Latency correlates with period in a model for signal-induced Ca2+ oscillations based on Ca2(+)-induced Ca2+ release

Modeling of Ca2+ transients initiated by GPCR agonists in mesenchymal stromal cells

The integrative study that included experimentation and mathematical modeling was carried out to analyze dynamic aspects of transient Ca²⁺ signaling induced by brief pulses of GPCR agonists in mesenchymal stromal cells from the human adipose tissue (AD-MSCs). The experimental findings argued for IP₃/Ca²⁺-regulated Ca²⁺ release via IP₃ receptors (IP₃Rs) as a key mechanism mediating agonist-dependent Ca²⁺ transients. The consistent signaling circuit was proposed to formalize coupling of agonist binding to Ca²⁺ mobilization for mathematical modeling. The model properly simulated the basic phenomenology of agonist transduction in AD-MSCs, which mostly produced single Ca²⁺ spikes upon brief stimulation. The spike-like responses were almost invariantly shaped at different agonist doses above a threshold, while response lag markedly decreased with stimulus strength. In AD-MSCs, agonists and IP₃ uncaging elicited similar Ca²⁺ transients but IP₃ pulses released Ca²⁺ without pronounced delay. This suggested that IP₃ production was rate-limiting in agonist transduction. In a subpopulation of AD-MSCs, brief agonist pulses elicited Ca²⁺ bursts crowned by damped oscillations. With properly adjusted parameters of IP₃R inhibition by cytosolic Ca²⁺, the model reproduced such oscillatory Ca²⁺ responses as well. GEM-GECO1 and R-CEPIA1er, the genetically encoded sensors of cytosolic and reticular Ca²⁺, respectively, were co-expressed in HEK-293 cells that also responded to agonists in an "all-or-nothing" manner. The experimentally observed Ca²⁺ signals triggered by ACh in both compartments were properly simulated with the suggested signaling circuit. Thus, the performed modeling of the transduction process provides sufficient theoretical basis for deeper interpretation of experimental findings on agonist-induced Ca²⁺ signaling in AD-MSCs.

Fundamental properties of Ca2+ signals

BACKGROUND

Ca2+ is a ubiquitous and versatile second messenger that transmits information through changes of the cytosolic Ca2+ concentration. Recent investigations changed basic ideas on the dynamic character of Ca2+ signals and challenge traditional ideas on information transmission.

SCOPE OF REVIEW

We present recent findings on key characteristics of the cytosolic Ca2+ dynamics and theoretical concepts that explain the wide range of experimentally observed Ca2+ signals. Further, we relate properties of the dynamical regulation of the cytosolic Ca2+ concentration to ideas about information transmission by stochastic signals.

MAJOR CONCLUSIONS

We demonstrate the importance of the hierarchal arrangement of Ca2+ release sites on the emergence of cellular Ca2+ spikes. Stochastic Ca2+ signals are functionally robust and adaptive to changing environmental conditions. Fluctuations of interspike intervals (ISIs) and the moment relation derived from ISI distributions contain information on the channel cluster open probability and on pathway properties.

GENERAL SIGNIFICANCE

Robust and reliable signal transduction pathways that entail Ca2+ dynamics are essential for eukaryotic organisms. Moreover, we expect that the design of a stochastic mechanism which provides robustness and adaptivity will be found also in other biological systems. Ca2+ dynamics demonstrate that the fluctuations of cellular signals contain information on molecular behavior. This article is part of a Special Issue entitled Biochemical, biophysical and genetic approaches to intracellular calcium signaling.

Chaotic pulse transmission and spiral formation in a calcium oscillation model

We study a two-dimensional reaction-diffusion equation for calcium oscillation with a pacemaker region. When the pacemaker entrains the whole system, circular waves are observed as a target pattern. However, if the pace of the pacemaker is too fast, the pulse propagation to the outer region sometimes fails in a chaotic manner. We find that spiral waves are spontaneously created at the interface between the pacemaker region and the outer region.

Intercellular waves propagation in an array of cells coupled through paracrine signaling: a computer simulation study

A linear chain of cells is considered in which calcium (Ca2+) fluctuations within a cell are described by a simple minimal model. Cells are coupled together by bidirectional paracrine signaling via calcium oscillations. Two typical zones of propagation are observed: a transition zone and a regular zone. The transition zone exhibits the same phenomena that can be observed in single cells, pairs or triplets of cells. Within the regular zone, simple periodic oscillations of calcium propagate and the Ca2+ signal is similar from one cell to another (same amplitude and same frequency). But, the signals are separated by a slight phase shift characterizing the propagation of Ca2+ waves due to the type of coupling used. We also consider the colonization of the lattice by the abnormal oscillations of sick 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.

A theoretical model of slow wave regulation using voltage-dependent synthesis of inositol 1,4,5-trisphosphate

A qualitative mathematical model is presented that examines membrane potential feedback on synthesis of inositol 1,4,5-trisphosphate (IP(3)), and its role in generation and modulation of slow waves. Previous experimental studies indicate that slow waves show voltage dependence, and this is likely to result through membrane potential modulation of IP(3). It is proposed that the observed response of the tissue to current pulse, pulse train, and maintained current injection can be explained by changes in IP(3), modulated through a voltage-IP(3) feedback loop. Differences underlying the tissue responses to current injections of opposite polarities are shown to be due to the sequence of events following such currents. Results from this model are consistent with experimental findings and provide further understanding of these experimental observations. Specifically, we find that membrane potential can induce, abolish, and modulate slow wave frequency by altering the excitability of the tissue through the voltage-IP(3) feedback loop.

The lifetime of inositol 1,4,5-trisphosphate in single cells

In many eukaryotic cell types, receptor activation leads to the formation of inositol 1,4,5-trisphosphate (IP3) which causes calcium ions (Ca) to be released from internal stores. Ca release was observed in response to the muscarinic agonist carbachol by fura-2 imaging of N1E-115 neuroblastoma cells. Ca release followed receptor activation after a latency of 0.4 to 20 s. Latency was not caused by Ca feedback on IP3 receptors, but rather by IP3 accumulation to a threshold for release. The dependence of latency on carbachol dose was fitted to a model in which IP3 synthesis and degradation compete, resulting in gradual accumulation to a threshold level at which Ca release becomes regenerative. This analysis gave degradation rate constants of IP3 in single cells ranging from 0 to 0.284 s-1 (0.058 +/- 0.067 s-1 SD, 53 cells) and a mean IP3 lifetime of 9.2 +/- 2.2 s. IP3 degradation was also measured directly with biochemical methods. This gave a half life of 9 +/- 2 s. The rate of IP3 degradation sets the time frame over which IP3 accumulations are integrated as input signals. IP3 levels are also filtered over time, and on average, large-amplitude oscillations in IP3 in these cells cannot occur with period < 10 s.

Properties of intracellular Ca2+ waves generated by a model based on Ca(2+)-induced Ca2+ release

Cytosolic Ca2+ waves occur in a number of cell types either spontaneously or after stimulation by hormones, neurotransmitters, or treatments promoting Ca2+ influx into the cells. These waves can be broadly classified into two types. Waves of type 1, observed in cardiac myocytes or Xenopus oocytes, correspond to the propagation of sharp bands of Ca2+ throughout the cell at a rate that is high enough to permit the simultaneous propagation of several fronts in a given cells. Waves of type 2, observed in hepatocytes, endothelial cells, or various kinds of eggs, correspond to the progressive elevation of cytosolic Ca2+ throughout the cell, followed by its quasi-homogeneous return down to basal levels. Here we analyze the propagation of these different types of intracellular Ca2+ waves in a model based on Ca(2+)-induced Ca2+ release (CICR). The model accounts for transient or sustained waves of type 1 or 2, depending on the size of the cell and on the values of the kinetic parameters that measure Ca2+ exchange between the cytosol, the extracellular medium, and intracellular stores. Two versions of the model based on CICR are considered. The first version involves two distinct Ca2+ pools sensitive to inositol 1,4,5-trisphosphate (IP3) and Ca2+, respectively, whereas the second version involves a single pool sensitive both to Ca2+ and IP3 behaving as co-agonists for Ca2+ release. Intracellular Ca2+ waves occur in the two versions of the model based on CICR, but fail to propagate in the one-pool model at subthreshold levels of IP3. For waves of type 1, we investigate the effect of the spatial distribution of Ca(2+)-sensitive Ca2+ stores within the cytosol, and show that the wave fails to propagate when the distance between the stores exceeds a critical value on the order of a few microns. We also determine how the period and velocity of the waves are affected by changes in parameters measuring stimulation, Ca2+ influx into the cell, or Ca2+ pumping into the stores. For waves of type 2, the numerical analysis indicates that the best qualitative agreement with experimental observations is obtained for phase waves. Finally, conditions are obtained for the occurrence of "echo" waves that are sometimes observed in the experiments.

Cellular and subcellular calcium signaling in gastrointestinal epithelium

Ca2+ is a critical second messenger in virtually all cell types, including the various epithelial cell types within the digestive system. When measured in cell populations, Ca2+ signals usually appear as a single transient or prolonged elevation. In individual epithelial cells, signaling patterns often vary from cell to cell and may contain more complex features such as Ca2+ oscillations. Subcellular Ca2+ signals show a further level of complexity, such as Ca2+ waves, and may relate to the polarized structure and function of epithelial cells. The approaches to detect cytosolic Ca2+ signals, the patterns and mechanisms of Ca2+ signaling, and the role of such signals in regulating the function of polarized epithelium within the gastrointestinal tract, pancreas, and liver are reviewed in this report.

Transitions of latency time and oscillation phase on parameter surfaces from models of intracellular calcium ion dynamics

The dynamics of two classical elementary compartmental models stimulating intracellular calcium ion oscillatory behavior are examined in terms of parameter surfaces. It has been found that, along certain lines of instability on surfaces defined by model parameters, the highly non-linear nature of these models produces sharp transitions in the latency time which determines the phase of oscillations once they commence. This sensitivity to initial conditions in deterministic models, along with the stochastic variance inevitably present in actual biological systems, illustrates how two seemingly identical cells activated by identical synchronous stimulation can exhibit oscillatory responses which are out of phase with respect to each other.

Calcium mobilization by dual receptors during fertilization of sea urchin eggs

Fertilization is accompanied by a transient increase in the concentration of intracellular Ca2+, which serves as a signal for initiating development. Some of the Ca2+ appears to be released from intracellular stores by the binding of inositol trisphosphate (IP3) to its receptor. However, in sea urchin eggs, other mechanisms appear to participate. Cyclic adenosine diphosphate--ribose (cADPR), a naturally occurring metabolite of nicotinamide adenine dinucleotide, is as potent as IP3 in mobilizing Ca2+ in sea urchin eggs. Experiments with antagonists of the cADPR and IP3 receptors revealed that both Ca2+ mobilizing systems were activated during fertilization. Blockage of either of the systems alone was not sufficient to prevent the sperm-induced Ca2+ transient. This study provides direct evidence for a physiological role of cADPR in the Ca2+ signaling process.

One-pool model for Ca2+ oscillations involving Ca2+ and inositol 1,4,5-trisphosphate as co-agonists for Ca2+ release

Experimental observations indicate that Ca(2+)-induced Ca2+ release (CICR) may underlie Ca2+ oscillations in a variety of cells. In its original version, a theoretical model for signal-induced Ca2+ oscillations based on CICR assumed the existence of two types of pools, one sensitive to inositol 1,4,5-trisphosphate (IP3) and the other one sensitive to Ca2+. Recent experiments indicate that Ca2+ channels may sometimes be sensitive to both IP3 and Ca2+. Such a regulation may be viewed as Ca(2+)-sensitized IP3-induced Ca2+ release or, alternatively, as a form of IP3-sensitized CICR. We show that sustained oscillations can still occur in a one-pool model, provided that the same Ca2+ channels are sensitive to both Ca2+ and IP3 behaving as co-agonists. This model and the two-pool model based on CICR both account for a number of experimental observations but differ in some respects. Thus, while in the two-pool model the latency and period of Ca2+ oscillations are of the same order of magnitude and correlate in a roughly linear manner, latency in the one-pool model is always brief and remains much shorter than the period of oscillations. Moreover, the first Ca2+ spike is much larger than the following ones in the one-pool model. These distinctive properties might provide an explanation for the differences in Ca2+ oscillations observed in various cell types.

Mechanisms of intercellular calcium signaling in glial cells studied with dantrolene and thapsigargin

Mechanical stimulation of a single cell in a primary mixed glial cell culture induced a wave of increased intracellular calcium concentration ([Ca2+]i) that was communicated to surrounding cells. Following propagation of the Ca2+ wave, many cells showed asynchronous oscillations in [Ca2+]i. Dantrolene sodium (10 microM) inhibited the increase in [Ca2+]i associated with this Ca2+ wave by 60-80%, and prevented subsequent Ca2+ oscillations. Despite the markedly decreased magnitude of the increase in [Ca2+]i, the rate of propagation and the extent of communication of the Ca2+ wave were similar to those prior to the addition of dantrolene. Thapsigargin (10 nM to 1 microM) induced an initial increase in [Ca2+]i ranging from 100 nM to 500 nM in all cells that was followed by a recovery of [Ca2+]i to near resting levels in most cells. Transient exposure to thapsigargin for 2 min irreversibly blocked communication of Ca2+ wave from the stimulated cell to adjacent cells. Glutamate (50 microM) induced an initial increase in [Ca2+]i in most cells that was followed by sustained oscillations in [Ca2+]i in some cells. Dantrolene (10 microM) inhibited this initial [Ca2+]i increase caused by glutamate by 65-90% and abolished subsequent oscillations. Thapsigargin (10 nM to 1 micron) abolished the response to glutamate in over 99% of cells. These results suggest that while both dantrolene and thapsigargin inhibit intracellular Ca2+ release, only thapsigargin affects the mechanism that mediates intercellular communication of Ca2+ waves. These findings are consistent with the hypothesis that inositol trisphosphate (IP3) mediates the propagation of Ca2+ waves whereas Ca(2+)-induced Ca2+ release amplifies Ca2+ waves and generates subsequent Ca2+ oscillations.

Oscillations and waves of cytosolic calcium: insights from theoretical models

Oscillations in cytosolic Ca2+ occur in a wide variety of cells, either spontaneously or as a result of external stimulation. This process is often accompanied by intracellular Ca2+ waves. A number of theoretical models have been proposed to account for the periodic generation and spatial propagation of Ca2+ signals. These models are reviewed and their predictions compared with experimental observations. Models for Ca2+ oscillations can be distinguished according to whether or not they rely on the concomitant, periodic variation in inositol 1,4,5-trisphosphate. Such a variation, however, is not required in models based on Ca(2+)-induced Ca2+ release. When Ca2+ diffusion is incorporated into these models, propagating waves of cytosolic Ca2+ arise, with profiles and rates comparable to those seen in the experiments.

Epidermal growth factor-stimulated calcium ion transients in individual A431 cells: initiation kinetics and ligand concentration dependence

The A431 epidermoid carcinoma cell line responds to epidermal growth factor (EGF) stimulation with a number of rapid changes, including alterations in free cytosolic calcium ion concentration ([Ca2+]i). At the single cell level, these changes in [Ca2+]i are known to proceed after a clear lag phase subsequent to EGF stimulus (Gonzalez et al., 1988). The present study explores the dependence on EGF concentration of this early [Ca2+]i signal. High levels of EGF (9.0-4.3 nM) produce a [Ca2+]i spike followed by an elevation of [Ca2+]i above basal levels. The time of initiation of the spike varies from 5 to 9 s at the high dose and from 8 to 32 s at the low dose in cells that respond. A lower level of EGF (1.5 nM) produces [Ca2+]i oscillations with no prolonged elevation over basal [Ca2+]i. The initiation of response at this [EGF] ranges from 20 to 410 s. Intermediate stimulus levels generate [Ca2+]i responses that are kinetic admixtures of these limiting responses. A simple model based on the enzymatically amplified signal cascade from ligand binding through Ca2+ release or influx is examined. The model predicts a prolonged lag phase followed by a rapid increase in the [CA2+]i signal that compares favorably with the data reported here.

Dose-dependency in spatial dynamics of [Ca2+]c in pancreatic acinar cells

Spatial dynamics of cytosolic concentration of Ca2+, [Ca2+]c, in stimulus-secretion coupling of rat pancreatic acinar cell was monitored by a digital image analysing technique using Fura-2. When freshly isolated acini were stimulated with lower concentrations of CCK-8 (5-30 pM), [Ca2+]c increase began at the region beneath the basolateral membrane and the [Ca2+]c increase depended on the presence of extracellular Ca2+ ([Ca2+]o). CCK-8 at higher concentrations (100 pM and 1 nM), however, caused [Ca2+]c increase even in the absence of [Ca2+]o. Low concentrations of G-protein activator, NaF (10 mM or lower), caused [Ca2+]o-dependent increase in [Ca2+]c, whereas higher concentrations of NaF (15 mM or higher) increased [Ca2+]c in the absence of [Ca2+]o. These results are compatible with the view that G-protein activated by a physiological concentration of secretagogue accelerates Ca2+ entry. This process is in contrast to the process of Ca2+ release from intracellular stores, which can be predominant when pharmacological or toxic concentration of the secretagogue was applied.

The brain ryanodine receptor: a caffeine-sensitive calcium release channel

The release of stored Ca2+ from intracellular pools triggers a variety of important neuronal processes. Physiological and pharmacological evidence has indicated the presence of caffeine-sensitive intracellular pools that are distinct from the well-characterized inositol 1,4,5,-trisphosphate (IP3)-gated pools. Here we report that the brain ryanodine receptor functions as a caffeine- and ryanodine-sensitive Ca2+ release channel that is distinct from the brain IP3 receptor. The brain ryanodine receptor has been purified 6700-fold with no change in [3H]ryanodine binding affinity and shown to be a homotetramer composed of an approximately 500 kd protein subunit, which is identified by anti-peptide antibodies against the skeletal and cardiac muscle ryanodine receptors. Our results demonstrate that the brain ryanodine receptor functions as a caffeine-sensitive Ca2+ release channel and thus is the likely gating mechanism for intracellular caffeine-sensitive Ca2+ pools in neurons.

Cytosolic Ca2+ oscillations in REF52 fibroblasts: Ca(2+)-stimulated IP3 production or voltage-dependent Ca2+ channels as key positive feedback elements

Oscillations in cytosolic free calcium concentrations ([Ca2+]i) can be elicited in REF52 fibroblasts by three different modes of stimulation. We have previously demonstrated that [Ca2+]i oscillations result when these cells are simultaneously depolarized and stimulated with a hormone linked to phosphoinositide breakdown. Further evidence is now presented that such oscillations are linked to fluctuations in the concentration of IP3 and the Ca2+ content of an IP3-sensitive Ca2+ store. [Ca2+]i oscillations can also be generated in REF52 cells either by direct stimulation of G-proteins with GTP gamma S or AlF4- or by destabilizing the membrane potential and opening voltage-dependent calcium channels. This report compares the different types of oscillations and their mechanisms.

Signal-induced Ca2+ oscillations: properties of a model based on Ca(2+)-induced Ca2+ release

We consider a simple, minimal model for signal-induced Ca2+ oscillations based on Ca(2+)-induced Ca2+ release. The model takes into account the existence of two pools of intracellular Ca2+, namely, one sensitive to inositol 1,4,5 trisphosphate (InsP3) whose synthesis is elicited by the stimulus, and one insensitive to InsP3. The discharge of the latter pool into the cytosol is activated by cytosolic Ca2+. Oscillations in cytosolic Ca2+ arise in this model either spontaneously or in an appropriate range of external stimulation; these oscillations do not require the concomitant, periodic variation of InsP3. The following properties of the model are reviewed and compared with experimental observations: (a) Control of the frequency of Ca2+ oscillations by the external stimulus or extracellular Ca2+; (b) correlation of latency with period of Ca2+ oscillations obtained at different levels of stimulation; (c) effect of a transient increase in InsP3; (d) phase shift and transient suppression of Ca2+ oscillations by Ca2+ pulses, and (e) propagation of Ca2+ waves. It is shown that on all these counts the model provides a simple, unified explanation for a number of experimental observations in a variety of cell types. The model based on Ca(2+)-induced Ca2+ release can be extended to incorporate variations in the level of InsP3 as well as desensitization of the InsP3 receptor; besides accounting for the phenomena described by the minimal model, the extended model might also account for the occurrence of complex Ca2+ oscillations.

Cytoplasmic calcium oscillations: a two pool model

Cytosolic calcium oscillations induced by a wide range of agonists, particularly those which stimulate phosphoinositide metabolism, are the result of a periodic release of stored calcium. The formation of inositol 1,4,5 trisphosphate (Ins(1,4,5)P3) seems to play an important role because it can initiate this periodic behaviour when injected or perfused into a variety of cells. A two pool model has been developed to explain how Ins(1,4, 5)P3 sets up these calcium oscillations. It is proposed that Ins(1,4,5)P3 acts through its specific receptor to create a constant influx of primer calcium (Ca2+p) made up of calcium released from the Ins(1,4,5)P3-sensitive pool (ISCS) together with an influx of external calcium. This Ca2+p fails to significantly elevate cytosolic calcium because it is rapidly sequestered by the Ins(1,4,5)P3-insensitive (IICS) stores of calcium distributed throughout the cytosol. Once the latter have filled, they are triggered to release their stored calcium through a process of calcium-induced calcium release to give a typical calcium spike (Ca2+s). In many cells, each Ca2+s begins at a discrete initiation site from which it then spreads through the cell as a wave. The two pool model can account for such waves if it is assumed that calcium released from one IICS diffused across to excite its neighbours thereby setting up a self-propagating wave based on calcium-induced calcium release.

Organization of intracellular calcium signals generated by inositol lipid-dependent hormones

Recent studies at the single cell level have demonstrated hitherto unsuspected complexities in the organization of intracellular Ca2+ homeostasis in both the temporal and spatial domains. Activation of receptors coupled to the phosphoinositide signalling system has been shown to generate [Ca2+]i oscillations in many cell types. These oscillations display diverse patterns, with variations in oscillation amplitude, latency and frequency which are often tissue and/or agonist dose specific. Furthermore, increases in [Ca2+]i can either occur uniformly or originate from a specific region and propagate throughout the cell in the form of a Ca2+ wave. The significance and underlying mechanisms responsible for these phenomena are discussed.