Abstract
Calcium (Ca2+) signaling is a fundamental molecular communication mechanism for the propagation of information in eukaryotic cells. Cytosolic calcium ions integrate a broad range of hormonal, mechanical and electrical stimuli within cells to modulate downstream cellular processes involved in organ development. However, how the spatiotemporal dynamics of calcium signaling are controlled at the organ level remains poorly understood. Here, we show that the spatiotemporal extent of calcium signaling within an epithelial system is determined by the class and level of hormonal stimulation and by the subdivision of the cell population into a small fraction of initiator cells surrounded by a larger fraction of standby cells connected through gap junction communication. To do so, we built a geometrically accurate computational model of intercellular Ca2+ signaling that spontaneously occurs within developing Drosophila wing imaginal discs. The multi-scale computational model predicts the regulation of the main classes of Ca2+ signaling dynamics observed in vivo: single cell Ca2+ spikes, intercellular transient bursts, intercellular waves and global fluttering. We show that the tuning of the spatial extent of Ca2+ dynamics from single cells to global waves emerges naturally as a function of global hormonal stimulation strength. Further, this model provides insight into how emergent properties of intercellular calcium signaling dynamics modulates cell growth within the tissue context. It provides a framework for analyzing second messenger dynamics in multicellular systems.
Significance Statement Intercellular calcium signaling is critical for epithelial morphogenesis and homeostasis. However, how cytosolic calcium concentration dynamics are regulated at the multicellular level are poorly understood. Here, we show using a novel multiscale computational model that the spatial extent of intercellular calcium communication is controlled by two factors: i) the relative strength of global hormonal stimulation, and ii) the presence of a subset of “initiator cells” among a population of “standby cells” that are connected by gap junctions. Localized multicellular calcium signals are associated with maximal organ growth while persistent calcium waves inhibit overall organ growth. This mechanism explains the broad range of spatiotemporal calcium signaling dynamics that occurs during epithelial development.
Calcium ions (Ca2+) mediate a large number of physiological and regulatory processes such as proliferation, differentiation, transcription, metabolism, cellular motility, fertilization, neuronal communication, muscle contraction, wound healing, cellular senescence and apoptosis (1–10). Such a broad range of functionality is primarily induced through coordinated variations in cytosolic free Ca2+ concentration in space and time (11). In addition to modulating cellular processes, Ca2+ signaling also regulates developmental processes at the multicellular level. For instance, Ca2+ is shown to regulate scale development in the butterfly (12) and mediates autophagic and apoptotic processes required for hearing acquisition in the developing cochlea (13, 14). A major challenge for understanding the emergent properties of Ca2+ signaling in multicellular systems is the lack of a suitable framework for analyzing, imaging and perturbing the stochastic signals systematically.
In our recent study, we found that Ca2+ dynamics correlates with final organ size during the development of the Drosophila larval wing disc, a genetic model for organogenesis (15). Specifically, Ca2+ dynamics in growing wing discs exhibit a progression from a global “fluttering” state in smaller, younger discs to infrequent single cell spikes in large, older discs as development proceeds. This ordinal progression is recapitulated by culturing ex vivo cultured wing discs with increasing concentrations of fly extract (FEX) titration, a serum-based stimulus of calcium activity. However, it remains unclear what might govern this progression mechanistically. This is important for decoding calcium signaling in developmental systems.
A major challenge in deciphering spontaneous calcium activity in tissues is the lack of computational models to quantify the multiplexed dynamics of the multiple regulators of Ca2+ activity in multicellular systems. Here, we have over-come this bottleneck by developing and validating a multi-scale model of Ca2+ signaling pathway that identifies the key parameters that determine transitions between tissue-wide calcium phenomena. This computational model provides key predictions on the underlying biophysical spatiotemporal patterning of parameters shaping calcium signaling dynamics needed to recapitulate the qualitative modes of calcium signaling dynamics that occur in epithelial systems: cellular Ca2+ spikes, multicellular transients, Ca2+ waves, or the global fluttering state (Fig. 1).
A second question in the field is how these different spatiotemporal modes of Ca2+ signaling impact downstream cellular or developmental processes. Here, we provide experimental evidence that local intercellular Ca2+ transients are linked to insulin signaling that directs promotion of tissue growth. In contrast, promotion of intercellular Ca2+ waves through over-expression of the Gαq subunit reduces wing size. Together these results support a novel model that links tissue-level calcium signaling dynamics to overall organ size regulation, which we term the “IP3 /Ca2+ shunt” model. This hypothesis views Ca2+ signaling as a readout of two physiological states: stimulation of calcium signaling can be either growth promoting or growth inhibiting depending on the overall net level of stimulated calcium activity. In this model, limited levels of stimulation, leading to localized cellular spikes and limited intercellular calcium transients, provide a readout of growth stimulation. However, high levels of Gαq /Phospholipase C activity are proposed to deplete PIP2 levels (16). This is likely due to substrate depletion of Phosphatidylinositol 4,5-bisphosphate PIP2 through promotion of IP3 generation and downstream Ca2+ activity by stimulation of Phospholipase C (PLC) activity. In turn, this would lead to reduced availability of PIP2 for conversion of PIP2 to Phosphatidylinositol-trisphosphate (PIP3), a key second messenger for stimulating protein kinase AKT and downstream growth promotion (17).
In this study, the Drosophila 3rd larval instar wing imaginal disc was used as a model platform to investigate the mechanisms governing Ca2+ signaling dynamics in epithelia. Fig. 1 summarizes the the experimental system and data. Different classes of patterns emerge at the tissue-level as the level of global stimulation increases: Ca2+ spikes, intercellular calcium transients (ICTs), intercellular calcium waves (ICWs) and global fluttering (15). However, a mechanistic under-standing linking hormonal stimulation levels to transitions in these qualitative classes of organ-level signaling remains a key question.
Here, we took a hierarchical modeling approach to recapitulate classes of spatiotemporal Ca2+ patterns. At the cellular level, we first extended a Ca2+ signaling model described in (18) (refer to Fig. 2 for a summary) and modified the activation rate of IP3 receptors to match the experimental data. This new modification of the model was necessary to match the temporal characteristics of Ca2+ oscillations derived from the model with the experimental observations (Fig. S1-S4). Next, a chain of cells (1D-model) connected by gap junctions (GJs) were considered in the model (Fig. S5). This led to the main factors affecting propagation of Ca2+ signals were identified through analysis of kymographs. We then built a geometrically accurate 2D-model depicted in Fig. 4 A and identified the circumstances underlying various spatiotemporal Ca2+ dynamics. Finally, we validated the model with experiments. This enabled us to map the qualitative classes of Ca2+ signaling to functional outcomes of relative tissue growth. Each step in hierarchical modeling approach is briefly described in Material and Methods, while the full description is given in Supporting Information. Finally, we summarize the results and propose a model linking the Ca2+ signaling readout to size control.
Results
Accounting for calcium-dependent regulation of oscillation duration is required to explain experimental measurements of calcium dynamics
In this study, we used a system of coupled Ordinary Differential Equations (ODEs) to model the basic Ca2+ signaling components (Fig.2A, B, see also associated SI text). The baseline model is adapted from (18). At the single cell level, the experimental Ca2+ signals in the wing imaginal discs exhibited much longer periods and width at half maximum (WHM) compared to the original model of (18). To match the experimental data, we modified the dynamical equation of r as highlighted in Fig. 2 B. The variable r encodes the rate at which the IP3 receptors can be activated by Ca2+. The proposed dynamical equation is given by where in comparison to the original model of (18), the time scale of r is modulated by Ca2+. The modification was necessary to match the temporal characteristics of the model with the experimental data. This modification enables simultaneous control over the frequency (by tuning τmax) and WHM (by tuning kτ) of Ca2+ oscillations. Fig. 2 C, D summarizes the main features of the calibrated model. This suggests that Ca2+ can self-regulate frequency and WHM of its oscillations by modulating the activation rate of IP3 receptors. Additional characteristics of the model are described in supporting information Fig. S2, S3. A similar correction (modifying dynamics of r by modulating the corresponding time scale with Ca2+) with an emphasis on frequency calibration of Ca2+ signals is reported in (19). However, the underling dynamical equations for modeling Ca2+ signaling reported there were slightly different. Specifically, in our model IP3 is described by a Ca2+ (and agonist) dependent ODE, while in their model IP3 is a pulse function.
In the single cell model, VPLC encodes the maximum production rate of IP3 (refer to IP3 dynamics in Fig. 2B). VPLC is a Hopf bifurcation parameter. Consequently, if VPLC is above a critical threshold value , Ca2+ oscillations arise (refer to Fig. S2). Otherwise, the Ca2+ levels remains at its rest value (basal level), and oscillations do not occur. Therefore, VPLC is considered the parameter that encodes the chemical stimulus (FEX) for the simulations.
To study the behavior of Ca2+ signaling in coupled cells, we first considered a simplified model consisting of a chain of cells connected by gap junctions (GJs). The details of the 1D model are described in Supporting Information, and insights are summarized below. The 1D model demonstrates that when VPLC is below , but very close to it, a small amount of diffusive IP3 can trigger Ca2+ spikes (refer to Fig. S11). Furthermore, the diffusive IP3 should have enough strength (defined in terms of energy of diffusive IP3 signal) to trigger Ca2+ signaling (refer to Fig. S12). This observation reveals that when VPLC is close to the Hopf bifurcation threshold, cells are much more prone to stimulate release of Ca2+ from the ER store into the cytosol due to diffusion of IP3. This important finding leads the way to understand the underlying principles for emergence of Ca2+ patterns at the tissue level. Another prediction from the 1D model is that when the gap junction permeability is increased, the triggering of Ca2+ signals in neighborhood cells occur faster. Therefore, permeability of GJs affect the speed of Ca2+ propagation. This is due to the fact that the accumulated IP3, which diffuses through GJs, is the key for triggering Ca2+ release from internal stores (See Supporting Information Fig. S5).
Gap junction communication coordinates and inhibits tissue-level Ca2+ signaling activity
Next, we built a geometrically accurate tissue model that consists of a collection of cells connected by GJ’s. Each cell has its own dynamical equations describing the Ca2+ signaling toolkit with additional terms corresponding to diffusion of IP3 and Ca2+ (Fig. 2 B). The 2D mathematical model suggests that the particular form of tissue-scale Ca2+ signaling present in the epithelium depends on two factors: (i) the spatial organization of IP3 production with respect to the Hopf bifurcation, and (ii) the relative strength of gap junction communication. Here, we provide experimental results to validate key predictions of the model. Throughout the rest of this study, Dp and Dc represent the effective diffusivity of IP3 and Ca2+, respectively.
Gap junction inhibition in the presence of a stimulus leads to asynchronous Ca2+ signaling
Cells exhibit oscillatory Ca2+ dynamics with no coordination among them when GJs were blocked in the presence of hormonal stimulation (FEX stimulation, Movies S1-S2). These results demonstrate the main role of gap junction communication is in the coordination of activity of spatiotemporal Ca2+ patterns between cells in the tissue. When the gap junctions are not blocked, a diverse range of spatiotemporal patterns emerges in the experimental data (Fig. 1C).
Inhibition of gap junction communication increases Ca2+ spikes
The experiment summarized in Fig. 3 provides evidence that reduction of gap junction communication increases Ca2+ signaling within individual cells under low levels of stimulation. Specifically, both control and test discs were cultured without using any external chemical stimulus such as FEX. The control shows almost no Ca2+ activity (Fig. 3A). However, when gap junction communication is blocked in the tissue, Ca2+ spikes appear (Fig. 3B). Fig. 3C represents the simulation results to recapitulate the transition from no Ca2+ activity to the emergence of spikes by decreasing gap junction permeability.
Most of the cells have VPLC below the Hopf bifurcation threshold to simulate no external stimulus, except a tiny fraction of cells that have VPLC slightly greater than the bifurcation threshold. We then varied the gap junction permeability and computed the average Ca2+ levels over the tissue by computing the average integrated Ca2+ levels Here, N is the total number of cells in the tissue, T is the simulation period (1 hour), and ci(t) is the Ca2+ signal for individual cells. When gap junctions are blocked, the average Ca2+ levels are higher. This increase is due to the occurrence of spontaneous Ca2+ spikes (Fig. 3C). When gap junctions are blocked, the IP3 produced in those cells, which are set to be slightly above the bifurcation threshold triggers Ca2+ spikes (there is no diffusion of IP3 to neighboring cells). When gap junctions are open, the produced IP3 diffuses to neighboring cells, and no Ca2+ spike can be triggered (due to insufficient accumulation of IP3). Thus, gap junction communication effectively raises the threshold needed for significant release of Ca2+ into the cytosol. This suggests that gap junction communication acts to ‘inhibit’ calcium signaling. Below, we discuss the necessary conditions for the main classes of Ca2+ patterns in the presence of a stimulus.
The distribution of VPLC with respect to the Hopf bifurcation governs transitions between spatiotemporal classes of tissue-level signaling dynamics
In experimental data Fig. 1 C, different tissue-level patterns of Ca2+ signaling are observed. The main classes include (i) Ca2+ local spikes, (ii) intercellular Ca2+ transients (ICTs), (iii) intercellular Ca2+ waves (ICWs), and (iv) global fluttering in ordinal progression by increasing stimulus. The first three classes have a common feature: a small fraction of cells in the tissue that serve as initiation sites for the onset of Ca2+ signals. However, in the global fluttering mode, most of the cells in the disc are in active state. Fig. 4 D-G summarizes the simulation results for spikes, ICTs, ICWs and global fluttering (also refer to SI simulation movies S4, S6, S8, S13). These results demonstrate that the spatial distribution of VPLC, with respect to the Hopf bifurcation threshold, is the key factor that determines the specific form of intercellular Ca2+ signaling. Fig. 4 C illustrates the distribution of VPLC, which leads to either Ca2+ spikes, ICTs or ICWs. As the distribution of IP3 production rates become closer to the Hopf bifurcation threshold, the spatial extent of Ca2+ signaling becomes larger. In other words, a subpopulation of initiator cells regulates the range of signal transmission by organizing IP3 production rate with respect to a Hopf bifurcation and in the presence of gap junction communication. This explains the ordinal progression of Ca2+ dynamics observed as the concentration of chemical stimulus such as FEX is increased. Fig. 4 H shows how Ca2+ waves can form based on patterning of maximum production of PLC activity (VPLC). As depicted in Fig. S20, reducing VPLC in a stripe along A/P axis, while keeping the rest of cells near Hopf bifurcation also leads to spiral form of Ca2+ waves (refer to SI simulation movie S10). An example of such an experimental observed spiral wave is depicted in the SI movie S9.
Gαq overexpression in the absence of stimulus induces Ca2+ waves and leads to reduced wing size
To further confirm our prediction that the position of VPLC with respect to Hopf bifurcation affects the overall Ca2+ dynamics, we experimentally tested the effect of overexpressing Gαq on the resulting Ca2+ dynamics using the Gal4/UAS system (23, 24). Gαq is one of the subunits of the G-protein that disassociates in response to GPCR activation. Dissociated Gαq activates phospholipase C to convert PIP2 to DAG and IP3 (25). Hence, altering the levels of Gαq increases activation of PLCs in the cytosol. We observed the robust formation of intercellular Ca2+ waves independent of FEX in the media (Fig. 5B, B’). The waves were periodic in nature and were similar to the FEX-induced waves. We did not observe significant global fluttering or spikes when we overexpressed Gαq in the wing disc. We also observed that overexpression of Gαq resulted in a decrease in the overall size of the wing (Fig. 5 B”). Taken together, our results indicate that the intercellular Ca2+ waves is a consequence of Gαq signaling, and that the relative level of stimulated Ca2+ signaling activities plays a key role in determining the final size of the adult wing.
Insulin signaling increases wing size but only generates localized Ca2+ signals
In addition to FEX, we asked whether other ligands added to the organ culture affects Ca2+ activity. In addition to FEX, insulin is added often to organ culture media to stimulate cell proliferation (26, 27). Hence, we asked whether activation of insulin signaling regulates Ca2+ activity. Using GAL4/UAS system, we upregulated and downregulated insulin signaling in the wing disc. Strikingly, we observed that activation of insulin signaling results in localized Ca2+ spikes and ICTs (Fig. 5 C, C’). However, we did not observe many ICWs. As a second experiment, we varied the concentration of insulin and found that a higher concentration of insulin increased the number of spikes and ICTs. However, we did not see the generation of periodic ICWs. In contrast, no spikes were observed when insulin signaling was inhibited by expressing a dominant negative form of the insulin receptor (Fig. 5 D, D’)(28). Furthermore, we did not observe periodic ICWs when insulin signaling was constitutively activated (Fig. 5 C, C’)(29). Thus, our results suggest that the localized Ca2+ spikes observed ex vivo is activated by insulin signaling. Upregulation of insulin signaling increases the wing size (Fig. 5 C”). Thus, localized Ca2+ signal correlates with increased wing size in contrast to global waves in response to GPCR signaling, which correlates with decreased wing size.
Discussion
The main finding of this work is the discovery of a parsimonious explanation that links global hormonal stimulation of calcium signaling to emergent spatiotemporal classes of signaling dynamics (Fig. 6). The model predicts that the distribution of IP3 production rate with respect to a Hopf bifurcation in the presence of gap junction communication determines the mode of Ca2+ signaling in epithelia, and each mode has a specific spatial range. As a consequence, the spatial range of Ca2+ signaling can be controlled by tuning tissue level IP3 production rates. We showed that (i) upregulation of insulin signaling induces localized Ca2+ signals with a corresponding increase in final wing size and (ii) Gαq overexpression in the absence of stimulus induces global Ca2+ waves and Gαq overexpression leads to reduced wing size,. To elucidate the impact of different modes of Ca2+ signaling on tissue growth, the computational model and experimental evidences provide key support for the “IP3 /Ca2+ shunt” hypothesis of tissue size regulation. In this model, tuning IP3 production levels enables control of the common substrate allocation between two different pathways, namely, Ca2+ signaling pathway and the PI3K/AKT signaling pathway (16). PIP2 is the precursor for IP3 and also modulate PI3K/AKT pathway (30). If more PIP2 is allocated for stimulating Ca2+ signaling (which induces global Ca2+ activity), less PIP2 is available for PI3K/AKT pathway (which inhibits the growth). This proposition paves the way on how to tune one signaling pathway to control another signaling pathway (e.g. PI3K/AKT), which are coupled at the substrate level.
A recent study on signal transmission in a bacterial community suggests that the transition from localized short-range signaling to global community-level communication is associated with a cost-benefit balance (31). In that context, long range signaling increases the overall fitness of the community against chemical attack, while the cost to individual cells is a reduction in growth rate. The proposed model in this work can also be characterized as a cost-benefit trade offs within the context of tissue level Ca2+ signaling. For instance, it has been suggested that the fast calcium waves facilitate migration and proliferation of the healing cells by inhibiting excessive apoptotic response during wound healing in epithelia (32). Fig. 6 summarizes the effects of different Ca2+ signaling modes in the context of tissue growth and development. Minimal calcium activity, as is observed when insulin signaling is inhibited, correlates with reduced growth, whereas intermediate levels of calcium signaling accompanies strong activation of insulin signaling. However, such signaling does not lead to recurring global calcium waves. GPCR-mediated ICWs lead to a net reduction in tissue growth and therefore are growth inhibiting. Within the context of the “IP3 /Ca2+ shunt” model, the strong induction of calcium waves will reduce the level of PIP2, a key substrate for growth. This analysis thus motivates future experimental work in this area, which will require careful quantification of PIP2 and PIP3 under genetic perturbations of GPCR signaling. Additionally, future work is needed to quantify the metabolic benefits and costs of calcium signaling during tissue growth.
A possible alternative interpretation would incorporate the coupling of calcium signaling dynamics to tissue growth through cell mechanics. A starting point of the proposed coupling equations can follow the recent proposed model where it was shown that calcium signals and contractions are coupled via a two-way mechanochemical feedback mechanism during apical constriction (33). Finally, a major implication for this work is the translational potential of deliberately shaping calcium signaling activities through spatiotemporally controlled modulation of calcium signaling dynamics in tissues, through a combination of global modulation and local perturbations, to treat or inhibit diseases such as cancer and birth defects.
Materials and Methods
In this study, the Drosophila wing imaginal disc in the late larval stages was used as a model platform to investigate the mechanisms governing Ca2+ signaling dynamics in epithelia (15, 34, 35). Wing imaginal discs are geometrically simple epithelial organs growing inside the larva. Imaginal discs form different parts of the adult wing and thorax after metamorphosis (36). We restrict the spatial domain of simulations to the wing pouch area, which will form the wing blade, as it is well defined through many genetic studies (see Fig. 1).
Fly stocks
A nub-GAL4, UAS-GCaMP6f reporter tester line was created by recombining nub-GAL4 and UAS-GCaMP6f lines (34). Additionally, a second tester line was used that also includes UAS-mcherry. Gene perturbations were generated by crossing the tester line to either RNAi-based transgenic lines (UAS-Gene XRNAi) or gene overexpression (UAS-Gene X). The following UAS transgenic lines were used: UAS-RyRRNAi(BL#31540)(37), UAS-Gq(BL#30734)(38), UAS-InsRCA (BL#8248)(39), UAS-InsRDN(BL#8252)(40). Progeny wing phenotypes are from F1 male progeny emerging form the nub-Gal4, UAS-GCaMP6f/CyO x UAS-X cross or nub-Gal4, UAS-GCaMP6f/CyO; UAS-mcherry x UAS-X cross. Flies were raised at 25C and on a 12-hour light cycle.
Live imaging
Wandering third instar larva approximately 6 days after egg laying were dissected in ZB media with 15% fly extract to obtain wing discs (41). ZB media + 15% fly extract contains 79.4% (v/v) ZB media, 0.6% (v/v) of 1 mg/ml of insulin (Sigma aldrich), 15% ZB-based fly extract and 5% pennicillin/streptomyocin (Gibco). Wing discs were loaded into the previously described REM-Chip (35) and imaged using Nikon Eclipse Ti confocal microscope with a Yokogawa spninning disc and MicroPoint laser ablation system. Image data were collected on an IXonEM+colled CCD camera (Andor technology, South Windsor, CT) using MetaMorph v7.7.9 software (Molecular devices, Sunnyvale, CA). Discs were imaged at three z-planes with a step size of 10 µm, 20x magnification and 10-seconds intervals for a total period of one hour, with 200 ms exposure time, and 50 nW, 488 nm laser exposure at 44 % laser intensity. We blocked gap junction by inhibiting innexin-2 using Carbenoxolone (Cbx, Sigma Aldrich) drug (34). Wing discs were incubated in ZB + 15% FEX with 30 µM Cbx for one hour before imaging. To induce Ca2+ transients, we imaged wing discs in ZB media + 2.5 % FEX. Ca2+ waves were induced by imaging the wing disc in ZB media + 15% FEX. Ca2+ fluttering was observed when discs were imaged in ZB media + 40% FEX respectively.
Quantification of adult wings
Total wing area was measured using imageJ. We traced the wing margin by following veins L1 and L5 and the wing hinge region was excluded from the size analysis.
Intracellular model
A modified model of Ca2+ signaling toolkit based on the Politi et al. model (18) was utilized in this work. The model is summarized in Fig. 2. A more comprehensive description can be found in Supporting Information. To recapitulate the same time resolution as the experiments, the simulation time is 1 hour and for generating videos, samples are obtained every 10s.
Tissue model
For constructing a realistic model of the tissue, we used experimental images of a wing pouch to build an accurate model of the tissue structure. Fig. 4 A,B depicts the structure of the tissue used for simulations and the statistics of the corresponding network. More detail on the geometry of the model are discussed in Supporting Information.
Intercellular model
The realistic model of the tissue was combined with proposed intracellular model. Diffusion of the second messengers IP3 and Ca2+ between adjacent cell was incorporated into the 2D model. Therefore, the tissue level model is a system of coupled ODE’s. A complete description of the model is provided in SI materials.
Data availability
All the data and simulation codes are available upon request.
ACKNOWLEDGMENTS
The work in this paper was supported by NIH Grant R35GM124935 and NSF Award CBET-1553826. The authors gratefully acknowledge the Notre Dame Center for Research Computing (CRC) for providing computational facilities. We would like to thank Alexander Dowling and Maria Unger for helpful discussions, and members of the Zartman lab for their supports and critiques.
Footnotes
↵2 The experimental data is imaged by Dharsan Soundarrajan.
The authors declare no conflict of interest.