An Excel-based model of Ca2+ diffusion and fura 2 measurements in a spherical cell

We wrote a program that runs as a Microsoft Excel spreadsheet to calculate the diffusion of Ca²⁺ in a spherical cell in the presence of a fixed Ca²⁺ buffer and two diffusible Ca²⁺ buffers, one of which is considered to be a fluorescent Ca²⁺ indicator. We modeled Ca²⁺ diffusion during and after Ca²⁺ influx across the plasma membrane with parameters chosen to approximate amphibian sympathetic neurons, mammalian adrenal chromaffin cells, and rat dorsal root ganglion neurons. In each of these cell types, the model predicts that spatially averaged intracellular Ca²⁺ activity ([Ca²⁺]_avg) rises to a high peak and starts to decline promptly on the termination of Ca²⁺ influx. We compared [Ca²⁺]_avg with predictions of ratiometric Ca²⁺ measurements analyzed in two ways. Method 1 sums the fluorescence at each of the two excitation or emission wavelengths over the N compartments of the model, calculates the ratio of the summed signals, and converts this ratio to Ca²⁺ ([Ca²⁺]_avg,M1). Method 2 sums the measured number of moles of Ca²⁺ in each of the N compartments and divides by the volume of the cell ([Ca²⁺]_avg,M2). [Ca²⁺]_avg,M1 peaks well after the termination of Ca²⁺ influx at a value substantially less than [Ca²⁺]_avg because the summed signals do not reflect the averaged free Ca²⁺ if the signals come from compartments containing gradients in free Ca²⁺ spanning nonlinear regions of the relationship between free Ca²⁺ and the fluorescence signals. In contrast, [Ca²⁺]_avg,M2 follows [Ca²⁺]_avg closely. intracellular calcium; kinetic model; diffusion coefficient; fura 2ff; furaptra     

Nonuniformity of calcium efflux from pancreatic acinar cells and its analysis by mathematical model of calcium diffusion and buffering in extracellular solution

We studied spatial and temporal patterns of Ca²⁺ extrusion from pancreatic acinar cells evoked by acetylcholine(ACh)-induced activation of plasma membrane calcium pumps. Using a modification of an earlier developed model, we estimated the time course of extracellular calcium concentration changes near the basal pole of a cell in the case, when calcium ions are released from the same site on the cell surface, and in the case when they are extruded from the apical pole and diffuse to the basal one. It is concluded that at the first stage of ACh-induced Ca²⁺ extrusion the appearance of Ca²⁺ elevation near the basal pole of the cells cannot be explained as a result of diffusion, but is mainly determined by Ca²⁺ efflux from this pole. The results also show that there are plasma membrane calcium pumps in both apical and basal parts of pancreatic acinar cells, but the activity of the pumps is substantially higher in the apical region.     

Dynamic buffering of mitochondrial Ca2+ during Ca2+ uptake and Na+-induced Ca2+ release

In cardiac mitochondria, matrix free Ca²⁺ ([Ca²⁺]_m) is primarily regulated by Ca²⁺ uptake and release via the Ca²⁺ uniporter (CU) and Na⁺/Ca²⁺ exchanger (NCE) as well as by Ca²⁺ buffering. Although experimental and computational studies on the CU and NCE dynamics exist, it is not well understood how matrix Ca²⁺ buffering affects these dynamics under various Ca²⁺ uptake and release conditions, and whether this influences the stoichiometry of the NCE. To elucidate the role of matrix Ca²⁺ buffering on the uptake and release of Ca²⁺, we monitored Ca²⁺ dynamics in isolated mitochondria by measuring both the extra-matrix free [Ca²⁺] ([Ca²⁺]_e) and [Ca²⁺]_m. A detailed protocol was developed and freshly isolated mitochondria from guinea pig hearts were exposed to five different [CaCl₂] followed by ruthenium red and six different [NaCl]. By using the fluorescent probe indo-1, [Ca²⁺]_e and [Ca²⁺]_m were spectrofluorometrically quantified, and the stoichiometry of the NCE was determined. In addition, we measured NADH, membrane potential, matrix volume and matrix pH to monitor Ca²⁺-induced changes in mitochondrial bioenergetics. Our [Ca²⁺]_e and [Ca²⁺]_m measurements demonstrate that Ca²⁺ uptake and release do not show reciprocal Ca²⁺ dynamics in the extra-matrix and matrix compartments. This salient finding is likely caused by a dynamic Ca²⁺ buffering system in the matrix compartment. The Na⁺- induced Ca²⁺ release demonstrates an electrogenic exchange via the NCE by excluding an electroneutral exchange. Mitochondrial bioenergetics were only transiently affected by Ca²⁺ uptake in the presence of large amounts of CaCl₂, but not by Na⁺- induced Ca²⁺ release.     

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.     

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+).     

Ca2+ buffering and action potential-evoked Ca2+ signaling in dendrites of pyramidal neurons.

The effect of the fluorescent Ca2+ indicator dye Fura-2 on Ca2+ dynamics was studied in proximal apical dendrites of neocortical layer V and hippocampal CA1 pyramidal neurons in rat brain slices using somatic whole-cell recording and a charge-coupled device camera. A single action potential evoked a transient increase of intradendritic calcium concentration ([Ca2+]i) that was reduced in size and prolonged when the Fura-2 concentration was increased from 20 to 250 microM. Extrapolation to zero Fura-2 concentration suggests that "physiological" transients at 37 degrees C have large amplitudes (150-300 nM) and fast decays (time constant < 100 ms). Assuming a homogeneous compartment model for the dendrite, 0.5-1% of the total Ca2+ entering during an action potential was estimated to remain free. Washout of cytoplasmic Ca2+ buffers was not detectable, suggesting that they are relatively immobile. During trains of action potentials, [Ca2+]i increased and rapidly reached a steady state (time constant < 200 ms), fluctuating around a plateau level which depended linearly on the action potential frequency. Thus, the mean dendritic [Ca2+]i encodes the action potential frequency during physiological patterns of electrical activity and may regulate Ca(2+)-dependent dendritic functions in an activity-dependent way.     

The rate of diffusion of Ca2+ and Ba2+ in a nerve cell body.

A spectrophotometric method was developed to directly measure the diffusion rate of Ca2+ and some other ions in nerve cell bodies, using pulsed ionophoretic injections and an optical microprobe to record locally absorbance changes of the dye arsenazo III. We report here that Ca2+ and Ba2+ diffuse at approximately the same rate in nerve soma cytoplasm, having effective diffusion coefficients in the range of 7-12 X 10(-7) cm2/s, while identical measurements conducted in an electrolytic solution yielded values of 5.2 X 10(-6) cm2/s for Ca and 5.4 X 10(-6) cm2/s for Ba. The results are discussed in relation to the mechanisms that regulate the intracellular concentration of free Ca.     

Deprivation of Na+, Ca2+ and Mg2+ from the extracellular solution increases cytosolic Ca2+ and stimulates catecholamine secretion from cultured bovine adrenal chromaffin cells

We report here that exposing cultured chromaffin cells to a low ionic strength medium (with sucrose in place of NaCl to maintain osmolarity) can induce a marked elevation in cytosolic Ca2+ concentration ([Ca2+]i) and catecholamine (CA) release. To determine the underlying mechanism, we first studied the effects of low [Na+]o on single cell [Ca2+]i (using fluo-3 as Ca2+ indicator) and CA release from many cells. In a Mg2+ and Ca2+-deficient medium, lowering the external concentration of Na2+ ([Na+]o) evoked CA secretion preceded by a transitory [Ca2+]i rise, the amplitude of which was inversely related to [Na+]o. By contrast, in the presence of either [Ca2+]o (2 mM) and [Mg2+]o (1.4 mM) or [Mg2+]o alone (3.4 mM), lowering the ionic strength was without effect. Furthermore, in a physiologic [Na+]o, [Ca2+]o and [Mg2+]o medium, two or three consecutive applications of the cholinergic agonist oxotremorine-M (oxo-M) consistently evoked a substantial [Ca2+]i rise. By contrast, consecutive applications of oxo-M in a Ca2+-deficient medium failed to evoke a rise in [Ca2+]i after the first exposure to the agonist. To clarify the underlying mechanism, we measured and compared the effects of low [Na+]o and the cholinergic agonists nicotine and oxo-M on changes in [Ca2+]i; we studied the effects of these agonists on both membrane potential, Vm (under current clamp conditions), and [Ca2+]i by single cell microfluorimetry (indo-1 as Ca2+ indicator). We observed that, in the presence of [Ca2+]o and [Mg2+]o, lowering [Na+]o had no effect on Vm. In a Ca2+-deficient medium, lowering [Na+]o depolarized the membrane from ca. –60 to –10 mV. As expected, we found that nicotine (10 M) depolarized the membrane (from ca. –60 to –20 mV) and simultaneously evoked a substantial [Ca2+]i rise that was [Ca2+]o-dependent. However, contrary to our expectations, we found that the muscarinic agonist oxo-M (50 M) also depolarized the membrane and induced an elevation in [Ca2+]i. Furthermore, both signals were blocked by D-tubocurarine, insinuating the nicotinic character of oxo-M in adrenal chromaffin cells from bovine. These results suggest that both nicotine and oxo-M stimulate Ca2+ entry, probably through voltage-gated Ca2+-channels. We also show here that oxo-M (and not low [Na+]o) stimulates phosphoinositide turnover.     

Sustained Ca2+ transfer across mitochondria is Essential for mitochondrial Ca2+ buffering,sore-operated Ca2+ entry,and Ca2+ store refilling

Mitochondria have been found to sequester and release Ca2+ during cell stimulation with inositol 1,4,5-triphosphate-generating agonists, thereby generating subplasmalemmal microdomains of low Ca2+ that sustain activity of capacitative Ca2+ entry (CCE). Procedures that prevent mitochondrial Ca2+ uptake inhibit local Ca2+ buffering and CCE, but it is not clear whether Ca2+ has to transit through or remains trapped in the mitochondria. Thus, we analyzed the contribution of mitochondrial Ca2+ efflux on the ability of mitochondria to buffer subplasmalemmal Ca2+, to maintain CCE, and to facilitate endoplasmic reticulum (ER) refilling in endothelial cells. Upon the addition of histamine, the initial mitochondrial Ca2+ transient, monitored with ratio-metric-pericam-mitochondria, was largely independent of extracellular Ca2+. However, subsequent removal of extracellular Ca2+ produced a reversible decrease in [Ca2+]mito, indicating that Ca2+ was continuously taken up and released by mitochondria, although [Ca2+]mito had returned to basal levels. Accordingly, inhibition of the mitochondrial Na+/Ca2+ exchanger with CGP 37157 increased [Ca2+]mito and abolished the ability of mitochondria to buffer subplasmalemmal Ca2+, resulting in an increased activity of BKCa channels and a decrease in CCE. Hence, CGP 37157 also reversibly inhibited ER refilling during cell stimulation. These effects of CGP 37157 were mimicked if mitochondrial Ca2+ uptake was prevented with oligomycin/antimycin A. Thus, during cell stimulation a continuous Ca2+ flux through mitochondria underlies the ability of mitochondria to generate subplasmalemmal microdomains of low Ca2+, to facilitate CCE, and to relay Ca2+ from the plasma membrane to the ER.     

Pulsatile Ca2+ extrusion from single pancreatic acinar cells during receptor-activated cytosolic Ca2+ spiking.

Ca2+ extrusion was measured simultaneously with the free intracellular Ca2+ concentration ([Ca2+]i) from single pancreatic acinar cells placed in microdroplets of extracellular solution (Tepikin, A. V., Voronina, S. G., Gallacher, D. V., and Petersen, O. H. (1992) J. Biol. Chem. 267, 3569-3572). Submaximal stimulation with cholecystokinin usually evoked discrete cytosolic Ca2+ spikes and each of these spikes was associated with a discrete and virtually synchronous pulse of Ca2+ extrusion into the extracellular microdroplet solution. When ACh evoked repetitive discrete [Ca2+]i spikes, each spike was also accompanied by a discrete pulse of Ca2+ extrusion. The velocity of Ca2+ extrusion oscillated with a time course similar to that of [Ca2+]i. The extracellular solution in our experiments had a low total calcium concentration (15-35 microM) and only a limited number of [Ca2+]i spikes (2-8) could be evoked. The magnitudes of the [Ca2+]i spikes and the amounts of Ca2+ extruded during each spike gradually decreased in each experiment. During the first cholecystokinin-evoked cytosolic Ca2+ spike the Ca2+ extrusion corresponded to a loss of 15-70% (mean value 39% +/- 12) of the mobilizable cellular calcium pool. The substantial pulsatile Ca2+ extrusion occurring synchronously with the receptor-activated cytosolic Ca2+ spikes is therefore an important element in repetitively bringing back [Ca2+]i to the resting level.     

Ca2+ and phosphate releases from calcified Chara cell walls in concentrated KCl solution

Ca2+ and P(i) (inorganic phosphate) releases from isolated calcified and uncalcified Chara cell walls were measured with a Ca(2+)-selective electrode and colorimetry, and their ionic relations were analysed on the basis of the electroneutrality rule. The results showed that (1) not only Ca2+ but also P(i) can be released from isolated calcified Chara cell walls into pure deionized water and 100 mM KCl solution, and (2) the positive charge due to the Ca2+ released cannot be neutralized only by the negative charge from the simultaneously released P(i). These findings suggest that calcium bands of calcified Chara cell walls are composed of mainly CaCO(3) and CaHPO(4) and some anions other than P(i) should be released simultaneously with the Ca2+ and P(i). More Ca2+ and P(i) can be solubilized from isolated Chara cell walls in 100 mM KCl solution than in pure deionized water. The pH value of 100 mM KCl solution in which isolated uncalcified young Chara cell walls have been immersed is a little lower than that of pure deionized water in which the same isolated uncalcified young Chara cell walls have been immersed, suggesting that some acidic substances are solubilized by 100 mM KCl. To explain this from the viewpoint of solution chemistry, the solubilities of pure CaCO(3) and pure CaHPO(4) in water and 100 mM KCl solution were measured with a Ca2+ -selective electrode and their pH values with a glass pH electrode. The conclusion reached was that the Ca2+ release from isolated Chara cell walls is accompanied by the release of P(i), CO(2-)(3) and acidic substances. This suggests that the so-called calcium bands and/or ionic relations, including ion exchange, in Chara cell walls are chemically or physicochemically more complex than they are currently considered to be.     

Calcium diffusion modeling in a spherical neuron. Relevance of buffering properties.

We have developed a calcium diffusion model for a spherical neuron which incorporates calcium influx and extrusion through the plasma membrane as well as three calcium buffer systems with different capacities, mobilities, and kinetics. The model allows us to calculate the concentration of any of the species involved at all locations in the cell and can be used to account for experimental data obtained with high-speed Ca imaging techniques. The influence of several factors on the Ca2+ transients is studied. The relationship between peak [Ca2+]i and calcium load is shown to be nonlinear and to depend on buffer characteristics. The time course of the Ca2+ signals is also shown to be dependent on buffer properties. In particular, buffer mobility strongly determines the size and time course of Ca2+ signals in the cell interior. The model predicts that the presence of exogenous buffer, such as fura-2, modifies the Ca2+ transients to a variable extent depending on its proportion relative to the natural, intrinsic buffers. The conclusions about natural calcium buffer properties that can be derived from Ca imaging experiments are discussed.     

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.     

Dietary calcium deficiency increases Ca2+ uptake and Ca2+ extrusion mechanisms in chick enterocytes

Ca2+ uptake and Ca2+ extrusion mechanisms were studied in enterocytes with different degree of differentiation from chicks adapted to a low Ca2+ diet as compared to animals fed a normal diet. Chicks adapted to a low Ca2+ diet presented hypocalcemia, hypophosphatemia and increased serum 1,25(OH)2D3 and Ca2+ absorption. Low Ca2+ diet increased the alkaline phosphatase (AP) activity, independently of the cellular maturation, but it did not alter gamma-glutamyl-transpeptidase activity. Ca2+ uptake, Ca2+-ATPase and Na(+)/Ca2+ exchanger activities and expressions were increased by the mineral-deficient diet either in mature or immature enterocytes. Western blots analysis shows that vitamin D receptor (VDR) expression was much higher in crypt cells than in mature cells. Low Ca2+ diet decreased the number of vitamin D receptor units in both kinds of cells. In conclusion, changes in Ca2+ uptake and Ca2+ extrusion mechanisms in the enterocytes by a low Ca2+ diet appear to be a result of enhanced serum levels of 1,25(OH)2D3, which would promote cellular differentiation producing cells more efficient to express vitamin D dependent genes required for Ca2+ absorption.