Ca2+ release via IP3 receptors shapes the cytosolic Ca2+ transient for hypertrophic signalling in ventricular cardiomyocytes
Hilary Hunt, Agne Tilunaite, Greg Bass, Christian Soeller, H. Llewelyn Roderick, Vijay Rajagopal, Edmund J. Crampin
MManuscript submitted to
Biophysical
Journal
Article Ca release via IP receptors shapes the cytosolic Ca transient for hypertrophic signalling in ventricularcardiomyocytes Hilary Hunt , Agn˙e Til¯unait˙e , Greg Bass , Christian Soeller , H. Llewelyn Roderick , Vijay Rajagopal * † , and Edmund J.Crampin * † Systems Biology Laboratory, School of Mathematics and Statistics and Melbourne School of Engineering, University ofMelbourne, Australia Living Systems Institute, University of Exeter, UK Laboratory of Experimental Cardiology, Department of Cardiovascular Sciences, KU Leuven, Belgium Cell Structure and Mechanobiology Group, Department of Biomedical Engineering, Melbourne School of Engineering,University of Melbourne, Australia ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, School of Chemical and Biomedical Engineering,University of Melbourne, Australia * Correspondence: [email protected]; [email protected] Calcium (Ca + ) plays a central role in mediating both contractile function and hypertrophic signalling in ventricularcardiomyocytes. L-type Ca channels trigger release of Ca + from ryanodine receptors (RyRs) for cellular contraction, whilesignalling downstream of Gq coupled receptors stimulates Ca release via inositol 1,4,5-trisphosphate receptors (IP Rs),engaging hypertrophic signalling pathways. Modulation of the amplitude, duration, and duty cycle of the cytosolic Ca + contractionsignal, and spatial localisation, have all been proposed to encode this hypertrophic signal. Given current knowledge of IP Rs,we develop a model describing the effect of functional interaction (cross-talk) between RyR and IP R channels on the Ca + transient, and examine the sensitivity of the Ca + transient shape to properties of IP R activation. A key result of our study isthat IP R activation increases Ca + transient duration for a broad range of IP R properties, but the effect of IP R activation onCa + transient amplitude is dependent on IP concentration. Furthermore we demonstrate that IP -mediated Ca release in thecytosol increases the duty cycle of the Ca + transient, the fraction of the cycle for which [Ca ] is elevated, across a broad rangeof parameter values and IP concentrations. When coupled to a model of downstream transcription factor (NFAT) activation,we demonstrate that there is a high correspondence between the Ca + transient duty cycle and the proportion of activatedNFAT in the nucleus. These findings suggest increased cytosolic Ca duty cycle as a plausible mechanism for IP -dependenthypertrophic signalling via Ca + -sensitive transcription factors such as NFAT in ventricular cardiomyocytes.SIGNIFICANCE Many studies have identified a role for IP R-mediated Ca + signalling in cardiac hypertrophy, howeverthe mechanism by which this signal is communicated within the cardiomyocyte remains unclear. We present a mathematicalmodel of functional interactions between RyR and IP R channels. We show that IP -mediated Ca + release is capableof providing a modest increase to the duty cycle of the calcium signal, which has been shown experimentally to lead toNFAT activation, and hence hypertrophic signalling. Through a parameter sensitivity analysis we demonstrate that theduty cycle is increased with IP over a broad parameter regime, indicating that this mechanism is robust, and we showthat an increase in Ca + duty cycle increases nuclear NFAT activation. These findings suggest a plausible mechanism forIP3R-dependent hypertrophic signalling in cardiomyocytes. INTRODUCTION
Calcium is a universal second messenger that plays a role in controlling many cellular processes across a wide variety of celltypes; ranging from fertilisation, cell contraction, and cell growth, to cell death (1, 2). Precisely how Ca + fulfills each of these † These authors contributed equally to the supervision of this work.
Manuscript submitted to Biophysical Journal a r X i v : . [ q - b i o . S C ] A ug unt, Til¯unait˙e et al. roles while also ensuring signal specificity remains unclear in many cases. Ca + can be used to transmit signals in a variety ofways. Signal localisation, and amplitude and frequency modulation have been widely explored (3–5), however, mechanismsfor information encoding in the cumulative signal (i.e. area under the curve (AUC), proportional-integral-derivative (PID)controller, or duty cycle (DC)) have also been proposed (6–8). Determining which method of information encoding is relevantto a specific signalling pathway requires determining what type of signal encoding the system is capable of, and whether thedownstream effector of the signal is capable of temporal signal integration, high or low pass filtering, or threshold filtering.In cardiac myocytes, discrete encoding of multiple Ca + -mediated signals is particularly pertinent because of the essentialand continuous role Ca + plays in excitation-contraction coupling (ECC). Of particular significance is the involvement of Ca + in hypertrophic growth signaling. How Ca + can communicate a signal in the hypertrophic signalling pathway concurrentwith the cytosolic Ca + fluxes that drive cardiac muscle contraction is still largely unresolved (9, 10). Understanding thismechanism is important as pathological hypertrophic remodelling is a precursor of heart failure and a common final pathway ofcardiovascular diseases including hypertension and coronary disease (11–13).During each heartbeat, on depolarisation of the membrane Ca + enters the cell via L-type Ca + channels (LTCC), triggeringlarger Ca + release from the sarcoplasmic reticulum (SR) via ryanodine receptors (RyRs), which then induces contraction.The activation of Ca + release via RyRs by the Ca + arising via LTCCs is known as calcium-induced calcium release(CICR), and results in a 10-fold increase in cytosolic Ca + concentration (relative to resting Ca + concentration of ∼
100 nM).Sarco-endoplasmic reticulum Ca + pumps (SERCA) and other Ca + sequestration mechanisms subsequently withdraw thereleased Ca + back into the SR and out of the cytosol (14, 15) reverting the cell to its relaxed state. Ca + also plays a centralrole in hypertrophic signalling. Hypertrophic stimuli such as endothelin-1 (ET-1) bind to G-protein-coupled receptors at thecell membrane to stimulate generation of the intracellular signalling molecule inositol 1,4,5-trisphosphate (IP ). After IP binds to and activates its cognate receptor, inositol 1,4,5-trisphosphate receptors (IP R), on the SR and nuclear envelope, Ca + is released into the cytosol and nucleus respectively (16, 17) (see Figure 1). This Ca signal arising from IP Rs has beenshown in multiple mammalian species to produce a distinct Ca signal that, through activation of pro-hypertrophic pathwaysincluding those involving NFAT, induces hypertrophy within cardiomyocytes. (16, 18, 19).In healthy adult rat ventricular myocytes (ARVMs), various effects of IP on global Ca transients associated with ECChave been described, summarised in Table 1. While application of GPCR agonists that stimulate IP generation produces robusteffects on ECC associated IP transients and contraction, the direct contribution of IP to these actions varies between studies(17, 20–24). For example, in rabbit the effect of ET-1 on Ca transient amplitude is sensitive to the IP R inhibitor 2-APB (22),whereas in healthy rats IP R inhibition with 2-APB was without effect (25). In mice 2-APB abrogated an increase in ECCassociated Ca transients brought about by AngII (24). Responses have also been variable when IP was directly applied tocardiac myocytes. In healthy rat, IP produced no or a modest effect on Ca transient amplitude (17, 21), whereas in rabbit(22) a more substantial effect was observed. These differences in the effect of IP have been ascribed in part to the greaterdependence of rat myocytes on SR Ca release to the Ca transient than rabbit myocytes(22). Notably, both ET-1 and IP elicit arrhythmogenic effects whereby they promote the generation of spontaneous calcium transients, manifest as a prolongedCa transient with additional peaks, and they increase the frequency of Ca sparks (17, 18, 21, 22). A more profound role forIP signalling is observed in hypertrophic ventricular myocytes, with ECC-associated Ca transients of greater amplitudereported. Underlying these effects, IP R expression is elevated in hypertrophy (26). Hence, a question remains as to whatindependent effect IP R activation has on the cytosolic Ca + transient in healthy ventricular cardiac myocytes. Cell State IP ET-1
Rat Amplitude:Duration:Basal Ca :SCTs: r (cid:115) (21) r (cid:117) (17) – r (cid:117) (17) r (cid:115) (21) r (cid:115) (17) r (cid:115) (21) r (cid:117) (16) r (cid:115) (17) – r (cid:117) (17) r (cid:115) (21) r (cid:115) (17) Other species Amplitude:Duration:Basal Ca :SCTs: m (cid:115) (20) m (cid:117) (27) – m (cid:115) (27) – h (cid:115) (20) m (cid:115) (20) – m (cid:115) (20) b (cid:115) (22) h (cid:115) (20) m (cid:115) (20) Table 1: Summary of experimentally observed changes to the Ca + transient in normal healthy ventricular myocytes in rat andother species following addition of IP and ET-1. SCTs: spontaneous Ca + transients; (cid:115) indicates an increase; (cid:116) a decrease; (cid:117) indicates no significant change reported; r indicates rat, b indicates rabbit, h indicates human, m indicates mouse; dashesindicate no data found. The model developed in this work is primarily parameterised with rat data.The individual behaviour of IP R channels and their dependence on Ca + , IP , and ATP in cardiac and other cell types has Manuscript submitted to Biophysical Journaln the role of IP R in cardiac hypertrophic signalling α β γ
CnANFAT CaMTnC
LTCC RyRPMCANCX GPCRNUCLEUS PLC
PIP IP IP R SarcoplasmicReticulum SERCACa Ca Ca Ca Ca Ca T-TUBULE
Figure 1: Schematic showing key Ca signalling pathways in the cardiomyocyte. ECC processes include ryanodine receptors(RyR), L-type Ca channel (LTCCs), sarco-endoplasmic reticulum Ca ATP-ase (SERCA), sodium calcium exchanger (NCX),sarcolemmal calcium pump (PMCA) and Troponin-C (TnC). Growth-related IP – CnA/NFAT signalling processes includeinositol 1,4,5-trisphosphate receptors (IP R), G protein-coupled receptor (GPCR), phospholipase C (PLC), phosphatidylinositol4,5-bisphosphate (PIP ), calmodulin (CaM), calcineurin (CnA) and nuclear factor of activated T-cells (NFAT). Manuscript submitted to Biophysical Journal unt, Til¯unait˙e et al. been explored in a number of studies (28–31). These studies have formed the basis of several computational models of IP Rtype I isoforms (30, 32, 33) fitted to stochastic single-channel data (34). However, properties of IP R channel activity within thecardiomyocyte, such as gating state transition rates and their dependency on IP and Ca , have not been directly measured. Inthis study we have taken the experimental studies on rat ventricular cardiomyocytes as a reference point for the observed effectsof IP R activation on cellular Ca + dynamics and extended a well-established model of beat-to-beat cytosolic Ca + transients inrat cardiac cells (14, 35) to include a model of type II IP R (33) channels. This deterministic, compartmental model of ECCenables us to investigate biophysically plausible mechanisms by which IP R activation could affect Ca + dynamics at the wholecell scale, while avoiding the computational complexity associated with detailed stochastic and spatial modelling. Specifically,it enables us to explore the parameter ranges of IP R-mediated Ca release that modify the global cytosolic Ca transient toencode information for hypertrophic signalling to the nucleus.A number of transcription factors transduce changes in Ca to activate hypertrophic gene transcription. Of particular note isNuclear Factor of Activated T-cells (NFAT). There are five known NFAT isoforms expressed in mammals, four of these are foundin cardiac cells (19, 36). To initiate hypertrophic remodelling, the hypertrophic Ca + signal, in conjunction with calmodulin(CaM) and calcineurin (CnA) leads to dephosphorylation of cytosolic NFAT. Upon dephosphorylation NFAT translocates to thenucleus where, in coordination with other proteins, it activates expression of genes responsible for hypertrophy (37). Severalstudies have focused on characterising the Ca + dynamics necessary to activate NFAT and initiate hypertrophy (8, 19, 38–43)and have shown NFAT to be a Ca + signal integrator (38). Furthermore, a recent study by Hannanta-anan and Chow (8) useddirect optogenetic control of cytosolic Ca + transients in HeLa cells to demonstrate that the transcriptional activity of NFAT4(also known as NFATc3), a necessary NFAT isoform in the hypertrophic pathway (36), can be up-regulated by increasing theresidence time of Ca + in the cytosol within each oscillation. The increased residence time of Ca + , referred to as the ‘dutycycle’, is the ratio between the area under the Ca + transient curve divided by the maximum possible area, as calculated by theproduct of transient amplitude and period (see Figure 2A). The Ca duty cycle is therefore distinct from the average Ca concentration. Hannanta-anan and Chow (8) showed that increasing the duty cycle had a proportionally greater effect on NFATtranscriptional activity than changing either the frequency or amplitude of the cytosolic Ca + oscillations. This suggests anincreased Ca duty cycle as a possible mechanism by which Ca + release through IP R channels can effect hypertrophicsignaling.Here, using a mathematical model of beat-to-beat cytosolic Ca + transients in rat ventricular myocytes, coupled to IP Rchannel Ca release, we show that IP R activation in the cytosol can increase the duty cycle of the cytosolic Ca + transient. Weestablish model feasibility through parameter sensitivity analysis, which shows that this behaviour does not depend sensitivelyon model parameter values. Furthermore we identify conditions necessary for IP R channel activation to alter Ca + transientamplitude, width, basal Ca and duty cycle, as identified in different experimental studies, and compare model simulations topublished experimental data summarised in Table 1. Finally, we couple simulations of cytosolic Ca dynamics to a model ofdownstream CaM/CnA/NFAT activation and show that the duty cycle of the Ca transient highly correlates with the activatednuclear NFAT (the proportion of NFAT which is dephosphorylated and translocated to the nucleus). These findings suggestIP R activity can increase the cytosolic Ca duty cycle, thus providing a mechanism for IP -dependent activation of NFAT forhypertrophic signalling in the cardiomyocyte. METHODS
We developed a computational model of RyR- and IP R-mediated Ca fluxes in the adult rat ventricular myocyte. Modelsimulations were performed using the ode15s ODE solver from MATLAB 2017b (The MathWorks Inc., Natick, Massachussetts)with relative and absolute tolerances 1 × − and 1 × − respectively. The model equations were simulated at 1 Hz, theoriginal pacing frequency of the Hinch et al. (14) model and at 0.3 Hz because it is another common pacing frequency inexperimental studies of IP and Ca + in cardiomyocytes (17, 21). The model was paced until the normalised root mean squaredeviation (NRMSD) between each subsequent beat was below 1 × − , and all but the last oscillation discarded to eliminatetransient behaviours (see Figure 2B). Initial conditions were set to the basal Ca level of the model at dynamic equilibriumwith inactive IP R channels, determined after running the base model until the NRMSD was also below 1 × − . Model Equations
The compartmental model of rat left ventricular cardiac myocyte Ca + dynamics is based on the Hinch et al. (14) model ofECC, with the addition of IP R Ca + release modelled using the Siekmann-Cao-Sneyd model (33). The Hinch model is anestablished whole cell model of rat cardiac Ca + dynamics that describes the flux through the major Ca + channels and pumpson the cell and SR membranes and the effects of applying a voltage across the cell membrane. The parameters for the Hinchcomponent of our model were maintained from the original except for those of the driving voltage. This was shortened to better Manuscript submitted to Biophysical Journaln the role of IP R in cardiac hypertrophic signalling approximate the rat action potential (44) (see Figure S1). The Ca + in the cytosol is governed by the following ODE:d [ Ca + ] cyt d t = β fluo · β CaM · (cid:16) I CaL + I RyR − I SERCA + I IP3R + I other (cid:17) (1) I other = I SRl + I NCX − I PMCA + I CaB + I TnC (2)A small Ca + flux through the LTCCs, I CaL , activates RyR channels to release Ca + from the SR into the cytosol at a rate of I RyR . Ca + is resequestered into the SR by SERCA at a rate I SERCA . β fluo is the rapid buffer coefficient (45) for the fluorescentdye in the cytosol and β CaM is the rapid buffer coefficient for calmodulin in the cytosol. I other includes Ca + fluxes such asexchange with the extracellular environment through the sodium-calcium exchanger, I NCX ; sarcolemmal Ca + -ATPase, I PMCA ;and the background leak current, I CaB ; as well as the SR leak current, I SRl ; and buffering on troponin C, I TnC . These fluxes aredefined in the SI (section 1).When the simulation is run with IP present, there is additionally a flux through the IP Rs : I IP3R = k f · N IP3R · P IP3R · (cid:16) [ Ca + ] SR − [ Ca + ] cyt (cid:17) (cid:46) V myo (3)Here V myo is the volume of the cell. k f is the maximum total flux through each IP R channel; this was chosen to be 0.45 µ m ms − unless otherwise stated to create a measurable effect on IP R channel activation while maintaining plausible totalflux. N IP3R is the number of IP R channels in the cell, this was set to 1/50th of the number of RyR channels (46). We studiedthe effect of varying k f on IP -induced changes to the cytosolic Ca transient in normal cardiomyocytes. Evidently, varying N IP3R and varying k f have the same effect on simulated calcium dynamics. While N IP3R is known to increase significantly indisease conditions, we have not emphasised it in this study due to our focus on normal cardiomyocytes. [ Ca + ] cyt and [ Ca + ] SR are the Ca concentrations in the cytosol and SR respectively. P IP3R is the [Ca ] and [IP ] dependent open probability of the IP R channels, and is determined using the Siekmann-Cao-Sneyd model (32, 33, 47), which has an in-built delay in response to changing Ca concentration, along with severalparameters governing channel activation and inactivation. This model describes P IP3R as: P IP3R = β (cid:46) (cid:0) β + k β · ( β + α ) (cid:1) (4)where k β is a transition term derived from single-channel Siekmann et al. (47), β describes the rate of activation and α the rateof inactivation: β = B · m · h (5) α = ( − B ) · ( − m · h ∞ ) (6)where h is time-dependent, and B , m , and h / h ∞ describe the dependence on IP , the dependence on Ca and the Ca -dependentdelay in IP R gating, respectively. Expressions for these variables are as follows: B = [ IP ] (cid:46) (cid:16) K p + [ IP ] (cid:17) (7) m = [ Ca + ] (cid:46) (cid:16) K c + [ Ca + ] (cid:17) (8) dhdt = (cid:16) ( h ∞ − h ) · (cid:16) K t + [ Ca + ] (cid:17)(cid:17) (cid:46) (cid:16) t max · K t (cid:17) (9) h ∞ = K h (cid:46) (cid:16) K h + [ Ca + ] (cid:17) (10)Here K c and K h are parameters which determine the Ca -dependence of IP R channel open probability, while K t and t max areparameters which affect the delay in IP R response to cytosolic changes. K t determines the influence of [Ca ] on the delay,while t max is a temporal scaling factor.We note that the SR leak flux, I SRl , is unchanged from the Hinch model, and would include the effects of diastolic IP RCa release at normal IP levels as that model did not explicity include IP R. However, in the presence of IP , IP R Ca flux during diastole is several orders of magnitude greater than I SRl , which is largely dependent on [ Ca + ] SR , and hence anydiscrepancy caused by this will have a negligible effect on overall Ca dynamics within the cell (see also Figure S4).Several experimental studies have investigated IP R activity across a range of Ca + concentrations with 1 µ M IP (28, 48).These studies suggest that IP R channels would be open, with almost constant P IP3R over the full range of cytosolic Ca + Manuscript submitted to Biophysical Journal unt, Til¯unait˙e et al. concentrations experienced during ECC in the cardiomyocyte. An IP R-facilitated SR-Ca leak has been reported to amplifysystolic concentrations (49, 50) as seen in most published experiments of IP enhanced Ca + transients tabulated in Table 1.Through parameter sensitivity analysis of this model, we show that in order to be consistent with these observations P IP3R mustbe significantly smaller at resting Ca concentrations than at higher concentrations. Coupling cytosolic Ca and NFAT activation We coupled the calcium model to the NFAT model developed by Cooling et al. (51), which determines the proportion of totalcellular NFAT that is dephosphorylated and translocated to the nucleus for a given cytosolic Ca signal. In this study we haveused the model parameters estimated from the data in Tomida et al. (38) who measured activation of NFAT4 in BHK cells. Fulldetails of the Cooling et al. (51) model are given in the Supplementary Information. RESULTS
An example of the model output when run with the original IP R channel parameter values determined by Sneyd et al. (33) fortype I IP R channels is shown in Figure 2C. Measurements of the properties of IP R channel activity and their dependence onCa within cardiomyocytes are sparse in the literature. Therefore we performed a parameter sensitivity analysis by runningmodel simulations over a variety of parameter ranges to explore the dependence of features of the cytosolic calcium transient toIP R channel parameters.A
AUC (U) [Ca ] Time A m p li t ud e ( A ) Period (T)Spike Width (∆)Threshold? Duty Cycle ( ! ) = ≈ ∆% B [IP ] increased Transient used C Time (ms) [ C a + ] ( M ) Cytosol
Time (ms) SR Time (ms) F l u x ( M / m s ) I RyR
Time (ms) I IP R Figure 2: (A) The duty cycle, a function of AUC, amplitude, and period, for the cytosolic Ca + transient. (B) Example ofCa + transients generated by the model. (C) Ca concentration in cytosol and SR, RyR flux, and IP R flux in the model withelevated IP (red) and without IP (blue). Here IP R parameters used are taken from Sneyd et al. (33), with maximum IP R flux k f = µ m ms − . Parameter sensitivity analysis
We conducted a parameter sensitivity analysis to determine the critical parameters related to IP R activation that affect the shapeof beat-to-beat cytosolic Ca + transients. We used the Jansen method (52) as described in Saltelli et al. (53) (and summarised inthe SI) to calculate the ‘main effect’ and ‘total effect’ coefficients of each of the parameters associated with IP R channel gatingin relation to changes in transient amplitude, full duration at half maximum (FDHM), diastolic Ca and duty cycle (see Table2). Saltelli et al. (53) describe the main effect coefficient as ‘the expected reduction in variance that would be obtained if [theparameter] could be fixed’ and the total effect coefficient as ‘the expected variance that would be left if all factors but [theparameter] could be fixed’, both normalised by the total variance. Both coefficients are included here to provide a completepicture of the impact of each parameter. Simulation parameter values were generated using the MATLAB sobolset function Manuscript submitted to Biophysical Journaln the role of IP R in cardiac hypertrophic signalling with leap 1 × and skip 1 × . Variance-based parameter sensitivity analysis
Main Effect Coefficients [IP ] t max K c K h K t k f Amplitude
Diastolic Ca [IP ] t max K c K h K t k f Amplitude
FDHM
Diastolic Ca Duty Cycle
Table 2: Main and total effects of the IP R gating parameters on Ca + transient amplitude, duration (FDHM), diastolic Ca + ,and duty cycle. Significant values are highlighted in bold font.Table 2 shows that the delay parameters t max and K t do not have a large effect on the cytosolic Ca transient. While theyare necessary to describe the effect of IP R-dominated Ca + dynamics (33), they contribute only a small amount to the variance.Therefore we decided to fix these parameters in our simulations.As expected, the coefficients show that cardiac cell Ca + dynamics during ECC are most highly sensitive to IP concentration([IP ]) and the maximal flux through each IP R ( k f ). The maximal flux k f has little effect on transient amplitude, but largeinfluence on duration and duty cycle; while [IP ] has the greatest effect on the change in amplitude and diastolic Ca concentration.The gating parameters K c and K h also influence the cytosolic Ca transient. K h affects the [Ca ] at which IP R channelsare inhibited and K c affects the [Ca ] at which IP R channels open. We illustrate how these two parameters affect IP R openprobability, P IP3R , in Figure 3. Figure 3 also shows how [IP ] affects the relationship between K c , K h , [Ca ] and P IP3R . It canbe seen that with K h = 80 nM, P IP3R will be close to zero regardless of the values of Ca or [IP ] or K c . At K h = µ M and[IP ] ≥ µ M P IP3R dependence on K c and Ca becomes apparent. Finally, at K h = µ M, P IP3R is still dependent on K c andCa values, but [IP ] does not change P IP3R significantly.From this analysis, we determine that in order for IP R channels to be active during ECC, K h must be sufficiently highthat IP Rs are not inhibited at diastolic [Ca ]. Conversely, K c must be low enough that IP R channels are active at Ca + concentrations below the systolic Ca peak. Therefore, in the remainder of this study, we fix K h at 2.2 µ M: high enough tofulfill this condition while low enough that IP R channels are still affected by [IP ]. We report simulation results only withinthe range of K c that exhibits experimentally plausible Ca + transient properties.With the plausible range of K h and K c established, we next show the effect of K c , k f and [IP ] on the ECC transient. IP concentration and IP R opening behaviour have the greatest impact on the Ca + transient As summarised in Table 1, different experimental studies suggest different effects of IP R activation on the ECC cytosolicCa + transient. Figures 4A-C show quantitative predictions of how much Ca transient properties could be affected by IP Ractivation across a range of [IP ] and Ca -dependent IP R gating parameter K c values. k f was fixed at 0.45 µ m ms − and K h was fixed at 2.2 µ M.The red region in Figure 4A corresponds to IP R activation parameters that produce the greatest increase in Ca amplitude.Noteworthy is that the red region depicts moderate changes in amplitude of ∼ K c values greaterthan 4 µ M and [IP ] greater than 2 µ M. With K h set at 2.2 µ M, this corresponds to the middle and far-right plots of P IP3R inFigure 3. The middle subfigure shows that with K c greater than 4 µ M IP R channels would open only at Ca concentrationsgreater than the diastolic concentration of ∼ µ M. The plot also shows that IP Rs would remain active at Ca greater than thesystolic peak concentration of ∼ µ M (54). Figure 4B further indicates that the increase in peak amplitude is accompanied byan increase in transient duration (FDHM). However, this change may be small, particularly at IP concentrations lower than 1 µ M. In Figure 4C it can be seen that the diastolic Ca + concentration decreases moderately ( ∼ + transient increases whenever IP Rs are active. This increase is greater with greater
Manuscript submitted to Biophysical Journal unt, Til¯unait˙e et al. Ca ( M) K c ( M ) Ca ( M) K c ( M ) Ca ( M) K c ( M ) Ca ( M) K c ( M ) Ca ( M) K c ( M ) Ca ( M) K c ( M ) Ca ( M) K c ( M ) Ca ( M) K c ( M ) Ca ( M) K c ( M ) Ca ( M) K c ( M ) Ca ( M) K c ( M ) Ca ( M) K c ( M ) K h = n M K h = . µ M K h = . µ M K h = . µ M Figure 3: The effect of [Ca ], [IP ], K c , and K h on P IP3R in the Siekmann-Cao-Sneyd IP R model (32, 33, 47). The colouredbars on the side of each plot show the proportion of IP R channels that will open for each set of parameters at steady state. Notethat IP Rs do not open at physiological Ca concentrations when K h is low (i.e. 80 nM or less). In subsequent simulations weused the value K h = µ M unless otherwise stated. Manuscript submitted to Biophysical Journaln the role of IP R in cardiac hypertrophic signalling
Change in Amplitude (%) [I P ] ( M ) K c ( M) -60-40-20020406080100120140160+ A Change in FDHM (%) [I P ] ( M ) K c ( M) -60-40-20020406080100120140160+ B Change in Baseline (%) [I P ] ( M ) K c ( M) -60-40-20020406080100120140160+ C Change regions K c ( M) I P ( M ) FDHM and Diastolic [Ca ] increase
Amplitude and FDHM increase
FDHM increases
No change [] D Figure 4: Effect of IP concentration and the parameter K c on the Ca + transient with pacing frequency 1 Hz. These twoparameters, along with maximum IP R flux, k f have the greatest impact when considering the effect of IP R activation on theCa + transient. To better resolve the range in which FDHM changes, all FDHM increases of 45% and over are shown in thesame colour. See Figure 5 for simulated transients at parameters indicated by crosses. We note that for ease of comparisonbetween figures, in this and in subsequent figures the maximum increase from baseline is cropped at 160%. Changes greaterthan this threshold are shown in the same colour. Manuscript submitted to Biophysical Journal unt, Til¯unait˙e et al. concentrations of IP and with lower values of K c . Figure 4C indicates that K c and [IP ] have a similar effect on the diastolicCa + concentration except that the location of the red and orange cross predicts a small ( ∼ . In allthree Figures (A-C) there is little change when [IP ] is low and K c is high (bottom right corner of each image). This is a regimein which the IP R channels barely open in response to ECC transients. For comparison, Supplementary Figure S2 shows thesame simulations as Figure 4 at a commonly used experimental pacing frequency of 0.3 Hz, showing similar trends.In order to compare our simulation results with the experimental observations summarised in Table 1 we divided theparameter space shown in Figures 4A-C into four regions, shown in Figure 4D. In the red region, amplitude and FDHM increase.In the orange region only FDHM increases. In the green region FDHM and diastolic [Ca ] increase but amplitude decreases.Comparing to the experimental observation of amplitude increase summarised in Table 1, the red region appears to describe themost plausible parameter range. Figure 4D also shows that there is no parameter set where both amplitude and diastolic Ca concentration increase. Furthermore, there is no region in which transients with increased amplitude and decreased duration areobserved, as has been reported in ET-1 treated rat ventricular myocyte experiments (55). Finally, with the exception of the blueregion in which there is no change, we observe that the FDHM increases in all parameter regimes.To examine these results further, we investigated model behaviour in different regions of Figure 4D, shown in Figure 5 andmarked as green, red and orange crosses in Figure 4A-C. Comparing the green cytosolic profiles (corresponding to the greenregion in Figure 4D) and blue cytosolic Ca profiles (corresponding to no IP R activation) in Figure 5, we find that IP Ropening at diastolic Ca + levels and IP R inhibition at Ca + levels below peak transient concentrations generates a flatter Ca + transient. This is the result of a gradual depletion of SR Ca + stores from IP Rs opening. This subsequently leads to lower Ca release through RyR and IP R channels.Interestingly, a delayed time to peak is observed with IP R activation in all regimes selected. With the reduction in SR loaddue to IP R activation, we find reduced Ca flux through RyRs. In order to maintain or increase Ca transient amplitude afteractivation, the IP R channels must compensate for the drop in RyR flux. As the spike in IP R flux is in response to Ca releasefrom RyR channels, and initial RyR-mediated Ca release is slower with lower SR Ca stores, it delays the time between cellstimulation and Ca transient peak.The increase in FDHM of the transient from IP R activation apparent in Figure 4B can be explained by continued release ofCa through IP R channels after RyRs have closed in Figure 5. The slower release through IP R channels after RyRs close is aresult of a smaller proportion of the channels opening and a decrease in SR Ca + store load. Maximum flux through IP Rs can increase signal duration
The parameter sensitivity analysis in Table 2 indicates that maximum flux through IP Rs ( k f ) has the greatest effect on Ca + transient duration. Therefore we next examined how increased k f values in our model affects the Ca + transient. Figure 6A-Cshow that for K c < µ M, increasing k f above 0.45 µ m m s − mostly increases transient duration but has only marginal effectson amplitude and baseline. However for large K c , the role of k f in modifying transient shape becomes more noticeable. There isa clear region where amplitude increases (red region), however this is more dependent on K c than k f . At 1 Hz, there is no valueof k f that reduces transient duration. With IP R activation the transient duration increases and k f merely determines by howmuch. However it is of note that, as shown in Figure 7, at a lower frequency of 0.3 Hz, when k f > µ m m s − and K c > µ M, there is a decrease in duration of the transient.To compare simulation results to experimental observations in Table 1, we divided the parameter space shown in Figures6A-C into three regions, shown in Figure 6D. The regions in this figure are consistent with the regions labelled in Figure4D. Figure 7D shows similar regions corresponding to simulations at 0.3 Hz. It can be seen that at 0.3 Hz, K c > µ M and k f > µ m m s − provide transients with increased amplitude and decreased duration, consistent with rat ET-1 experimentssummarized in Table 1. However this value of k f results in an unrealistic flux through IP R channels. Additionally, in vivo , thecell would be paced at a faster frequency and this result is unlikely without the cell being able to return to resting Ca + . We havenot been able to identify a parameter set that would provide a simultaneous increase in both amplitude and diastolic Ca . RyR and IP R interaction increases the intracellular Ca duty cycle Having establishing reasonable parameters ranges for IP R activation based on the influence on ECC Ca + transient properties(amplitude, FDHM, and diastolic Ca ), we investigated the possibility that cytosolic Ca + plays a role in hypertrophicremodelling through changing the duty cycle. Given the time scale involved in hypertrophic remodelling, and the signalintegration properties of NFAT, the IP R -modified cytosolic Ca + transient could cumulatively encode hypertrophic signalling.Using optogenetic encoding of cytosolic Ca transients in HeLa cells, Hannanta-anan and Chow (8) demonstrated that thetranscriptional activity of NFAT4 can be up-regulated by increasing cytosolic Ca + duty cycle. This is a plausible mechanismof signal encoding that is likely to be less susceptible to noise than either amplitude or frequency encoding. Therefore, we Manuscript submitted to Biophysical Journaln the role of IP R in cardiac hypertrophic signalling [ C a + ] ( M ) Cytosol SR F l u x ( M / m s ) I RyR I SERCA
Time (ms) F l u x ( M / m s ) I IP R Time (ms) -20-100 10 -3 I NCX
Figure 5: Simulated ECC transient and fluxes in the absence (blue) and presence of IP , corresponding to low (green), medium(orange) and high (red) values of K c . With K c = µ M (orange), IP R channels open only at Ca concentrations greater than0.1 µ M. This results in increased peak in cytosolic Ca transients and depleted SR Ca stores. Parameters here were selectedto show: absence of IP R channels (blue), increased transient amplitude (orange, red) and IP Rs parameterised as described inthe original Siekmann-Cao-Sneyd model (green). IP concentration is 10 µ M and pacing frequency 1 Hz in all simulations. Thesign of I NCX indicates whether Ca + is moving into (positive) or out of (negative) the cell. Manuscript submitted to Biophysical Journal unt, Til¯unait˙e et al. Change in Amplitude (%) k f ( m / m s ) K c ( M) -60-40-20020406080100120140160+ A Change in FDHM (%) k f ( m / m s ) K c ( M) -60-40-20020406080100120140160+ B Change in Baseline (%) k f ( m / m s ) K c ( M) -60-40-20020406080100120140160+ C Change regions K c ( M) k f ( m / m s ) Amplitude and FDHM increase
FDHM increases
No change FDHM and Diastolic [Ca ] increase D Figure 6: Effect of maximum IP R flux k f and the Ca + -sensitivity parameter K c on the Ca + transient at 1 Hz. Maximum IP Rflux has the greatest impact on transient duration. In these simulations [IP ] = µ M. See Figure 5 for simulated transients atparameters indicated by crosses. Manuscript submitted to Biophysical Journaln the role of IP R in cardiac hypertrophic signalling
Change in Amplitude (%) k f ( m / m s ) K c ( M) -60-40-20020406080100120140160+ A Change in FDHM (%) k f ( m / m s ) K c ( M) -60-40-20020406080100120140160+ B Change in Baseline (%) k f ( m / m s ) K c ( M) -60-40-20020406080100120140160+ C Change regions K c ( M) k f ( m / m s ) FDHM and Diastolic [Ca ] increase
Amplitude and FDHM increase
FDHM increases
No change A m p li t ude i n c r ea s e s , F DH M de c r ea s e s D Figure 7: Effect of maximum IP R flux k f and the Ca + sensitivity parameter K c on the Ca + transient at 0.3 Hz. MaximumIP R flux has the greatest impact on transient duration. In these simulations [IP ] = µ M. See Figure S3 for simulatedtransients at parameter values indicated by crosses.
Manuscript submitted to Biophysical Journal unt, Til¯unait˙e et al. examined the cytosolic Ca + duty cycle as a hypertrophic signalling mechanism.We calculated the duty cycle for the Ca transients in the plausible parameter ranges for IP R activation as the ratiobetween the area under the Ca transient curve and the area of the bounded box defined by the amplitude and period of the Ca transient (shown in Figure 2). Figure 8 shows the effects of [IP ], k f , and K c on the duty cycle of the cytosolic Ca + transient.The Figure shows that the Ca + duty cycle increases with IP R activation across the broad parameter range shown.
NFAT activation increases with an increase in calcium duty cycle
Having established that IP R activation results in increased calcium transient duty cycle, we coupled the model of cytosolicARVM calcium dynamics to the model of NFAT activation developed by Cooling et al. (51). We then tested the effect of varyingIP concentration over a range of IP R parameter values on the proportion of dephosphorylated nuclear NFAT comparedto that in the phosphorylated inactive state in the cytosol (Figure 9). These simulation data clearly show that increased IP and alteration in Ca transient duty cycle positively influences NFAT activation and thus provides a mechanism to coupleIP -induced Ca release and activation of hypertrophic gene expression. DISCUSSION
Here we have presented what is, to our knowledge, the first modelling study to investigate the effect of IP R channel activity onthe cardiac ECC Ca + transient and possible information encoding mechanisms. We extended a well-established model ofthe ECC Ca transient by Hinch et al. (14) to include a model of IP R activation and Ca release. The model, upon IP Ractivation, simulates the influence of IP R activation on Ca transients in non-hypertrophic adult rat left ventricular cardiacmyocytes.Parameter sensitivity analysis (Table 2) showed the maximal IP -induced Ca release through individual IP R ( k f ) had thegreatest influence on the Ca transient duration and duty cycle. [IP ] had the biggest influence on the Ca amplitude anddiastolic Ca concentration. We found that under fixed maximum IP R flux, k f = µ m m s − , IP R activation increasesthe duration of the Ca + transient, but Ca amplitude is IP -dependent. The Ca transient duration can be reduced only byincreasing k f to physiologically unrealistic values.The finding that the Ca transient duty cycle increases with [IP ] (see Figure 8) provides a plausible explanation for themechanism by which IP -dependent Ca release from IP Rs can enhance pro-hypertrophic NFAT activity.
Does IP -induced Ca release modify the ECC transient? Figures 4, 6 and 7 show that IP Rs can influence the ECC Ca transient and the effect is dependent on the IP R propertiesand IP concentration. Our model simulations predict that Ca transient amplitude increases approximately 15% when IP Rproperties are such that IP Rs remain inhibited from opening at diastolic Ca but release Ca once RyRs are activated andremain open when Ca concentration is above 1 µ M. The IP R parameter combination marked by a red cross in the contourplots is a representative example of this type of effect of IP Rs. There is also a narrow parameter range at [IP ] of 10 µ M( K h = µ M, K c = µ M) where the amplitude does not change more than 5% (see Figure 4). The orange cross marks anexample of IP R effects in this parameter range. These simulation predictions are consistent with the experimental studies thateither show increased amplitude or no change in amplitude (Table 1).Model simulations predict that IP R activation only increases diastolic [Ca ] when IP R are open at resting [Ca ] of ∼ µ M (see Figure 4D). Harzheim et al. (17) reported no measurable differences in diastolic [Ca ] between ARVMs stimulatedwith an agonist, known to induce hypertrophy in healthy ARVMs, and those treated with a saline buffer (although effects havebeen observe in disease ventricular cardiomyocytes and atrial cardiomyocytes). Examination of simulated Ca transientswithin a regime that results in diastolic [Ca ] increase (green traces in Figure 5) shows that the transients do not resemble anyof the observed experimental measurements in the literature. Therefore the comparison of model simulations and experimentalmeasurements of diastolic [Ca ] and Ca transient amplitude suggest that the most likely regime of IP R activation liesbetween the orange and red regions in Figure 4D. Using these comparisons we propose that IP R activation makes modestchanges to the ECC Ca transient which are often hidden within the measurement variability in experiments. The biological significance of the duty cycle
We showed that while amplitude, duration, and diastolic Ca can increase or decrease depending on IP R parameter values andpacing frequency, the duty cycle, as defined by Hannanta-anan and Chow (8) always increases with IP , consistent with effectsseen in (21). The implication of this observation is that IP R activation is sufficient to provide a signal to drive NFAT nucleartranslocation and hence hypertrophic gene expression in the manner described by Hannanta-anan and Chow (8). Manuscript submitted to Biophysical Journaln the role of IP R in cardiac hypertrophic signalling
Change in Duty cycle (%) [I P ] ( M ) K c ( M) -60-40-20020406080100120140160+ A Change in Duty cycle (%) k f ( m / m s ) K c ( M) -60-40-20020406080100120140160+ B Change in Duty cycle (%) [I P ] ( M ) K c ( M) -60-40-20020406080100120140160+ C Change in Duty cycle (%) k f ( m / m s ) K c ( M) -60-40-20020406080100120140160+ D Figure 8: Effects on the Ca + transient duty cycle of (A) IP concentration and the Ca + sensitivity parameter K c with pacingfrequency 1 Hz; (B) of maximum IP R flux k f and K c with pacing frequency 1 Hz; (C) of IP concentration and K c with pacingfrequency 0.3 Hz; and (D) of maximum IP R flux k f and the K c at pacing frequency 0.3 Hz. The colour bar indicates the %change from a simulation run with identical parameters but no IP R channels. The coloured crosses indicate the parametersused for the corresponding plots in Figure 5. Hannanta-anan and Chow (8) report a transcription rate increase of approximately30% with a duty cycle increase of 50% in Figure 2 of their paper. The duty cycle of the Ca + transient when IP Rs are inactiveis 0.127.
Manuscript submitted to Biophysical Journal unt, Til¯unait˙e et al. Dephosphorylated nuc NFAT (%) [I P ] ( M ) K c ( M) -60-40-20020406080100120140160+ Figure 9: Effect of [IP ] and K c on the concentration of dephosphorylated nuclear NFAT (NFAT n ). Simulations were paced at 1Hz. The colour bar indicates the % change from a simulation run with identical parameters but no IP .Hannanta-anan and Chow (8) found that, when comparing Ca + oscillations of the same amplitude, oscillations with greaterduty cycle had a greater effect on NFAT dephosphorylation and translocation to the nucleus. In their study, duty cycle, γ , wascalculated as the area under the curve, U , divided by the maximum area under the curve (for Ca + oscillations of the sameamplitude, A , and period of oscillation, T ), i.e. γ = U / AT (see Figure 2A). An alternative definition is γ = ∆ / T , where ∆ is thetransient duration and T the period of oscillation. This alternate formulation is used by Tomida et al. (38) and Salazar et al. (56)but is less well defined for analogue signals. The duty cycle in Figure 8 was calculated using the former definition. This can becompared with the latter definition when remembering that duty cycle will now vary with FDHM (Figures 4C and 6C).The duty cycle in this system essentially reflects the fraction of each period of the Ca + cycle for which cytosolic Ca + issufficiently elevated to affect the downstream proteins in the CnA/NFAT signalling pathway. The greater sensitivity of NFAT toCa + oscillations with sustained elevation in intracellular Ca + is well established (19, 39, 57). While it is difficult to determinewhere this threshold is, NFAT is a Ca + integrator and a clear correlation has been found between Ca + duty cycle and NFATactivation (8). Increasing duty cycle increases the time NFAT spends in the dephosphorylated state, which is required to bothenter and maintain it in the nucleus and hence effect transcription (58); NFAT responds to changes in duty cycle while beinginsensitive to both amplitude and frequency changes. We see in simulations too that the proportion of NFAT that is in thedephosphorylated nuclear state is highest when the duty cycle of the Ca transient is high (Figures 8 and 9).In experiments, IP stimulation has been shown to lead to an increase in systolic Ca + in cardiac cells, but significant changein duration has not been reported (although as in Harzheim et al. (17) and Proven et al. (21), increased spontaneous calciumtransients are observed which could function to prolong the duration of the Ca + transient). Based on the definition of the dutycycle presented in Hannanta-anan and Chow (8), there is a negative effect on duty cycle, and hence NFAT activation, whenCa transient amplitude is increased. However, within the physiologically plausible parameter range we find that simulationswith increased Ca transient amplitude also have increased transient duration. We postulate that NFAT may be responsiveto the Ca + transient through the latter definition of the duty cycle – i.e. the duration of time that Ca + is elevated over athreshold divided by the period. This is more consistent with both the biological mechanism and the potential increase in peakCa + concentration in the hypertrophic pathway, which may be a side-effect of a corresponding increase in duration over thisthreshold. Further research, both theoretical and experimental, is required in order to determine the validity of this assumption.Figure 9 shows a strong correlation between [Ca ]-dependent NFAT activation and Ca transient duty cycle in the Coolinget al. (51) model: the correspondence between Figure 8A and Figure 9 is striking. A caveat, however, is that the original Coolinget al. (51) study showed that the NFAT model is also sensitive to any average increase in cytosolic calcium. Therefore, whileincreasing Ca transient duty cycle is shown to be sufficient for NFAT activation in this model, further experimental validationis required to confirm this mechanism in cardiomyocytes. Manuscript submitted to Biophysical Journaln the role of IP R in cardiac hypertrophic signalling
Experimental evidence of an IP -induced increase in calcium duty cycle? An increase in duty cycle without an increase in frequency requires an increase in transient duration. While this increase isobserved in our simulations for a broad range of parameter values, it has not however been reported in experiments involving IP stimulation. The possible reasons for this are many and varied, however, as discussed earlier, using different IP concentrations tothose that occur in vivo may result in different effects on the shape of the Ca + oscillations, leading to inconsistent observations.Furthermore, small variations in Ca concentrations may not be experimentally discernible, or may be hidden by the effectof Ca -sensitive dyes (59). A small, but prolonged variation in transient duration can produce a comparatively large changein duty cycle. Hence it remains to be confirmed experimentally whether IP R-dependent Ca flux does indeed lead to anincreased Ca duty cycle in cardiomyocytes. Limitations of the study
In this study we have considered generation of voltage-driven cytosolic Ca + transients using deterministic models of each ionchannel in a compartmental model. There are several physiological features of cardiomyocyte Ca dynamics which are notrepresented, and hence not considered in this approach. In particular, our model does not represent any of the stochastic eventsassociated with IP R channels. Further modelling of combined stochastic channel gating may be necessary to elucidate theentire impact of IP R interaction with the cytosolic Ca machinery. While cell structure is known to play a role in cardiacCa + dynamics (60–62), effects beyond the synchronising function of the dyad are not considered in this compartmental study.Furthermore we have not considered the spatial IP R distribution. Our model is developed primarily using parameters fitted byHinch et al. (14) and Sneyd et al. (33), and makes no distinction between IP R channels located within or outside the dyad(63, 64). These and other structural features of the cell could alter the Ca available to regulate IP R channels and may bedetected in the Ca + transient. Distinct effects of IP signalling in the cytosol and the nucleus are also not considered. CytosolicCa is thought to promote translocation of NFAT into the nucleus, while nuclear Ca maintains it there (16). We have onlyinvestigated the former role for Ca + signalling within the CnA/NFAT pathway.We have explored model behaviour at pacing frequencies of 1 Hz and 0.3 Hz, rather than higher, more physiologicalfrequencies, primarily because the majority of parameters were derived from in vitro experiments conducted at room temperature.Extrapolation of parameters and hence model behaviour to in vivo temperature and correspondingly higher pacing frequencyremains challenging. Therefore model predictions must be interpreted cautiously in relation to higher pacing frequencies.Additionally, not all components of this signalling pathway have been considered in this study. Ca /calmodulin-dependentkinases II and Class IIa histone deacetylases, for example, are both known Ca -mediated components of the hypertrophicpathway that are activated by IP signalling (65) but are not included. Here we have focused only on the impact of IP Ractivation on the cytosolic Ca + dynamics and how this relates to the mechanism of NFAT activation. In order to explorebroader context for IP mediated hypertrophic signalling, it remains to couple this model to upstream events including modelsof IP production through activation of cell membrane receptors (66, 67). This would allow the profile and extent of the rise inIP concentration due to the activation of the hypertrophic pathway in cardiomyocytes to be determined. We have focused onthe effect of an elevated IP concentration of 10 µ M as many experimental studies into the effect of IP on Ca dynamics usesaturating [IP ]. However, Remus et al. (68) found stimulation of adult cat ventricular myocytes with 100 nM ET-1 induced acell-averaged increase in IP concentration of only 10 nM indicating a much lower concentration than used in experiments.This, together with known differences between species, suggests the IP concentration detected by IP R receptors in ARVMsin vivo could be lower than the simulated 10 µ M . However we note qualitatively similar effects on the Ca transient inparameter regimes with lower [IP ] in our model (Figures 4 and S2) albeit with more modest effects on the transient shape.Additionally, ET-1 receptors are localised to t-tubule membranes (69) so IP may be generated very close to IP R channels(64, 70), increasing the concentration they detect.Finally, IP R-induced Ca release is a part of a larger hypertrophic signalling network. It remains to couple this model toother signalling pathways involved in bringing about hypertrophic remodelling (71). How cytosolic Ca interacts with nuclearCa in regulation of NFAT nuclear residence and activity also remains to be determined. Conclusion
The sensitivity of NFAT translocation to the Ca + duty cycle demonstrated by Hannanta-anan and Chow (8) raises the questionas to whether IP R flux can increase the Ca + duty cycle in cardiomyocytes during hypertrophic signalling. Here we haveshown using mathematical modelling that an increase in cytosolic Ca + transient duration can occur following addition ofIP , and furthermore that this increase is sufficient to increase NFAT activation. Together, these results suggest a plausiblemechanism for hypertrophic signalling via IP R activation in cardiomyocytes. While it cannot be ruled out that a significantrole is played by components of this pathway that are not considered here, the computational evidence provided in this study,
Manuscript submitted to Biophysical Journal unt, Til¯unait˙e et al. along with the previous experimental findings, suggests encoding of the hypertrophic signal through alteration of the durationof cytosolic Ca + oscillations to be a feasible mechanism for IP -dependent hypertrophic signalling. AUTHOR CONTRIBUTIONS
EJC, VR, HLR, CS, and GB conceived of the study; EJC and VR supervised the project; HH, AT, VR and EJC developed themodelling approach. HH implemented the simulations. HLR, CS, and GB provided critical feedback. All authors contributed towriting the manuscript.
ACKNOWLEDGEMENTS
This research was supported in part by the Australian Government through the Australian Research Council Discovery Projectsfunding scheme (project DP170101358). HLR wishes to acknowledge financial support from the Research Foundation Flanders(FWO) through Project Grant G08861N and Odysseus programme Grant 90663.
SUPPORTING CITATIONS
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