Buffering of calcium in the vicinity of a channel pore.

The function of calcium entry or release channels is often modulated by the cytosolic free calcium concentration. When such channels are studied in isolation, calcium buffer solutions are usually used to control the free calcium at the cytosolic face of the channel. Such solutions are generally formulated on the basis of equilibrium considerations. We calculate the gradient of [Ca2+] in the vicinity of a channel pore, in the presence of such buffers. We find that the effective degree of buffering near the pore is markedly affected by kinetic considerations. Commonly used EGTA solutions are completely ineffective in buffering [Ca2+] within macromolecular distances of the pore. In order to achieve useful buffering, the fastest buffers (e.g. BAPTA derivatives) must be used, in concentrations very much higher than those conventionally employed. Because of the diffusion limit on the maximum rate of binding of calcium to the buffer ligand, it is physically impossible to achieve good control of [Ca2+] at cytosolic levels at distances of less than a few nm from a pore conducting pico-ampere calcium current.     

Time courses of calcium and calcium-bound buffers following calcium influx in a model cell.

Fixed and diffusible calcium (Ca) buffers shape the spatial and temporal distribution of free Ca following Ca entry through voltage-gated ion channels. This modeling study explores intracellular Ca levels achieved near the membrane and in deeper locations following typical Ca currents obtained with patch clamp experiments. Ca ion diffusion sets an upper limit on the maximal average Ca concentration achieved near the membrane. Fixed buffers restrict Ca elevation spatially to the outermost areas of the cell and slow Ca equilibration. Fixed buffer bound with Ca near the membrane can act as Ca source after termination of Ca influx. The relative contribution of fixed versus diffusible buffers to shaping the Ca transient is determined to a large extent by the binding rate of each buffer, with diffusible buffer dominating at equal binding rates. In the presence of fixed buffers, diffusible buffers speed Ca equilibration throughout the cell. The concentration profile of Ca-bound diffusible buffer differs from the concentration profile of free Ca, reflecting theoretical limits on the temporal resolution which can be achieved with commonly used diffusible Ca indicators. A Ca indicator which is fixed to an intracellular component might more accurately report local Ca concentrations.     

Exocytotic dynamics and calcium cooperativity effects in the calyx of Held synapse: a modelling study

A stochastic computational approach to the study of secretory processes at the calyx of Held synapse is presented in this paper. The calyx of Held is a giant synapse located in the brainstem which is widely used for experimental recording of neurotransmitter release. We focus on the study of the exocytotic dynamics for a pool of readily releasable vesicles using a Monte Carlo simulation scheme that includes models for the P-type calcium channels, the kinetic reactions of endogenous and exogenous (mobile) buffers, the kinetic reactions for the secretory vesicles, as well as the microscopic diffusion of mobile buffers and calcium ions. The simulations are performed in a 3-D orthogonal grid which approximates a cylindrical domain representing an active zone of the presynaptic terminal of the calyx. For this domain, we quantify the release rates related to calcium currents in response to depolarizing voltage pulses. The influence on simulated pulse/action potential depolarization protocols of the kinetic scheme for the calcium sensor of vesicles and the geometry of calcium channels for the kinetic cooperativity for release, is analyzed at a microdomain level. Among other aspects, our results suggest that the spatial organization of Ca ^2 + channels could have measurable effects in the kinetic cooperativity which could reflect developing changes in the calyx of Held synapse.     

Two-dimensional determination of the cellular Ca2+ binding in bovine chromaffin cells.

The spatiotemporal profile of intracellular calcium signals is determined by the flux of calcium ions across different biological membranes as well as by the diffusional mobility of calcium and different calcium buffers in the cell. To arrive at a quantitative understanding of the determinants of these signals, one needs to dissociate the flux contribution from the redistribution and buffering of calcium. Since the cytosol can be heterogeneous with respect to its calcium buffering property, it is essential to assess this property in a spatially resolved manner. In this paper we report on two different methods to estimate the cellular calcium binding of bovine adrenal chromaffin cells. In the first method, we use voltage-dependent calcium channels as a source to generate calcium gradients in the cytosol. Using imaging techniques, we monitor the dissipation of these gradients to estimate local apparent calcium diffusion coefficients and, from these, local calcium binding ratios. This approach requires a very high signal-to-noise ratio of the calcium measurement and can be used when well-defined calcium gradients can be generated throughout the cell. In the second method, we overcome these problems by using calcium-loaded DM-nitrophen as a light-dependent calcium source to homogeneously and quantitatively release calcium in the cytosol. By measuring [Ca2+] directly before and after the photorelease process and knowing the total amount of calcium being released photolytically, we get an estimate of the fraction of calcium ions which does not appear as free calcium and hence must be bound to either the indicator dye or the endogenous calcium buffer. This finally results in a two-dimensional map of the distribution of the immobile endogenous calcium buffer. We did not observe significant variations of the cellular calcium binding at a spatial resolution of approximately 2 micron. Furthermore, the calcium binding is not reduced by increasing the resting [Ca2+] to levels as high as 1.1 microM. This is indicative of a low calcium affinity of the corresponding buffers and is in agreement with a recent report on the affinity of these buffers (Xu, T., M. Naraghi, H. Kang, and E. Neher. 1997. Biophys. J. 73:532-545). In contrast to the homogeneous distribution of the calcium buffers, the apparant calcium diffusion coefficient did show inhomogeneities, which can be attributed to restricted diffusion at the nuclear envelope and to rim effects at the cell membrane.     

Co-localization of vesicles and P/Q Ca2+-channels explains the preferential distribution of exocytotic active zones in neurites emitted by bovine chromaffin cells.

We have taken advantage of the differences between the preferential localization of secretion in the terminals of neurite-emitting bovine chromaffin cells in contrast with the random distribution secretion in spherical cells to study the possible molecular factors determining such localization by using immunofluorescence and confocal microscopy techniques. By analyzing the distribution of dopamine beta-hydroxylase present in the membrane of chromaffin granules, we found that vesicles migrate and accumulate in dense packages in the terminals of neurite processes. Neither members of the fusion core complex such as SNAP-25, nor nicotinic receptors are preferentially located in the terminals as would be expected from elements defining sites of release, thereby suggesting the presence of additional factors. Interestingly, we observed a preferential distribution of the P/Q subtype of Ca2+ channels in these neurite terminals and co-localization with vesicles present in these structures, in sharp contrast with the overall distribution of the L subtype channels. Using the same immunofluorescence techniques we were unable to detect N-type calcium channels. In addition, omega-agatoxin IVA was able to block 70% of the exocytotic release occurring into the neurites, whereas L-type blockers had a weak effect. Taken together our results strongly indicate that the co-localization of vesicles and clusters of P/Q Ca2+ channels may explain the precise localization of exocytotic sites in the terminals of neurite-emitting chromaffin cells, whereas the distribution of secretory sites in round cells may arise from the random presence of these factors as indicated by their partial co-localization.     

Modeling study of the effects of overlapping Ca2+ microdomains on neurotransmitter release.

Although single-channel Ca2+ microdomains are capable of gating neurotransmitter release in some instances, it is likely that in many cases the microdomains from several open channels overlap to activate vesicle fusion. We describe a mathematical model in which transmitter release is gated by single or overlapping Ca2+ microdomains produced by the opening of nearby Ca2+ channels. This model accounts for the presence of a mobile Ca2+ buffer, provided either that the buffer is unsaturable or that it is saturated near an open channel with Ca2+ binding kinetics that are rapid relative to Ca2+ diffusion. We show that the release time course is unaffected by the location of the channels (at least for distances up to 50 nm), but paired-pulse facilitation is greater when the channels are farther from the release sites. We then develop formulas relating the fractional release following selective or random channel blockage to the cooperative relationship between release and the presynaptic Ca2+ current. These formulas are used with the transmitter release model to study the dependence of this form of cooperativity, which we call Ca2+ current cooperativity, on mobile buffers and on the local geometry of Ca2+ channels. We find that Ca2+ current cooperativity increases with the number of channels per release site, but is considerably less than the number of channels, the theoretical upper bound. In the presence of a saturating mobile buffer the Ca2+ current cooperativity is greater, and it increases more rapidly with the number of channels. Finally, Ca2+ current cooperativity is an increasing function of channel distance, particularly in the presence of saturating mobile buffer.     

The probability of quantal secretion within an array of calcium channels of an active zone

A Monte Carlo analysis has been made of calcium dynamics in submembranous domains of active zones in which the calcium contributed by the opening of many channels is pooled. The kinetics of calcium ions in these domains has been determined using simulations for channels arranged in different geometries, according to the active zone under consideration: rectangular grids for varicosities and boutons and lines for motor-nerve terminals. The effects of endogenous fixed and mobile buffers on the two-dimensional distribution of free calcium ions at these active zones are then given, together with the extent to which these are perturbed and can be detected with different affinity calcium indicators when the calcium channels open stochastically under an action potential. A Monte Carlo analysis of how the dynamics of calcium ions in the submembranous domains determines the probability of exocytosis from docked vesicles is also presented. The spatial distribution of exocytosis from rectangular arrays of secretory units is such that exocytosis is largely excluded from the edges of the array, due to the effects of endogenous buffers. There is a steeper than linear increase in quantal release with an increase in the number of secretory units in the array, indicating that there is not just a local interaction between secretory units. Conditioning action potentials promote an increase in quantal release by a subsequent action potential primarily by depleting the fixed and mobile buffers in the center of the array. In the case of two parallel lines of secretory units exocytosis is random, and diffusion, together with the endogenous calcium buffers, ensures that the secretory units only interact over relatively short distances. As a consequence of this and in contrast to the case of the rectangular array, there is a linear relationship between the extent of quantal secretion from these zones and their length, for lengths greater than a critical value. This Monte Carlo analysis successfully predicts the relationship between the size and geometry of active zones and the probability of quantal secretion at these, the existence of quantal versus multiquantal release at different active zones, and the origins of the F1 phase of facilitation in synapses possessing different active zone geometries.     

The immediately releasable vesicle pool: highly coupled secretion in chromaffin and other neuroendocrine cells

In neuroendocrine cells, such as adrenal chromaffin cells, the exocytosis of hormone-filled vesicles is triggered by a localized Ca(2+) increase that develops after the activation of voltage-dependent Ca(2+) channels. To reach the fusion competent state, vesicles have to go through a series of maturation steps that involve the detachment from cytoskeletal proteins, docking and priming. However, the fusion readiness of vesicles will also depend on their proximity to the calcium source. The immediately releasable pool is a small group of ready-to-fuse vesicles, whose fusion is tightly coupled to Ca(2+) entry through channels. Recent work indicates that such coupling is not produced by a random distribution between vesicles and channels, but would be the result of a specific interaction of immediately releasable vesicles with particular Ca(2+) channel subtypes. The immediately releasable pool is able to sustain, with high efficiency, the secretion triggered by the small and localized Ca(2+) gradients produced by brief depolarizations at low frequencies, like action potentials at basal conditions in adrenal chromaffin cells.     

Stochastic properties of Ca(2+) release of inositol 1,4,5-trisphosphate receptor clusters

Intracellular Ca(2+) release is controlled by inositol 1,4,5-trisphosphate (IP(3)) receptors or ryanodine receptors. These receptors are typically distributed in clusters with several or tens of channels. The random opening and closing of these channels introduces stochasticity into the elementary calcium release mechanism. Stochastic release events have been experimentally observed in a variety of cell types and have been termed sparks and puffs. We put forward a stochastic version of the Li-Rinzel model (the deactivation binding process is described by a Markovian scheme) and a computationally more efficient Langevin approach to model the stochastic Ca(2+) oscillation of single clusters. Statistical properties such as Ca(2+) puff amplitudes, lifetimes, and interpuff intervals are studied with both models and compared with experimental observations. For clusters with tens of channels, a simply decaying amplitude distribution is typically observed at low IP(3) concentration, while a single peak distribution appears at high IP(3) concentration.     

A model-independent algorithm to derive Ca2+ fluxes underlying local cytosolic Ca2+ transients

Local intracellular Ca(2+) signals result from Ca(2+) flux into the cytosol through individual channels or clusters of channels. To gain a mechanistic understanding of these events we need to know the magnitude and spatial distribution of the underlying Ca(2+) flux. However, this is difficult to infer from fluorescence Ca(2+) images because the distribution of Ca(2+)-bound dye is affected by poorly characterized processes including diffusion of Ca(2+) ions, their binding to mobile and immobile buffers, and sequestration by Ca(2+) pumps. Several methods have previously been proposed to derive Ca(2+) flux from fluorescence images, but all require explicit knowledge or assumptions regarding these processes. We now present a novel algorithm that requires few assumptions and is largely model-independent. By testing the algorithm with both numerically generated image data and experimental images of sparklets resulting from Ca(2+) flux through individual voltage-gated channels, we show that it satisfactorily reconstructs the magnitude and time course of the underlying Ca(2+) currents.     

Synaptic vesicle recruitment for release explored by Monte Carlo stimulation at the crayfish neuromuscular junction

Neurotransmission at chemically transmitting synapses requires calcium-mediated fusion of synaptic vesicles with the presynaptic membrane. Utilizing ultrastructural information available for the crustacean excitatory neuromuscular junction, we developed a model that employs the Monte Carlo simulation technique to follow the entry and movement of Ca2+ ions at a presynaptic active zone, where synaptic vesicles are preferentially docked for release. The model includes interaction of Ca2+ with an intracellular buffer, and variable separation between calcium channels and vesicle-associated Ca(2+)-binding targets that react with Ca2+ to trigger vesicle fusion. The end point for vesicle recruitment for release was binding of four Ca2+ ions to the target controlling release. The results of the modeling experiments showed that intracellular structures that interfere with Ca2+ diffusion (in particular synaptic vesicles) influence recruitment or priming of vesicles for release. Vesicular recruitment is strongly influenced by the separation distance between an opened calcium channel and the target controlling release, and by the concentration and binding properties of the intracellular buffers, as in previous models. When a single opened calcium channel is very close to the target, a single synaptic vesicle can be recruited. However, many of the single-channel openings actuated by a nerve impulse are likely to be ineffective for release, although they contribute to the buildup of total intracellular Ca2+. Thus, the overall effectiveness of single calcium channels in causing vesicles to undergo exocytosis is likely quite low.     

Local positive feedback by calcium in the propagation of intracellular calcium waves.

In many types of eukaryotic cells, the activation of surface receptors leads to the production of inositol 1,4,5-trisphosphate and calcium release from intracellular stores. Calcium release can occur in complex spatial patterns, including waves of release that traverse the cytoplasm. Fluorescence video microscopy was used to view calcium waves in single mouse neuroblastoma cells. The propagation of calcium waves was slowed by buffers that bind calcium quickly, such as BAPTA, but not by a buffer with slower on-rate, EGTA. This shows that a key feedback event in wave propagation is rapid diffusion of calcium occurring locally on a scale of < 1 micron. The length-speed product of wavefronts was used to determine that calcium acting in feedback diffuses at nearly the rate expected for free diffusion in aqueous solution. In cytoplasm, which contains immobile Ca2+ buffers, this rate of diffusion occurs only in the first 0.2 ms after release, within 0.4 micron of a Ca2+ release channel mouth. Calcium diffusion from an open channel to neighboring release sites is, therefore, a rate-determining regenerative step in calcium wave propagation. The theoretical limitations of the wave front analysis are discussed.     

Slow Ca2'-binding Mg2+- EDTA buffer for intracellular perfusion

In studies of currents in perfused cells or their membrane fragments containing potential-dependent Ca channels and Ca2+-activated channels, a buffer slowly binding Ca2+ appears useful in some cases. A buffer with EDTA in excess of Mg2+ has been proposed, and its kinetic characteristics have been calculated. It has been shown that this buffer, depending on its component proportions, may provide Ca2+ binding with a characteristic time of up to tens of milliseconds. For comparison, in the cytoplasm, this time does not exceed 1 ms even with a large calcium signal, as follows from calculations.     

Development and dissipation of Ca(2+) gradients in adrenal chromaffin cells

We used pulsed laser imaging to measure the development and dissipation of Ca(2+) gradients evoked by the activation of voltage-sensitive Ca(2+) channels in adrenal chromaffin cells. Ca(2+) gradients appeared rapidly (<5 ms) upon membrane depolarization and dissipated over several hundred milliseconds after membrane repolarization. Dissipation occurred with an initial fast phase, as the steep gradient near the membrane collapsed, and a slower phase as the remaining shallow gradient dispersed. Inhibition of active Ca(2+) uptake by the endoplasmic reticulum (thapsigargin) and mitochondria (carbonylcyanide p-trifluoro-methoxyphenylhydrazone/oligomycin) had no effect on the size of Ca(2+) changes or the rate of gradient dissipation, suggesting that passive endogenous Ca(2+) buffers are responsible for the slow Ca(2+) redistribution. We used a radial diffusion model incorporating Ca(2+) diffusion and binding to intracellular Ca(2+) buffers to simulate Ca(2+) gradients. We included a 3D optical sectioning model, simulating the effects of out-of-focus light, to allow comparison with the measured gradients. Introduction of a high-capacity immobile Ca(2+) buffer, with a buffer capacity on the order of 1000 and appropriate affinity and kinetics, approximated the size of the Ca(2+) increases and rate of dissipation of the measured gradients. Finally, simulations without exogenous buffer suggest that the Ca(2+) signal due to Ca(2+) channel activation is restricted by the endogenous buffer to a space less than 1 microm from the cell membrane.     

Diffusion barriers limit the effect of mobile calcium buffers on exocytosis of large dense cored vesicles

Fast exocytosis in melanotropic cells, activated by calcium entry through voltage-gated calcium channels, is very sensitive to mobile calcium buffers (complete block at 800 microM ethylene glycol bis(beta-aminoethyl ether)-N,N,N'N'-tetraacetic acid (EGTA)). This indicates that calcium diffuses a substantial distance from the channel to the vesicle. Surprisingly, 1, 2-bis(2-aminophenoxy)ethane-N,N,N',N'-tetraacetic acid (BAPTA), having a similar KD for calcium as EGTA but a approximately 100 times faster binding rate, blocked exocytosis only twice as effectively as EGTA. Using computer simulations, we demonstrate that this result cannot be explained by free diffusion and buffer binding rates. We hypothesized that local saturation of calcium buffers is involved. A diffusion barrier for both calcium and buffer molecules, located 50-300 nm from the membrane and reducing diffusion 1000 to 10,000 times, generated similar calcium concentrations for specific concentrations of EGTA and BAPTA. With such barriers, calcium rise phase kinetics upon short step depolarizations (2-20 ms) were faster for EGTA than for BAPTA, implying that short depolarizations should allow exocytosis with 50 microM EGTA but not with 25 microM BAPTA. This prediction was confirmed experimentally with capacitance measurements. Coupling exocytosis to calcium dynamics in the model, we found that a barrier with a approximately 3000 times reduced diffusion at approximately 130 nm beneath the membrane best explains the experimentally observed effects of EGTA and BAPTA on block and kinetics of release.     

Cytosolic organelles shape calcium signals and exo-endocytotic responses of chromaffin cells

The concept of stimulus-secretion coupling was born from experiments performed in chromaffin cells 50 years ago. Stimulation of these cells with acetylcholine enhances calcium (Ca(2+)) entry and this generates a transient elevation of the cytosolic Ca(2+) concentration ([Ca(2+)](c)) that triggers the exocytotic release of catecholamines. The control of the [Ca(2+)](c) signal is complex and depends on various classes of plasmalemmal calcium channels, cytosolic calcium buffers, the uptake and release of Ca(2+) from cytoplasmic organelles, such as the endoplasmic reticulum, mitochondria, chromaffin vesicles and the nucleus, and Ca(2+) extrusion mechanisms, such as the plasma membrane Ca(2+)-stimulated ATPase, and the Na(+)/Ca(2+) exchanger. Computation of the rates of Ca(2+) fluxes between the different cell compartments support the proposal that the chromaffin cell has developed functional calcium tetrads formed by calcium channels, cytosolic calcium buffers, the endoplasmic reticulum, and mitochondria nearby the exocytotic plasmalemmal sites. These tetrads shape the Ca(2+) transients occurring during cell activation to regulate early and late steps of exocytosis, and the ensuing endocytotic responses. The different patterns of catecholamine secretion in response to stress may thus depend on such local [Ca(2+)](c) transients occurring at different cell compartments, and generated by redistribution and release of Ca(2+) by cytoplasmic organelles. In this manner, the calcium tetrads serve to couple the variable energy demands due to exo-endocytotic activities with energy production and protein synthesis.     

The role of fixed and mobile buffers in the kinetics of proton movement

We derive a simple expression for the effective diffusion coefficient of protons in Fick's second law, Deff, when both spatially fixed, HF, and mobile, HM, buffers are present. These buffers are present at moderately high concentrations ([Ftot], [Mtot] greater than 1 mM) in most biological systems. We consider only the case where the protonation reactions remain at equilibrium during the diffusion process. When the pH is to the alkaline side of the pK values of the fixed and mobile buffers ([H+] less than KF, KM), the effective diffusion coefficient of protons in Ficks second law is: (Formula: see text) where DH is the diffusion coefficient of the protons free in the aqueous phase and DHM is the diffusion coefficient of the mobile buffer. The equation illustrates three features of diffusion in a buffered system. Firstly, the effective diffusion coefficient of protons is always lower than the diffusion coefficient of free protons. Secondly, increasing the concentration of fixed buffers always decreases Deff. Thirdly, increasing the concentration of mobile buffer can increase Deff when fixed buffers are present.     

Effects of Lead Ions on Events Associated with Exocytosis in Isolated Bovine Adrenal Medullary Cells

Lead buffers (citrate and Tiron) were used to investigate the effects of low concentrations (0.1-6 microM) of Pb2+ on stimulus-secretion coupling in isolated bovine chromaffin cells. Nicotinic agonists and high K elicit secretion by enhancing Ca2+ influx into chromaffin cells. Pb2+ inhibited the catecholamine secretion in response to 500 microM carbachol and 77 mM K+ depolarization but was without significant effect on basal secretion. Pb2+ also inhibited the influx of 45Ca occurring in response to these agents. The K0.5 values for inhibition suggest that the carbachol-evoked flux is more sensitive to Pb2+ than influx in response to a direct depolarization. When extracellular calcium was lowered in the absence of Pb2+, both secretion and 45Ca entry were reduced. The effects of Pb2+ were comparable to those of lowered Ca2+. 22Na influx through nicotinic receptor-mediated channels, measured in the presence of tetrodotoxin (2 microM) and ouabain (50 microM), was inhibited by Pb2+. The results suggest that Pb2+ inhibits exocytotic catecholamine secretion by inhibiting Ca2+ influx. The differential sensitivity to Pb2+ of K- and carbachol-evoked 45Ca flux, coupled with the 22Na measurements, indicates that Pb2+ inhibits the movement of ions through acetylcholine-induced channels as well as through voltage-sensitive calcium channels.