Analytical calculation of intracellular calcium wave characteristics

We present a theoretical analysis of intracellular calcium waves propagated by calcium feedback at the inositol 1,4,5-trisphosphate (IP3) receptor. The model includes essential features of calcium excitability, but is still analytically tractable. Formulas are derived for the wave speed, amplitude, and width. The calculations take into account cytoplasmic Ca buffering, the punctate nature of the Ca release channels, channel inactivation, and Ca pumping. For relatively fast buffers, the wave speed is well approximated by V(infinity) = (J(eff)D(eff)/C0)1/2, where J(eff) is an effective, buffered source strength; D(eff) is the effective, buffered diffusion constant of Ca; and C(0) is the Ca threshold for channel activation. It is found that the saturability and finite on-rate of buffers must be taken into account to accurately derive the wave speed and front width. The time scale governing Ca wave propagation is T(r), the time for Ca release to reach threshold to activate further release. Because IP3 receptor inactivation is slow on this time scale, channel inactivation does not affect the wave speed. However, inactivation competes with Ca removal to limit wave height and front length, and for biological parameter ranges, it is inactivation that determines these parameters. Channel discreteness introduces only small corrections to wave speed relative to a model in which Ca is released uniformly from the surface of the stores. These calculations successfully predict experimental results from basic channel and cell parameters and explain the slowing of waves by exogenous buffers.     

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.     

Sustained activation of the tyrosine kinase Syk by antigen in mast cells requires local Ca2+ influx through Ca2+ release-activated Ca2+ channels

Mast cell activation involves cross-linking of IgE receptors followed by phosphorylation of the non-receptor tyrosine kinase Syk. This results in activation of the plasma membrane-bound enzyme phospholipase Cgamma1, which hydrolyzes the minor membrane phospholipid phosphatidylinositol 4,5-bisphosphate to generate diacylglycerol and inositol trisphosphate. Inositol trisphosphate raises cytoplasmic Ca2+ concentration by releasing Ca2+ from intracellular stores. This Ca2+ release phase is accompanied by sustained Ca2+ influx through store-operated Ca2+ release-activated Ca2+ (CRAC) channels. Here, we find that engagement of IgE receptors activates Syk, and this leads to Ca2+ release from stores followed by Ca2+ influx. The Ca2+ influx phase then sustains Syk activity. The Ca2+ influx pathway activated by these receptors was identified as the CRAC channel, because pharmacological block of the channels with either a low concentration of Gd3+ or exposure to the novel CRAC channel blocker 3-fluoropyridine-4-carboxylic acid (2',5'-dimethoxybiphenyl-4-yl)amide or RNA interference knockdown of Orai1, which encodes the CRAC channel pore, all prevented the increase in Syk activity triggered by Ca2+ entry. CRAC channels and Syk are spatially close together, because increasing cytoplasmic Ca2+ buffering with the fast Ca2+ chelator 1,2-bis(2-aminophenoxy)ethane-N,N,N',N'-tetraacetic acid tetrakis failed to prevent activation of Syk by Ca2+ entry. Our results reveal a positive feedback step in mast cell activation where receptor-triggered Syk activation and subsequent Ca2+ release opens CRAC channels, and the ensuing local Ca2+ entry then maintains Syk activity. Ca2+ entry through CRAC channels therefore provides a means whereby the Ca2+ and tyrosine kinase signaling pathways can interact with one another.     

Mice null for calsequestrin 1 exhibit deficits in functional performance and sarcoplasmic reticulum calcium handling

In skeletal muscle, the release of calcium (Ca(2+)) by ryanodine sensitive sarcoplasmic reticulum (SR) Ca(2+) release channels (i.e., ryanodine receptors; RyR1s) is the primary determinant of contractile filament activation. Much attention has been focused on calsequestrin (CASQ1) and its role in SR Ca(2+) buffering as well as its potential for modulating RyR1, the L-type Ca(2+) channel (dihydropyridine receptor, DHPR) and other sarcolemmal channels through sensing luminal [Ca(2+)]. The genetic ablation of CASQ1 expression results in significant alterations in SR Ca(2+) content and SR Ca(2+) release especially during prolonged activation. While these findings predict a significant loss-of-function phenotype in vivo, little information on functional status of CASQ1 null mice is available. We examined fast muscle in vivo and in vitro and identified significant deficits in functional performance that indicate an inability to sustain contractile activation. In single CASQ1 null skeletal myofibers we demonstrate a decrease in voltage dependent RyR Ca(2+) release with single action potentials and a collapse of the Ca(2+) release with repetitive trains. Under voltage clamp, SR Ca(2+) release flux and total SR Ca(2+) release are significantly reduced in CASQ1 null myofibers. The decrease in peak Ca(2+) release flux appears to be solely due to elimination of the slowly decaying component of SR Ca(2+) release, whereas the rapidly decaying component of SR Ca(2+) release is not altered in either amplitude or time course in CASQ1 null fibers. Finally, intra-SR [Ca(2+)] during ligand and voltage activation of RyR1 revealed a significant decrease in the SR[Ca(2+)](free) in intact CASQ1 null fibers and a increase in the release and uptake kinetics consistent with a depletion of intra-SR Ca(2+) buffering capacity. Taken together we have revealed that the genetic ablation of CASQ1 expression results in significant functional deficits consistent with a decrease in the slowly decaying component of SR Ca(2+) release.     

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.     

A three-dimensional model of intercellular calcium signaling in epithelial cells

We have developed a fully three-dimensional (3D) model of calcium signaling in epithelial cells based on a set of reaction diffusion equations that are solved on a large-scale finite-element code in three dimensions. We have explicitly included the cellular compartments including the cell nucleus, cytoplasm, and gap junctions. The model allows for buffering of free Ca2+, calcium-induced calcium release, and the explicit inclusion of mobile buffers. To make quantitative comparisons to experimental results, we used fluorescence microscopy images of cells to generate an accurate mesh describing cell morphology. We found that Ca2+ wave propagation through the tissue is a function of both initial conditions used to start the wave and various geometrical parameters that affect propagation such as gap junction density and distribution, and the presence of nuclei. The exogenous dyes used in experimental imaging also affect wave propagation.     

Respiring mitochondria determine the pattern of activation and inactivation of the store-operated Ca(2+) current I(CRAC)

In eukaryotic cells, hormones and neurotransmitters that engage the phosphoinositide pathway evoke a biphasic increase in intracellular free Ca(2+) concentration: an initial transient release of Ca(2+) from intracellular stores is followed by a sustained phase of Ca(2+) influx. This influx is generally store dependent. Most attention has focused on the link between the endoplasmic reticulum and store-operated Ca(2+) channels in the plasma membrane. Here, we describe that respiring mitochondria are also essential for the activation of macroscopic store-operated Ca(2+) currents under physiological conditions of weak intracellular Ca(2+) buffering. We further show that Ca(2+)-dependent slow inactivation of Ca(2+) influx, a widespread but poorly understood phenomenon, is regulated by mitochondrial buffering of cytosolic Ca(2+). Thus, by enabling macroscopic store-operated Ca(2+) current to activate, and then by controlling its extent and duration, mitochondria play a crucial role in all stages of store-operated Ca(2+) influx. Store-operated Ca(2+) entry reflects a dynamic interplay between endoplasmic reticulum, mitochondria and plasma membrane.     

In retinal cones, membrane depolarization in darkness activates the cGMP-dependent conductance. A model of Ca homeostasis and the regulation of guanylate cyclase

We measured outer segment currents under voltage clamp in solitary, single cone photoreceptors isolated from the retina of striped bass. In darkness, changes in membrane voltage to values more positive than 10 mV activate a time- and voltage-dependent outward current in the outer segment. This dark, voltage-activated current (DVAC) increases in amplitude with a sigmoidal time course up to a steady-state value, reached in 0.75-1.5 s. DVAC is entirely suppressed by light, and its current-voltage characteristics and reversal potential are the same as those of the light-sensitive currents. DVAC, therefore, arises from the activation by voltage in the dark of the light-sensitive, cGMP-gated channels of the cone outer segment. Since these channels are not directly gated by voltage, we explain DVAC as arising from a voltage- dependent decrease in cytoplasmic Ca concentration that, in turn, activates only guanylate cyclase and results in net synthesis of cGMP. This explanation is supported by the finding that the Ca buffer BAPTA, loaded into the cytoplasm of the cone outer segment, blocks DVAC. To link a decrease in cytoplasmic Ca concentration to the synthesis of cGMP and the characteristics of DVAC, we develop a quantitative model that assumes cytoplasmic Ca concentration can be continuously calculated from the balance between passive Ca influx via the cGMP- gated channel and its active efflux via a Na/Ca,K exchanger, and that further assumes that guanylate cyclase is activated by decreasing cytoplasmic Ca concentration with characteristics identical to those described for the enzyme in rods. The model successfully simulates experimental data by adjusting the Ca conductance of the cGMP-gated channels as a function of voltage and the Ca buffering power of the cytoplasm. This success suggests that the activity of guanylate cyclase in cone outer segments is indistinguishable from that in rods.     

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.     

Free calcium wave upon activation in Xenopus eggs

Eggs of Xenopus laevis were preloaded with aequorin and the spatial and temporal pattern of free calcium release in the egg cortex on artificial activation was determined by the aequorin luminescence emitted from the thin cortical layer of naturally opaque eggs. The aequorin luminescence was detected with a photonic microscope system consisting of a light microscope and a two-dimensional photon-counting system with an image processor. A free calcium increase was initiated around the point of prick activation. The state of increased Ca2+ propagated in the cortical cytoplasm of the egg as a wave with a velocity of about 8 micron/sec at 22 degrees C. This wave reached the antipode by 5 to 6 min of prick activation. The spatial pattern of the Ca2+ wave was similar to that of changes in brightness of the egg surface on activation, termed the "activation wave" by K. Hara and P. Tydeman (1979, Wilhelm Roux's Arch. Dev. Biol. 186, 91-94). To examine the temporal correlation between the Ca2+ wave and the activation wave, images of aequorin luminescence and those of the egg cortex taken by incident light illumination were recorded alternately in the same egg. The zone of free calcium increase corresponded to the light (relaxation) zone of the activation wave, where exocytosis of cortical granules and elongation of microvilli were taking place.     

Intercellular Ca2+ wave propagation through gap-junctional Ca2+ diffusion: a theoretical study

Intercellular regenerative calcium waves in systems such as the liver and the blowfly salivary gland have been hypothesized to spread through calcium-induced calcium release (CICR) and gap-junctional calcium diffusion. A simple mathematical model of this mechanism is developed. It includes CICR and calcium removal from the cytoplasm, cytoplasmic and gap-junctional calcium diffusion, and calcium buffering. For a piecewise linear approximation of the calcium kinetics, expressions in terms of the cellular parameters are derived for 1) the condition for the propagation of intercellular waves, and 2) the characteristic time of the delay of a wave encountered at the gap junctions. Intercellular propagation relies on the local excitation of CICR in the perijunctional space by gap-junctional calcium influx. This mechanism is compatible with low effective calcium diffusivity, and necessitates that CICR can be excited in every cell along the path of a wave. The gap-junctional calcium permeability required for intercellular waves in the model falls in the range of reported gap-junctional permeability values. The concentration of diffusive cytoplasmic calcium buffers and the maximal rate of CICR, in the case of inositol 1,4,5-trisphosphate (IP3) receptor calcium release channels set by the IP(3) concentration, are shown to be further determinants of wave behavior.     

Calcium-Activated K+ Channels and Calcium-Induced Calcium Release by Slow Vacuolar Ion Channels in Guard Cell Vacuoles Implicated in the Control of Stomatal Closure

Stomatal closing requires the efflux of K+ from the large vacuolar organelle into the cytosol and across the plasma membrane of guard cells. More than 90% of the K+ released from guard cells during stomatal closure originates from the guard cell vacuole. However, the corresponding molecular mechanisms for the release of K+ from guard cell vacuoles have remained unknown. Rises in the cytoplasmic Ca2+ concentration have been shown to trigger ion efflux from guard cells, resulting in stomatal closure. Here, we report a novel type of largely voltage-independent K+-selective ion channel in the vacuolar membrane of guard cells that is activated by physiological increases in the cytoplasmic Ca2+ concentration. These vacuolar K+ (VK) channels had a single channel conductance of 70 pS with 100 mM KCI on both sides of the membrane and were highly selective for K+ over NH4+ and Rb+. Na+, Li+, and Cs+ were not measurably permeant. The Ca2+, voltage, and pH dependences, high selectivity for K+, and high density of VK channels in the vacuolar membrane of guard cells suggest a central role for these K+ channels in the initiation and control of K+ release from the vacuole to the cytoplasm required for stomatal closure. The activation of K+-selective VK channels can shift the vacuolar membrane to more positive potentials on the cytoplasmic side, sufficient to activate previously described slow vacuolar cation channels (SV-type). Analysis of the ionic selectivity of SV channels demonstrated a Ca2+ over K+ selectivity (permeability ratio for Ca2+ to K+ of ~3:1) of these channels in broad bean guard cells and red beet vacuoles, suggesting that SV channels play an important role in Ca2+-induced Ca2+ release from the vacuole during stomatal closure. A model is presented suggesting that the interaction of VK and SV channel activities is crucial in regulating vacuolar K+ and Ca2+ release during stomatal closure. Furthermore, the possibility that the ubiquitous SV channels may represent a general mechanism for Ca2+-induced Ca2+ release from higher plant vacuoles is discussed.     

Energized mitochondria increase the dynamic range over which inositol 1,4,5-trisphosphate activates store-operated calcium influx

In eukaryotic cells, activation of cell surface receptors that couple to the phosphoinositide pathway evokes a biphasic increase in intracellular free Ca2+ concentration: an initial transient phase reflecting Ca2+ release from intracellular stores, followed by a plateau phase due to Ca2+ influx. A major component of this Ca2+ influx is store-dependent and often can be measured directly as the Ca2+ release-activated Ca2+ current (I(CRAC)). Under physiological conditions of weak intracellular Ca2+ buffering, respiring mitochondria play a central role in store-operated Ca2+ influx. They determine whether macroscopic I(CRAC) activates or not, to what extent and for how long. Here we describe an additional role for energized mitochondria: they reduce the amount of inositol 1,4,5-trisphosphate (InsP3) that is required to activate I(CRAC). By increasing the sensitivity of store-operated influx to InsP3, respiring mitochondria will determine whether modest levels of stimulation are capable of evoking Ca2+ entry or not. Mitochondrial Ca2+ buffering therefore increases the dynamic range of concentrations over which the InsP3 is able to function as the physiological messenger that triggers the activation of store-operated Ca2+ influx.     

Differential release of amino acids, neuropeptides, and catecholamines from isolated nerve terminals

We have investigated transmitter release from small and large dense-core vesicles in nerve terminals isolated from guinea pig hippocampus. Small vesicles are found in clusters near the active zone, and large dense-core vesicles are located at ectopic sites. The abilities of Ca2+ channel activation and uniform elevation of Ca2+ concentration (with ionophores) to evoke secretion of representative amino acids, catecholamines, and neuropeptides were compared. For a given increase in Ca2+ concentration, ionophore was less effective than Ca2+ channel activation in releasing amino acids, but not in releasing cholecystokinin-8. Titration of the average Ca2+ concentration showed that the Ca2+ affinity for cholecystokinin-8 secretion was higher than that for amino acids. Catecholamine release showed intermediate behavior. It is concluded that neuropeptide release is triggered by small elevations in the Ca2+ concentration in the bulk cytoplasm, whereas secretion of amino acids requires higher elevations, as produced in the vicinity of Ca2+ channels.     

Activation of the calcium release channel (ryanodine receptor) by heparin and other polyanions is calcium dependent.

Heparin has been used as a potent competitive inhibitor of inositol 1,4,5-trisphosphate (IP3)-binding to IP3 receptors and to block IP3-gated calcium channels in bilayer experiments. In contrast to the effect on the IP3-gated channel, heparin (0.1-1 micrograms/ml) opened the Ca release channel (ryanodine receptor). Other polyanions such as pentosan polysulfate and polyvinyl sulfate also activated the Ca release channel. The effect of polyanions on the Ca release channel was Ca dependent. Polyanion addition activated the Ca release channel when free Ca was > 80 nM, but was ineffective when free Ca was < 20 nM. The level of channel activation could be altered by manipulating the free Ca concentration. These results suggest that the polyanions act by increasing the local concentration of Ca near regulatory sites on the channel complex. As most cells have both types of intracellular channels, the opposite effects of the polyanions on the two channel types suggests that addition of polyanions to intact cells may produce multiple effects.     

Activation of single cardiac and skeletal ryanodine receptor channels by flash photolysis of caged Ca2+.

Single ryanodine-sensitive sarcoplasmic reticulum (SR) Ca2+ release channels isolated from rabbit skeletal and canine cardiac muscle were reconstituted in planar lipid bilayers. Single channel activity was measured in simple solutions (no ATP or Mg2+) with 250 mM symmetrical Cs+ as charge carrier. A laser flash was used to photolyze caged-Ca2+ (DM-nitrophen) in a small volume directly in front of the bilayer. The free [Ca2+] in this small volume and in the bulk solution was monitored with Ca2+ electrodes. This setup allowed fast, calibrated free [Ca2+] stimuli to be applied repetitively to single SR Ca2+ release channels. A standard photolytically induced free [Ca2+] step (pCa 7-->6) was applied to both the cardiac and skeletal release channels. The rate of channel activation was determined by fitting a single exponential to ensemble currents generated from at least 50 single channel sweeps. The time constants of activation were 1.43 +/- 0.65 ms (mean +/- SD; n = 5) and 1.28 +/- 0.61 ms (n = 5) for cardiac and skeletal channels, respectively. This study presents a method for defining the fast Ca2+ regulation kinetics of single SR Ca2+ release channels and shows that the activation rate of skeletal SR Ca2+ release channels is consistent with a role for CICR in skeletal muscle excitation-contraction coupling.     

Intracellular axial current in Chara corallina reflects the altered kinetics of ions in cytoplasm under the influence of light

Recent experiments demonstrate that the concentration of Ca2+ in cytoplasm of Chara corallina internodal cells plays important role in electrical excitation of the plasma membrane. The concentration of free Ca2+ in the cytoplasm -[Ca2+]c is also sensitive to visible light. Both phenomena were simultaneously studied by noninvasive measuring action potential (AP) and magnetic field with a superconducting quantum interference device magnetometer in very close vicinity of electrically excited internodal C. corallina cells. A temporal shift in the depolarization maximum, which progressively occurred after transferring cells from the dark into the light, can be explained by the extended Othmer model. Assuming that the change in membrane voltage during the depolarization part of AP is the direct consequence of an activation of [Ca2+]c sensitive Cl- channels, the model simulations compare well with the experimental data. We can say that we have an example of electrically elicited AP that is of biochemical nature. Electric and magnetic measurements are in good agreement.     

Glutamatergically induced pattern of Ca2+ driving potential as a mechanism of postsynaptic plasticity.

Simulation studies were performed in a model of neuronal dendrite with Na+ and K+ channels and with ionotropic and metabotropic glutamate receptors. The ionotropic receptors were either N-methyl-D-aspartate (NMDA)-sensitive, voltage-dependent, and permeable to Ca2+, Na+, and K+, or non-NMDA-sensitive, voltage-independent, and permeable to Na+ and K+. The metabotropic receptors provided a catalytic effect on Ca2+-induced Ca2+ release from intracellular stores. Local intracellular concentration [Ca2+]i in the cytoplasm was changed because of exchange with the stores, axial diffusion, and transmembrane inward passive and outward pump fluxes. Tonic activation of ionotropic and metabotropic receptors in a particular range of intensities triggered the formation of spatially periodic [Ca2+]i hot and cold bands arising from an initial uniform state. The period and width of the bands were smaller at higher levels of tonic NMDA activation and higher metabotropically controlled rates of Ca2+-induced Ca2+ release. The bandwidths also depended on the dendrite diameter, the specific membrane, and cytoplasm resistivity. This activity-induced pattern led to long-term, spatially inhomogeneous change in local excitatory postsynaptic potentials (EPSPs) of NMDA synapses phasically activated with the same presynaptic intensity. The phasic EPSPs were potentiated if the synapse occurred in the hot band.