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.     

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.     

An estimate of rapid cytoplasmic calcium buffering in a single smooth muscle cell

Cytoplasmic calcium increments in the absence of sarco (endo) plasmic reticulum function were measured with a low-affinity fluorophore Indo-1FF in single isolated smooth muscle cells from guinea-pig urinary bladder. To evaluate the Ca(2+)-buffering properties of the myoplasm, Ca2+ influx, measured as time integral of the Ica (integral of Ica), was compared with corresponding free Ca2+ increments (delta [Ca2+]i) in the cytoplasm. The ratio between integral of ICa and delta [Ca2+]i (integral Ica/delta [Ca2+]i), reflecting the Ca2+ buffering properties of the cytosol, was in the range of 4.9-9.3 pC/microM (mean 6.2 +/- 1.2, n = 12). It remained approximately constant (6.4 +/- 1.4 pC/microM, n = 8) during recordings lasting up to 25 min, suggesting that cytoplasmic Ca2+ binding does not change markedly during cell dialysis and that the endogenous Ca2+ buffer is not significantly washed out of the cell through the patch pipette. Wash-in or wash-out of BAPTA, a mobile high-affinity Ca2+ buffer, into or from the cell markedly changed the relationship between Ca2+ influx through Ca2+ channels and delta [Ca2+]i within minutes. Changes in integral of ICa/delta [Ca2+]i during the sequence of depolarizing steps, which increased free [Ca2+]i up to 5 microM, suggested lower limits for the apparent affinity of a rapid Ca2+ buffer (16 microM) and for the total buffer concentration (530 microM). Introduction of 4 mM DPTA (Kd for Ca2+ = 81 microM) into the cell more than doubled the total cytoplasmic Ca2+ buffer capacity. These results suggest that cytoplasmic Ca2+ buffer in smooth muscle cells has a low affinity for free Ca2+. The Ca(2+)-binding ratio of the cytoplasm in most cells was estimated to be between 30 and 40. The Ca(2+)-binding ratio did not differ markedly between cells isolated from neonatal (< or = 5 days) and adult animals.     

Calcium fluxes and calcium buffering in human neutrophils

Neutrophils loaded with the calcium indicator quin-2 and challenged with the ionophore ionomycin or the chemotactic peptide fMet-Leu-Phe were examined in the light of a theory that relates time-dependent changes in the fluorescence of the indicator to cytosolic calcium fluxes and levels. The cytosolic binding capacity was estimated from the theory to be 1.5 +/- 0.6 X 10(8) sites/cell (0.76 mM based on a cell volume of 330 micron 3, irrespective of water content and the distribution of sites), each site having an apparent average single class dissociation constant of 0.55 +/- 0.2 microM. Some 20% of the total available cytosolic calcium sites of the normal resting cell appear to be occupied when no quin-2 is present. In a calcium-free medium, the amount of calcium released by fMet-Leu-Phe from storage pool locations that are distinct from the cytosolic sites is sufficient to further raise the cytosolic site occupancy level to 50%, at which point the calcium buffering capacity of the cytosol is maximal. In a calcium-containing medium, however, simultaneous influx from the outside appears to supply enough additional calcium to saturate most of the remaining sites. The combined initial rate of storage pool calcium release plus influx through the plasma membrane was roughly twice the initial rate at which calcium was released from storage locations alone, suggesting that stimulus-induced influx from the outside may be comparable in importance to storage pool mobilization in determining physiological calcium levels in stimulated cells.     

Saltatory propagation of Ca2+ waves by Ca2+ sparks.

Punctate releases of Ca2+, called Ca2+ sparks, originate at the regular array of t-tubules in cardiac myocytes and skeletal muscle. During Ca2+ overload sparks serve as sites for the initiation and propagation of Ca2+ waves in myocytes. Computer simulations of spark-mediated waves are performed with model release sites that reproduce the adaptive Ca2+ release observed for the ryanodine receptor. The speed of these waves is proportional to the diffusion constant of Ca2+, D, rather than D, as is true for reaction-diffusion equations in a continuous excitable medium. A simplified "fire-diffuse-fire" model that mimics the properties of Ca2+-induced Ca2+ release (CICR) from isolated sites is used to explain this saltatory mode of wave propagation. Saltatory and continuous wave propagation can be differentiated by the temperature and Ca2+ buffer dependence of wave speed.     

The role of calcium in buffering soils

Abstract. Calcium is the soluble cation that occurs in largest amount in most soils. It does not take part directly in the proton transfer reactions involved in pH-buffering, but it provides the cation charge balance for these reactions. It is also the complementary cation in formulations of chemical potential for many other ions in soils. The presence of free calcium carbonate in calcareous soils. The presence of free calcium carbonate in calcareous soils ensures a very high soil buffer capacity; d AB/ d pH ≃ 1000 Eq. m⁻³.
In acid mineral soils, dissolution and precipitation of aluminium ions contribute to the buffering processes, but most of the buffering in non-calcareous soils is caused by specific ion adsorption at variable-charge sites, in particular those associated with the dissociation of humus acids. Typical buffer capacity values of non-calcareous soils vary from 10 Eq. m⁻³ for sandy soils to 100 Eq. m⁻³ for peats. The pH changes associated with buffering are produced by leaching of calcium from soil, or by adding calcium to soil in liming materials.     

Estimating intracellular calcium concentrations and buffering without wavelength ratioing

We describe a method for determining intracellular free calcium concentration ([Ca(2+)]) from single-wavelength fluorescence signals. In contrast to previous single-wavelength calibration methods, the proposed method does not require independent estimates of resting [Ca(2+)] but relies on the measurement of fluorescence close to indicator saturation during an experiment. Consequently, it is well suited to [Ca(2+)] indicators for which saturation can be achieved under physiological conditions. In addition, the method requires that the indicators have large dynamic ranges. Popular indicators such as Calcium Green-1 or Fluo-3 fulfill these conditions. As a test of the method, we measured [Ca(2+)] in CA1 pyramidal neurons in rat hippocampal slices using Oregon Green BAPTA-1 and 2-photon laser scanning microscopy (BAPTA: 1,2-bis(2-aminophenoxy)ethane-N,N,N', N'-tetraacetic acid). Resting [Ca(2+)] was 32-59 nM in the proximal apical dendrite. Monitoring action potential-evoked [Ca(2+)] transients as a function of indicator loading yielded estimates of endogenous buffering capacity (44-80) and peak [Ca(2+)] changes at zero added buffer (178-312 nM). In young animals (postnatal days 14-17) our results were comparable to previous estimates obtained by ratiometric methods (, Biophys. J. 70:1069-1081), and no significant differences were seen in older animals (P24-28). We expect our method to be widely applicable to measurements of [Ca(2+)] and [Ca(2+)]-dependent processes in small neuronal compartments, particularly in the many situations that do not permit wavelength ratio imaging.     

Expression of a rapid,low-voltage threshold K current in insulin-secreting cells is dependent on intracellular calcium buffering

Summary Depolarization-activated outward currents ranging in amplitude from 100–1000 pA were studied in cultured, insulinsecreting HIT cells and mouse B-cells using the whole-cell patch clamp. Outward current was identified as a K current since it was blocked by K channel blockers and its tail current reversed nearE _K. The K currents of HIT cells dialyzed with internal solutions containing 0.1–10mm EGTA with no added calcium (Ca), or 10mm EGTA with 2mm added Ca, activated rapidly with depolarization. However, the stronger Ca buffer BAPTA (5mm; no added Ca) blocked the rapidly activating current to reveal an underlying more slowly activating K current. With intracellular EGTA, application of the Ca channel blocker cadmium mimicked the effect of intracellular BAPTA. These data suggest that the rapid K current was mediated by low-voltage threshold, Ca-activated K channels while the slower K current was mediated by high threshold delayed rectifier K channels. Mouse B-cells also had both K current components. Dialyzing these cells with either BAPTA (5mm, no added Ca) or high EGTA (10mm with 2mm Ca) blocked the rapid Ca-activated K current observed when cells were filled with 0.1 to 1mm EGTA. It is concluded that the extent of Ca-activated K current activation in either HIT or adult mouse B-cells depends on the degree of intracellular Ca buffering.     

Fast calcium waves

Calcium waves are propagated in five main speed ranges which cover a billion-fold range of speeds. We define the fast speed range as 3-30μm/s after correction to a standard temperature of 20°C. Only waves which are not fertilization waves are considered here. 181 such cases are listed here. These are through organisms in all major taxa from cyanobacteria through mammals including human beings except for those through other bacteria, higher plants and fungi. Nearly two-thirds of these speeds lie between 12 and 24μm/s. We argue that their common mechanism in eukaryotes is a reaction-diffusion one involving calcium-induced calcium release, in which calcium waves are propagated along the endoplasmic reticulum. We propose that the gliding movements of some cyanobacteria are driven by fast calcium waves which are propagated along their plasma membranes. Fast calcium waves may drive materials to one end of developing embryos by cellular peristalsis, help coordinate complex cell movements during development and underlie brain injury waves. Moreover, we continue to argue that such waves greatly increase the likelihood that chronic injuries will initiate tumors and cancers before genetic damage occurs. Finally we propose numerous further studies.     

Paradoxical buffering of calcium by calsequestrin demonstrated for the calcium store of skeletal muscle

Contractile activation in striated muscles requires a Ca²⁺ reservoir of large capacity inside the sarcoplasmic reticulum (SR), presumably the protein calsequestrin. The buffering power of calsequestrin in vitro has a paradoxical dependence on [Ca²⁺] that should be valuable for function. Here, we demonstrate that this dependence is present in living cells. Ca²⁺ signals elicited by membrane depolarization under voltage clamp were compared in single skeletal fibers of wild-type (WT) and double (d) Casq-null mice, which lack both calsequestrin isoforms. In nulls, Ca²⁺ release started normally, but the store depleted much more rapidly than in the WT. This deficit was reflected in the evolution of SR evacuability, E, which is directly proportional to SR Ca²⁺ permeability and inversely to its Ca²⁺ buffering power, B. In WT mice E starts low and increases progressively as the SR is depleted. In dCasq-nulls, E started high and decreased upon Ca²⁺ depletion. An elevated E in nulls is consistent with the decrease in B expected upon deletion of calsequestrin. The different value and time course of E in cells without calsequestrin indicate that the normal evolution of E reflects loss of B upon SR Ca²⁺ depletion. Decrement of B upon SR depletion was supported further. When SR calcium was reduced by exposure to low extracellular [Ca²⁺], release kinetics in the WT became similar to that in the dCasq-null. E became much higher, similar to that of null cells. These results indicate that calsequestrin not only stores Ca²⁺, but also varies its affinity in ways that progressively increase the ability of the store to deliver Ca²⁺ as it becomes depleted, a novel feedback mechanism of potentially valuable functional implications. The study revealed a surprisingly modest loss of Ca²⁺ storage capacity in null cells, which may reflect concurrent changes, rather than detract from the physiological importance of calsequestrin.     

Intracellular calcium buffering capacity in isolated squid axons

Changes in ionized calcium were studied in axons isolated from living squid by measuring absorbance of the Ca binding dye Arsenazo III using multiwavelength differential absorption spectroscopy. Absorption changes measured in situ were calibrated in vitro with media of ionic composition similar to axoplasm containing CaEGTA buffers. Calcium loads of 50-2,500 μmol/kg axoplasm were induced by microinjection, by stimulation in 112 mM Ca seawater, or by soaking in choline saline with 1-10 mM Ca. Over this range of calcium loading of intact axoplasm, the ionized calcium in the axoplasm rose about 0.6 nM/μM load. Similar loading in axons preteated with carbonyl cyanide 4- trifluoromethoxyphenylhydrazone (FCCP) to inhibit the mitochondrial proton gradient increased ionized calcium by 5-7 percent of the imposed load, i.e. 93-95 percent of the calcium load was buffered by a process insensitive to FCCP. This FCCP- insensitive buffer system was not saturated by the largest calcium loads imposed, indicating a capacity of at least several millimolar. Treatment of previously loaded axons with FCCP or apyrase plus cyanide produced rises in ionized calcium which could be correlated with the extent of the load. Analysis of results indicated that, whereas only 6 percent of the endogenous calcium in fresh axons is stored in the FCCP-sensitive (presumably mitochondrial) buffer system, about 30 percent of an imposed exogenous load in the range of 50-2,500 μM is taken up by this system.     

A rapid assessment of the sedimentary buffering capacity towards free sulphides

Combined field surveys and laboratory studies were conducted in two Italian coastal lagoons, which differ for geomorphology, hydrodynamics and eutrophication degree (Sacca di Goro and Lesina lagoons, Adriatic Sea). Research aimed at assessing with a rapid technique the potential buffering capacity of sedimentary iron towards sulphides. In Spring and Summer 2004, the main pools of iron and sulphides were analysed in the uppermost sediment horizon (0–5 cm) at four stations in each lagoon. In parallel, experiments with laboratory incubations of sediment slurries were carried out at two sites in each lagoon in order to assess the sediment capacity of binding and retaining sulphides. Sediment slurries were kept stirred and anoxic with N₂ purging. Aliquots of dissolved sulphides (DS) were then added and DS concentrations were monitored until they were undetectable. On average, the total reactive iron (RFe), extracted with 6 N HCl, ranged from 170 to 400 μmol cm⁻³ in the Sacca di Goro stations, and comprised between 40 and 150 μmol cm⁻³ in the Lesina sites. The labile iron ferric quota (LFe: extractable with 0.5 N HCl) is considered representative of the microbially reducible iron fraction and was highest in spring in Sacca di Goro (up to 20 μmol cm⁻³). Differences among stations evidenced by PCA analysis, can be inferred from RFe, LFe and AVS, which represent the iron buffer and its saturation status, respectively. The sedimentary DS uptake was 6 μmol cm⁻³ of fresh sediment in Lesina and 8–12 μmol cm⁻³ in Sacca di Goro, indicating a direct relationship between DS removal and iron availability. Guest editors: A. Razinkovas, Z. R. Gasiūnaitė, J. M. Zaldivar & P. Viaroli European Lagoons and their Watersheds: Function and Biodiversity     

Hepatocyte growth factor-induced calcium waves in hepatocytes as revealed with rapid scanning confocal microscopy

Cytosolic Ca²⁺ transients induced by hepatocyte growth factor (HGF) were imaged in primary cultured rat hepatocytes using newly developed rapid scanning confocal microscopes and Indo-1. HGF (40 ng/ml) increased cytosolic free Ca²⁺ concentration ([Ca²⁺]i) in about 60% of hepatocytes, in 45% of which the increases were oscillatory. In each of the oscillatory hepatocytes, the repetitive increases in [Ca²⁺]i originated from a specific same region adjacent to the cell membrane and propagated across the cell like waves. Phenylephrine (10 μM) also induced Ca²⁺ waves. The locus where HGF-induced Ca²⁺ waves and phenylephrine-induced Ca²⁺ waves were originated was the same, and there was a correlation in the peak height between HGF-induced Ca²⁺ waves and phenylephrine-induced Ca²⁺ waves in each cell, although the mechanisms of inositol 1,4,5-trisphosphate (Ins(1,4,5)P₃) formation induced by HGF should be different from those by phenylephrine. On the other hand, there was no correlation between sensitivity of each cell to HGF and that to phenylephrine which were measured as latent periods prior to Ca²⁺ rises after an addition of the agonists. These results suggested the following: the spatial patterns of Ca²⁺ waves were decided by a common mechanism, probably not the propagation of Ins(1,4,5)P₃ but the distribution of Ins(1,4,5)P₃-sensitive Ca²⁺ pools; sensitivities of each cell to the agonists did not mainly depend on the common mechanism.     

Surfing on calcium waves

A key question in brain development is how migration of neuronal precursors is guided to establish the ordered laminar layers. In the April 20, 2007 issue of Cell, Guan et al. show that the leading process of migrating cerebellar granule neurons senses repulsive Slit molecules by generating a Ca(2+) wave that propagates to the soma to cause reversal of cell polarity and migration.     

Signals and calcium waves at fertilization

The study of sperm egg interactions and the signals they trigger, have made remarkable progress from the time of the seminal discovery of calcium waves 30 years ago. In this special issue of Seminars in Cell and Developmental Biology, 3 short pieces and 10 expert reviews survey this recent past and brings us up to date with current developments in this fertile field. Jaffe, Steinhardt and Whitaker recall the historical years while Miyazaki, Dumas, Rubinstein, Swann, Fissore, Sato, Foltz, Stricker, and their co-authors bring us up to date with current developments in sperm egg interaction, egg activation and calcium signalling. Dumollard, Duchen and Sardet and Ducibella, Schultz and Ozil deal with the pleiotropic consequences of stereotyped calcium signals from the cytoplasmic and cortical reorganizations they trigger including the stimulation of mitochondrial respiration, cell cycle regulation, the activation of protein synthesis, and subsequent developmental events. A list of interesting web sites giving access to video archives of fertilization and calcium waves is also provided.     

Classes and mechanisms of calcium waves

The best known calcium waves move at about 5–30 μm/s (at 20°C) and will be called fast waves to distinguish them from slow (contractile) ones which move at 0.1-1 μm/s as well as electrically propagated, ultrafast ones. Fast waves move deep within cells and seem to underlie most calcium signals. Their velocity and hence mechanism has been remarkably conserved among all or almost all eukaryotic cells. In fully active (but not overstimulated) cells of all sorts, their mean speeds lie between about 15–30 μm/s at 20°C. Their amplitudes usually lie between 3–30 μM and their frequencies from one per 10–300 s. They are propagated by a reaction diffusion mechanism governed by the Luther equation in which Ca²⁺ ions are the only diffusing propagators, and calcium induced calcium release, or CICR, the only reaction; although this reaction traverses various channels which are generally modulated by IP₃ or cADPR. However, they may be generally initiated by a second, lumenal mode of CICR which occurs within the ER. Moreover, they are propagated between cells by a variety of mechanisms. Slow intracellular waves, on the other hand, may be mechanically propagated via stretch sensitive calcium channels.     

Taurine increases mitochondrial buffering of calcium: role in neuroprotection

Summary. We have determined the role of mitochondria in the sequestration of calcium after stimulation of cerebellar granule cells with glutamate. In addition we have evaluated the neuroprotective role of taurine in excitotoxic cell death. Mitochondrial inhibitors were used to determine the calcium buffering capacity of mitochondria, as well as how taurine regulates the ability of mitochondria to buffer intracellular calcium during glutamate depolarization and excitotoxicity. We report here that pre-treatment of cerebellar granule cells with taurine (1 mM, 24 h) significantly counteracted glutamate excitotoxicity. The neuroprotective role of taurine was mediated through regulation of cytoplasmic free calcium ([Ca²⁺] _i ), and intra-mitochondrial calcium homeostasis, as determined by fluo-3 and ⁴⁵Ca²⁺-uptake. Furthermore, the overall mitochondrial function was increased in the presence of taurine, as assessed by rhodamine accumulation into mitochondria and total cellular ATP levels. We specifically tested the hypothesis that taurine reduces glutamate excitotoxicity through both the enhancement of mitochondrial function and the regulation of intracellular (cytoplasmic and intra-mitochondrial) calcium homeostasis. The role of taurine in modulating mitochondrial calcium homeostasis could be of particular importance under pathological conditions that are characterized by excessive calcium overloads. Taurine may serve as an endogenous neuroprotective molecule against brain insults. Authors’ address: Abdeslem El Idrissi, Biology Department and Center for Developmental Neuroscience, College of Staten Island/CUNY, 6S-134 Staten Island, NY 10314, U.S.A.