Modeling the intracellular organization of calcium signaling.

Advanced Review

Modeling the intracellular organization of calcium signaling ` Dupont∗ Genevieve Calcium (Ca2+ ) is a key signaling ion that plays a fundamental role in many cellular processes in most types of tissues and organisms. The versatility of this signaling pathway is remarkable. Depending on the cell type and the stimulus, intracellular Ca2+ increases can last over different periods, as short spikes or more sustained signals. From a spatial point of view, they can be localized or invade the whole cell. Such a richness of behaviors is possible thanks to numerous exchange processes with the external medium or internal Ca2+ pools, mainly the endoplasmic or sarcoplasmic reticulum and mitochondria. These fluxes are also highly regulated. In order to get an accurate description of the spatiotemporal organization of Ca2+ signaling, it is useful to resort to modeling. Thus, each flux can be described by an appropriate kinetic expression. Ca2+ dynamics in a given cell type can then be simulated by a modular approach, consisting of the assembly of computational descriptions of the appropriate fluxes and regulations. Modeling can also be used to get insight into the mechanisms of decoding of the Ca2+ signals responsible for cellular responses. Cells can use frequency or amplitude coding, as well as take profit of Ca2+ oscillations to increase their sensitivity to small average Ca2+ increases. © 2014 Wiley Periodicals, Inc. How to cite this article:

WIREs Syst Biol Med 2014, 6:227–237. doi: 10.1002/wsbm.1261

INTRODUCTION

A

variety of cellular functions are driven by changes in the level of intracellular calcium (Ca2+ ) that are highly organized in time and space. This organization relies on the dynamical regulation of the intracellular Ca2+ channels mediating Ca2+ exchanges with the extracellular medium or with the intracellular stores. Metabolism of the Ca2+ -releasing messengers, such as inositol 1,4,5-trisphosphate (InsP3 ), Ca2+ buffers, and Ca2+ diffusion also play a primary role in the shaping of the hormone-induced Ca2+ responses (Figure 1). Since the first observation of Ca2+ oscillations in mouse oocytes,1 intracellular Ca2+ dynamics has been extensively studied, from both an experimental and a modeling perspective. Thus, it is known that in a large number of cell types, Ca2+ release is initiated by a rise in InsP3 concentration, ∗

Correspondence to: [email protected]

Unité de Chronobiologie Théorique, Faculté des Sciences, Université Libre de Bruxelles (ULB), Brussels, Belgium Conflict of interest: The author has declared no conflicts of interest for this article.

Volume 6, May/June 2014

generated in response to the external stimulus through a well-characterized signaling cascade.2 InsP3 triggers Ca2+ release from the endoplasmic reticulum (ER). Because of the dual regulation exerted by Ca2+ on the Ca2+ -releasing activity of the InsP3 receptor (InsP3 R), oscillations occur in the levels of Ca2+ in the cytoplasm and in the ER. In some cases, the Ca2+ rise occurs sequentially in the different regions of the cell, thus leading to the propagation of a Ca2+ wave. These waves are particularly spectacular at fertilization, where they are a prerequisite for cell cycle resumption and egg development. The Ca2+ -releasing activity of a small number of InsP3 R, corresponding to a subcellular region of a few hundred nanometers wide, has also been largely investigated. This activity can occur either spontaneously or at submaximal InsP3 concentrations. As can be expected from the low number of channels involved in the generation of this small-scale Ca2+ signals, these events are stochastic and can last from 70 to 400 milliseconds.3 Given that (irregular) subcellular Ca2+ signals and (much more regular) Ca2+ oscillations and waves can be observed in the same cell for different

© 2014 Wiley Periodicals, Inc.

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PMCA AI

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a dri on och Mit

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FIGURE 1 | Schematic representation of the main intracellular

processes playing an important role in Ca2+ homeostasis. Hormonal stimulation leads to the activation of the phospholipase C (PLC) that synthesizes inositol 1,4,5-trisphosphate (InsP3 ). This messenger can be phosphorylated into InsP4 or dephosphorylated into InsP2 . InsP3 binds to InsP3 receptors (IP3 Rs) on the surface of the endoplasmic reticulum (ER) and thereby initiates Ca2+ release. Ca2+ can also be released from the ER through ryanodine receptors (RyRs). SERCA pumps are Ca2+ ATPases that actively transport Ca2+ from the cytosol into the ER. The filling state of the ER is sensed by STIM, the Ca2+ -unbound state of which can bind to Orai and thereby initiate the influx of Ca2+ from the extracellular medium into the cytosol. PMCAs are plasma membrane Ca2+ ATPases that actively transport Ca2+ from the cytosol into the extracellular medium. In the cytosol, and in the intracellular organelles, Ca2+ reversibly binds to Ca2+ buffers. Ca2+ exchanges between the cytosol and mitochondria are also important for cellular Ca2+ homeostasis. Ca2+ enters in mitochondria through the Ca2+ uniporter (UNI) and is released through the Na+ /Ca2+ exchanger. Upon conditions of very high Ca2+ load, permeability transition pores (PTP) open thereby releasing Ca2+ as well as proapoptotic agents.

levels of stimulus, the study of Ca2+ dynamics offers the fascinating possibility to study the transition from a stochastic- to a deterministic-like regime. It is most of the time assumed that this transition corresponds to the emergence of a macroscopic self-organized system, which is a central concern in cellular biology.4,5 However, other groups conclude that Ca2+ dynamics remain a stochastic process even at the cellular level, mainly because of the poor communication between Ca2+ -releasing channels due to the low diffusivity of Ca2+ inside the cytoplasm.3,6,7 Nonetheless, these authors assume that the interspike interval contains both a deterministic and a stochastic part, thus rendering the deterministic approach an appropriate tool to describe cellular Ca2+ dynamics in most situations. Thus, in the following, I will focus on a deterministic description of intracellular Ca2+ dynamics. In the course of time, the large cell-to-cell variations in Ca2+ dynamics have become more and 228

more evident. Even if InsP3 R-based Ca2+ oscillations occur in most cell types, their detailed shape and characteristics much vary. These differences are both quantitative (periods, duration of spikes, etc.) and qualitative (requirement for extracellular Ca2+ or not, regulation by receptor phosphorylation, etc).8 Moreover, for a given cell type, different agonists can induce widely different Ca2+ responses. For example, in hepatocytes, stimulation by vasopressin generally induces the regular repetition of sharp spikes, whereas stimulation by noradrenaline leads to smaller spikes on an elevated plateau level.9,10 Finally, hepatocytes stimulated by ATP display oscillations of a complex type, reminiscent of the bursting behavior of electrical activity seen in voltage-sensitive cells.11,12 Thus, the current view in the field of modeling Ca2+ signaling is that each cell type requires a distinctive description taking into account the fluxes and the biochemical processes that have been shown to be important in this cell type stimulated by a specified agonist. In this framework, the modeler combines appropriate kinetic expressions for the processes involved. This is the modeling formalization of the concept of ‘Ca2+ toolkit’ developed by the experimentalists.13,14 Some newly identified players in intracellular Ca2+ dynamics have not been modeled yet, mostly because their kinetics and regulations are still too vague to be described quantitatively. In this review, after a brief reminder of the well-characterized Ca2+ exchange processes between the ER and the cytosol, I will describe other feature of Ca2+ dynamics that are less, or have been more recently incorporated in computational models. I will also mention those that have been experimentally uncovered but, to my knowledge, not considered yet in any modeling approach.

Ca2+ EXCHANGES BETWEEN THE CYTOSOL AND THE ER At rest, Ca2+ concentration is low (30–100 nM) in the cytosol and high in the ER (0.5–1 mM). This huge concentration gradient allows for a rapid increase in cytosolic Ca2+ following the opening of the InsP3 R and ryanodine receptors (RyRs), which are Ca2+ channels specifically located in the ER membrane. These channels play a primary role in cell signaling. On the other hand, maintenance of these gradients requires a very active, ATP-dependent Ca2+ pumping. The dynamical regulation of the InsP3 R has been investigated by many models. Most of these models take into account the tetrameric nature of this protein as well as its biphasic regulation by cytosolic Ca2+ . In particular, they all include the autocatalytic regulation through which Ca2+ activates its own release in the



WIREs Systems Biology and Medicine

Intracellular organization of calcium signaling

cytoplasm, as this regulation plays a major role in the occurrence of the well-known Ca2+ oscillations observed in most nonexcitable cells.2 It is also well established that this autocatalytic activation is much faster than Ca2+ -induced inhibition. In models, this time-scale difference is a prerequisite to get oscillations and the period is fixed by the time taken by the receptor to be relieved from inhibition. Besides these deterministic models (see Ref 14 for review), more recent stochastic models are also available in the literature. These models aim at understanding single-channel data.15,16 These data indeed reveal that the InsP3 R exhibits mode changes: the average open probability jumps between two levels even when ligand (Ca2+ , InsP3 , or ATP) concentrations are kept constant. These modes, corresponding to several channel states, are referred to as drive (highly active) and park (inactive) modes by Siekmann et al.17 Using a statistical analysis, these authors propose the most complex model, implying six channel states, which can be built unambiguously from the experimental data. The RyR, mostly expressed in excitable cells, much resembles the InsP3 R. Its main activator is Ca2+ itself and, as for the InsP3 R, excess Ca2+ has an inhibitory effect, although the level of Ca2+ required for inhibition much depends on the receptor subtype. Other factors that modulate the activity of the RyR are caffeine, ryanodine, and the second messenger cyclic ADP ribose, which has been proposed to be the endogenous activator of the channel. As many studies suggest that inactivation does not play a significant role for RyR-mediated Ca2+ release, the activity of this Ca2+ channel can be adequately described by an algebraic function of cytosolic and ER Ca2+ concentrations.18 Stochastic models, taking into account the existence of an inactivated state and the regulation of the channel activity by ER Ca2+ , have also been proposed.19 Modeling also emphasizes the crucial physiological role of the prominent apposition of RyR with L-type Ca2+ channels, in particular for cardiac cell dynamics.20 Sarcoplasmic or endoplasmic Ca2+ ATPases (SERCA) play a major role in the maintenance of a low resting level of Ca2+ in the cytoplasm. On the basis of data from Lytton et al.,21 this pumping activity can be modeled by a Hill expression, with a cooperativity coefficient equal to 2. The value of K1/2 depends on the ATPase subtype but is roughly around 300 nM, in agreement with the role of this pump to keep the basal Ca2+ level at concentrations around 100 nM. More complex models also take into account the possible bidirectionality of these pumps, arising when ER Ca2+ gets unusually high.22 Volume 6, May/June 2014

Together, the InsP3 R, the RyR, and the SERCA pumps govern most Ca2+ exchanges between the cytosol and the ER. When combined in a cellular model, they can explain most qualitative observations about signal-induced Ca2+ oscillations and waves and these models have been very helpful in improving our understanding of the Ca2+ oscillatory mechanism.

SIGNAL-STIMULATED Ca2+ ENTRY In electrically excitable cells, Ca2+ spikes are mainly carried out by Ca2+ entry from the extracellular medium through voltage-gated Ca2+ channels that are able to generate large Ca2+ increases in a few milliseconds. These Ca2+ changes are important for neuronal function, as the development and maintenance of neuronal circuits, secretion and exocytosis, or axonal guidance. By contrast, in other cell types, Ca2+ entry from the exterior plays a less important role, as it mostly modulates Ca2+ release from the intracellular stores and allows the latter release to be maintained on extended periods of time.23 Release of stored Ca2+ indeed activates influx through store-operated Ca2+ (SOC) channels.24 The major components of the SOC pathway are stromal interaction molecules (STIM1 or 2) and Orai (1, 2, or 3). STIM and Orai reside in the ER and plasma membrane, respectively. STIM has a Ca2+ -binding EF motif in the N-terminus, which is directed toward the lumen of the ER. When Ca2+ is bound, STIM proteins are found as dimers, whereas Ca2+ dissociation induces a conformational change in STIM, resulting in the formation of oligomers that translocate toward ER–plasma membrane junctions. There, STIM proteins bind to Orai and trigger their opening, thus provoking an influx of Ca2+ from the extracellular medium into the cytosol. Until now, attempts to model this Orai–STIM influx pathways have been scarce and rather preliminary. Liu et al.25 developed a model that well reproduces the steady-state dependence of the SOC current26 on the level of ER Ca2+ . Assuming a cooperative binding of ER Ca2+ to STIM, the evolution equation for the concentration of unbound STIM reads: d [Stim] s + bs [Stim]tot − [Stim] , = −fs [Stim] cnER dt (1) where f s and bs stand for the binding and dissociation rate constants of ER Ca2+ to STIM, respectively. If the time required for STIM to translocate to the ER–plasma membrane junction is small when


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compared with other processes, this process can be neglected and the formation of Orai/STIM complexes (to form an active SOC channel) obeys the following equation: d [SO] = f0 (1 − [SO]) [Stim] − b0 [SO] , dt

(2)

where f 0 and b0 stand for the binding and dissociation rates between STIM and Orai, respectively. Given the simplicity of the equations, the model can be solved analytically at steady state to get: [SO]ss =

f0 bs [Stim]tot . s b0 bs + f0 bs [Stim]tot + b0 fs cnER

(3)

Using a parameter fitting procedure, the authors found a set of kinetic constants providing an excellent agreement with the experimental data of Luik et al.,26 although their model does not consider the formation of STIM oligomers. Nonetheless, Eqs (1)–(3) together with the kinetic constants given in Liu et al.25 provide a useful ad hoc description of SOC-mediated Ca2+ entry at steady state. Another heuristic description of this influx pathway has been introduced by Croisier et al.27 in their modeling of Ca2+ dynamics in airway smooth muscle cells. On the basis of the observation that the diffusion of STIM within the ER membrane is a slow process,28 they model the evolution of the fraction of STIM/Orai complexes by: ∞ PSO (cER ) − PSO dPSO . (4) = dt τS As this current must be an increasing function of Ca2+ store depletion (i.e., a decreasing function of cER ), the authors assume that P∞ SO (cER ) =

K4S K4S + c4ER

.

(5)

In Eq (4), the value for τ S equals 30 seconds. Thus, it introduces a delay between store emptying and Orai opening when oscillations are rather fast. As an example, in the airway smooth muscle cells studied by Croisier et al.,27 the period of Ca2+ oscillations is of the order of 5 seconds; thus, Ca2+ entry activates slowly upon store depletion when compared with cytosolic Ca2+ changes. In other cell types, as hepatocytes or oocytes where the period can be a few minutes long, store refilling occurs faster than repetitive spiking and the steady-state assumption made by Liu et al.25 is reasonable. A closely related model, which furthermore considers that STIM is 230

sensitive to the Ca2+ concentration near the ER membrane rather than in the bulk ER, has been proposed by Ong et al.29 There are also a number of experimental publications mentioning TRPC (canonical transient receptor potential) cation channels, instead of Orai, as channels interacting with STIM.30,31 TRPCs comprise one of the six families of the nonselective TRP channels. However, Ca2+ influx represents their most common and investigated function. Although their influence on Ca2+ signaling is well established,32 their possible role in SOC entry is still rather uncertain, mainly because these channels display an unusually wide variety of activation mechanisms ranging from ligand binding to physical stimuli such as pressure or temperature.

REGULATION OF PLASMA MEMBRANE RECEPTOR ACTIVITY In most cell types, Ca2+ signaling is initiated by the binding of an agonist to a G-protein-coupled receptor (GPCR) embedded in the plasma membrane. These receptors are themselves dynamically regulated by a variety of intracellular processes: they can diffuse, form oligomers, be phosphorylated or internalized, and recycled. Although modeling33 is also widely used in the field of G-protein-mediated signaling (a domain that is of utmost importance in pharmacology), the dynamical regulation of GPCR has not much been incorporated in models for intracellular Ca2+ dynamics. Some models12,34 have empirically taken into account the existence of feedbacks on the receptor by combining several inhibitory regulations exerted by Ca2+ on the cascade leading to InsP3 synthesis. In particular, these models have put forward the role of these regulations in the generation of complex Ca2+ oscillations of the bursting type that are sometimes observed in response to stimulation by specific agonists. In the case of mGluR5 receptors (metabotropic receptor of type 5), the detailed molecular mechanism regulating their activity has been well characterized. These receptors to glutamate, the most abundant excitatory neurotransmitter in the central nervous system, are highly expressed in neurons and astrocytes. Upon stimulation, receptor dimers first activate the usual phospholipase C–InsP3 –Ca2+ release pathway, but later undergo rapid and reversible phosphorylation that uncouples the receptor from its downstream signaling pathway. This phosphorylation is mediated by a protein kinase C of the novel type (nPKC), which is activated by diacylglycerol (DAG). DAG is produced at the same time as InsP3 . This reversible phosphorylation mechanism is





able to generate Ca2+ oscillations. When mGluR5 phosphorylation drives Ca2+ oscillations, they are accompanied by an oscillating level of InsP3. 35,36 This network of interactions is schematized in Figure 2 and can be modeled by adding two differential and two algebraic equations to a classical model describing InsP3 -induced Ca2+ oscillations.37 It is assumed that mGluR5 receptors fulfill their signaling function as covalently linked dimers, whose formation is supposed to be much faster than the other processes considered. The first equation describes the evolution of the fraction of active, nonphosphorylated dimers:

are assumed to be proportional to the concentration of active receptor dimer. Thus, D dD = kPLC DIM − vMD . dt KMD + D

(7)

As InsP3 is synthesized together with DAG, its evolution is described by Eq. (7), with D being changed into InsP3 . PKC is the fraction of active kinase, which obeys the following equation: dPKC D = kact (1 − PKC) − kdes PKC. dt KAD + D

(8)

DIMP dDIM = k+ R2 L2 − k− DIM + VM1 dt KA1 + DIMP DIM − VPKC PKC , (6) KA + DIM

The rate equation for ligand binding and unbinding to and from mGluR5 reads:

where the superscript P indicates a phosphorylated form. R2 and L stand for the concentrations of free mGluR5 dimers and extracellular ligand (glutamate), respectively. The rates of InsP3 and DAG(D) synthesis

where k+ and k− are the kinetic constants of ligand binding and unbinding, respectively. Quasisteady-state assumption can be made on Eq. (9). The conservation relation of the total amount of Glu

Glu Glu Glu

5

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FIGURE 2 | Schematic representation of the core model for mGlu5 receptor-stimulated Ca2+ oscillations. Glutamate-bound dimers of mGlu5 receptor activate phospholipase C (PLC) through Gα q/11 proteins that are not considered explicitly in the model. This results in an increase in inositol 1,4,5-trisphosphate (InsP3 ) and diacylglycerol (DAG). InsP3 triggers Ca2+ release from the endoplasmic reticulum (ER). This process is regulated by cytosolic Ca2+ , both positively and negatively. Cytosolic Ca2+ can be resequestered by the ER through a Ca2+ -ATPase (SERCA). DAG activates a protein kinase C of the novel PKC family, which phosphorylates the mGlu5 receptor. This phosphorylation uncouples the receptor from the transduction mechanism leading to PLC activation. As shown in the lower panel, this model accounts for the existence of oscillations in the concentration of cytosolic Ca2+ (blue curve) that are driven by changes in the phosphorylation status of mGluR5 (red curve).



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mGluR5 allows to compute the concentration of phosphorylated dimers: DIM =

Rtot −

√ Kdi R2 − 2R2 − 2DIM , 2

where Rtot is the total concentration of mGluR5 (in the monomeric form) and Kdi is the dimerization constant of this receptor. When simulating Eqs (6)–(10), Ca2+ oscillations resulting from a mechanism of ‘dynamic uncoupling’ occur in an appropriate range of parameter values (Figure 2): ligand-bound unphosphorylated mGluR5 first activates PLC, which provokes an increase in the concentration of both InsP3 that releases Ca2+ and DAG that activates PKC. This kinase then phosphorylates mGluR5, thus terminating the synthesis of InsP3 and DAG, which both decrease, provoking the decreases of Ca2+ and PKC activity, respectively. Phosphatases dephosphorylate the receptors, thus allowing them to reactivate PLC and beginning a new cycle. During oscillations, active, nonphosphorylated mGlu5 receptors peak first, followed by InsP3 and DAG (that peak together), then rapidly by Ca2+ , and later by active PKC. Interestingly, the frequency of Ca2+ oscillations based on this mechanism is insensitive to the level of stimulation, while the level of receptor expression is a key determinant of oscillation frequency in both the model and experiments.37,38 Related models, although considering other PKC isoforms as well as many additional regulatory feedbacks, have been used to study Ca2+ dynamics in astrocytes. Thus, Kang and Othmer39 show that the strength of the interaction between PKC and PLC can be used to predict the Ca2+ response pattern, including spiking, sinusoidal oscillations, and transients with a plateau. Another interesting consequence of this dual control of oscillations is that it endows the system with an oscillatory mechanism favoring mixed frequency and amplitude encoding mode.40

Ca2+ HANDLING BY MITOCHONDRIA It is known for long that mitochondria also affect cytosolic Ca2+ signals, both by buffering ER-mediated Ca2+ increases and by releasing Ca2+ .41,42 At rest, intramitochondrial and cytosolic Ca2+ concentrations are similar.43,44 When the level of Ca2+ increases in the cytosol, it enters into mitochondria through a complex, multistep mechanism (Figure 3). It relies on the presence of a negative potential difference across the inner mitochondrial membrane ( m ), due to the activity of the respiratory chain that extrudes 232

PT

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tra Ele ns ctro po rt c n ha in

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H+

FIGURE 3 | Schematic representation of the main processes driving

the Ca2+ exchanges between the cytoplasm and the mitochondria. Processes shown in red are part of mitochondrial metabolism and transform pyruvate into NADH that will feed the electron transport chain. Shown in blue are the proton fluxes: H+ is extruded by using the electrochemical energy provided by the electron transport chain, while the F0/F1 ATPase uses the energy provided by the proton gradient to phosphorylate ADP into ATP. Ca2+ enters and leaves mitochondria through the processes indicated in black. The proton and Ca2+ gradients across the mitochondrial membrane are responsible for the voltage difference between the outer and inner sides of mitochondria. (Reprinted with permission from Ref 45. Copyright 2001 Elsevier; Reprinted with permission from Ref 46. Copyright 2011 Elsevier).

protons out of the mitochondria. This allows a uniporter to transport Ca2+ inside mitochondria when cytosolic Ca2+ locally reaches high concentrations, which arises in the close vicinity of ER Ca2+ release sites.47 However, this Ca2+ entry depolarizes mitochondria, thus reducing its own driving force. Also, exchangers such as the Na+ /Ca2+ and H+ /Ca2+ become slowly activated and thus bring mitochondrial Ca2+ concentration back to its resting value. Mitochondrial Ca2+ handling shapes cytosolic 2+ Ca changes. Ca2+ pumping by mitochondria reduces the amplitude of cytosolic Ca2+ spikes.48,49 The effect of Ca2+ release from this organelle depends on the Ca2+ content of mitochondria. Upon reduced load, mitochondrial Ca2+ primes Ca2+ release from the ER through the InsP3 R, thus accelerating the oscillations.50 In conditions of massive Ca2+ load, the mitochondrial permeable transition pore (mPTP) can activate and release massive amounts of Ca2+ , thereby triggering the release of apoptogenic proteins and cell death.51,52 In nonpathological conditions, Ca2+ increases in mitochondria allow for the enhancement of mitochondrial ATP production, which can coordinate energy production to cellular needs.53 Given these intertwined relationships between mitochondrial variables, models for Ca2+ handling by mitochondria need to describe the activity of the





PHYSIOLOGICAL EFFECTS OF Ca2+ OSCILLATIONS One of the main reasons why it is so important to get a profound understanding of intracellular Ca2+ dynamics is that Ca2+ plays a crucial role in a variety of vital physiological processes such as fertilization, gene transcription, muscle contraction, or secretion. Most of these processes appear to be sensitive to the spatiotemporal organization of the Ca2+ rises. The mechanism by which the cell machinery responsible Volume 6, May/June 2014

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respiratory chain as well as the evolution of the mitochondrial membrane voltage. Thus, they need to include a large number of variables. Moreover, most of the fluxes are themselves regulated by many factors. To quote only one example, the activity of the uniporter that translocates Ca2+ from the cytosol to mitochondria depends on voltage as well as on mitochondrial and cytosolic Ca2+ concentrations in an allosteric manner. The reference modeling work in the field has been performed by Magnus and Keizer, who provided an original and detailed description of mitochondrial function in the pancreatic β-cell.54,55 This model has been simplified by Fall and coworkers,45,46 who kept only six variables and updated the equations to include the permeability transition pore. In agreement with experimental observations, simulated oscillations of cytosolic and mitochondrial Ca2+ are accompanied by changes in mitochondrial potential (Figure 4). These models also account for the negative effect of metabolic substrates on the frequency of Ca2+ oscillations or for the properties of Ca2+ waves propagating in mitochondrial suspensions.41,57 More recently, this model has also been used to investigate the effect of Hint2, a mitochondrial protein that interferes with the electron transport chain, on cytosolic Ca2+ dynamics in hepatocytes.56 Interestingly, it was found that by activating the respiratory chain, Hint2 decreases the frequency of cytoplasmic Ca2+ oscillations. On the other hand, because it favors Ca2+ entry into mitochondria, Hint2 induces an earlier opening of the permeability transition pore. This effect is physiologically relevant in view of the known downregulation of Hint2 in hepatocarcinoma.58 Because of their complexity, these models are difficult to use and their behaviors sometimes are hard to understand. One of the most successful attempts to further simplify the computational description of mitochondrial Ca2+ handling has been performed by Bertram et al.59 who proposed plainer kinetic expressions for most fluxes represented in Figure 3. It is also clearer in this model how changes in parameter values will affect fluxes and regulations.

0 1500

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FIGURE 4 | Computational simulations of the Ca2+ exchanges between the cytosol and mitochondria during inositol 1,4,5-trisphosphate (InsP3 )-induced Ca2+ oscillations. The model combines a classical description of InsP3 -mediated Ca2+ oscillations due to the biphasic regulation of the IP3 R and the model of Fall and Keizer45 for mitochondria (see Ref 56). As shown in the lower panel, Ca2+ increases (blue) in mitochondria lead to mitochondrial depolarization (red).

for mediating the cellular response can be sensitive to the dynamics of Ca2+ changes has early attracted the attention of modelers.60–62 Besides these general approaches, it is also useful to question these concepts in physiologically concrete situations. In the last part of this review, I shall evoke some of these processes, emphasizing the possible detailed molecular mechanisms allowing for their sensitivity to the kinetics of the Ca2+ increases. It was early proposed that the frequency of Ca2+ oscillations determines the effectiveness of the stimulus-response coupling. In line with this hypothesis, the ubiquitous Ca2+ -calmodulin kinase II has been shown to be selectively activated, depending on the frequency of the stimulatory Ca2+ spikes.63 Each subunit of this multimeric kinase can be phosphorylated in a Ca2+ -dependent manner. This frequency sensitivity relies on the possibility of the kinase to autophosphorylate via an intersubunit reaction and thereby acquire a Ca2+ insensitive autonomous activity64 ; if the time interval between two Ca2+ spikes is too large, subunits will dephosphorylate because of Ca2+ dissociation rather than autophosphorylate their neighboring subunits. However, the frequency sensitivity of the kinase occurs


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only in the range of 1–10 Hz, which corresponds to the frequency of Ca2+ spikes in neurons, but is much higher than that observed in most electrically nonexcitable cells. Most studies on Ca2+ oscillations and their frequency sensitivity are performed on mammalian cells, although this signaling mode is much more widespread. Interestingly, Ca2+ oscillations in fish hepatocytes appear to be amplitude- rather than frequency-coded, although they are triggered by the same hormonal stimuli as in mammalian hepatocytes.65 For example, in these cells, doubling the concentration of extracellular phenylephrine does not decrease the oscillation period but increases their amplitude by about 50%. In their accompanying modeling approach, the authors identify the relative time scales of Ca2+ uptake and release as the main factors responsible for this difference. In agreement with this theoretical prediction, in mammalian hepatocytes, Ca2+ release from the ER is much faster than Ca2+ uptake by the ER, whereas both fluxes have similar kinetics in fish cells. From a theoretical point of view, frequency and amplitude coding are associated with oscillations emanating, respectively, from a subcritical and supercritical Hopf bifurcation, as already emphasized by De Pitta` et al.66 In many instances, an oscillatory Ca2+ signal is more efficient in inducing a physiological response than a constant one of the same average, although neither the frequency nor the amplitude seems to dictate the extent of the response. By reducing the effective average Ca2+ threshold for activating transcription factors NF-AT and NF-κB, Ca2+ oscillations increase the efficiency of Ca2+ signaling for gene transcription.61,67 During each Ca2+ spike, Ca2+ can indeed transiently activate a process characterized by a sharp threshold, whereas there is no response to a constant increase of this messenger, as long as the threshold is not reached. A similar mechanism could also explain why Ca2+ oscillations favor glucagon secretion by pancreatic αcells. In response to low glucose, some of these cells develop low-amplitude, irregular Ca2+ oscillations, while others respond by a steady increase in Ca2+ . Interestingly, secretion of glucagon is higher in cells exhibiting Ca2+ oscillations. Modeling reveals that this is due to the highly nonlinear relationship that exists between the Ca2+ level and the secretion rate: Ca2+ indeed primes and activates the granules of glucagon for fusion with the plasma membrane and secretion through a multistep mechanism that brings about a steep relationship between Ca2+ and secretion.68 As a last example, one can mention contraction of airway or arteriole smooth muscle 234

cells in response to Ca2+ oscillations. Contraction is also favored by an oscillatory signal, because the high level of Ca2+ reached at the peak causes a more pronounced phosphorylation of the myosin light chain, and thus a larger contractile force. Contraction also increases with frequency; when the time interval between two Ca2+ spikes decreases, a smaller fraction of myosin detaches from actin.69 Thus, it appears that different cell types, although characterized by distinct physiological functions and time scale of responses, have developed appropriate strategies to take profit of the oscillatory nature of Ca2+ signaling. One should note, however, that this is not a general rule. There are indeed some examples where the extent of the physiological response depends only on the average level of Ca2+ , whatever its temporal evolution. This is the case in saliva-secreting acinar cells, where mean Ca2+ concentration is found to be the most significant factor in determining the amount of secretion.70 Finally, another level of complexity arises when considering not only the temporal but also the spatial organization of Ca2+ signals. At fertilization in mammals, the sperm-induced intracellular movements of Ca2+ cause contractions of the actomyosin skeleton and cytoplasmic flows that are important for the development of the embryo.71 In cardiac atrial myocytes, the spatial profile of the Ca2+ signals occurring during excitation–contraction coupling plays a key role in the onset of the ‘atrial kick’, which increases the blood pumping activity of the heart.20 As a last example, the features of Ca2+ wave propagation and distribution in epidermal keratinocytes report information about the stimuli, damage status, and the skin pathology.72 The level of complexity of these processes that are regulated by the spatiotemporal organization of Ca2+ signals further increases the richness of the dynamical repertoire for the encoding of the information.

CONCLUDING REMARKS Ca2+ is a ubiquitous intracellular messenger. Evidence is accumulating at an increasing pace about the importance and sophistication of this signaling mode. This sophistication appears as a way to discriminate between different responses, given the large number of cellular processes that are controlled by the concentration of this ion. In the past 20 years, our understanding of this signaling pathway and of its physiological implications has much increased. We have uncovered the main basic principles allowing cells to use this ion, which is highly toxic at large concentrations, as a messenger. However, details are





clearly different from one cell type to another, and in order to be able to selectively interfere with one or the other Ca2+ -mediated response, one needs an accurate knowledge of Ca2+ signaling in each case. One can

hope that, in a near future, the combination between experiments and modeling will allow for a modular description of the various elements of the Ca2+ toolkit and for a deep understanding of their networking.

ACKNOWLEDGMENTS GD is a Senior Research Associate at the Belgian FNRS and acknowledges support from the ‘Fonds de la Recherche Scientifique Médicale’ (grant # 3.4636.04).

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Modeling of progesterone-induced intracellular calcium signaling in human spermatozoa.

Translating intracellular calcium signaling into models.

Intracellular calcium signaling in the fertilized eggs of Annelida.

Evolution of the Calcium-Based Intracellular Signaling System.

Analysis of Intracellular Calcium Signaling in Human Embryonic Stem Cells.

Cyst formation following disruption of intracellular calcium signaling.

Measurement of intracellular free calcium to investigate receptor-mediated calcium signaling.

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

Intracellular signaling in the gonads.

Genome organization: experiments and modeling.

On the structural organization of the intracellular domains of CFTR.

Apoptosis of alcohol-exposed human placental cytotrophoblast cells is downstream of intracellular calcium signaling.

Quantification of platelet-surface interactions in real-time using intracellular calcium signaling.

Curve-Fitting the Intracellular Calcium Dynamics.

Intracellular calcium channels in protozoa.

Intracellular calcium: molecules and pools.

14-3-3 Proteins Buffer Intracellular Calcium Sensing Receptors to Constrain Signaling.

Intracellular signaling of cardiac fibroblasts.

Stress-induced dissociations between intracellular calcium signaling and insulin secretion in pancreatic islets.

The effect of cholesterol on the accumulation of intracellular calcium.

Use of photoproteins as intracellular calcium indicators.

Fluorescence lifetime imaging of intracellular calcium.

Intracellular calcium during photodynamic permeabilization of cardiomyocytes.

The role of extracellular calcium in the regulation of intracellular calcium and cell function.