Simplification and analysis of models of calcium dynamics based on IP3-sensitive calcium channel kinetics

Understanding complex signaling networks through models and metaphors

Signaling networks are complex both in terms of the chemical and biophysical events that underlie them, and in the sheer number of interactions. Computer models are powerful tools to deal with both aspects of complexity, but their utility goes beyond simply replicating signaling events in silicon. Their great advantage is as a tool to understanding. The completeness of the description demanded by computer models highlights gaps in knowledge. The quantitative description in models facilitates a mapping between different kinds of analysis methods for complex systems. Systems analysis methods can highlight stable states of signaling networks and describe the transitions between them. Modeling also reveals functional similarities between signaling network properties and other well-understood systems such as electronic devices and neural networks. These suggest various metaphors as a tool to understanding. Based on such descriptions, it is possible to regard signaling networks as systems that decode complex inputs in time, space and chemistry into combinatorial output patterns of signaling activity. This would provide a natural interface to the combinatorial input patterns required by genetic circuits. Thus, a combination of computer modeling methods to capture the complexity and details, and useful abstractions revealed by these models, is necessary to achieve both rigorous description as well as human understanding.

Buffers and oscillations in intracellular Ca2+ dynamics

I model the behavior of intracellular Ca(2+) release with high buffer concentrations. The model uses a spatially discrete array of channel clusters. The channel subunit dynamics is a stochastic representation of the DeYoung-Keizer model. The calculations show that the concentration profile of fast buffer around an open channel is more localized than that of slow buffers. Slow buffers allow for release of larger amounts of Ca(2+) from the endoplasmic reticulum and hence bind more Ca(2+) than fast buffers with the same dissociation constant and concentration. I find oscillation-like behavior for high slow buffer concentration and low Ca(2+) content of the endoplasmic reticulum. High concentration of slow buffer leads to oscillation-like behavior by repetitive wave nucleation for high Ca(2+) content of the endoplasmic reticulum. Localization of Ca(2+) release by slow buffer, as used in experiments, can be reproduced by the modeling approach.

On the role of stochastic channel behavior in intracellular Ca2+ dynamics

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.

Simulations of inositol phosphate metabolism and its interaction with InsP(3)-mediated calcium release

Inositol phosphates function as second messengers for a variety of extracellular signals. Ins(1,4,5)P(3) generated by phospholipase C-mediated hydrolysis of phosphatidylinositol bisphosphate, triggers numerous cellular processes by regulating calcium release from internal stores. The Ins(1,4,5)P(3) signal is coupled to a complex metabolic cascade involving a series of phosphatases and kinases. These enzymes generate a range of inositol phosphate derivatives, many of which have signaling roles of their own. We have integrated published biochemical data to build a mass action model for InsP(3) metabolism. The model includes most inositol phosphates that are currently known to interact with each other. We have used this model to study the effects of a G-protein coupled receptor stimulus that activates phospholipase C on the inositol phosphates. We have also monitored how the metabolic cascade interacts with Ins(1,4,5)P(3)-mediated calcium release. We find temporal dynamics of most inositol phosphates to be strongly influenced by the elaborate networking. We also show that Ins(1,3,4,5)P(4) plays a key role in InsP(3) dynamics and allows for paired pulse facilitation of calcium release. Calcium oscillations produce oscillatory responses in parts of the metabolic network and are in turn temporally modulated by the metabolism of InsP(3).

Mechanisms for temporal tuning and filtering by postsynaptic signaling pathways

Networks of signaling pathways perform complex temporal decoding functions in diverse biological systems, including the synapse, development, and bacterial chemotaxis. This paper examines temporal filtering and tuning properties of synaptic signaling pathways as a possible substrate for emergent temporal decoding. A mass action kinetic model of 16 synaptic signaling pathways was used to dissect out the contribution of these pathways in linear cascades and when coupled to form a network. The model predicts two primary mechanisms of temporal tuning of pathways: a weighted summation of responses of pathways with different timings and the presence of biochemical feedback loop(s) with emergent dynamics. Regulatory inputs act differently on these two tuning mechanisms. In the first case, regulators act like a gain-control on pathways with different intrinsic tuning. In the case of feedback loops, the temporal properties of the loop itself are changed. These basic tuning mechanisms may underlie specialized temporal tuning functions in more complex signaling systems in biology.

Control and plasticity of intercellular calcium waves in astrocytes: a modeling approach

Intercellular Ca2+ waves in astrocytes are thought to serve as a pathway of long-range signaling. The waves can propagate by the diffusion of molecules through gap junctions and across the extracellular space. In rat striatal astrocytes, the gap-junctional route was shown to be dominant. To analyze the interplay of the processes involved in wave propagation, a mathematical model of this system has been developed. The kinetic description of Ca2+ signaling within a single cell accounts for inositol 1,4,5-trisphosphate (IP3) generation, including its activation by cytoplasmic Ca2+, IP3-induced Ca2+ liberation from intracellular stores and various other Ca2+ transports, and cytoplasmic diffusion of IP3 and Ca2+. When cells are coupled by gap junction channels in a two-dimensional array, IP3 generation in one cell triggers Ca2+ waves propagating across some tens of cells. The spatial range of wave propagation is limited, yet depends sensitively on the Ca2+-mediated regeneration of the IP3 signal. Accordingly, the term "limited regenerative signaling" is proposed. The gap-junctional permeability for IP3 is the crucial permissive factor for wave propagation, and heterogeneity of gap-junctional coupling yields preferential pathways of wave propagation. Processes involved in both signal initiation (activation of IP3 production caused by receptor agonist) and regeneration (activation of IP3 production by Ca2+, loading of the Ca2+ stores) are found to exert the main control on the wave range. The refractory period of signaling strongly depends on the refilling kinetics of the Ca2+ stores. Thus the model identifies multiple steps that may be involved in the regulation of this intercellular signaling pathway.

Control and plasticity of intercellular calcium waves in astrocytes: a modeling approach

Intercellular Ca2+ waves in astrocytes are thought to serve as a pathway of long-range signaling. The waves can propagate by the diffusion of molecules through gap junctions and across the extracellular space. In rat striatal astrocytes, the gap-junctional route was shown to be dominant. To analyze the interplay of the processes involved in wave propagation, a mathematical model of this system has been developed. The kinetic description of Ca2+ signaling within a single cell accounts for inositol 1,4,5-trisphosphate (IP3) generation, including its activation by cytoplasmic Ca2+, IP3-induced Ca2+ liberation from intracellular stores and various other Ca2+ transports, and cytoplasmic diffusion of IP3 and Ca2+. When cells are coupled by gap junction channels in a two-dimensional array, IP3 generation in one cell triggers Ca2+ waves propagating across some tens of cells. The spatial range of wave propagation is limited, yet depends sensitively on the Ca2+-mediated regeneration of the IP3 signal. Accordingly, the term "limited regenerative signaling" is proposed. The gap-junctional permeability for IP3 is the crucial permissive factor for wave propagation, and heterogeneity of gap-junctional coupling yields preferential pathways of wave propagation. Processes involved in both signal initiation (activation of IP3 production caused by receptor agonist) and regeneration (activation of IP3 production by Ca2+, loading of the Ca2+ stores) are found to exert the main control on the wave range. The refractory period of signaling strongly depends on the refilling kinetics of the Ca2+ stores. Thus the model identifies multiple steps that may be involved in the regulation of this intercellular signaling pathway.

Modelling of simple and complex calcium oscillations. From single-cell responses to intercellular signalling

This review provides a comparative overview of recent developments in the modelling of cellular calcium oscillations. A large variety of mathematical models have been developed for this wide-spread phenomenon in intra- and intercellular signalling. From these, a general model is extracted that involves six types of concentration variables: inositol 1,4,5-trisphosphate (IP3), cytoplasmic, endoplasmic reticulum and mitochondrial calcium, the occupied binding sites of calcium buffers, and the fraction of active IP3 receptor calcium release channels. Using this framework, the models of calcium oscillations can be classified into 'minimal' models containing two variables and 'extended' models of three and more variables. Three types of minimal models are identified that are all based on calcium-induced calcium release (CICR), but differ with respect to the mechanisms limiting CICR. Extended models include IP3--calcium cross-coupling, calcium sequestration by mitochondria, the detailed gating kinetics of the IP3 receptor, and the dynamics of G-protein activation. In addition to generating regular oscillations, such models can describe bursting and chaotic calcium dynamics. The earlier hypothesis that information in calcium oscillations is encoded mainly by their frequency is nowadays modified in that some effect is attributed to amplitude encoding or temporal encoding. This point is discussed with reference to the analysis of the local and global bifurcations by which calcium oscillations can arise. Moreover, the question of how calcium binding proteins can sense and transform oscillatory signals is addressed. Recently, potential mechanisms leading to the coordination of oscillations in coupled cells have been investigated by mathematical modelling. For this, the general modelling framework is extended to include cytoplasmic and gap-junctional diffusion of IP3 and calcium, and specific models are compared. Various suggestions concerning the physiological significance of oscillatory behaviour in intra- and intercellular signalling are discussed. The article is concluded with a discussion of obstacles and prospects.

A dynamic model of the type-2 inositol trisphosphate receptor

The dynamic properties of the inositol (1,4,5)-trisphosphate (IP(3)) receptor are crucial for the control of intracellular Ca(2+), including the generation of Ca(2+) oscillations and waves. However, many models of this receptor do not agree with recent experimental data on the dynamic responses of the receptor. We construct a model of the IP(3) receptor and fit the model to dynamic and steady-state experimental data from type-2 IP(3) receptors. Our results indicate that, (i) Ca(2+) binds to the receptor using saturating, not mass-action, kinetics; (ii) Ca(2+) decreases the rate of IP(3) binding while simultaneously increasing the steady-state sensitivity of the receptor to IP(3); (iii) the rate of Ca(2+)-induced receptor activation increases with Ca(2+) and is faster than Ca(2+)-induced receptor inactivation; and (iv) IP(3) receptors are sequentially activated and inactivated by Ca(2+) even when IP(3) is bound. Our results emphasize that measurement of steady-state properties alone is insufficient to characterize the functional properties of the receptor.

Sparks and puffs in oligodendrocyte progenitors: cross talk between ryanodine receptors and inositol trisphosphate receptors

Investigating how calcium release from the endoplasmic reticulum (ER) is triggered and coordinated is crucial to our understanding of how oligodendrocyte progenitor cells (OPs) develop into myelinating cells. Sparks and puffs represent highly localized Ca(2+) release from the ER through ryanodine receptors (RyRs) and inositol trisphosphate receptors (IP(3)Rs), respectively. To study whether sparks or puffs trigger Ca(2+) waves in OPs, we performed rapid high-resolution line scan recordings in fluo-4-loaded OP processes. We found spontaneous and evoked sparks and puffs, and we have identified functional cross talk between IP(3)Rs and RyRs. Local events evoked using the IP(3)-linked agonist methacholine (MeCh) showed significantly different morphology compared with events evoked using the caffeine analog 3,7-dimethyl-1-propargylxanthine (DMPX). Pretreatment with MeCh potentiated DMPX-evoked events, whereas inhibition of RyRs potentiated events evoked by low concentrations of MeCh. Furthermore, activation of IP(3)Rs but not RyRs was critical for Ca(2+) wave initiation. Using immunocytochemistry, we show OPs express the specific Ca(2+) release channel subtypes RyR3 and IP(3)R2 in patches along OP processes. RyRs are coexpressed with IP(3)Rs in some patches, but IP(3)Rs are also found alone. This differential distribution pattern may underlie the differences in local and global Ca(2+) signals mediated by these two receptors. Thus, in OPs, interactions between IP(3)Rs and RyRs determine the spatial and temporal characteristics of calcium signaling, from microdomains to intracellular waves.

Sparks and puffs in oligodendrocyte progenitors: cross talk between ryanodine receptors and inositol trisphosphate receptors

Investigating how calcium release from the endoplasmic reticulum (ER) is triggered and coordinated is crucial to our understanding of how oligodendrocyte progenitor cells (OPs) develop into myelinating cells. Sparks and puffs represent highly localized Ca(2+) release from the ER through ryanodine receptors (RyRs) and inositol trisphosphate receptors (IP(3)Rs), respectively. To study whether sparks or puffs trigger Ca(2+) waves in OPs, we performed rapid high-resolution line scan recordings in fluo-4-loaded OP processes. We found spontaneous and evoked sparks and puffs, and we have identified functional cross talk between IP(3)Rs and RyRs. Local events evoked using the IP(3)-linked agonist methacholine (MeCh) showed significantly different morphology compared with events evoked using the caffeine analog 3,7-dimethyl-1-propargylxanthine (DMPX). Pretreatment with MeCh potentiated DMPX-evoked events, whereas inhibition of RyRs potentiated events evoked by low concentrations of MeCh. Furthermore, activation of IP(3)Rs but not RyRs was critical for Ca(2+) wave initiation. Using immunocytochemistry, we show OPs express the specific Ca(2+) release channel subtypes RyR3 and IP(3)R2 in patches along OP processes. RyRs are coexpressed with IP(3)Rs in some patches, but IP(3)Rs are also found alone. This differential distribution pattern may underlie the differences in local and global Ca(2+) signals mediated by these two receptors. Thus, in OPs, interactions between IP(3)Rs and RyRs determine the spatial and temporal characteristics of calcium signaling, from microdomains to intracellular waves.

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

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 this - and other - cell types has much improved. Many of these signals are mediated by a rise in the level of inositol 1,4,5-trisphosphate (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.

Stochastic spreading of intracellular Ca(2+) release

We study the spreading of calcium-induced calcium release with the stochastic DeYoung-Keizer-model of the inositol 1,4,5-trisphosphate receptor channel. The model shows a transition from isolated release events to steadily propagating waves with increasing IP3 concentration. A state--stochastic backfiring--was found in the regime of steady propagation. The model can be reduced by an adiabatic elimination of the partial differential equation for the Ca(2+) concentration to a lattice of stochastic channel clusters.

Dispersion gap and localized spiral waves in a model for intracellular Ca2+ dynamics

The dispersion relation is the dependence of the velocity of periodic planar wave trains on their wavelength. We study the occurrence of a velocity gap in the dispersion relation in a bistable three component reaction-diffusion system modeling intracellular Ca2+ dynamics. In two spatial dimensions, localized pinned spirals are observed, if their wavelength falls into the dispersion gap. Destruction of free spirals occurs already for conditions where the asymptotic planar wave train exists and the dispersion gap is absent.

Asynchronous Ca(2+) waves in intact venous smooth muscle

The rabbit inferior vena cava (IVC) is a large-capacitance vessel that displays typical contractile dose-response curves for caffeine and phenylephrine (PE). Using confocal microscopy on the endothelium-denuded IVC, we undertook experiments to correlate these whole-tissue contractile dose-response curves with changes in subcellular [Ca(2+)](i) signals in the in situ vascular smooth muscle cells (VSMCs). We observed that both caffeine and PE initially elicited Ca(2+) waves in individual VSMCs. The [Ca(2+)](i) in cells challenged with caffeine subsequently returned to baseline whereas the [Ca(2+)](i) in cells challenged with PE exhibited repetitive asynchronous Ca(2+) waves. These [Ca(2+)](i) oscillations were related to Ca(2+) release from the sarcoplasmic reticulum as they were inhibited by ryanodine and caffeine. The lack of synchronicity of the [Ca(2+)](i) oscillations between VSMCs can explain the observed tonic contraction at the whole-tissue level. The nature of these Ca(2+) waves was further characterized. For caffeine, the amplitude was all-or-none in nature, with individual cells differing in sensitivity, leading to their recruitment at different concentrations of the agonist. This concentration dependency of recruitment appears to form the basis for the concentration dependency of caffeine-induced contraction. Furthermore, the speed of the Ca(2+) waves correlated positively with the concentration of caffeine. In the case of PE, we observed the same characteristics with respect to wave speed, amplitude, and recruitment. Increasing concentrations of PE also enhance the frequency of the [Ca(2+)](i) oscillations. We therefore conclude that PE stimulates whole-tissue contractility through differential recruitment of VSMCs and enhancement of the frequency of asynchronous [Ca(2+)](i) oscillations once the cells are recruited.

Mechanism of receptor-oriented intercellular calcium wave propagation in hepatocytes

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 receptor-oriented intercellular calcium wave propagation in hepatocytes.

Impact of mitochondrial Ca2+ cycling on pattern formation and stability

Energization of mitochondria significantly alters the pattern of Ca2+ wave activity mediated by activation of the inositol (1,4,5) trisphosphate (IP3) receptor (IP3R) in Xenopus oocytes. The number of pulsatile foci is reduced and spiral Ca2+ waves are no longer observed. Rather, target patterns of Ca2+ release predominate, and when fragmented, fail to form spirals. Ca2+ wave velocity, amplitude, decay time, and periodicity are also increased. We have simulated these experimental findings by supplementing an existing mathematical model with a differential equation for mitochondrial Ca2+ uptake and release. Our calculations show that mitochondrial Ca2+ efflux plays a critical role in pattern formation by prolonging the recovery time of IP3Rs from a refractory state. We also show that under conditions of high energization of mitochondria, the Ca2+ dynamics can become bistable with a second stable stationary state of high resting Ca2+ concentration.

Agonist-dependent phosphorylation of the inositol 1,4,5-trisphosphate receptor: A possible mechanism for agonist-specific calcium oscillations in pancreatic acinar cells

The properties of inositol 1,4,5-trisphosphate (IP3)-dependent intracellular calcium oscillations in pancreatic acinar cells depend crucially on the agonist used to stimulate them. Acetylcholine or carbachol (CCh) cause high-frequency (10-12-s period) calcium oscillations that are superimposed on a raised baseline, while cholecystokinin (CCK) causes long-period (>100-s period) baseline spiking. We show that physiological concentrations of CCK induce rapid phosphorylation of the IP3 receptor, which is not true of physiological concentrations of CCh. Based on this and other experimental data, we construct a mathematical model of agonist-specific intracellular calcium oscillations in pancreatic acinar cells. Model simulations agree with previous experimental work on the rates of activation and inactivation of the IP3 receptor by calcium (DuFour, J.-F., I.M. Arias, and T.J. Turner. 1997. J. Biol. Chem. 272:2675-2681), and reproduce both short-period, raised baseline oscillations, and long-period baseline spiking. The steady state open probability curve of the model IP3 receptor is an increasing function of calcium concentration, as found for type-III IP3 receptors by Hagar et al. (Hagar, R.E., A.D. Burgstahler, M.H. Nathanson, and B.E. Ehrlich. 1998. Nature. 396:81-84). We use the model to predict the effect of the removal of external calcium, and this prediction is confirmed experimentally. We also predict that, for type-III IP3 receptors, the steady state open probability curve will shift to lower calcium concentrations as the background IP3 concentration increases. We conclude that the differences between CCh- and CCK-induced calcium oscillations in pancreatic acinar cells can be explained by two principal mechanisms: (a) CCK causes more phosphorylation of the IP3 receptor than does CCh, and the phosphorylated receptor cannot pass calcium current; and (b) the rate of calcium ATPase pumping and the rate of calcium influx from the outside the cell are greater in the presence of CCh than in the presence of CCK.

Regulation of type 1 inositol 1,4,5-trisphosphate-gated calcium channels by InsP3 and calcium: Simulation of single channel kinetics based on ligand binding and electrophysiological analysis

Cytosolic calcium acts as both a coagonist and an inhibitor of the type 1 inositol 1,4,5-trisphosphate (InsP3)-gated Ca channel, resulting in a bell-shaped Ca dependence of channel activity (Bezprozvanny, I., J. Watras, and B.E. Ehrlich. 1991. Nature. 351:751-754; Finch, E.A., T.J. Turner, and S.M. Goldin. 1991. Science. 252: 443-446; Iino, M. 1990. J. Gen. Physiol. 95:1103-1122). The ability of Ca to inhibit channel activity, however, varies dramatically depending on InsP3 concentration (Combettes, L., Z. Hannaert-Merah, J.F. Coquil, C. Rousseau, M. Claret, S. Swillens, and P. Champeil. 1994. J. Biol. Chem. 269:17561-17571; Kaftan, E.J., B.E. Ehrlich, and J. Watras. 1997. J. Gen. Physiol. 110:529-538). In the present report, we have extended the characterization of the effect of cytosolic Ca on both InsP3 binding and InsP3-gated channel kinetics, and incorporated these data into a mathematical model capable of simulating channel kinetics. We found that cytosolic Ca increased the Kd of InsP3 binding approximately 3.5-fold, but did not influence the maximal number of binding sites. The ability of Ca to decrease InsP3 binding is consistent with the rightward shift in the bell-shaped Ca dependence of InsP3-gated Ca channel activity. High InsP3 concentrations are able to overcome the Ca-dependent inhibition of channel activity, apparently due to a low affinity InsP3 binding site (Kaftan, E.J., B.E. Ehrlich, and J. Watras. 1997. J. Gen. Physiol. 110:529-538). Constants from binding analyses and channel activity determinations were used to develop a mathematical model that fits the complex Ca-dependent regulation of the type 1 InsP3-gated Ca channel. This model accurately simulated both steady state data (channel open probability and InsP3 binding) and kinetic data (channel activity and open time distributions), and yielded testable predictions with regard to the regulation of this intracellular Ca channel. Information gained from these analyses, and our current molecular model of this Ca channel, will be important for understanding the basis and regulation of intracellular Ca waves and oscillations in intact cells.

Highly selective sigma receptor ligands elevate inositol 1,4,5-trisphosphate production in rat cardiac myocytes

Exposure of cardiac myocytes from adult rat ventricles to the highly selective, high affinity sigma receptor ligands 1S,2 R-cis-N-[2-(3,4-dichlorophenyl)ethyl]-N-methyl-2-(1-pyrrolidinyl)-cycloh exylamine (BD-737) (0.1-100 nM) and N-[2-(3,4-dichlorophenyl)ethyl]-N,N',N'-trimethylethylenediamine (BD-1047) (0.01-10 nM), caused potentiation of electrically-evoked amplitudes of contraction and Ca2+ transients, while exposure to 100 nM BD-1047 caused attenuation of these amplitudes. In addition, BD-737 (1-100 nM) and BD-1047 (10-100 nM) caused an increase in the incidence of spontaneous twitches. These effects were inhibited when the incubation with BD-737 was done in the presence of the phospholipase C inhibitor, neomycin, or after pre-incubation with thapsigargin or caffeine which deplete the sarcoplasmic reticulum Ca2+ stores. Inositol 1,4,5-trisphosphate (IP3) production in cardiac myocytes was determined by the IP3 binding protein assay. Both substances caused an increase in the intracellular concentration of IP3. BD-737 caused a rapid transient increase to 3.2-fold in 1 min and stabilization at 2.1-fold of control thereafter. BD-1047 caused a gradual increase reaching 4.4-fold after 5 min. The results suggest that the effects of these sigma receptor ligands on contractility and spontaneous contractions are mediated by activation of phospholipase C and elevation of intracellular IP3 level.

Theoretical insights into the mechanism of spiral Ca2+ wave initiation in Xenopus oocytes

Spiral waves of intracellular Ca2+ have often been observed in Xenopus oocytes. Such waves can be accounted for by most realistic models for Ca2+ oscillations taking diffusion of cytosolic Ca2+ into account, but their initiation requires rather demanding and unphysiological initial conditions. Here, it is shown by means of numerical simulations that these spiral Ca2+ waves naturally arise if the cytoplasm is assumed to be heterogeneous both at the level of the synthesis and metabolism of D-myo-inositol 1,4,5-trisphosphate [Ins(1,4,5)P3] and at the level of the distribution of the Ins(1,4, 5)P3 receptors. In such conditions, a spiral can be initiated in the simulations after an increase in Ins(1,4,5)P3 concentration, with the direction of rotation being determined by the position of the region of high receptor density with respect to the locus of Ins(1,4, 5)P3 production.

Stochastic simulation of a single inositol 1,4,5-trisphosphate-sensitive Ca2+ channel reveals repetitive openings during 'blip-like' Ca2+ transients

Confocal microscope studies with fluorescent dyes of inositol 1,4,5-trisphosphate (InsP3)-induced intracellular Ca2+ mobilization recently established the existence of 'elementary' events, dependent on the activity of individual InsP3-sensitive Ca2+ channels. In the present work, we try by theoretical stochastic simulation to explain the smallest signals observed in those studies, which were referred to as Ca2+ 'blips' [Parker I., Yao Y. Ca2+ transients associated with openings of inositol trisphosphate-gated channels in Xenopus oocytes. J Physiol Lond 1996; 491: 663-668]. For this purpose, we assumed a simple molecular model for the InsP3-sensitive Ca2+ channel and defined a set of parameter values accounting for the results obtained in electrophysiological bilayer experiments [Bezprozvanny I., Watras J., Ehrlich B.E. Bell-shaped calcium-response curves of Ins(1,4,5)P3- and calcium-gated channels from endoplasmic reticulum of cerebellum. Nature 1991; 351: 751-754; Bezprozvanny I., Ehrlich B.E. Inositol (1,4,5)-trisphosphate (InsP3)-gated Ca channels from cerebellum: conduction properties for divalent cations and regulation by intraluminal calcium. J Gen Physiol 1994; 104: 821-856]. With a stochastic procedure which considered cytosolic Ca2+ diffusion explicitly, we then simulated the behaviour of a single channel, placed in a realistic physiological environment. An attractive result was that the simulated channel exhibited bursts of activity, arising from repetitive channel openings, which were responsible for transient rises in Ca2+ concentration and were reminiscent of the relatively long-duration experimental Ca2+ blips. The influence of the values chosen for the various parameters (affinity and diffusion coefficient of the buffers, luminal Ca2+ concentration) on the kinetic characteristics of these theoretical blips is analyzed.

Effects of sympathetic nerve stimulation on membrane potential, [Ca2+]i and force in the arrested sinus venosus of the toad, Bufo marinus

1. The effects of sympathetic nerve stimulation on membrane potential and on the intracellular concentration of calcium ions, [Ca2+]i, were recorded concurrently from the sinus venosus of the toad, Bufo marinus, in preparations where beating had been abolished by adding an organic calcium antagonist to the physiological saline. In a separate set of experiments the effects of sympathetic nerve stimulation on force production were examined. 2. Stimulation of the sympathetic nerves caused a membrane depolarization and a simultaneous increase in [Ca2+]i. Both responses were reduced by dihydroergotamine (20 microM). 3. The membrane depolarization and increase in [Ca2+]i evoked by sympathetic nerve stimulation were abolished by ryanodine (10 microM), or caffeine (3 mM). The effects of caffeine, but not those of ryanodine, were fully reversible. 4. Although the Ca(2+)-ATPase inhibitor thapsigargin (30 microM) itself had little effect on the responses to sympathetic nerve stimulation, in its presence caffeine (3 mM) irreversibly abolished the responses. 5. In the presence of nifedipine (10 microM), sympathetic nerve stimulation caused contractions of the sinus venosus. These responses were abolished by either ryanodine (10 microM) or caffeine (3 mM). 6. The results suggest that neuronally released transmitter activates a complex biochemical pathway which triggers the release of Ca2+ from internal stores.

Calcium waves in a model with a random spatially discrete distribution of Ca2+ release sites

We study the propagation of intracellular calcium waves in a model that features Ca2+ release from discrete sites in the endoplasmic reticulum membrane and random spatial distribution of these sites. The results of our simulations qualitatively reproduce the experimentally observed behavior of the waves. When the level of the channel activator inositol trisphosphate is low, the wave undergoes fragmentation and eventually vanishes at a finite distance from the region of initiation, a phenomenon we refer to as an abortive wave. With increasing activator concentration, the mean distance of propagation increases. Above a critical level of activator, the wave becomes stable. We show that the heterogeneous distribution of Ca2+ channels is the cause of this phenomenon.

Inositol 1,4,5-trisphosphate (InsP3) and calcium interact to increase the dynamic range of InsP3 receptor-dependent calcium signaling

The inositol 1,4,5-trisphosphate (InsP3)-gated Ca channel in cerebellum is tightly regulated by Ca (Bezprozvanny, I., J. Watras, and B.E. Ehrlich. 1991. Nature (Lond.). 351:751-754; Finch, E.A., T. J. Turner, and S.M. Goldin. 1991. Science (Wash. DC). 252:443-446; Hannaert-Merah, Z., J.F. Coquil, L. Combettes, M. Claret, J.P. Mauger, and P. Champeil. 1994. J. Biol. Chem. 269:29642-29649; Iino, M. 1990. J. Gen. Physiol. 95:1103-1122; Marshall, I., and C. Taylor. 1994. Biochem. J. 301:591-598). In previous single channel studies, the Ca dependence of channel activity, monitored at 2 microM InsP3, was described by a bell-shaped curve (Bezprozvanny, I., J. Watras, and B.E. Ehrlich. 1991. Nature (Lond.). 351:751-754). We report here that, when we used lower InsP3 concentrations, the peak of the Ca-dependence curve shifted to lower Ca concentrations. Unexpectedly, when we used high InsP3 concentrations, channel activity persisted at Ca concentrations as high as 30 microM. To explore this unexpected response of the channel, we measured InsP3 binding over a broad range of InsP3 concentrations. We found the well-characterized high affinity InsP3 binding sites (with Kd < 1 and 50 nM) (Maeda, N., M. Niinobe, and K. Mikoshiba. 1990. EMBO (Eur. Mol. Biol. Organ.) J. 9:61-67; Mignery, G., T.C. Sudhof, K. Takei, and P. De Camilli. 1989. Nature (Lond.). 342:192-195; Ross, C.A., J. Meldolesi, T.A. Milner, T. Satoh, S. Supattapone, and S.H. Snyder. 1989. Nature (Lond.). 339:468-470) and a low affinity InsP3 binding site (Kd = 10 microM). Using these InsP3 binding sites, we developed a new model that accounts for the shift in the Ca-dependence curve at low InsP3 levels and the maintained channel activity at high Ca and InsP3 levels. The observed Ca dependence of the InsP3-gated Ca channel allows the cell to abbreviate the rise of intracellular Ca in the presence of low levels of InsP3, but also provides a means of maintaining high intracellular Ca during periods of prolonged stimulation.

Simulations of the effects of inositol 1,4,5-trisphosphate 3-kinase and 5-phosphatase activities on Ca2+ oscillations

Inositol 1,4,5-trisphosphate (Ins-1,4,5-P3) is responsible for Ca2+ mobilization in response to external stimulation in many cell types. The latter phenomenon often occurs as repetitive Ca2+ spikes. In this study, the effect of the two Ins-1,4,5-P3 metabolizing enzymes (Ins-1,4,5-P3 3-kinase and 5-phosphatase) on the temporal pattern of Ca2+ oscillations has been investigated. On the basis of the well-documented Ins-1,4,5-P3 3-kinase stimulation by the Ca2+/calmodulin complex and of the experimentally-determined kinetic characteristics of these enzymes, we predict that 5-phosphatase primarily controls the levels of Ins-1,4,5-P3 and, thereby, the occurrence and frequency of Ca2+ oscillations. Consequently, the model reproduces the experimental observation performed in Chinese hamster ovary cells that 5-phosphatase overexpression has a much more pronounced effect on the pattern of Ca2+ oscillations than 3-kinase overexpression. We also investigated, in more detail, under which conditions a similar effect could be observed in other cell types expressing various Ins-1,4,5-P3 3-kinase activities.

Defective excitation-contraction coupling in experimental cardiac hypertrophy and heart failure

Cardiac hypertrophy and heart failure caused by high blood pressure were studied in single myocytes taken from hypertensive rats (Dahl SS/Jr) and SH-HF rats in heart failure. Confocal microscopy and patch-clamp methods were used to examine excitation-contraction (EC) coupling, and the relation between the plasma membrane calcium current (ICa) and evoked calcium release from the sarcoplasmic reticulum (SR), which was visualized as "calcium sparks." The ability of ICa to trigger calcium release from the SR in both hypertrophied and failing hearts was reduced. Because ICa density and SR calcium-release channels were normal, the defect appears to reside in a change in the relation between SR calcium-release channels and sarcolemmal calcium channels. beta-Adrenergic stimulation largely overcame the defect in hypertrophic but not failing heart cells. Thus, the same defect in EC coupling that develops during hypertrophy may contribute to heart failure when compensatory mechanisms fail.

Quantal release, incremental detection, and long-period Ca2+ oscillations in a model based on regulatory Ca2+-binding sites along the permeation pathway

Quantal release, incremental detection, and oscillations are three types of Ca2+ responses that can be obtained in different conditions, after stimulation of the intracellular Ca2+ stores by submaximum concentrations of inositol 1,4,5-triphosphate (InsP3). All three phenomena are thought to occur through the regulatory properties of the InsP3 receptor/Ca2+ channel. In the present study, we perform further analysis of the model (Swillens et al., 1994, Proc. Natl. Acad. Sci. USA. 91:10074-10078) previously proposed for transient InsP3-induced Ca2+ release, based on the bell-shaped dependence of the InsP3 receptor activity on the Ca2+ level and on the existence of an intermediate Ca2+ domain located around the mouth of the channel. We show that Ca2+ oscillations also arise in the latter model. Conditions for the occurrence of the various behaviors are investigated. Numerical simulations also show that the existence of an intermediate Ca2+ domain can markedly increase the period of oscillations. Periods on the order of 1 min can indeed be accounted for by the model when one assigns realistic values to the kinetic constants of the InsP3 receptor, which, in the absence of a domain, lead to oscillations with periods of a few seconds. Finally, theoretical support in favor of a positive cooperativity in the regulation of the InsP3 receptor by Ca2+ is presented.

Calcium dynamics and homeostasis in a mathematical model of the principal cell of the cortical collecting tubule

Calcium (Ca) dynamics are incorporated into a mathematical model of the principal cell in the cortical collecting tubule developed earlier in Strieter et al. (1992a. Am. J Physiol. 263:F1063-1075). The Ca components are modeled after the Othmer-Tang model for IP(3)-sensitive calcium channels (1993, in Experimental and Theoretical Advances in Biological Pattern Formation, 295-319). There are IP(3)-sensitive Ca channels and ATP-driven pumps on the membrane of the endoplasmic reticulum. Calcium enters the cell passively down its electrochemical gradient. A Ca pump and Na/Ca exchange in the basolateral membrane are responsible for the extrusion of cytoplasmic calcium. Na/Ca exchange can also operate in reverse mode to transport Ca into the cell. Regulatory effects of cytoplasmic Ca on the apical Na channels are modeled after experimental data that indicate apical Na permeability varies inversely with cytoplasmic Ca concentration. Numerical results on changes in intracellular Ca caused by decreasing NaCl in the bath and the lumen are similar to those from experiments in Bourdeau and Lau (1990. Am. J Physiol. 258:F1497-1503). This match of simulation and experiment requires the synergistic action of the Na/Ca exchanger and the Ca regulated apical Na permeability. In a homogeneous medium, cytoplasmic Ca becomes oscillatory when extracellular Na is severely decreased, as observed in experiments of cultured principal cells (Koster, H., C. van Os and R. Bindels. 1993. Kidney Int.43:828-836). This essentially pathological situation arises because the hyperpolarization of membrane potential caused by Na-free medium increases Ca influx into the cell, while the Na/Ca exchanger is inactivated by the low extracellular Na and can no longer move Ca out of the cell effectively. The raising of the total amount of intracellular Ca induces oscillatory Ca movement between the cytoplasm and the endoplasmic reticulum. Ca homeostasis is investigated under the condition of severe extracellular Ca variations. As extracellular Ca is decreased, Ca regulation is greatly impaired if Ca does not regulate apical ionic transport. The simulations indicate that the Na/Ca exchanger alone has only limited regulatory capacity. The Ca regulated apical sodium or potassium permeability are essential for regulation of cytoplasmic Ca in the principal cell of the cortical collecting tubule.