Calmodulin can induce and control damped oscillations in plasma membrane Ca<Superscript>2+</Superscript>-ATPase activity: A kinetic model

Plasma membrane Ca²⁺-ATPase is the pump that extrudes calcium ions from cells using ATP hydrolysis to maintain low Ca²⁺ concentrations in the cell. Calmodulin stimulates Ca²⁺-ATPase by binding to the autoinhibitory enzyme domain, which allows the access of cytoplasmic ATP and Ca²⁺ to the catalytic and transport sites. Our kinetic model predicts damped oscillations of the enzyme activity and interprets the known nonmonotonic kinetic behavior of the enzyme in the presence of calmodulin. For parameters close to experimental data, the kinetic model explains the dependence of the frequency and damping factor of the oscillatory enzyme activity on the calmodulin concentration. The calculated pre-steady-state curves fit well to known experimental data. Kinetic analysis allows us to assign Ca²⁺-ATPase to hysteretic enzymes exhibiting activity oscillations in open systems.     

Induction of cortical oscillations in spreading cells by depolymerization of microtubules

Actomyosin-based cortical contractility is a common feature of eukaryotic cells but the capability to produce rhythmic contractions is found in only a few types such as cardiomyocytes. Mechanisms responsible for the acquisition of this capability remain largely unknown. Rhythmic contractility can be induced in non-muscle cells by microtubule depolymerization. Spreading epithelial cells and fibroblasts in which microtubules were depolymerized with nocodazole or colcemid underwent rhythmic oscillations of the body that lasted for several hours before the cells acquired a stable, flattened shape. By contrast, control cells spread and flattened into discoid shapes in a smooth and regular manner. Quantitative analysis of the oscillations showed that they have a period of about 50 seconds. The kinase inhibitors, HA 1077 and H7, and the more specific rho-kinase inhibitor, Y 27632, caused the oscillations to immediately cease and the cells to become flat. Transient increases in cytoplasmic calcium preceded the contractile phase of the oscillations. Wrinkle formation by cells plated on elastic substrata indicated that the contractility of colcemid-treated cells increased in comparison to controls but was drastically decreased after HA 1077 addition. These data suggest that an intact microtubular system normally prevents pulsations by moderating excessive rho-mediated actin myosin contractility. Possible mechanistic interactions between rho-mediated and calcium activated contractile pathways that could produce morphological oscillations are discussed.     

Cell proliferation, calcium influx and calcium channels

Both increases in the basal cytosolic calcium concentration ([Ca²⁺]_cyt) and [Ca²⁺]_cyt transients play major roles in cell cycle progression, cell proliferation and division. Calcium transients are observed at various stages of cell cycle and more specifically during late G₁ phase, before and during mitosis. These calcium transients are mainly due to calcium release and reuptake by the endoplasmic reticulum (ER) and are observed over periods of hours in oocytes and mammalian cells. Calcium entry sustains the ER Ca²⁺ load and thereby helps to maintain these calcium transients for such a long period. Calcium influx also controls cell growth and proliferation in several cell types. Various calcium channels are involved in this process and the tight relation between the expression and activity of cyclins and calcium channels also suggests that calcium entry may be needed only at particular stages of the cell cycle. Consistent with this idea, the expression of l-type and T-type calcium channels and SOCE amplitude fluctuate along the cell cycle. But, as calcium influx regulates several other transduction pathways, the presence of a specific connection to trigger activation of proliferation and cell division in mammalian cells will be discussed in this review.     

Modelling mechanism of calcium oscillations in pancreatic acinar cells

We present a simple model for calcium oscillations in the pancreatic acinar cells. This model is based on the calcium release from two receptors, inositol trisphosphate receptors (IPR) and ryanodine receptors (RyR) through the process of calcium induced calcium release (CICR). In pancreatic acinar cells, when the Ca²⁺ concentration increases, the mitochondria uptake it very fast to restrict Ca²⁺ response in the cell. Afterwards, a much slower release of Ca²⁺ from the mitochondria serves as a calcium supply in the cytosol which causes calcium oscillations. In this paper we discuss a possible mechanism for calcium oscillations based on the interplay among the three calcium stores in the cell: the endoplasmic reticulum (ER), mitochondria and cytosol. Our model predicts that calcium shuttling between ER and mitochondria is a pacemaker role in the generation of Ca²⁺oscillations. We also consider the calcium dependent production and degradation of (1,4,5) inositol-trisphosphate (IP₃), which is a key source of intracellular calcium oscillations in pancreatic acinar cells. In this study we are able to predict the different patterns of calcium oscillations in the cell from sinusoidal to raised-baseline, high frequency and low-frequency baseline spiking.     

Simulation of Spontaneous Ca Oscillations in Astrocytes Mediated by Voltage-Gated Calcium Channels

The purpose of this computational study was to investigate the possible role of voltage-gated Ca²⁺ channels in spontaneous Ca²⁺ oscillations of astrocytes. By incorporating different types of voltage-gated Ca²⁺ channels and a previous model, this study reproduced typical Ca²⁺ oscillations in silico. Our model could mimic the oscillatory phenomenon under a wide range of experimental conditions, including resting membrane potential (−75 to −60 mV), extracellular Ca²⁺ concentration (0.1 to 1500 μM), temperature (20 to 37°C), and blocking specific Ca²⁺ channels. By varying the experimental conditions, the amplitude and duration of Ca²⁺ oscillations changed slightly (both <25%), while the frequency changed significantly (∼400%). This indicates that spontaneous Ca²⁺ oscillations in astrocytes might be an all-or-none process, which might be frequency-encoded in signaling. Moreover, the properties of Ca²⁺ oscillations were found to be related to the dynamics of Ca²⁺ influx, and not only to a constant influx. Therefore, calcium channels dynamics should be used in studying Ca²⁺ oscillations. This work provides a platform to explore the still unclear mechanism of spontaneous Ca²⁺ oscillations in astrocytes.     

Glucose modulates [Ca2+]i oscillations in pancreatic islets via ionic and glycolytic mechanisms

Pancreatic islets of Langerhans display complex intracellular calcium changes in response to glucose that include fast (seconds), slow ( approximately 5 min), and mixed fast/slow oscillations; the slow and mixed oscillations are likely responsible for the pulses of plasma insulin observed in vivo. To better understand the mechanisms underlying these diverse patterns, we systematically analyzed the effects of glucose on period, amplitude, and plateau fraction (the fraction of time spent in the active phase) of the various regimes of calcium oscillations. We found that in both fast and slow islets, increasing glucose had limited effects on amplitude and period, but increased plateau fraction. In some islets, however, glucose caused a major shift in the amplitude and period of oscillations, which we attribute to a conversion between ionic and glycolytic modes (i.e., regime change). Raising glucose increased the plateau fraction equally in fast, slow, and regime-changing islets. A mathematical model of the pancreatic islet consisting of an ionic subsystem interacting with a slower metabolic oscillatory subsystem can account for these complex islet calcium oscillations by modifying the relative contributions of oscillatory metabolism and oscillatory ionic mechanisms to electrical activity, with coupling occurring via K(ATP) channels.     

L-type Ca2+ channels and K+ channels specifically modulate the frequency and amplitude of spontaneous Ca2+ oscillations and have distinct roles in prolactin release in GH3 cells

GH3 cells showed spontaneous rhythmic oscillations in intracellular calcium concentration ([Ca2+]i) and spontaneous prolactin release. The L-type Ca2+ channel inhibitor nimodipine reduced the frequency of Ca2+ oscillations at lower concentrations (100nM-1 microM), whereas at higher concentrations (10 microM), it completely abolished them. Ca2+ oscillations persisted following exposure to thapsigargin, indicating that inositol 1,4,5-trisphosphate-sensitive intracellular Ca2+ stores were not required for spontaneous activity. The K+ channel inhibitors Ba2+, Cs+, and tetraethylammonium (TEA) had distinct effects on different K+ currents, as well as on Ca2+ oscillations and prolactin release. Cs+ inhibited the inward rectifier K+ current (KIR) and increased the frequency of Ca2+ oscillations. TEA inhibited outward K+ currents activated at voltages above -40 mV (grouped within the category of Ca2+ and voltage-activated currents, KCa,V) and increased the amplitude of Ca2+ oscillations. Ba2+ inhibited both KIR and KCa,V and increased both the amplitude and the frequency of Ca2+ oscillations. Prolactin release was increased by Ba2+ and Cs+ but not by TEA. These results indicate that L-type Ca2+ channels and KIR channels modulate the frequency of Ca2+ oscillations and prolactin release, whereas TEA-sensitive KCa,V channels modulate the amplitude of Ca2+ oscillations without altering prolactin release. Differential regulation of these channels can produce frequency or amplitude modulation of calcium signaling that stimulates specific pituitary cell functions.     

Calmodulin can induce and control damping oscillations in the plasma membrane Ca2+ -ATPase activity: a kinetic model

Plasma membrane Ca2+-ATPase is the calcium pump that extrudes calcium ions from cells using ATP hydrolisis for the maintenance of low Ca2+ concentrations in the cell. Calmodulin stimulates Ca2+-ATPase by binding to the autoinhibitory enzyme domain, which allows the access of cytoplasmic ATP and Ca2+ to the active and transport cites. Our kinetic model predicts damped oscillations in the enzyme activity and interprets the known nonmonotonous kinetic behavior of the enzyme in the presence of calmodulin. For the parameters close to the experimental ones, the kinetic model explains the changes in frequency and damping factor of the oscillatory enzyme activity, as dependent on calmodulin concentration. The calculated pre-steady-state curves fit well the known experimental data. The kinetic analysis allows us to assign Ca2+-ATPase to the hysteretic enzymes exhibiting activity oscillations in open systems.     

Modeling the Calcium Signaling in Stomatal Guard Cells under the Action of Abscisic Acid

A theoretical model of calcium signaling is presented that simulates oscillations of cytoplasmic calcium concentration ([Ca²⁺]_cyt) in stomatal guard cells under the action of abscisic acid. The model is based on the kinetics of inositol 1,4,5-trisphosphate-sensitive calcium channels of endoplasmic reticulum and cyclic ADP-ribose-sensitive calcium channels of the tonoplast. The operation of two energy-dependent pumps—the Ca²⁺-ATPase of the endoplasmic reticulum and the Ca²⁺/H⁺ antiporter of the tonoplast—is also included in the model. It is shown that the removal of excessive Ca²⁺ from the cytoplasm by the tonoplast Ca²⁺/H⁺ antiporter is the main factor accounting for generation of [Ca²⁺]_cyt oscillations at a wide range of ABA concentrations (0.01–1 M). The long period of [Ca²⁺]_cyt oscillations in plant cells is explained by a slow release from inhibition of inositol 1,4,5-trisphosphate-gated calcium channels.     

A model of oscillation generation by molluscan neurons

A model describing slow oscillations of membrane potential in molluscan neurons is suggested. It is based on the view that the depolarization phase is due to the slow calcium current, whereas the hyperpolarization phase is due to the potassium current activated by intracellular Ca ions. It is shown that depending on values of the parameters of the model there are three possible types of electrical activity of the neurons: stable membrane hyperpolarization up to the resting potential which is between ?49 and ?53 mV; slow oscillations of membrane potential from ?30 to ?60 mV, with a period of 12–17 sec, and stable membrane depolarization to between ?40 and ?30 mV, which may lead to the onset of stable rhythmic activity of these neurons. Dependence of the amplitude of the oscillations of potential on the extracellular concentration of Ca, K, and Na ions was calculated and agrees qualitatively with the experimental data of Barker and Gainer [4].     

High Cell Density Upregulates Calcium Oscillation by Increasing Calcium Store Content via Basal Mitogen-Activated Protein Kinase Activity

Calcium releases of non-excitable cells are generally a combination of oscillatory and non-oscillatory patterns, and factors affecting the calcium dynamics are still to be determined. Here we report the influence of cell density on calcium increase patterns of clonal cell lines. The majority of HeLa cells seeded at 1.5 x 10⁴/cm² showed calcium oscillations in response to histamine and ATP, whereas cells seeded at 0.5 x 10⁴/cm² largely showed transient and sustained calcium increases. Cell density also affected the response of HEK293 cells to ATP in a similar manner. High cell density increased the basal activity of the mitogen-activated protein (MAP) kinase and calcium store content, and both calcium oscillation and calcium store content were down-regulated by a MAP kinase inhibitor, U0126. Thus, MAP kinase-mediated regulation of calcium store likely underlie the effect of cell density on calcium oscillation. Calcium increase patterns of HeLa cells were conserved at any histamine concentrations tested, whereas the overexpression of histamine H1 receptor, which robustly increased histamine-induced inositol phospholipid hydrolysis, converted calcium oscillations to sustained calcium increases only at high histamine concentrations. Thus, the consequence of modulating inositol phospholipid metabolism was distinct from that of changing cell density, suggesting the effect of cell density is not attributed to inositol phospholipid metabolism. Collectively, our results propose that calcium increase patterns of non-excitable cells reflect calcium store, which is regulated by the basal MAP kinase activity under the influence of cell density.     

Mathematical investigation of IP<Subscript>3</Subscript>-dependent calcium dynamics in astrocytes

We study evoked calcium dynamics in astrocytes, a major cell type in the mammalian brain. Experimental evidence has shown that such dynamics are highly variable between different trials, cells, and cell subcompartments. Here we present a qualitative analysis of a recent mathematical model of astrocyte calcium responses. We show how the major response types are generated in the model as a result of the underlying bifurcation structure. By varying key channel parameters, mimicking blockers used by experimentalists, we manipulate this underlying bifurcation structure and predict how the distributions of responses can change. We find that store-operated calcium channels, plasma membrane bound channels with little activity during calcium transients, have a surprisingly strong effect, underscoring the importance of considering these channels in both experiments and mathematical settings. Variation in the maximum flow in different calcium channels is also shown to determine the range of stable oscillations, as well as set the range of frequencies of the oscillations. Further, by conducting a randomized search through the parameter space and recording the resulting calcium responses, we create a database that can be used by experimentalists to help estimate the underlying channel distribution of their cells.     

Cardiotoxicity of calmidazolium chloride is attributed to calcium aggravation, oxidative and nitrosative stress, and apoptosis

The intracellular calcium concentration ([Ca]_i) regulates cell viability and contractility in myocardial cells. Elevation of the [Ca]_i level occurs by entry of calcium ions (Ca²⁺) through voltage-dependent Ca²⁺ channels in the plasma membrane and release of Ca²⁺ from the sarcoplasmic reticulum. Calmidazolium chloride (CMZ), a subgroup II calmodulin antagonist, blocks L-type calcium channels as well as voltage-dependent Na⁺ and K⁺ channel currents. This study elaborates on the events that contribute to the cytotoxic effects of CMZ on the heart. We hypothesized that apoptotic cell death occurs in the cardiac cells through calcium accumulation, production of reactive oxygen species, and the cytochrome c-mediated PARP activation pathway. CMZ significantly increased the production of superoxide (O₂^•–) and nitric oxide (NO) as detected by FACS and confocal microscopy. CMZ induced mitochondrial damage by increasing the levels of intracellular calcium, lowering the mitochondrial membrane potential, and thereby inducing cytochrome c release. Apoptotic cell death was observed in H9c2 cells exposed to 25 μM CMZ for 24 h. This is the first report that elaborates on the mechanism of CMZ-induced cardiotoxicity. CMZ causes apoptosis by decreasing mitochondrial activity and contractility indices and increasing oxidative and nitrosative stress, ultimately leading to cell death via an intrinsic apoptotic pathway.     

Spontaneous oscillations of intracellular calcium and growth hormone secretion

A novel combination of two single cell assays allowed the simultaneous measurement of intracellular calcium concentration and hormone secretion in normal pituitary cells. [Ca2+]i was recorded using the fluorescent Ca2+ indicator fura-2 and digital imaging microscopy. This technique was combined with a reverse hemolytic plaque assay for growth hormone in order to identify somatotropes and quantitate the amount of hormone released. A dynamic profile of rhythmic calcium oscillations was found in spontaneously secreting somatotropes. Each somatotrope displayed a distinct frequency (one pulse every 5-30 s) and amplitude (range 50-450 nM) generated asynchronously from cell to cell. The amount of growth hormone (GH) released correlated directly with both the frequency and amplitude of calcium oscillations at the level of single GH cells. Furthermore, calcium excursions in somatotropes were rapidly suppressed by either (i) removal of extracellular calcium, (ii) somatostatin (1 mM), or (iii) the calcium channel blockers cobalt (2 mM) and verapamil (100 microM). These observations demonstrate that spontaneous calcium oscillations are characteristic for normal somatotropes. These oscillations are related to spontaneous hormone secretion and due to influx through calcium channels in the membrane. Somatostatin, the physiologic inhibitor of GH secretion, suppresses calcium transients. These findings suggest that the intracellular signaling information may be encoded both in the frequency and amplitude of calcium oscillations.     

A membrane model for cytosolic calcium oscillations. A study using Xenopus oocytes.

Cytosolic calcium oscillations occur in a wide variety of cells and are involved in different cellular functions. We describe these calcium oscillations by a mathematical model based on the putative electrophysiological properties of the endoplasmic reticulum (ER) membrane. The salient features of our membrane model are calcium-dependent calcium channels and calcium pumps in the ER membrane, constant entry of calcium into the cytosol, calcium dependent removal from the cytosol, and buffering by cytoplasmic calcium binding proteins. Numerical integration of the model allows us to study the fluctuations in the cytosolic calcium concentration, the ER membrane potential, and the concentration of free calcium binding sites on a calcium binding protein. The model demonstrates the physiological features necessary for calcium oscillations and suggests that the level of calcium flux into the cytosol controls the frequency and amplitude of oscillations. The model also suggests that the level of buffering affects the frequency and amplitude of the oscillations. The model is supported by experiments indirectly measuring cytosolic calcium by calcium-induced chloride currents in Xenopus oocytes as well as cytosolic calcium oscillations observed in other preparations.     

Calcium oscillations in a triplet of pancreatic acinar cells

We use a mathematical model of calcium dynamics in pancreatic acinar cells to investigate calcium oscillations in a ring of three coupled cells. A connected group of cells is modeled in two different ways: 1), as coupled point oscillators, each oscillator being described by a spatially homogeneous model; and 2), as spatially distributed cells coupled along their common boundaries by gap-junctional diffusion of inositol trisphosphate and/or calcium. We show that, although the point-oscillator model gives a reasonably accurate general picture, the behavior of the spatially distributed cells cannot always be predicted from the simpler analysis; spatially distributed diffusion and cell geometry both play important roles in determining behavior. In particular, oscillations in which two cells are in synchrony, with the third phase-locked but not synchronous, appears to be more dominant in the spatially distributed model than in the point-oscillator model. In both types of model, intercellular coupling leads to a variety of synchronous, phase-locked, or asynchronous behaviors. For some parameter values there are multiple, simultaneous stable types of oscillation. We predict 1), that intercellular calcium diffusion is necessary and sufficient to coordinate the responses in neighboring cells; 2), that the function of intercellular inositol trisphosphate diffusion is to smooth out any concentration differences between the cells, thus making it easier for the diffusion of calcium to synchronize the oscillations; 3), that groups of coupled cells will tend to respond in a clumped manner, with groups of synchronized cells, rather than with regular phase-locked periodic intercellular waves; and 4), that enzyme secretion is maximized by the presence of a pacemaker cell in each cluster which drives the other cells at a frequency greater than their intrinsic frequency.     

Functional Modeling of the Shift in Cellular Calcium Dynamics at the Onset of Synchronization in Smooth Muscle Cells

In the present paper we address the nature of synchronization properties found in populations of mesenteric artery smooth muscle cells. We present a minimal model of the onset of synchronization in the individual smooth muscle cell that is manifested as a transition from calcium waves to whole-cell calcium oscillations. We discuss how different types of ion currents may influence both amplitude and frequency in the regime of whole-cell oscillations. The model may also explain the occurrence of mixed-mode oscillations and chaotic oscillations frequently observed in the experimental system.     

NAD causes dissociation of neural networks into subpopulations of neurons by inhibiting the network synchronous hyperactivity evoked by ammonium ions

The mechanisms of hyperexcitability of neuronal networks by ammonium ions and inhibition of this activity by coenzyme NAD were investigated on mixed neuro-glial cultures of rat hippocampus. Ammonium ions cause activation of silent or spontaneously active neuronal networks inducing a bursting electrical activity of neurons and high-frequency synchronous calcium oscillations. In control conditions NAD completely inhibits spontaneous activity of the neuronal network. NAD added after NH₄Cl disrupts synchronous oscillation in neurons and splits the network into five populations of neurons. In 4% of cells NAD decreased the amplitude of Ca²⁺ oscillations, preserving initial mode of oscillations. In 32% of cells, a transient suppression of the neuronal oscillations was observed: inhibition was followed by restoration of the synchronous periodic activity. In 10% of cells, NAD produced a gradual decrease of Ca²⁺ oscillations down to a complete termination of the initial periodic activity induced by ammonium. Fast and total inhibition of Ca²⁺ oscillations by NAD was observed in two small groups of neurons. First group (A) participated in the initial spontaneous network activity (5% of cells) with a period of 66–100 s. Second group (B), on the contrary, did not participate in the spontaneous activity. This group of neurons began to pulse with a high frequency (with a period of 6–8 s) synchronously with other neurons in the network after the addition of NH₄Cl. Based on the comparison of calcium responses of different cell groups to the depolarization caused by KCl and NH₄Cl and to the application of domoic acid, as well as on the results obtained in experiments with fluorescent antibodies against GAD 65/67, parvalbumin, calretinin, and calbindin, we propose that neurons of populations (A) and (B) may belong to GABAergic neurons containing calbindin and parvalbumin, respectively. Further analysis of specificity of the NAD effect on these neuronal groups may allow identification of the main targets of the ammonium toxic action in the brain. Thus, we have shown that NAD selectively inhibits neuronal activity and high-frequency synchronous Ca²⁺ oscillations in GABAergic neurons containing calcium-binding proteins. The inhibition is accompanied by desynchronization of oscillations and dissociation of neuronal network into several populations.     

Slow oscillations of free intracellular calcium ion concentration in human fibroblasts responding to mechanical stretch

Calcium transients in single, human gingival fibroblasts were studied after mechanical stretching of flexible culture substrates. A model system was developed to reproducibly stretch and rapidly (< 1 sec) refocus cells in the same focal plane so that changes in the concentration of free intracellular calcium ions ([Ca²⁺]_i) were monitored without delay. Attached cells were grown on flexible bottom Petriperm dishes, loaded with fura-2/AM, and stretched by 1% or 2.8% of substrate area. The stretch caused no significant cell detachment or membrane lesions. A 1% stretch induced no calcium response, but a 2.8% stretch stimulated an initial calcium transient and the subsequent generation of [Ca²⁺]_i oscillations of up to 2,000 sec. At 1% stretch, there was no calcium response. Cell shape and plating time were important determinants in the calcium response to mechanical stimulation: the responder cells were small and round without long processes. Major calcium transients were inhibited completely by 5 mM EGTA or by 10 μM gadolinium ions, by 50 μM nifedipine, or 250 μM verapamil, suggesting an influx of calcium through stretch-activated (SA) channels and L-type calcium channels. Depolarization by high KCl (144 mM) in the extracellular medium enhanced the amplitude of calcium transients by 54%. Calcium oscillations were not inhibited by preincubation with thapsigargin, caffeine, cholera toxin, staurosporine or 1-(5-isoquinolinesulfonyl)-2-methylpiperazine (H-7), indicating that IP₃ sensitive pools, IP₃ insensitive pools, G₅α subunits, and protein kinase C, respectively, were not involved in the generation of calcium oscillations. Pretreatment with genistein, a specific tyrosine kinase inhibitor or cytochalasin D, an inhibitor of actin polymerization, or pertussis toxin, an inhibitor of G_iα and G_oα subunits, completely abolished calcium transients and oscillations. These results indicate that Ca²⁺ flux due to mechanical stretching is likely mediated through SA ion channe s and is dependent on tyrosine kinases, pertussis toxin-sensitive subunits of G-proteins, and actin filaments. © 1994 Wiley-Liss, Inc.