiments demonstrate that the accessibility of a DP4-directed, conformationally sensitive fluorescence probe linked to the RyR1 N-terminal domain is increased in the presence of domain-specific antibodies, consistent with the view that these antibodies produce unzipping of interacting domains that are of hindered accessibility to the surrounding aqueous environment. Our results suggest that domain-specific antibody binding induces a conformational change resulting in channel activation, and are consistent with the hypothesis that interacting N-terminal and central domains are intimately involved in the regulation of RyR1 channel function.

Computing transient gating charge movement of voltage-dependent ion channels.

The opening of voltage-gated sodium, potassium, and calcium ion channels has a steep relationship with voltage. In response to changes in the transmembrane voltage, structural movements of an ion channel that precede channel opening generate a capacitative gating current. The net gating charge displacement due to membrane depolarization is an index of the voltage sensitivity of the ion channel activation process. Understanding the molecular basis of voltage-dependent gating of ion channels requires the measurement and computation of the gating charge, Q. We derive a simple and accurate semianalytic approach to computing the voltage dependence of transient gating charge movement (Q-V relationship) of discrete Markov state models of ion channels using matrix methods. This approach allows rapid computation of Q-V curves for finite and infinite length step depolarizations and is consistent with experimentally measured transient gating charge. This computational approach was applied to Shaker potassium channel gating, including the impact of inactivating particles on potassium channel gating currents.

Monte Carlo evaluation of quantal analysis in the light of Ca2+ dynamics and the geometry of secretion.

Using the Monte Carlo technique, Ca2+ dynamics were simulated in the absence and presence of vesicles to gain better insight into what governs quantal release. A vesicle, represented as a flat, infinitely thin surface, was positioned parallel to the plasma membrane at a chosen distance from the locus of Ca2+ entry. Because vesicles act as important diffusion barriers after the synchronous opening of Ca2+ channels (as occurs during evoked release), [Ca2+] close to the plasma membrane reaches higher levels than it would in the absence of vesicles. The rise in [Ca2+] is greater under larger vesicles close to the plasma membrane, which thus have a higher probability of release. The power-law relationship between the [Ca2+] and the probability of release, and the cubic relationship between the vesicular diameter and its volume can make this relationship very steep. In contrast, when release occurs owing to fluctuations of [Ca2+]--as a result of Ca2+ release from an internal store or asynchronous opening of Ca2+ channels (during spontaneous release)--the effect of vesicles as diffusion barriers is less pronounced and vesicles of different sizes should have a similar probability of release. Since the preferential release of large vesicles depends on how the Ca2+ needed for secretion is raised (synchronously versus asynchronously), the quantal size of evoked and spontaneous release should differ. The main factors influencing the preferential release of large vesicles are the distance between vesicles and the plasma membrane, the concentration of Ca2+ buffers, and single-channel Ca2+ flux. Vesicles also have a pronounced effect on Ca2+ binding to buffers and on the spatio-temporal distribution of bound buffers. The greater the vesicular size and the closer their position to the plasma membrane, the more fixed buffers will be bound near the plasma membrane because of limited diffusion of Ca2+. Since bound fixed buffers act as "memory elements", such a change in their spatial distribution will further enhance the probability of release of large vesicles during stimulation.

Assessment of the role of the inositol 1,4,5-trisphosphate receptor in the activation of transient receptor potential channels and store-operated Ca2+ entry channels.

The mechanism for coupling between Ca(2+) stores and store-operated channels (SOCs) is an important but unresolved question. Although SOCs have not been molecularly identified, transient receptor potential (TRP) channels share a number of operational parameters with SOCs. The question of whether activation of SOCs and TRP channels is mediated by the inositol 1,4,5-trisphosphate receptor (InsP(3)R) was examined using the permeant InsP(3)R antagonist, 2-aminoethoxydiphenyl borate (2-APB) in both mammalian and invertebrate systems. In HEK293 cells stably transfected with human TRPC3 channels, the actions of 2-APB to block carbachol-induced InsP(3)R-mediated store release and carbachol-induced Sr(2+) entry through TRPC3 channels were both reversed at high agonist levels, suggesting InsP(3)Rs mediate TRPC3 activation. However, electroretinogram recordings of the light-induced current in Drosophila revealed that the TRP channel-mediated responses in wild-type as well as trp and trpl mutant flies were all inhibited by 2-APB. This action of 2-APB is likely InsP(3)R-independent since InsP(3)Rs are dispensable for the light response. We used triple InsP(3)R knockout DT40 chicken B-cells to further assess the role of InsP(3)Rs in SOC activation. (45)Ca(2+) flux analysis revealed that although DT40 wild-type cells retained normal InsP(3)Rs mediating 2-APB-sensitive Ca(2+) release, the DT40InsP(3)R-k/o cells were devoid of functional InsP(3)Rs. Using intact cells, all parameters of Ca(2+) store function and SOC activation were identical in DT40wt and DT40InsP(3)R-k/o cells. Moreover, in both cell lines SOC activation was completely blocked by 2-APB, and the kinetics of action of 2-APB on SOCs (time dependence and IC(50)) were identical. The results indicate that (a) the action of 2-APB on Ca(2+) entry is not mediated by the InsP(3)R and (b) the effects of 2-APB provide evidence for an important similarity in the function of invertebrate TRP channels, mammalian TRP channels, and mammalian store-operated channels.