What can we learn from the irregularity of Ca[sup 2+] oscillations? (original) (raw)

Stochastic Aspects of Oscillatory Ca2+ Dynamics in Hepatocytes

Biophysical Journal, 2008

Signal-induced Ca 21 oscillations have been observed in many cell types and play a primary role in cell physiology. Although it is the regular character of these oscillations that first catches the attention, a closer look at time series of Ca 21 increases reveals that the fluctuations on the period during individual spike trains are far from negligible. Here, we perform a statistical analysis of the regularity of Ca 21 oscillations in norepinephrine-stimulated hepatocytes and find that the coefficient of variation lies between 10% and 15%. Stochastic simulations based on Gillespie's algorithm and considering realistic numbers of Ca 21 ions and inositol trisphosphate (InsP 3 ) receptors account for this variability if the receptors are assumed to be grouped in clusters of a few tens of channels. Given the relatively small number of clusters (;200), the model predicts the existence of repetitive spikes induced by fluctuations (stochastic resonance). Oscillations of this type are found in hepatocytes at subthreshold concentrations of norepinephrine. We next predict with the model that the isoforms of the InsP 3 receptor can affect the variability of the oscillations. In contrast, possible accompanying InsP 3 oscillations have no impact on the robustness of signal-induced repetitive Ca 21 spikes.

Stochastic effects in intercellular calcium spiking in hepatocytes

2001

We carry out a Monte Carlo simulation of stochastic effects for two models of intercellular calcium wave propagation in rat hepatocytes. Both models involve gap junction diffusion by a second messenger. We find that, in general, the stochastic effects improve agreement with experiment, for a reasonable choice of model parameters. Both stochastic models exhibit baseline fluctuations and variations in the peak heights of Ca2+.

Mechanism of intracellular Ca2+ oscillations and interspike interval distributions

Proc. of SPIE Vol. 6602, 66020M, (2007), 2007

The dynamics of cytosolic Ca 2+ concentration exhibits oscillations with a wide range of periods. It was suggested in recent years by several modelling studies that these oscillations do not result from an oscillatory local dynamics but that fluctuations drive the formation of spatial and temporal structures in a non-oscillatory dynamic regime. Fluctuations arise from the random opening and closing of release channels on the membrane of the endoplasmic reticulum. Consequently, the interspike interval (ISI) has not a sharp value as with regular oscillations but distributions of ISI arise. We present these distributions and relate them to underlying processes. Oscillations with long average ISI can be comprehended as repetitive wave triggering. The standard deviation of the ISI approximates the inverse of the triggering rate. Oscillations with short average ISI are often complex oscillations consisting of base line oscillations and intermittent oscillations on an elevated cytosolic Ca 2+ level.

Switching from Simple to Complex Oscillations in Calcium Signaling

Biophysical Journal, 2000

We present a new model for calcium oscillations based on experiments in hepatocytes. The model considers feedback inhibition on the initial agonist receptor complex by calcium and activated phospholipase C, as well as receptor type-dependent self-enhanced behavior of the activated G ␣ subunit. It is able to show simple periodic oscillations and periodic bursting, and it is the first model to display chaotic bursting in response to agonist stimulations. Moreover, our model offers a possible explanation for the differences in dynamic behavior observed in response to different agonists in hepatocytes.

Complex intracellular calcium oscillations A theoretical exploration of possible mechanisms

Biophysical Chemistry, 1997

Intracellular Ca'+ oscillations are commonly observed in a large number of cell types in response to stimulation by an extracellular agonist. In most cell types the mechanism of regular spiking is well understood and models based on Ca2+-induced Ca*+ release (CICR) can account for many experimental observations. However, cells do not always exhibit simple Ca*+ oscillations. In response to given agonists, some cells show more complex behaviour in the form of bursting, i.e. trains of Ca2+ spikes separated by silent phases. Here we develop several theoretical models, based on physiologically plausible assumptions, that could account for complex intracellular Ca'+ oscillations. The models are all based on one-or two-pool models based on CICR. We extend these models by (i) considering the inhibition of the Ca*+-release channel on a unique intracellular store at high cytosolic Ca2+ concentrations, (ii> taking into account the Ca*+-activated degradation of inositol 1,4,5trisphosphate (IP& or (iii) considering explicitly the evolution of the Ca2' concentration in two different pools, one sensitive and the other one insensitive to IP,. Besides simple periodic oscillations, these three models can all account for more complex oscillatory behaviour in the form of bursting. Moreover, the model that takes the kinetics of IP, into account shows chaotic behaviour.

On the Role of Stochastic Channel Behavior in Intracellular Ca2+ Dynamics

Biophysical Journal, 2003

I present a stochastic model for intracellular Ca(2+) oscillations. The model starts from stochastic binding and dissociation of Ca(2+) to binding sites on a single subunit of the IP(3)-receptor channel but is capable of simulating large numbers of clusters for many oscillation periods too. I find oscillations with variable periods ranging from 17 s to 120 s and a standard deviation well in the experimentally observed range. Long period oscillations can be perceived as nucleation phenomenon and can be observed for a large variety of single channel dynamics. Their period depends on the geometric characteristics of the cluster array. Short periods are in the range of the time scale of channel dynamics. Both long and short period oscillations occur for parameters with a nonoscillatory deterministic regime.

Hierarchical organization of calcium signals in hepatocytes: from experiments to models

Biochimica et Biophysica Acta (BBA) - Molecular Cell Research, 2000

The proper working of the liver largely depends on the fine tuning of the level of cytosolic Ca 2 in hepatocytes. Thanks to the development of imaging techniques, our understanding of the spatio-temporal organization of intracellular Ca 2 in thisâ nd other^cell types has much improved. Many of these signals are mediated by a rise in the level of inositol 1,4,5trisphosphate (InsP 3 ), a second messenger which can activate the release of Ca 2 from the endoplasmic reticulum. Besides the now well-known hepatic Ca 2 oscillations induced by hormonal stimulation, intra-and intercellular Ca 2 waves have also been observed. More recently, subcellular Ca 2 increases associated with the coordinated opening of a few Ca 2 channels have been reported. Given the complexity of the regulations involved in the generation of such processes and the variety of time and length scales necessary to describe those phenomena, theoretical models have been largely used to gain a precise and quantitative understanding of the dynamics of intracellular Ca 2 . Here, we review the various aspects of the spatio-temporal organization of cytosolic Ca 2 in hepatocytes from the dual point of view provided by experiments and modeling. We first focus on the description and the mechanism of intracellular Ca 2 oscillations and waves. Second, we investigate in which manner these repetitive Ca 2 increases are coordinated among a set of hepatocytes coupled by gap junctions, a phenomenon known as`intercellular Ca 2 waves'. Finally, we focus on the so-called elementary Ca 2 signals induced by low InsP 3 concentrations, leading to Ca 2 rises having a spatial extent of a few microns. Although these small-scale events have been mainly studied in other cell types, we theoretically infer general properties of these localized intracellular Ca 2 rises that could also apply to hepatocytes. ß 0167-4889 / 00 / $^see front matter ß 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 -4 8 8 9 ( 0 0 ) 0 0 0 9 0 -2 * Corresponding

Mechanism of receptor-oriented intercellular calcium wave propagation in hepatocytes

The FASEB Journal, 2000

Intercellular calcium signals are propagated in multicellular hepatocyte systems as well as in the intact liver. The stimulation of connected hepatocytes by glycogenolytic agonists induces reproducible sequences of intracellular calcium concentration increases, resulting in unidirectional intercellular calcium waves. Hepatocytes are characterized by a gradient of vasopressin binding sites from the periportal to perivenous areas of the cell plate in hepatic lobules. Also, coordination of calcium signals between neighboring cells requires the presence of the agonist at each cell surface as well as gap junction permeability. We present a model based on the junctional coupling of several hepatocytes differing in sensitivity to the agonist and thus in the intrinsic period of calcium oscillations. In this model, each hepatocyte displays repetitive calcium spikes with a slight phase shift with respect to neighboring cells, giving rise to a phase wave. The orientation of the apparent calcium wave is imposed by the direction of the gradient of hormonal sensitivity. Calcium spikes are coordinated by the diffusion across junctions of small amounts of inositol 1,4,5-trisphosphate (InsP 3 ). Theoretical predictions from this model are confirmed experimentally. Thus, major physiological insights may be gained from this model for coordination and spatial orientation of intercellular signals.-Dupont, G., Tordjmann, T., Clair, C., Swillens, S., Claret, M., Combettes, L. Mechanism of receptororiented intercellular calcium wave propagation in hepatocytes. FASEB J. 14, 279 -289 (2000)