Hormone-induced calcium oscillations in liver cells can be explained by a simple one pool model

Hormone-induced oscillations of the free intracellular calcium concentration are thought to be relevant for frequency encoding of hormone signals. In liver cells, such Ca2+ oscillations occur in response to stimulation by hormones acting via phosphoinositide breakdown. This observation may be explained by cooperative, positive feedback of Ca2+ on its own release from one inositol 1,4,5-trisphosphate-sensitive pool, obviating oscillations of inositol 1,4,5-trisphosphate. The kinetic rate laws of the associated model have a mathematical structure reminiscent of the Brusselator, a hypothetical chemical model involving a rather improbable trimolecular reaction step, thus giving a realistic biological interpretation to this hallmark of dissipative structures. We propose that calmodulin is involved in mediating this cooperativity and positive feedback, as suggested by the presented experiments. For one, hormone-induced calcium oscillations can be inhibited by the (nonphenothiazine) calmodulin antagonists calmidazolium or CGS 9343 B. Alternatively, in cells overstimulated by hormone, as characterized by a non-oscillatory elevated Ca2+ concentration, these antagonists could again restore sustained calcium oscillations. The experimental observations, including modulation of the oscillations by extracellular calcium, were in qualitative agreement with the predictions of our mathematical model.     

Mechanical stimuli modulate intracellular calcium oscillations: a pathological model without chemical cues

Objective

To control the oscillatory behavior of the intracellular calcium ([Ca²⁺]_i) concentration in endothelial cells via mechanical factors (i.e., various hydrostatic pressures) because [Ca²⁺]_i in these cells is affected by blood pressure.

Results

Quantitative analyses based on real-time imaging showed that [Ca²⁺]_i oscillation frequency and relative concentration increased significantly when 200 mm Hg pressure, mimicking hypertension, was applied for >10 min. Peak height and peak width decreased significantly at 200 mm Hg. These trends were more marked as the duration of the 200 mm Hg pressure was increased. However, no change was observed under normal blood pressure conditions 100 mm Hg.

Conclusion

We generated a simple in vitro model to study [Ca²⁺]_i behavior in relation to various pathologies and diseases by eliminating possible complicating effects induced by chemical cues.

     

Effectors of the frequency of calcium oscillations in HEK-293 cells: wavelet analysis and a computer model

Oscillations of the intracellular concentration of Ca²⁺ in cultured HEK-293 cells, which heterologously expressed the calcium-sensing receptor, were recorded with the fluorophore Fura-2 using fluorescence microscopy. HEK-293 cells are extremely sensitive to small perturbations in extracellular calcium concentrations. Resting cells were attached to cover slips and perifused with saline solution containing physiologically relevant extracellular Ca²⁺ concentrations in the range 0.5–5 mM. Acquired digitized images of the cells showed oscillatory fluctuations in the intracellular Ca²⁺ concentration over the time course, and were processed as a function of the change in Fura-2 excitation ratio and frequency at 12–37°C. Newly developed data processing techniques with wavelet analysis were used to estimate the frequency at which the rectified sinusoidal oscillations occurred; we estimated ~4 min⁻¹ under normal conditions. Temperature variations revealed an Arrhenius relationship in oscillation frequency. A critical Ca²⁺ concentration of ~2 mM was estimated, below which oscillations did not occur. These data were used to develop a kinetic model of the system that was simulated using Mathematica; kinetic parameter values were adjusted to match the experimentally observed oscillations of intracellular Ca²⁺ concentration as a function of extracellular Ca²⁺ concentration, and temperature; and from these, limit cycles were obtained and control coefficients were estimated for all parameters.     

Cytoplasmic calcium stimulates exocytosis in a plant secretory cell

Although exocytosis is likely to occur in plant cells, the control of this process is the subject of speculation, as no direct measurements of vesicle fusion to the plasma membrane have been made. We used the patch clamp technique to monitor the secretory activity of single aleurone protoplasts by measuring membrane capacitance (C_m), while dialyzing the cytosol with different Ca²⁺ containing solutions. Secretory activity increased with [Ca²⁺]_i ~ 1 μM. This demonstrates directly the existence of exocytosis in plant cells, and suggests that both plant and animal cells share common mechanisms (cytosolic Ca²⁺) for the control of exocytotic secretion.     

Emergence of oscillations in a model of weakly coupled two Bonhoeffer-van der Pol equations

Bifurcations of periodic solutions in a model of weakly coupled two Bonhoeffer-van der Pol equations are studied. The model realizes a half-center model with reciprocal inhibition, a typical model used in the field of neural motor control to account for the generation of alternating rhythmic bursts observed in motoneurons and spinal neural networks. Several oscillatory solutions such as in-phase, anti-phase as well as out-of-phase solutions emerge from the model's equilibrium as one of the parameters of the model changes. Among the variety of bifurcations exhibited by the model, we analyze Hopf bifurcations, by which several periodic solutions emerge, and illustrate generation mechanisms of alternating oscillations in the model.     

A mathematical model of spontaneous calcium(II) oscillations in astrocytes

Astrocytes exhibit oscillations and waves of Ca²⁺ ions within their cytosol and it appears that this behavior helps facilitate the astrocyte's interaction with its environment, including its neighboring neurons. Often changes in the oscillatory behavior are initiated by an external stimulus such as glutamate, recently however, it has been observed that oscillations are also initiated spontaneously. We propose here a mathematical model of how spontaneous Ca²⁺ oscillations arise in astrocytes. This model uses the calcium-induced calcium release and inositol cross-coupling mechanisms coupled with a receptor-independent method for producing inositol (1,4,5)-trisphosphate as the heart of the model. By computationally mimicking experimental constraints we have found that this model provides results that are qualitatively similar to experiment.     

Localization of a thrombin-sensitive calcium pool in platelets.

Electron microscopic x-ray microprobe analysis of pyroantimonate precipitates in platelets fixed in osmium tetroxide-pyroantimonate revealed calcium localization in the nucleoids of alpha-granules. This pool of calcium had largely disappeared within 10 sec after stimulation of platelets by thrombin. Such a rapid change suggests that this calcium pool may have a regulatory role in stimulus-response coupling.     

Protein phosphorylation driven by intracellular calcium oscillations: a kinetic analysis.

Given the ubiquitous nature of signal-induced Ca2+ oscillations, the question arises as to how cellular responses are affected by repetitive Ca2+ spikes. Among these responses, we focus on those involving protein phosphorylation. We examine, by numerical simulations of a theoretical model, the situation where a protein is phosphorylated by a Ca(2+)-activated kinase and dephosphorylated by a phosphatase. This reversible phosphorylation system is coupled to a mechanism generating cytosolic Ca2+ oscillations; for definiteness, this oscillatory mechanism is based on the process of Ca(2+)-induced Ca2+ release. The analysis shows that the average fraction of phosphorylated protein increases with the frequency of repetitive Ca2+ spikes; the latter frequency generally rises with the extent of external stimulation. Protein phosphorylation therefore provides a mechanism for the encoding of the external stimulation in terms of the frequency of signal-induced Ca2+ oscillations. Such a frequency encoding requires precise kinetic conditions on the Michaelis-Menten constants of the kinase and phosphatase, their maximal rates, and the degree of cooperativity in kinase activation by Ca2+. In particular, the most efficient encoding of Ca2+ oscillations based on protein phosphorylation occurs in conditions of zero-order ultrasensitivity, when the kinase and phosphatase are saturated by their protein substrate. The kinetic analysis uncovers a wide variety of temporal patterns of phosphorylation that could be driven by signal-induced Ca2+ oscillations.     

Inositol trisphosphate and calcium oscillations

InsP3 has two important functions in generating Ca2+ oscillations. It releases Ca2+ from the internal store and it can contribute to Ca2+ entry. A hypothesis has been developed to describe a mechanism for Ca2+ oscillations with particular emphasis on the way agonist concentration regulates oscillator frequency. The main idea is that the InsP3 receptors are sensitized to release Ca2+ periodically by cyclical fluctuations of Ca2+ within the lumen of the endoplasmic reticulum. Each time a pulse of Ca2+ is released, the luminal level of Ca2+ declines and has to be replenished before the InsP3 receptors are resensitized to deliver the next pulse of Ca2+. It is this loading of the internal store that explains why frequency is sensitive to external Ca2+ and may also account for how variations in agonist concentration are translated into changes in oscillation frequency. Variations in agonist-induced entry of external Ca2+, which can occur through different mechanisms, determine the variable rates of store loading responsible for adjusting the sensitivity of the InsP3 receptors to produce the periodic pulses of Ca2+. The Ca2+ oscillator is an effective analogue-to-digital converter in that variations in the concentration of the external stimulus are translated into a change in oscillator frequency.     

Frequency decoding of calcium oscillations

Background

Calcium (Ca^2 +) oscillations are ubiquitous signals present in all cells that provide efficient means to transmit intracellular biological information. Either spontaneously or upon receptor ligand binding, the otherwise stable cytosolic Ca^2 + concentration starts to oscillate. The resulting specific oscillatory pattern is interpreted by intracellular downstream effectors that subsequently activate different cellular processes. This signal transduction can occur through frequency modulation (FM) or amplitude modulation (AM), much similar to a radio signal. The decoding of the oscillatory signal is typically performed by enzymes with multiple Ca^2 + binding residues that diversely can regulate its total phosphorylation, thereby activating cellular program. To date, NFAT, NF-κB, CaMKII, MAPK and calpain have been reported to have frequency decoding properties.

Scope of review

The basic principles and recent discoveries reporting frequency decoding of FM Ca^2 + oscillations are reviewed here.

Major conclusions

A limited number of cellular frequency decoding molecules of Ca^2 + oscillations have yet been reported. Interestingly, their responsiveness to Ca^2 + oscillatory frequencies shows little overlap, suggesting their specific roles in cells.

General significance

Frequency modulation of Ca^2 + oscillations provides an efficient means to differentiate biological responses in the cell, both in health and in disease. Thus, it is crucial to identify and characterize all cellular frequency decoding molecules to understand how cells control important cell programs.     

Forced oscillations in a windkessel model

Volume elasticity of the arterial system and its component parts is developed starting from a Windkessel^*-model, which is defined in 4 points. Emphasis is laid on the simplicity of the derived equations and accessibility to experimental verification. The theory is an extension of earlier work achieved by Wetterer and Pieper (1953), who introduced an essentially physical method for the indirect determination of volume elasticity in situ, by creating forced sinusoidal oscillations in the arterial system, using a special pump operated at a considerably lower frequency than the mean heart frequency. The elegance of both experimental technique and the derived equations incited us to investigate the mathematical foundation and possible generalization of the method.     

Forced oscillations in a windkessel model

Volume elasticity of the arterial system and its component parts is developed starting from a Windkessel^*-model, which is defined in 4 points. Emphasis is laid on the simplicity of the derived equations and accessibility to experimental verification. The theory is an extension of earlier work achieved by Wetterer and Pieper (1953), who introduced an essentially physical method for the indirect determination of volume elasticity in situ, by creating forced sinusoidal oscillations in the arterial system, using a special pump operated at a considerably lower frequency than the mean heart frequency. The elegance of both experimental technique and the derived equations incited us to investigate the mathematical foundation and possible generalization of the method.     

Cytoplasmic maturation of mammalian oocytes: development of a mechanism responsible for sperm-induced Ca2+ oscillations

The oocytes of most mammalian species, including mouse and human, are fertilized in metaphase of the second meiotic division. A fertilizing spermatozoon introduces an oocyte-activating factor, phospholipase C zeta, triggering oscillations of the cytoplasmic concentration of free calcium ions ([Ca(2+)](i)) in the oocyte. [Ca(2+)](i) oscillations are essential for the activation of the embryonic development. They trigger processes such as resumption and completion of meiosis, establishment of the block to polyspermy and recruitment of maternal mRNAs necessary for the activation of the embryo genome. Moreover, it has been recently shown that [Ca(2+)](i) oscillations may also influence the development of the embryo. The ability to generate [Ca(2+)](i) oscillations develops in mammalian oocytes during meiotic maturation and requires several cytoplasmic changes, including: 1/ reorganization of endoplasmic reticulum, the main stockpile of calcium in the oocyte, 2/ increase in the number of 1,4,5-inositol triphosphate (IP(3)) receptors, 3/ changes in their biochemical properties (e.g.: sensitivity to IP3), and possibly both 4/ an increase in the concentration of Ca(2+) ions stored in endoplasmic reticulum (ER) and 5/ redistribution of Ca(2+)-binding ER proteins. The aim of this review is to present the state of current knowledge about these processes.     

Amplitude-encoded calcium oscillations in fish cells

The reaction of intracellular Ca(2+) to different agonist stimuli in primary hepatocytes from rainbow trout (Oncorhynchus mykiss) as well as the permanent fish cell line RTL-W1 was investigated systematically. In addition to "classical" agonists such as phenylephrine and ATP, model environmental toxicants like 4-nitrophenol and 3,4-dichloroaniline were used to elucidate possible interactions between toxic effects and Ca(2+) signaling. We report Ca(2+) oscillations in response to several stimuli in RTL-W1 cells and to a lesser extent in primary hepatocytes. Moreover, these Ca(2+) oscillations are amplitude-encoded in contrast to their mammalian counterpart. Bioinformatics and computational analysis were employed to identify key players of Ca(2+) signaling in fish and to determine likely causes for the experimentally observed differences between the Ca(2+) dynamics in fish cells compared to those in mammalian liver cells.     

Intercellular communication via intracellular calcium oscillations

In this letter, we present the results of a simple model for intercellular communication via calcium oscillations, motivated in part by a recent experimental study. The model describes two cells (a "donor" and "sensor") whose intracellular dynamics involve a calcium-induced, calcium release process. The cells are coupled by assuming that the input of the sensor cell is proportional to the output of the donor cell. As one varies the frequency of calcium oscillations of the donor cell, the sensor cell passes through a sequence of N : M phase-locked regimes and exhibits a "Devil's staircase" behavior. Such a phase-locked response has been seen experimentally in pulsatile stimulation of single cells. We also study a stochastic version of the coupled two-cell model. We find that phase locking holds for realistic choices for the cell volume.     

Non-Gaussian noise-optimized intracellular cytosolic calcium oscillations

We have numerically studied the effect of a particular kind of non-Gaussian colored noise (NGN), characterized by the deviation q from Gaussian noise (q = 1), on intracellular cytosolic calcium (Ca²⁺) oscillations. It is found that, as q is increased, the Ca²⁺ oscillation regularity increases and reaches a best performance at an optimal q, and then decreases with further increasing q, which represents the occurrence of coherence resonance, i.e., the most regular Ca²⁺ oscillations. Similar phenomena occur for different values of noise intensity and correlation time of the NGN. This phenomenon of deviation-optimized Ca²⁺ oscillations show that, external non-Gaussian noises of different types can enhance and even optimize the intracellular Ca²⁺ oscillations. This result provides new insights into the constructive roles and potential applications of non-Gaussian noises in intracellular cytosolic Ca²⁺ oscillations.     

Selective use of a reserved mechanism for inducing calcium oscillations

Concentration-dependent transformation of hormone- and neurotransmitter-induced calcium oscillation is a common phenomenon in diverse types of cells especially of the secretory type. The rodent submandibular acinar cells are an exception to this rule, which show elevated plateau increase in intracellular calcium under all stimulatory concentrations of both norepinephrine and acetylcholine. However, under depolarized state this cell type could also show a variation of periodic calcium changes. This reserved mechanism of calcium oscillation is jump-started by depolarization only with muscarinic cholinergic stimulation, but not with adrenergic stimulation. This latter effect is attributable to receptor activation, not due to simultaneous activation of and β receptors, with β receptor activation only serving to enhance the magnitude. These data suggest that this reserved mechanism for inducing calcium oscillation can be selectively used only by specific receptor-signaling pathways, and may therefore partly explain the long-known differences between secretion induced by sympathetic and parasympathetic stimulation in the submandibular gland.     

Sandy: a new mouse model for platelet storage pool deficiency

Sandy (sdy) is a mouse mutant with diluted pigmentation which recently arose in the DBA/2J strain. Genetic tests indicate it is caused by an autosomal recessive mutation on mouse Chromosome 13 near the cr and Xt genetic loci. This mutation is different genetically and hematologically from previously described mouse pigment mutations with storage pool deficiency (SPD). The sandy mutant has diluted pigmentation in both eyes and fur, is fully viable and has prolonged bleeding times. Platelet serotonin levels are extremely low although ATP dependent acidification activity of platelet organelles appears normal. Also, platelet dense granules are extremely reduced in number when analysed by electron microscopy of unfixed platelets. Platelets have abnormal uptake and flashing of the fluorescent dye mepacrine. Secretion of lysosomal enzymes from kidney and from thrombin-stimulated platelets is depressed 2- and 3-fold, and ceroid pigment is present in kidney. Sandy platelets have a reduced rate of aggregation induced by collagen. The sandy mutant has an unusually severe dense granule defect and thus may be an appropriate model for cases of human Hermansky-Pudlak syndrome with similarly extreme types of SPD. It represents the tenth example of a mouse mutant with simultaneous defects in melanosomes, lysosomes and/or platelet dense granules.     

How to determine a regional species pool: a study in two Swedish regions

The species pool hypothesis has been proposed as one of the possible explanations for the local species richness of plant communities. For testing and validating this theory, it is of crucial importance to determine the dimension of the regional pool, which is the reservoir of species that are potentially able to exist in a community. The main purpose of this study was to develop and test different methods for the determination of the regional species pool. Two regions in Sweden served as study areas, Öland and Uppland. In both regions, three different vegetation types were treated: dry calcareous grasslands, coastal meadows and deciduous forests. For the determination of the regional pool two main groups of methods are proposed: 1) six ecological approaches, based on Ellenberg species indicator values, and 2) two phytosociological approaches, based on the occurrence of species in different syntaxa in the framework of the Braun-Blanquet system. The different screening methods were tested using Sørensen's index expressing the similarity between the community species pool and the regional species pool. Two types of error were recognized which may result in low index values. For the six ecological methods Sørensen's index values were below 50%. The methods differed considerably from each other in accuracy, due to large differences in errors of both types. The phytosociological methods resulted in higher similarity values of up to almost 70%. The two approaches differed in error type but gave similar results.