Analytical steady-state solution to the rapid buffering approximation near an open Ca2+ channel.

We derive an analytical steady-state solution for the Ca2+ profile near an open Ca2+ channel based on a transport equation which describes the buffered diffusion of Ca2+ in the presence of rapid stationary and mobile Ca2+ buffers (Wagner and Keizer, 1994). This steady-state rapid buffering approximation gives an upper bound on local Ca2+ elevations such as Ca2+ puffs or sparks when conditions for the validity of the rapid buffering approximation are met and is an alternative to approximations that assume that mobile buffers are unsaturable. This result also provides an analytical estimate of the cytosolic Ca2+ domain concentration ([Ca2+]d) near a channel pore and shows the dependence of [Ca2+]d on moderate concentrations of endogenous mobile buffer, Ca2+ indicator dye, and bulk cytosolic Ca2+. Assuming a simple relationship between [Ca2+]d and the lumenal depletion domain of an intracellular Ca2+ channel, lumenal and cytosolic Ca2+ profiles are matched to give an implicit analytical expression for the effect of bulk lumenal Ca2+ on [Ca2+]d.     

On the roles of Ca2+ diffusion, Ca2+ buffers, and the endoplasmic reticulum in IP3-induced Ca2+ waves.

We have investigated the effects of Ca2+ diffusion, mobile and stationary Ca2+ buffers in the cytosol, and Ca2+ handling by the endoplasmic reticulum on inositol 1,4,5-trisphosphate-induced Ca2+ wave propagation. Rapid equilibration of free and bound Ca2+ is used to describe Ca2+ sequestration by buffers in both the cytosol and endoplasmic reticulum (ER) lumen. Cytosolic Ca2+ regulation is based on a kinetic model of the inositol 1,4,5-trisphosphate (IP3) receptor of De Young and Keizer that includes activation and inhibition of the IP3 receptor Ca2+ channel in the ER membrane and SERCA Ca2+ pumps in the ER. Diffusion of Ca2+ in the cytosol and the ER and the breakdown and diffusion of IP3 are also included in our calculations. Although Ca2+ diffusion is severely limited because of buffering, when conditions are chosen just below the threshold for Ca2+ oscillations, a pulse of IP3 or Ca2+ results in a solitary trigger wave that requires diffusion of Ca2+ for its propagation. In the oscillatory regime repetitive wave trains are observed, but for this type of wave neither the wave shape nor the speed is strongly dependent on the diffusion of Ca2+. Local phase differences lead to waves that are predominately kinematic in nature, so that the wave speed (c) is related to the wavelength (lambda) and the period of the oscillations (tau) approximately by the formula c = lambda/tau. The period is determined by features that control the oscillations, including [IP3] and pump activity, which are related to recent experiments. Both solitary waves and wave trains are accompanied by a Ca2+ depletion wave in the ER lumen, similar to that observed in cortical preparations from sea urchin eggs. We explore the effect of endogenous and exogenous Ca2+ buffers on wave speed and wave shape, which can be explained in terms of three distinct effects of buffering, and show that exogenous buffers or Ca2+ dyes can have considerable influence on the amplitude and width of the waves.     

Different patterns of receptor-activated cytoplasmic Ca2+ oscillations in single pancreatic acinar cells: dependence on receptor type, agonist concentration and intracellular Ca2+ buffering.

Agonist-specific cytosolic Ca2+ oscillation patterns can be observed in individual cells and these have been explained by the co-existence of separate oscillatory mechanisms. In pancreatic acinar cells activation of muscarinic receptors typically evokes sinusoidal oscillations whereas stimulation of cholecystokinin (CCK) receptors evokes transient oscillations consisting of Ca2+ waves with long intervals between them. We have monitored changes in the cytosolic Ca2+ concentration ([Ca2+]i) by measuring Ca2(+)-activated Cl- currents in single internally perfused mouse pancreatic acinar cells. With minimal intracellular Ca2+ buffering we found that low concentrations of both ACh (50 nM) and CCK (10 pM) evoked repetitive short-lasting Ca2+ spikes of the same duration and frequency, but the probability of a spike being followed by a longer and larger Ca2+ wave was low for ACh and high for CCK. The probability that the receptor-evoked shortlasting Ca2+ spikes would initiate more substantial Ca2+ waves was dramatically increased by intracellular perfusion with solutions containing high concentrations of the mobile low affinity Ca2+ buffers citrate (10-40 mM) or ATP (10-20 mM). The different Ca2+ oscillation patterns normally induced by ACh and CCK would therefore appear not to be caused by separate mechanisms. We propose that specific receptor-controlled modulation of Ca2+ signal spreading, either by regulation of Ca2+ uptake into organelles and/or cellular Ca2+ extrusion, or by changing the sensitivity of the Ca2(+)-induced Ca2+ release mechanism, can be mimicked experimentally by different degrees of cytosolic Ca2+ buffering and can account for the various cytosolic Ca2+ spike patterns.     

Endogenous and exogenous Ca2+ buffers differentially modulate Ca2+-dependent inactivation of Ca(v)2.1 Ca2+ channels

Voltage-gated Ca2+ channels undergo a negative feedback regulation by Ca2+ ions, Ca2+-dependent inactivation, which is important for restricting Ca2+ signals in nerve and muscle. Although the molecular details underlying Ca2+-dependent inactivation have been characterized, little is known about how this process might be modulated in excitable cells. Based on previous findings that Ca2+-dependent inactivation of Ca(v)2.1 (P/Q-type) Ca2+ channels is suppressed by strong cytoplasmic Ca2+ buffering, we investigated how factors that regulate cellular Ca2+ levels affect inactivation of Ca(v)2.1 Ca2+ currents in transfected 293T cells. We found that inactivation of Ca(v)2.1 Ca2+ currents increased exponentially with current amplitude with low intracellular concentrations of the slow buffer EGTA (0.5 mm), but not with high concentrations of the fast Ca2+ buffer BAPTA (10 mm). However, when the concentration of BAPTA was reduced to 0.5 mm, inactivation of Ca2+ currents was significantly greater than with an equivalent concentration of EGTA, indicating the importance of buffer kinetics in modulating Ca2+-dependent inactivation of Ca(v)2.1. Cotransfection of Ca(v)2.1 with the EF-hand Ca2+-binding proteins, parvalbumin and calbindin, significantly altered the relationship between Ca2+ current amplitude and inactivation in ways that were unexpected from behavior as passive Ca2+ buffers. We conclude that Ca2+-dependent inactivation of Ca(v)2.1 depends on a subplasmalemmal Ca2+ microdomain that is affected by the amplitude of the Ca2+ current and differentially modulated by distinct Ca2+ buffers.     

Presynaptic Ca2+ dynamics, Ca2+ buffers and synaptic efficacy

In synapses neurotransmitter release is triggered by elevation of Ca2+ concentration at a Ca2+ sensor of the release machinery. The Ca2+ concentration at the release site at the given time point is determined by Ca2+ dynamics within presynaptic terminal. It depends on a source of Ca2+ (usually voltage-gated Ca2+ channels), diffusional distance between the source of Ca2+ and the Ca2+ sensor and Ca2+ buffering by endogenous Ca2+ buffers. In many synapses transmitter release can be enhanced (facilitated) during repetitive activity of neurons. The main source of facilitation is activity-dependent increase of Ca2+ concentration at the release site. Several mechanisms of facilitation have been proposed, namely, accumulation of residual Ca2+, multi-site (X receptor) mechanism and partial Ca2+ buffer saturation mechanism. In this review we discuss theoretical and experimental evidence in favor of one or the other of proposed mechanisms.     

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.     

The spatial relationship between Ca2+ channels and Ca2+-activated channels and the function of Ca2+-buffering in avian sensory neurons

In order to learn about the endogenous Ca2+-buffering in the cytoplasm of chick dorsal root ganglion (DRG) neurons and the distance separating the ryanodine receptor Ca2+ release channels (RyRs) from the plasma membrane, we monitored the amplitude and time course of Ca2+-activated Cl- currents (I(ClCa)) in protocols that manipulated Ca2+-buffering. I(ClCa)was activated by Ca2+ influx via voltage-gated Ca2+ channels or by Ca2+ release via RyRs activated by 10 mM caffeine. I(ClCa)was measured in neurons at 20 degrees C and 35 degrees C using the amphotericin perforated patch technique that preserves endogenous Ca2+-buffering, or at 20 degrees C in neurons dialyzed with pipette solutions designed to replace the endogenous Ca2+ buffers. The amplitude of I(ClCa)activated by Ca2+ influx or Ca2+ at 20 degrees C was similar in the amphotericin neurons and neurons dialyzed with an 'unbuffered' pipette solution containing 10 mM citrate and 3 mM ATP as the only Ca2+ binding molecules. Thus, endogenous mobile Ca2+ buffers are relatively unimportant in chick DRG neurons. Warming the neurons from 20 degrees C to 35 degrees C increased the amplitude and the rate of deactivation of I(ClCa)consistent with an increased rate of Ca2+ buffering by fixed endogenous Ca2+-buffers. Dialysis with 2 mM EGTA/0.1 microM free Ca2+ reduced the amplitude and increased the rate of deactivation of I(ClCa)activated by Ca2+ influx and abolished I(ClCa)activated by Ca2+ release. Dialysis with 2 mM BAPTA/0.1 microM free Ca2+ abolished I(ClCa)activated by Ca2+ influx or release. Dialysis with 42 mM HEEDTA/0.5 microM free Ca2+ caused the persistent activation of I(ClCa). Calculations using a Ca2+-diffusion model suggest that the voltage-gated Ca2+ channels and the Ca2+-activated Cl- channels are separated by 50-400 nm and that the RyRs are more than 600 nm from the plasma membrane.     

Endoplasmic reticulum Ca2+ store: regulation of Ca2+ release and reuptake by intracellular and extracellular Ca2+ in pancreatic acinar cells

We investigated the effect of cytosolic and extracellular Ca2+ on Ca2+ signals in pancreatic acinar cells by measuring Ca2+ concentration in the cytosol([Ca2+]c) and in the lumen of the ER([Ca2+]Lu). To control buffers and dye in the cytosol, a patch-clamp microelectrode was employed. Acetylcholine released Ca2+ mainly from the basolateral ER-rich part of the cell. The rate of Ca2+ release from the ER was highly sensitive to the buffering of [Ca2+]c whereas ER Ca2+ refilling was enhanced by supplying free Ca2+ to the cytosol with [Ca2+]c clamped at resting levels with a patch pipette containing 10 mM BAPTA and 2 mM Ca2+. Elevation of extracellular Ca2+ to 10 mM from 1 mM raised resting [Ca2+]c slightly and often generated [Ca2+]c oscillations in single or clustered cells. Although pancreatic acinar cells are reported to have extracellular Ca2+-sensing receptors linked to phospholipase C that mobilize Ca2+ from the ER, exposure of cells to 10 mM Ca2+ did not decrease [Ca2+]Lu but rather raised it. From these findings we conclude that 1) ER Ca2+ release is strictly regulated by feedback inhibition of [Ca2+]c, 2) ER Ca2+ refilling is determined by the rate of Ca2+ influx and occurs mainly in the tiny subplasmalemmal spaces, 3) extracellular Ca2+-induced [Ca2+]c oscillations appear to be triggered not by activation of extracellular Ca2+-sensing receptors but by the ER sensitised by elevated [Ca2+]c and [Ca2+]Lu.     

Spatiotemporal features of Ca2+ buffering and diffusion in atrial cardiac myocytes with inhibited sarcoplasmic reticulum

Ca(2+) signaling in cells is largely governed by Ca(2+) diffusion and Ca(2+) binding to mobile and stationary Ca(2+) buffers, including organelles. To examine Ca(2+) signaling in cardiac atrial myocytes, a mathematical model of Ca(2+) diffusion was developed which represents several subcellular compartments, including a subsarcolemmal space with restricted diffusion, a myofilament space, and the cytosol. The model was used to quantitatively simulate experimental Ca(2+) signals in terms of amplitude, time course, and spatial features. For experimental reference data, L-type Ca(2+) currents were recorded from atrial cells with the whole-cell voltage-clamp technique. Ca(2+) signals were simultaneously imaged with the fluorescent Ca(2+) indicator Fluo-3 and a laser-scanning confocal microscope. The simulations indicate that in atrial myocytes lacking T-tubules, Ca(2+) movement from the cell membrane to the center of the cells relies strongly on the presence of mobile Ca(2+) buffers, particularly when the sarcoplasmic reticulum is inhibited pharmacologically. Furthermore, during the influx of Ca(2+) large and steep concentration gradients are predicted between the cytosol and the submicroscopically narrow subsarcolemmal space. In addition, the computations revealed that, despite its low Ca(2+) affinity, ATP acts as a significant buffer and carrier for Ca(2+), even at the modest elevations of [Ca(2+)](i) reached during influx of Ca(2+).     

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.     

Ca2+-calmodulin-dependent facilitation and Ca2+ inactivation of Ca2+ release-activated Ca2+ channels

In non-excitable cells, one major route for Ca2+ influx is through store-operated Ca2+ channels in the plasma membrane. These channels are activated by the emptying of intracellular Ca2+ stores, and in some cell types store-operated influx occurs through Ca2+ release-activated Ca2+ (CRAC) channels. Here, we report that intracellular Ca2+ modulates CRAC channel activity through both positive and negative feedback steps in RBL-1 cells. Under conditions in which cytoplasmic Ca2+ concentration can fluctuate freely, we find that store-operated Ca2+ entry is impaired either following overexpression of a dominant negative calmodulin mutant or following whole-cell dialysis with a calmodulin inhibitory peptide. The peptide had no inhibitory effect when intracellular Ca2+ was buffered strongly at low levels. Hence, Ca2+-calmodulin is not required for the activation of CRAC channels per se but is an important regulator under physiological conditions. We also find that the plasma membrane Ca2+ATPase is the dominant Ca2+ efflux pathway in these cells. Although the activity of the Ca2+ pump is regulated by calmodulin, the store-operated Ca2+ entry is more sensitive to inhibition by the calmodulin mutant than by Ca2+ extrusion. Hence, these two plasmalemmal Ca2+ transport systems may differ in their sensitivities to endogenous calmodulin. Following the activation of Ca2+ entry, the rise in intracellular Ca2+ subsequently feeds back to further inhibit Ca2+ influx. This slow inactivation can be activated by a relatively brief Ca2+ influx (30-60 s); it reverses slowly and is not altered by overexpression of the calmodulin mutant. Hence, the same messenger, intracellular Ca2+, can both facilitate and inactivate Ca2+ entry through store-operated CRAC channels and through different mechanisms.     

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.     

Supralinear Ca2+ signaling by cooperative and mobile Ca2+ buffering in Purkinje neurons

Endogenous high-affinity Ca2+ buffering and its roles were investigated in mouse cerebellar Purkinje cells with the use of a low-affinity Ca2+ indicator and a high-affinity caged Ca2+ compound. Increases in the cytosolic Ca2+ concentration ([Ca2+]i) were markedly facilitated during repetitive depolarization, resulting in the generation of steep micromolar Ca2+ gradients along dendrites. Such supralinear Ca2+ responses were attributed to the saturation of a large concentration (0.36 mM) of a mobile, high-affinity (dissociation constant, 0.37 microM) Ca2+ buffer with cooperative Ca2+ binding sites, resembling calbindin-D28K, and to an immobile, low-affinity Ca2+ buffer. These data suggest that the high-affinity Ca2+ buffer operates as the neuronal computational element that enables efficient coincidence detection of the Ca2+ signal and that facilitates spatiotemporal integration of the Ca2+ signal at submicromolar [Ca2+]i.     

Validity of the rapid buffering approximation near a point source of calcium ions.

In the presence of rapid buffers the full reaction-diffusion equations describing Ca2+ transport can be reduced using the rapid buffering approximation to a single transport equation for [Ca2+]. Here we simulate the full and reduced equations, exploring the conditions necessary for the validity of the rapid buffering approximation for an isolated Ca2+ channel or a cluster of channels. Using a point source and performing numerical simulations of different durations, we quantify the error of the rapid buffering approximation as a function of buffer and source parameters as well as the time and spatial scale set by the resolution of confocal microscopic measurements. We carry out simulations of Ca2+ "sparks" and "puffs," both with and without the indicator dye Ca2+ Green-1, and find that the rapid buffering approximation is excellent. These calculations also show that the traditional calculation of [Ca2+] from a fluorescence signal may grossly underestimate the true value of [Ca2+] near a source. Finally, we use the full model to simulate the transient Ca2+ domain near the pore of an open Ca2+ channel in a cell dialyzed with millimolar concentrations of 1,2-bis(2-aminophenoxy)ethane-N,N,N,N-tetraacetic acid or EGTA. In this regime, where the rapid buffering approximation is poor. Neher's equation for the steady-state Ca2+ profile is shown to be a reliable approximation adjacent to the pore.     

Calbindin-D28K dynamically controls TRPV5-mediated Ca2+ transport

In Ca(2+)-transporting epithelia, calbindin-D(28K) (CaBP(28K)) facilitates Ca(2+) diffusion from the luminal Ca(2+) entry side of the cell to the basolateral side, where Ca(2+) is extruded into the extracellular compartment. Simultaneously, CaBP(28K) provides protection against toxic high Ca(2+) levels by buffering the cytosolic Ca(2+) concentration ([Ca(2+)](i)) during high Ca(2+) influx. CaBP(28K) consistently colocalizes with the epithelial Ca(2+) channel TRPV5, which constitutes the apical entry step in renal Ca(2+)-transporting epithelial cells. Here, we demonstrate using protein-binding analysis, subcellular fractionation and evanescent-field microscopy that CaBP(28K) translocates towards the plasma membrane and directly associates with TRPV5 at a low [Ca(2+)](i). (45)Ca(2+) uptake measurements, electrophysiological recordings and transcellular Ca(2+) transport assays of lentivirus-infected primary rabbit connecting tubule/distal convolute tubule cells revealed that associated CaBP(28K) tightly buffers the flux of Ca(2+) entering the cell via TRPV5, facilitating high Ca(2+) transport rates by preventing channel inactivation. In summary, CaBP(28K) acts in Ca(2+)-transporting epithelia as a dynamic Ca(2+) buffer, regulating [Ca(2+)] in close vicinity to the TRPV5 pore by direct association with the channel.     

Ca2+ transients in cardiac myocytes measured with high and low affinity Ca2+ indicators.

Intracellular calcium ion ([Ca2+]i) transients were measured in voltage-clamped rat cardiac myocytes with fura-2 or furaptra to quantitate rapid changes in [Ca2+]i. Patch electrode solutions contained the K+ salt of fura-2 (50 microM) or furaptra (300 microM). With identical experimental conditions, peak amplitude of stimulated [Ca2+]i transients in furaptra-loaded myocytes was 4- to 6-fold greater than that in fura-2-loaded cells. To determine the reason for this discrepancy, intracellular fura-2 Ca2+ buffering, kinetics of Ca2+ binding, and optical properties were examined. Decreasing cellular fura-2 concentration by lowering electrode fura-2 concentration 5-fold, decreased the difference between the amplitudes of [Ca2+]i transients in fura-2 and furaptra-loaded myocytes by twofold. Thus, fura-2 buffers [Ca2+]i under these conditions; however, Ca2+ buffering is not the only factor that explains the different amplitudes of the [Ca2+]i transients measured with these indicators. From the temporal comparison of the [Ca2+]i transients measured with fura-2 and furaptra, the apparent reverse rate constant for Ca2+ binding of fura-2 was at least 65s-1, much faster than previously reported in skeletal muscle fibers. These binding kinetics do not explain the difference in the size of the [Ca2+]i transients reported by fura-2 and furaptra. Parameters for fura-2 calibration, Rmin, Rmax, and beta, were obtained in salt solutions (in vitro) and in myocytes exposed to the Ca2+ ionophore, 4-Br A23187, in EGTA-buffered solutions (in situ). Calibration of fura-2 fluorescence signals with these in situ parameters yielded [Ca2+]i transients whose peak amplitude was 50-100% larger than those calculated with in vitro parameters. Thus, in vitro calibration of fura-2 fluorescence significantly underestimates the amplitude of the [Ca2+]i transient. These data suggest that the difference in amplitude of [Ca2+]i transients in fura-2 and furaptra-loaded myocytes is due, in part, to Ca2+ buffering by fura-2 and use of in vitro calibration parameters.     

Extension of Rapid Buffering Approximation to Ca2+ Buffers with Two Binding Sites

Fundamental cell processes such as synaptic neurotransmitter release, endocrine hormone secretion, and myocyte contraction are controlled by highly localized calcium (Ca²⁺) signals resulting from brief openings of trans-membrane Ca²⁺ channels. On short temporal and spatial scales, the corresponding local Ca²⁺ nanodomains formed in the vicinity of a single or several open Ca²⁺ channels can be effectively approximated by quasi-stationary solutions. The rapid buffering approximation (RBA) is one of the most powerful of such approximations, and is based on the assumption of instantaneous equilibration of the bimolecular Ca²⁺ buffering reaction, combined with the conservation condition for the total Ca²⁺ and buffer molecule numbers. Previously, RBA has been generalized to an arbitrary arrangement of Ca²⁺ channels on a flat membrane, in the presence of any number of simple Ca²⁺ buffers with one-to-one Ca²⁺ binding stoichiometry. However, many biological buffers have multiple binding sites. For example, buffers and sensors phylogenetically related to calmodulin consist of two Ca²⁺-binding domains (lobes), with each domain binding two Ca²⁺ ions in a cooperative manner. Here we consider an extension of RBA to such buffers with two interdependent Ca²⁺ binding sites. We show that in the presence of such buffers, RBA solution is given by the solution to a cubic equation, analogous to the quadratic equation describing RBA in the case of a simple, one-to-one Ca²⁺ buffer. We examine in detail the dependence of RBA accuracy on buffering parameters, to reveal conditions under which RBA provides sufficient precision.     

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.     

Characterization of (Ca2+ + Mg2+)-ATPase of sarcoplasmic reticulum by laser-excited europium luminescence

The molecular environment of Ca2+ translocating sites of skeletal muscle sarcoplasmic reticulum (SR) (Ca2+ + Mg2+)-ATPase has been studied by pulsed-laser excited luminescence of Eu3+ used as a Ca2+ analogue. Interaction of Eu3+ with SR was characterized by investigating its effect on partial reactions of the Ca2+ transport cycle. In native SR vesicles, Eu3+ was found to inhibit Ca2+ binding, phosphoenzyme formation, ATP hydrolysis activity and Ca2+ uptake in parallel fashion. The non-specific binding of Eu3+ to acidic phospholipids associated with the enzyme was prevented by purifying (Ca2+ + Mg2+)-ATPase and exchanging the endogenous lipids with a neutral phospholipid, dioleoylglycerophosphocholine. The results demonstrate that the observed inhibition of Ca2+ transport by Eu3+ is due to its binding to Ca2+ translocating sites. The 7F0----5D0 transition of Eu3+ bound to these sites was monitored. The non-Lorentzian nature of the excitation profile and a double-exponential fluorescence decay revealed the heterogeneity of the two sites. Measurement of fluorescence decay rates in H2O/D2O mixture buffers further distinguished the sites. The number of water molecules in the first co-ordination sphere of Eu3+ bound at transport sites were found to be 4 and 1.5. Addition of ATP reduced these numbers to zero and 0.6. These data show that the calcium ions in translocating sites are well enclosed by protein ligands and are further occluded down to zero or one water molecule of solvation during the transport process.