Translating Intracellular Calcium Signaling into Models
Abstract
The rich experimental data on intracellular calcium has put theoreticians in an ideal position to derive models of intracellular calcium signaling. Over the last 25 years, a large number of modeling frameworks have been suggested. Here, I will review some of the milestones of intracellular calcium modeling with a special emphasis on calcium-induced calcium release (CICR) through inositol-1,4,5-trisphosphate and ryanodine receptors. I will highlight key features of CICR and how they are represented in models as well as the challenges that theoreticians face when translating our current understanding of calcium signals into equations. The selected examples demonstrate that a successful model provides mechanistic insights into the molecular machinery of the Ca2+ signaling toolbox and determines the contribution of local Ca2+ release to global Ca2+ patterns, which at the moment cannot be resolved experimentally.
INTRODUCTION
One of the most fascinating features of calcium (Ca2+) as a second messenger is its versatility (Berridge et al. 2000). Almost every cell type shows Ca2+ signals, and even within a single cell the number of signaling pathways that involve Ca2+ is huge. From a modeler's perspective the broad spectrum of interactions renders Ca2+ an intriguing yet challenging study object. The fascination originates from the large dynamic repertoire of Ca2+ signals. Most Ca2+ responses begin with the elevation of the cytosolic Ca2+ concentration through either Ca2+ entry from the extracellular space or Ca2+ liberation from intracellular organelles such as the endoplasmic or sarcoplasmic reticulum (ER/SR). Although the molecular details of the ion channels that are responsible for the increase in the cytosolic Ca2+ concentration differ, in all cases, Ca2+ forms a plume of high concentration around the site of influx just after a channel opens. These microdomains form the smallest functional unit of intracellular Ca2+ signals (Berridge 2006) from which larger Ca2+ patterns are formed. For example, it is the orchestrated action of microdomains that gives rise to cellular responses such as Ca2+ waves and Ca2+ oscillations (Bootman et al. 1997). Some Ca2+ waves travel through the entire cell, while others only spread through parts of the cytoplasm resulting in abortive waves. The existence of Ca2+ microdomains and Ca2+ waves already points to a defining characteristic of intracellular Ca2+ signals—they vary largely in their temporal duration and their spatial spread. On the temporal scale, intracellular Ca2+ signals range from events faster than microseconds (binding and unbinding of Ca2+ to target molecules) to cellular Ca2+ transients that last minutes (Ca2+ waves and oscillations). At the same time, intracellular Ca2+ operates on length scales from a few nanometers (molecular binding sites) up to hundreds of micrometers (Ca2+ waves). The challenge for modelers arises from the realization that a complete account of intracellular Ca2+ requires us to incorporate the entire spatiotemporal spread, that is, more than eight orders of magnitude in space and more than six orders of magnitude in time.
The large range of length and time scales of intracellular Ca2+ patterns has led to various modeling approaches. A common research practice has been to focus on one class of Ca2+ signals at a time. For example, detailed investigations of the inositol-1,4,5-trisphosphate (IP3) receptor (IP3R) have been conducted that have greatly facilitated our mechanistic understanding of localized Ca2+ release events such as Ca2+ blips and puffs (Thul and Falcke 2004a; Rüdiger et al. 2007; Shuai et al. 2007; Taufiq-Ur-Rahman et al. 2009; Thul et al. 2009b; Swaminathan et al. 2009). More recently, a number of studies have addressed the interaction between different levels of the Ca2+ signaling hierarchy in a three-dimensional cellular environment. To cope with the increased computational demand of simulating three spatial dimensions, all approaches had to introduce approximations. For instance, the coupling between IP3R clusters with a detailed stochastic gating scheme for the receptor was achieved at the cost of a small number of IP3R clusters and an idealized spherical cellular geometry (Skupin and Falcke 2009; Skupin et al. 2010; Thurley and Falcke 2011). In a study of an atrial myocytes (Thul et al. 2012), the authors used a realistic distribution of ryanodine receptor (RyR) clusters but a simplified threshold dynamics for Ca2+ liberation. By focusing on a small number of RyR clusters in a cardiac myocyte, Izu et al. could incorporate detailed stochastic dynamics for RyRs (Izu et al. 2006). A combination of a small number of IP3R clusters and an approximation of the Ca2+ concentration profile around a cluster was studied in Solovey et al. (2008). In contrast to the spatially extended models, each Ca2+ ion is treated separately in a fully stochastic simulation for a point model of a hepatocyte in Dupont et al. (2008).
In this article, I will illustrate modeling concepts and applications with Ca2+ liberation from the ER or SR through either the IP3R or the RyR. The main motivation for this selection comes from the fact that these receptors present an integral component in the generation of Ca2+ waves and oscillations and, therefore, are vital for mounting a physiological response to extracellular stimuli (Thul et al. 2008a; Dupont et al. 2011; Parekh 2011). It is worth noting that IP3Rs and RyRs differ significantly from each other in their molecular structure, their gating properties and expression patterns (Foskett et al. 2007; Zalk et al. 2007). Different tissues and cell-lines express various isoforms, each tailored to specific signaling needs. Therefore, conclusions drawn for the IP3R cannot necessarily be transferred to the RyR.
The modeling studies mentioned above highlight some of the latest developments in a long evolution of Ca2+ models. In what follows I will describe three modeling approaches of increasing complexity that are stepping stones toward the more sophisticated modeling frameworks that we use today.
THE WELL-STIRRED CELL
A common and historically an often used assumption is that a cell presents a well-stirred bioreactor. In this setting, the
Ca2+ concentration is the same at all points within each cellular compartment such as the cytosol, the ER/SR, or across all mitochondria.
From a mathematical point of view, this translates into describing the dynamics of the Ca2+ concentration in each compartment with an ordinary differential equation (ODE). For example, the rate of change of the cytosolic
Ca2+ concentration (c) equals the sum of all Ca2+ fluxes into the cytoplasm (Jin) minus the sum of all Ca2+ fluxes out of the cytosol (Jout):
(1)
This simple relation has spawned a large number of cellular Ca2+ models, most of which differ in the details of the Ca2+ influx. Assuming that the main contribution to changes in the intracellular Ca2+ concentration results from the IP3R, various schemes have been put forward for the receptor as outlined in, for example, Meyer and Stryer (1988), Goldbeter et al. (1990), De Young and Keizer (1992), Li and Rinzel (1994), Sneyd and Dufour (2002) and Mak et al. (2003) and see Sneyd and Falcke (2005) for a review. The value of all of these IP3R models is that they provide different mechanistic interpretations of the experimental data sets that they were fitted to. Some of these models assume that Ca2+ and IP3 can associate in any order with their respective binding sites, while other models stipulate a strict sequential binding order or an allosteric transformation to the active state.
Another assumption of such models is that a given value of the cytosolic Ca2+ concentration results in exactly one fraction of active IP3Rs, that is, the Ca2+ release flux through the IP3R is completely deterministic. However, this is in stark contrast to experiments in, for example, Xenopus oocytes that showed the spontaneous emergence of Ca2+ puffs (Parker and Yao 1996; Sun et al. 1998). To reflect such random initiation of Ca2+ liberation, modelers replaced the deterministic Ca2+ flux through the IP3R with a stochastic function. The simplest implementation of this modeling approach is to take any of the deterministic ODE models listed above and to change the description of the IP3R Ca2+ flux to its stochastic counterpart by treating the IP3R as a Markov chain (Shuai and Jung 2002).
While ODE models of intracellular Ca2+ dynamics—whether deterministic or stochastic—have proven popular in the past, the richness of new experimental data prompts questions about the validity of this approach. A different interpretation of an ODE representation of the intracellular Ca2+ dynamics is that the equation describes the average Ca2+ concentration in the cell. This is indeed a good approximation if the Ca2+ concentration varies marginally across the cell and hence every point in the cell experiences an almost identical Ca2+ concentration. However, the presence of spatially localized IP3R clusters and Ca2+ microdomains already indicates that the Ca2+ concentration can change drastically from one part of the cell to another. For example, the cytosolic Ca2+ concentration increases to >150 µm at an open IP3R cluster, whereas the basal Ca2+ concentration is ∼50–150 nm (Thul and Falcke 2004a). This represents more than 3 orders of magnitude, and given the sharp gradients of the Ca2+ concentration around an active IP3R cluster, averaging does not capture the true concentration profiles. The issue of largely distinct Ca2+ concentrations also affects the mechanistic interpretation of ion channel models. Based on thermodynamic principles, the binding rate of Ca2+ to a designated binding site is proportional to the Ca2+ concentration. Averaged Ca2+ concentrations usually peak around 2 µm. Since realistic values of the Ca2+ concentration may exceed the average by a factor of 100, the binding rate is 100 times faster in the latter case than in the former. This has important consequences for processes such as Ca2+-induced activation or Ca2+-induced inhibition. Only realistic values of the cellular Ca2+ concentration can unravel the mechanistic details of Ca2+-dependent molecules and, in turn, faithfully represent the cellular Ca2+ dynamics.
It is worth remembering that models are designed to answer a particular research question and to make predictions. Models should not be limited to reproducing experimental findings. Often, an ODE model for averaged Ca2+ concentrations provides preliminary insights into the problem at hand and guides researchers toward more sophisticated approaches. From a practical point of view, ODE models frequently serve as a starting point to explore new signaling pathways, partly because there might not be sufficient experimental data to construct a more detailed Ca2+ model, and partly because the mathematical analysis of ODEs is well established and computationally cheap. Moreover, powerful analytical tools exist that give deeper insights into the mathematical details of such models. Therefore, ODE models for the averaged Ca2+ concentration may prove useful, despite being a poor reflection of the underlying physiology.
FROM ONE COMPARTMENT TO THE NEXT
It became apparent early on that for models of cardiac action potentials and for local control models of excitation–contraction
coupling that averaged Ca2+ concentrations across the cell presented a poor description of the cellular environment (DiFrancesco and Noble 1985; Stern 1992). The latter serves as a prime example of how details of the spatial arrangement of Ca2+ conducting ion channels lead to predictive modeling. To trigger contraction, Ca2+ enters the cell through L-type voltage-dependent Ca2+ channels (VDCCs) on depolarization of the plasma membrane. In turn, RyRs open through Ca2+-induced Ca2+ release (CICR) (Bers 2002). A key feature of VDCCs and RyRs is that they often co-localize within a distance of ∼15 nm, hence providing RyRs with a
privileged access to the Ca2+ influx through VDCCs. It is this localized Ca2+ entry that controls CICR, not a whole-cell averaged L-type Ca2+ current. Indeed, excitation–contraction coupling can only be explained through a spatially nonuniform distribution of VDCCs-RyRs
clusters (Soeller and Cannell 2004; Cannell and Kong 2012). Such spatial heterogeneity is also at the heart of the model by DiFrancesco and Noble (1985). To reproduce experimental time courses of the intracellular Ca2+ concentration, the authors had to assume two compartments within the SR: one pool that resequesters Ca2+ from the cytosol and one pool that releases Ca2+ into the cytosol. This highlights what is known as compartmentalized modeling. In Stern's model the two conceptual compartments
are the dyadic cleft and the bulk cytosol, while DiFrancesco and Noble distinguish between the junctional and nonjunctional
SR as well as the bulk cytosol. Note that compartmentalized models differ from whole-cell models introduced in the previous
section because they allow the division of morphologically continuous cellular compartments into functional subspaces (e.g.,
junctional and nonjunctional SR). In turn, this leads to spatially varying Ca2+ concentrations as opposed to spatially homogenous Ca2+ concentrations in the well-stirred cell. From a mathematical point of view, compartmentalized models take on the form of
coupled ODEs between the different compartments. For example, the model in DiFrancesco and Noble (1985) can be written as
where c, cup, and crel denote the Ca2+ concentration in the cytosol, the uptake pool and the release pool of the SR, respectively, with corresponding volumes Vi, Vup, and Vrel. The three concentrations change because of the ionic flux Jion across the plasma membrane, the release flux Jrel from the release pool into the cytosol, the uptake flux Jup from the cytosol into the uptake pool, and the transfer flux Jtr from the uptake compartment to the release compartment.
The challenge for modelers lies in finding descriptions for all these fluxes, which often reflect mechanistic insights into
the underlying dynamics. In this respect, compartmentalized models demand the same input as ODE models for averaged Ca2+ concentrations. One major difference, however, is that some of the fluxes that are assumed to be present across the entire
cell in models for the averaged Ca2+ concentration only occur for certain compartments. For example, the uptake current is usually assumed to operate throughout
a well-stirred cell, but is restricted to the uptake compartment in DiFrancesco and Noble (1985). From a mechanistic point of view, the uptake current is often carried by sarco-endoplasmic Ca2+ ATPase (SERCA) pumps and can be described by
where vm and K represent the maximal uptake current and the value of the Ca2+ concentration at which pumps work at half their maximal uptake rate (EC50), respectively. The above equation assumes that
the Ca2+ flux is unidirectional and only determined by the cytosolic Ca2+ concentration. However, experimental measurements strongly suggest that first luminal Ca2+ feeds back to SERCA pump dynamics and second Ca2+ movement between the cytosol and the ER/SR proceeds along multiple distinct states of the SERCA pump molecule. These experimental
results have led to more comprehensive models of SERCA pumps such as in Sneyd et al. (2003), Shannon et al. (2004), Higgins et al. (2006), Koivumäki et al. (2009), and Tran et al. (2009).
The advantage of compartmentalized models lies in the computational ease in accounting for largely varying Ca2+ concentrations and spatial gradients. A single point model cannot incorporate the different peak values and time courses of, for example, the subsarcolemmal and bulk Ca2+ concentration in cardiac myocytes. On the other hand, a two-compartment model accomplishes this easily.
Compartmentalized models have significantly advanced our understanding of Ca2+ handling and the interaction between the membrane potential and the intracellular Ca2+ concentration in cardiac myocytes (Shiferaw et al. 2003; Shannon et al. 2004; Shiferaw and Karma 2006; Koivumäki et al. 2011). However, deriving multi-compartment descriptions for intracellular Ca2+ signaling suffers from two major shortcomings. First, it is not clear a priori how many compartments are needed to account for experimental measurements. Different models use different numbers of compartments and yet describe the same physiology (see, e.g., Table 1 in Fink et al. [2011]). Second, compartmentalized models depend on the volumes of the compartments. It might appear straightforward to estimate the volume of the dyadic cleft, but it is less intuitive where to draw the line between the junctional and nonjunctional SR or the bulk and the subsarcolemmal cytosolic space. The last point illustrates the fact that some of the compartments do not correspond to actual physical entities but to functional units that organize Ca2+ handling. Moreover, the spatial extent of these functional compartments may change over time because of molecular interactions, which in turn renders the volume estimation difficult to make. A prime example for this scenario is the impact of buffers on Ca2+ release through IP3 channels. Especially mobile buffers can increase the effective size of a microdomain around an open IP3R cluster. Ca2+ buffers are molecules that bind Ca2+ and hence increase the cellular Ca2+ capacity. It is worth noting that >90% of cellular Ca2+ is buffered under normal conditions and that buffers significantly affect local and global Ca2+ signals (Keener and Sneyd 2001; Falcke 2003a; Dargan and Parker 2003; Zeller et al. 2009). In addition, varying the number of IP3Rs in a cluster changes the functional volume and hence the dynamics of compartmentalized IP3R clusters such as those modeled in Williams et al. (2008).
The conceptual simplicity of compartmentalized models makes them ideal candidates to start exploring cellular heterogeneity with low computational demand. However, no matter how many compartments are used and how sophisticated they are, any compartmentalized model suffers from the above shortcomings. The only way to circumvent these issues is to treat the cellular space as what it is: a continuous representation of a cell where the only boundaries are those of the plasma membrane and intracellular organelles. In the next section, we will examine some more realistic models of intracellular Ca2+ dynamics. However, a better representation of the physiological reality comes at a price. Larger computational overheads are required and more involved mathematical analysis is needed, if it is feasible at all.
SPATIALLY EXTENDED CELL MODELS
Ca2+ waves, whether spontaneous or triggered, abortive or cell-wide, correspond to one of the most common forms of Ca2+ signals. To fully map the large dynamic repertoire of Ca2+ waves, modelers have to go beyond the framework of ODEs discussed so far and turn to partial differential equations (PDEs).
In contrast to the ODEs discussed above where the Ca2+ concentration only depends on time, PDEs treat the Ca2+ concentration as dependent on both space x and time t, that is, c = c(x, t). In its simplest form, the spatiotemporal evolution of the Ca2+ concentration is captured by
(2)
where D denotes the (effective) diffusion coefficient of Ca2+ in the cytosol and f describes the local Ca2+ dynamics, that is, Ca2+ release through IP3Rs and RyRs or Ca2+ resequestration by SERCA pumps from the cytosol to the ER or SR. In this respect, Ca2+ dynamics, as modeled by PDEs, has a direct connection to the ODEs outlined above, because the function f in Equation (2) is the same as the right-hand side of Equation (1). The effective diffusion coefficient reflects the impact of Ca2+ buffers on Ca2+ transport. Essentially, Ca2+ diffuses through the cytosol either as a free ion or bound to mobile buffers. Since buffers are much larger than Ca2+, buffer-bound Ca2+ diffuses more slowly than free Ca2+. An effective diffusion coefficient accounts for these different transport velocities. One method to compute D is the fast buffer approximation (Wagner and Keizer 1994). To date, Ca2+ waves have been studied in great detail, and I refer the reader to Sneyd and Tsaneva-Atanasova (2003) and Falcke (2004) for recent reviews on Ca2+ wave propagation. Here, I would like to focus on some selected aspects of Ca2+ waves.
The main driving force behind Ca2+ waves is CICR. Suppose Ca2+ is liberated at one Ca2+ release site while all neighboring Ca2+ release sites are quiescent. Calcium then diffuses from the active Ca2+ release site to the dormant sites, which increases the probability of these channels to open. Once these channels open, Ca2+ is liberated and in turn diffuses to adjacent Ca2+ release sites where a new round of Ca2+ liberation is triggered. In this way, a saltatory Ca2+ wave propagates through a cell. For IP3Rs, the notion of CICR is often illustrated by the bell-shaped dependence of the stationary open probability of the IP3R on the cytosolic Ca2+ concentration (Bezprozvanny et al. 1991; Foskett et al. 2007). A small increase of the cytosolic Ca2+ concentration above the base level leads to a significant increase in the IP3R open probability. However, steady-state data do not necessarily capture the true dynamics of an IP3R, neither is a bell-shaped dependence of the open probability necessary to explain observed Ca2+ signals (Sneyd and Falcke 2005). As a consequence, it is more appropriate to conceptualize CICR as Ca2+ excitability (Keizer et al. 1995). Borrowing ideas from nonlinear dynamical systems, Ca2+ excitability refers to the fact that Ca2+ liberation is only initiated at a cluster of closed Ca2+-releasing channels if the cluster state is sufficiently perturbed. One such perturbation is the increase in the cytosolic Ca2+ concentration, others include an increase of the IP3 concentration or phosphorylation of the receptor molecules. One class of models for Ca2+ wave propagation that builds on the notion of a critical value of the cytosolic Ca2+ concentration to trigger Ca2+ release are those of the fire-diffuse-fire (FDF) type (Pearson and Ponce-Dawson 1998; Keizer et al. 1998; Dawson et al. 1999). Also known as threshold models, Ca2+ liberation starts as soon as the cytosolic Ca2+ concentration reaches a critical value. Calcium release continues for a fixed duration, comparable to the lifetime of a Ca2+ puff or spark, then the release site closes and becomes refractory. The beauty of FDF models is that they are amenable to a rigorous mathematical analysis and computationally inexpensive. The first property makes them ideal candidates to study large portions of parameter space since expressions for key features of traveling waves such as the wave speed are available in closed form. Instead of running a large number of simulations all that is needed is to evaluate analytical expressions, which can be performed in a fraction of the time that is required for the numerical simulations. For example, the impact of SERCA pumps on Ca2+ wave propagation has been studied in Coombes (2001), and investigating the interplay between the cytosol and the SR provided explanations for two novel wave types: tango waves (Li 2003; Thul et al. 2008b) and sensitization waves (Keller et al. 2007; Thul et al. 2009a). While deterministic models such as the original FDF description are still instrumental in advancing our understanding of intracellular Ca2+ waves, hybrid frameworks that incorporate the stochastic nature of Ca2+ release have gained considerable attention. In this respect, threshold models are ideally suited to capture the random opening of IP3Rs and RyRs, and to study stochastic Ca2+ waves. In these models, the constant threshold for Ca2+ liberation is replaced by a fluctuating value which can in principle be derived from experiments (Izu et al. 2001; Coombes and Timofeeva 2003).
The above examples for Ca2+ waves all represent a cell as a one-dimensional line. From an experimentalist's point of view, this might appear to be a crude approximation to the real cellular shape and morphology. The value of one-dimensional models is their ability to identify key mechanisms of Ca2+ wave propagation and to provide a thorough mathematical underpinning of the intracellular processes that drive Ca2+ waves. In turn, this establishes confidence in the chosen modeling framework to explore two- and three-dimensional models while avoiding spurious results.
Coupled with the stochastic description of Ca2+ release, two-dimensional models of the intracellular Ca2+ concentration have provided intriguing insights into the generation and propagation of Ca2+ waves (see Fig. 1). For example, a stochastic FDF model shows spatially synchronized oscillations, that is, every point in the cell oscillates with the same phase as its neighbors and the averaged Ca2+ concentration shows regular oscillations (Coombes and Timofeeva 2003). However, as soon as the random opening of the Ca2+ releasing channels is turned off, the oscillations disappear. Although the cell-wide signal looks deterministic and homogenous, an ODE framework as discussed above fails to provide the right mechanism. It is the interplay between the spatial arrangement of the Ca2+ release channels and the fluctuations of channel opening that are important, neither of which are captured by ODEs. Similarly, the results in Falcke (2003b) suggest that Ca2+ waves are initiated by the random formation of a critical nucleus. Only if a sufficient number of IP3R clusters open at the same time in close proximity will a Ca2+ wave be born. Two-dimensional simulations have been instrumental in providing first estimates for the number of IP3Rs per cluster, which is still hard to determine experimentally because of the small cluster diameter (Swillens et al. 1999; Shuai and Jung 2003a,b), but see Smith and Parker (2009) for a recent experimental measurement.
Ca2+ waves in a stochastic two-dimensional FDF model. The eight panels show snapshots of multiple Ca2+ waves (time runs from left to right, top to bottom). The first wave (top left) is triggered at the beginning of the simulation, while all other waves emerge spontaneously because of fluctuations of Ca2+ release. For a three-dimensional stochastic FDF model, I refer the reader to Thul et al. (2012).
The success of two-dimensional simulations and the availability of more powerful computing facilities have promoted the study of Ca2+ signals in a three-dimensional cellular environment (Izu et al. 2006; Means et al. 2006; Rüdiger et al. 2007; Li and Holden 2009; Skupin et al. 2010; Solovey et al. 2011; Thurley and Falcke 2011; Thul et al. 2012). Each of these studies focuses on a particular aspect of Ca2+ signaling such as a realistic distribution of Ca2+ release sites, ER geometry, or the interaction of a small number of IP3Rs and IP3R clusters with detailed gating schemes. Taken together, this research provides a kaleidoscopic view of the nature of intracellular Ca2+ signals and highlights two of the main characteristics of intracellular Ca2+ dynamics. First, intracellular Ca2+ is an intrinsic stochastic medium. The random state transitions that occur at a cluster of IP3Rs is caused by the continuous binding and unbinding of Ca2+ and IP3 to a small number of binding sites and is instrumental in generating Ca2+ puffs. The large Ca2+ concentrations that occur at an open cluster saturate any deterministic binding dynamics and hence cannot explain experimentally observed puff statistics (Thul and Falcke 2004a,b). As a consequence intracellular Ca2+ oscillations emerge at the cellular level through the stochastic orchestration of Ca2+ puffs. Single puff sites do not show oscillatory dynamics (Thurley et al. 2011). Second, the true nature of Ca2+ dynamics can only be captured in spatially extended models. Microdomains and Ca2+ waves clearly indicate that cells are not well-stirred bioreactors where the Ca2+ concentration is the same across the entire cell. The generation and molecular readout of Ca2+ signals depends on the local environment, not on properties of the bulk Ca2+ concentration.
THE ROAD AHEAD
Modeling intracellular Ca2+ dynamics has already come a long way and has significantly advanced our understanding of this most versatile second messenger. So far, we have gained great insight into individual levels of the Ca2+ signaling hierarchy, for example, for Ca2+ blips, puffs and sparks or whole-cell Ca2+ waves. The challenge for the future is to construct models that span the entire spatiotemporal range (Thurley et al. 2012). For IP3-mediated Ca2+ patterns, this means computational frameworks that take us from the stochastic binding of Ca2+ and IP3 to their respective binding sites on the IP3R, to a cellular response accounting for the often irregular three-dimensional geometry of cells and the spatially heterogeneous expression of large numbers of IP3R clusters. The constant advances in computational power will certainly help us to achieve this goal. At the same time, modelers have to improve existing models and to develop novel techniques that characterize intracellular Ca2+ dynamics more efficiently without sacrificing details of the Ca2+ signaling toolkit. Constructing models that are firmly rooted in experimental findings and successfully predict experimental results, while at the same time providing mechanistic interpretations of signaling pathways, will serve as a guiding principle for future research both in modeling and experiment.
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