Ca²⁺ Release via IP₃ Receptors Shapes the Cardiac Ca²⁺ Transient for Hypertrophic Signaling

Abstract

Calcium (Ca²⁺) plays a central role in mediating both contractile function and hypertrophic signaling in ventricular cardiomyocytes. L-type Ca²⁺ channels trigger release of Ca²⁺ from ryanodine receptors for cellular contraction, whereas signaling downstream of G-protein-coupled receptors stimulates Ca²⁺ release via inositol 1,4,5-trisphosphate receptors (IP₃Rs), engaging hypertrophic signaling pathways. Modulation of the amplitude, duration, and duty cycle of the cytosolic Ca²⁺ contraction signal and spatial localization have all been proposed to encode this hypertrophic signal. Given current knowledge of IP₃Rs, we develop a model describing the effect of functional interaction (cross talk) between ryanodine receptor and IP₃R channels on the Ca²⁺ transient and examine the sensitivity of the Ca²⁺ transient shape to properties of IP₃R activation. A key result of our study is that IP₃R activation increases Ca²⁺ transient duration for a broad range of IP₃R properties, but the effect of IP₃R activation on Ca²⁺ transient amplitude is dependent on IP₃ concentration. Furthermore we demonstrate that IP₃-mediated Ca²⁺ release in the cytosol increases the duty cycle of the Ca²⁺ transient, the fraction of the cycle for which [Ca²⁺] is elevated, across a broad range of parameter values and IP₃ concentrations. When coupled to a model of downstream transcription factor (NFAT) activation, we demonstrate that there is a high correspondence between the Ca²⁺ transient duty cycle and the proportion of activated NFAT in the nucleus. These findings suggest increased cytosolic Ca²⁺ duty cycle as a plausible mechanism for IP₃-dependent hypertrophic signaling via Ca²⁺-sensitive transcription factors such as NFAT in ventricular cardiomyocytes.

Significance

Many studies have identified a role for inositol 1,4,5-trisphosphate receptor (IP₃R)-mediated Ca²⁺ signaling in cardiac hypertrophy; however, the signaling mechanism remains unclear. Here we present a mathematical model of functional interactions between ryanodine receptors (RyRs) and IP₃Rs, and show that IP₃-mediated Ca²⁺ release can increase the Ca²⁺ duty cycle, which has been shown experimentally to lead to NFAT activation and hypertrophic signaling. Through a parameter sensitivity analysis, we demonstrate that the duty cycle increases with IP₃ over a broad parameter regime, indicating that this mechanism is robust, and furthermore we show that increasing Ca²⁺ duty cycle raises nuclear NFAT activation. These findings suggest a plausible mechanism for IP₃R-dependent hypertrophic signaling in cardiomyocytes.

Introduction

Calcium is a universal second messenger that plays a role in controlling many cellular processes across a wide variety of cell types, ranging from fertilization, cell contraction, and cell growth to cell death (1,2). Precisely how Ca²⁺ fulfills each of these roles while also ensuring signal specificity remains unclear in many cases. Ca²⁺ can be used to transmit signals in a variety of ways. Signal localization and amplitude and frequency modulation have been widely explored (3, 4, 5); however, mechanisms for information encoding in the cumulative signal (i.e., area under the curve, proportional-integral-derivative controller, or duty cycle) have also been proposed (6, 7, 8). Determining which method of information encoding is relevant to a specific signaling pathway requires determining what type of signal encoding the system is capable of and whether the downstream 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 Ca²⁺-mediated signals is particularly pertinent because of the essential and continuous role Ca²⁺ plays in excitation-contraction coupling (ECC). Of particular significance is the involvement of Ca²⁺ in hypertrophic growth signaling. How Ca²⁺ can communicate a signal in the hypertrophic signaling pathway concurrent with the cytosolic Ca²⁺ fluxes that drive cardiac muscle contraction is still largely unresolved (9,10). Understanding this mechanism is important because pathological hypertrophic remodeling is a precursor of heart failure and a common final pathway of cardiovascular diseases, including hypertension and coronary disease (11, 12, 13).

During each heartbeat, on depolarization of the membrane Ca²⁺ enters the cell via L-type Ca²⁺ channels (LTCCs), triggering larger Ca²⁺ release from the sarcoplasmic reticulum (SR) via ryanodine receptors (RyRs), which then induces contraction. The activation of Ca²⁺ release via RyRs by the Ca²⁺ arising via LTCCs is known as calcium-induced calcium release and results in a 10-fold increase in cytosolic Ca²⁺ concentration (relative to resting Ca²⁺ concentration of ∼100 nM). Sarcoendoplasmic reticulum Ca²⁺ pumps (SERCA) and other Ca²⁺ sequestration mechanisms subsequently withdraw the released Ca²⁺ back into the SR and out of the cytosol (14,15), reverting the cell to its relaxed state. Ca²⁺ also plays a central role in hypertrophic signaling. Hypertrophic stimuli such as endothelin-1 (ET-1) bind to G-protein-coupled receptors at the cell membrane to stimulate generation of the intracellular signaling molecule inositol 1,4,5-trisphosphate (IP₃). After IP₃ binds to and activates its cognate receptor, inositol 1,4,5-trisphosphate receptors (IP₃Rs), on the SR and nuclear envelope, Ca²⁺ is released into the cytosol and nucleus, respectively (see Fig. 1; (16,17)). This Ca²⁺ signal arising from IP₃Rs has been shown in multiple mammalian species to produce a distinct Ca²⁺ signal that through activation of pro-hypertrophic pathways, including those involving nuclear factor of activated T cells (NFAT), induces hypertrophy within cardiomyocytes (16,18,19).

Figure 1.

Schematic showing key Ca²⁺signaling pathways in the cardiomyocyte. ECC processes include ryanodine receptors (RyRs), L-type Ca²⁺ channels (LTCCs), SERCA, sodium-calcium exchanger (NCX), sarcolemmal calcium pump (PMCA), and troponin C (TnC). Growth-related IP₃-CnA/NFAT signaling processes include inositol 1,4,5-trisphosphate receptors (IP₃Rs), G-protein-coupled receptor (GPCR), phospholipase C (PLC), phosphatidylinositol 4,5-bisphosphate (PIP₂), calmodulin (CaM), calcineurin (CnA), and nuclear factor of activated T cells (NFAT). To see this figure in color, go online.

In healthy adult rat ventricular myocytes (ARVMs), various effects of IP₃ on global Ca²⁺ transients associated with ECC have been described, summarized in Table 1. Although application of G-protein-coupled receptor agonists that stimulate IP₃ generation produces robust effects on ECC-associated IP₃ transients and contraction, the direct contribution of IP₃ to these actions varies between studies (17,20, 21, 22, 23, 24). For example, in rabbits the effect of ET-1 on Ca²⁺ transient amplitude is sensitive to the IP₃R inhibitor 2-APB (22), whereas in healthy rats, IP₃R inhibition with 2-APB was without effect (25). In mice, 2-APB abrogated an increase in ECC-associated Ca²⁺ transients brought about by AngII (24). Responses have also been variable when IP₃ was directly applied to cardiac myocytes. In healthy rats, IP₃ produced no or a modest effect on Ca²⁺ transient amplitude (17,21), whereas in rabbits (22), a more substantial effect was observed. These differences in the effect of IP₃ have been ascribed in part to the greater dependence of rat myocytes on SR Ca²⁺ release to the Ca²⁺ transient than rabbit myocytes (22). Notably, both ET-1 and IP₃ elicit arrhythmogenic effects whereby they promote the generation of spontaneous calcium transients, manifest as a prolonged Ca²⁺ transient with additional peaks, and increase the frequency of Ca²⁺ sparks (17,18,21,22). A more profound role for IP₃ signaling is observed in hypertrophic ventricular myocytes, with ECC-associated Ca²⁺ transients of greater amplitude reported. Underlying these effects, IP₃R expression is elevated in hypertrophy (26). Hence, a question remains as to what independent effect IP₃R activation has on the cytosolic Ca²⁺ transient in healthy ventricular cardiac myocytes.

Table 1.

Summary of Experimentally Observed Changes to the Ca²⁺ Transient in Normal Healthy Ventricular Myocytes in Rat and Other Species after Addition of IP₃ and ET-1

Cell State		IP3	ET-1
Rat	Amplitude:	r▲(21) r♦(17)	r▲(21) r♦(16) r▲(17)
	Duration:	–	–
	Basal Ca2+:	r♦(17)	r♦(17)
	SCTs:	r▲(21) r▲(17)	r▲(21) r▲(17)
Other species	Amplitude:	m▲(20) m♦(73)	h▲(20) m▲(20)
	Duration:	–	–
	Basal Ca2+:	m▲(73)	m▲(20), b▲(22)
	SCTs:	–	h▲(20) m▲(20)

SCT, spontaneous Ca²⁺ transient. ▲ indicates an increase, ▼ a decrease, and ♦ indicates no significant change reported; r indicates rat, b indicates rabbit, h indicates human, and m indicates mouse; dashes indicate no data found. The model developed in this work is primarily parameterized with rat data.

The individual behavior of IP₃R channels and their dependence on Ca²⁺, IP₃, and ATP in cardiac and other cell types has been explored in a number of studies (27, 28, 29, 30). These studies have formed the basis of several computational models of IP₃R type I isoforms (29,31,32) fitted to stochastic single-channel data (33). However, properties of IP₃R channel activity within the cardiomyocyte, such as gating state transition rates and their dependency on IP₃ and Ca²⁺, have not been directly measured. In this study, we have taken the experimental studies on rat ventricular cardiomyocytes as a reference point for the observed effects of IP₃R activation on cellular Ca²⁺ dynamics and extended a well-established model of beat-to-beat cytosolic Ca²⁺ transients in rat cardiac cells (14,34) to include a model of type II IP₃R (32) channels. This deterministic, compartmental model of ECC enables us to investigate biophysically plausible mechanisms by which IP₃R activation could affect Ca²⁺ dynamics at the whole-cell scale while avoiding the computational complexity associated with detailed stochastic and spatial modeling. Specifically, it enables us to explore the parameter ranges of IP₃R-mediated Ca²⁺ release that modify the global cytosolic Ca²⁺ transient to encode information for hypertrophic signaling to the nucleus.

A number of transcription factors transduce changes in Ca²⁺ to activate hypertrophic gene transcription. Of particular note is NFAT. There are five known NFAT isoforms expressed in mammals; four of these are found in cardiac cells (19,35). To initiate hypertrophic remodeling, the hypertrophic Ca²⁺ signal, in conjunction with calmodulin (CaM) and calcineurin (CnA), leads to dephosphorylation of cytosolic NFAT. Upon dephosphorylation, NFAT translocates to the nucleus, where, in coordination with other proteins, it activates expression of genes responsible for hypertrophy (36). Several studies have focused on characterizing the Ca²⁺ dynamics necessary to activate NFAT and initiate hypertrophy (8,19,37, 38, 39, 40, 41, 42) and have shown NFAT to be a Ca²⁺ signal integrator (37). Furthermore, a recent study by Hannanta-anan and Chow (8) used direct optogenetic control of cytosolic Ca²⁺ transients in HeLa cells to demonstrate that the transcriptional activity of NFAT4 (also known as NFATc3), a necessary NFAT isoform in the hypertrophic pathway (35), can be upregulated by increasing the residence time of Ca²⁺ in the cytosol within each oscillation. The increased residence time of Ca²⁺, referred to as the “duty cycle,” is the ratio between the area under the Ca²⁺ transient curve divided by the maximal possible area, as calculated by the product of transient amplitude and period (see Fig. 2 A). The Ca²⁺ duty cycle is therefore distinct from the average Ca²⁺ concentration. Hannanta-anan and Chow (8) showed that increasing the duty cycle had a proportionally greater effect on NFAT transcriptional activity than changing either the frequency or amplitude of the cytosolic Ca²⁺ oscillations. This suggests an increased Ca²⁺ duty cycle as a possible mechanism by which Ca²⁺ release through IP₃R channels can affect hypertrophic signaling.

Figure 2.

(A) The duty cycle, a function of area under the curve, amplitude, and period, for the cytosolic Ca²⁺ transient. (B) An example of Ca²⁺ transients generated by the model is shown. (C) Ca²⁺ concentration in cytosol and SR, RyR flux, and IP₃R flux in the model with elevated IP₃ (red) and without IP₃ (blue) are shown. Here, IP₃R parameters used are taken from (32), with maximal IP₃R flux k_f = 0.003 μm³ ms⁻¹. To see this figure in color, go online.

Here, using a mathematical model of beat-to-beat cytosolic Ca²⁺ transients in rat ventricular myocytes, coupled to IP₃R channel Ca²⁺ release, we show that IP₃R activation in the cytosol can increase the duty cycle of the cytosolic Ca²⁺ transient. We establish model feasibility through parameter sensitivity analysis, which shows that this behavior does not depend sensitively on model parameter values. Furthermore, we identify conditions necessary for IP₃R channel activation to alter Ca²⁺ transient amplitude, width, basal Ca²⁺, and duty cycle, as identified in different experimental studies, and compare model simulations to published experimental data summarized in Table 1. Finally, we couple simulations of cytosolic Ca²⁺ dynamics to a model of downstream CaM/CnA/NFAT activation and show that the duty cycle of the Ca²⁺ transient highly correlates with the activated nuclear NFAT (the proportion of NFAT that is dephosphorylated and translocated to the nucleus). These findings suggest IP₃R activity can increase the cytosolic Ca²⁺ duty cycle, thus providing a mechanism for IP₃-dependent activation of NFAT for hypertrophic signaling in the cardiomyocyte.

Methods

We developed a computational model of RyR- and IP₃R-mediated Ca²⁺ fluxes in the adult rat ventricular myocyte. Model simulations were performed using the ode15s ODE solver from MATLAB 2017b (The MathWorks, Natick, MA) with relative and absolute tolerances 1 × 10⁻³ and 1 × 10⁻⁶, respectively. The model equations were simulated at 1 Hz, the original pacing frequency of the Hinch et al. (14) model, and at 0.3 Hz because it is another common pacing frequency in experimental studies of IP₃ and Ca²⁺ in cardiomyocytes (17,21). The model was paced until the normalized root mean-square deviation between each subsequent beat was below 1 × 10⁻³, and all but the last oscillation were discarded to eliminate transient behaviors (see Fig. 2 B). Initial conditions were set to the basal Ca²⁺ level of the model at dynamic equilibrium with inactive IP₃R channels, determined after running the base model until the normalized root mean-square deviation was also below 1 × 10⁻³.

Model equations

The compartmental model of rat left ventricular cardiac myocyte Ca²⁺ dynamics is based on the Hinch et al. (14) model of ECC, with the addition of IP₃R Ca²⁺ release modeled using the Siekmann-Cao-Sneyd model (32). The Hinch model is an established whole-cell model of rat cardiac Ca²⁺ dynamics that describes the flux through the major Ca²⁺ channels and pumps on the cell and SR membranes and the effects of applying a voltage across the cell membrane. The parameters for the Hinch component of our model were maintained from the original, except for those of the driving voltage. This was shortened to better approximate the rat action potential (43) (see Fig. S1). The Ca²⁺ in the cytosol is governed by the following ODE:

$$\frac{\text{d}{\left[{\text{Ca}}^{2+}\right]}_{\text{cyt}}}{\text{d}t}={\beta }_{\text{fluo}}\times {\beta }_{\text{CaM}}\times \left(I_{\text{CaL}}+I_{\text{RyR}}-I_{\text{SERCA}}+I_{{\text{IP}}_3\text{R}}+I_{\text{other}}\right),$$ (1)

$$I_{\text{other}}=I_{\text{SRl}}+I_{\text{NCX}}-I_{\text{PMCA}}+I_{\text{CaB}}+I_{\text{TnC}}.$$ (2)

A small Ca²⁺ flux through the LTCCs, I_CaL, activates RyR channels to release Ca²⁺ from the SR into the cytosol at a rate of I_RyR. Ca²⁺ is resequestered into the SR by SERCA at a rate I_SERCA. β_fluo is the rapid buffer coefficient (44) for the fluorescent dye in the cytosol, and β_CaM is the rapid buffer coefficient for calmodulin in the cytosol. I_other includes Ca²⁺ fluxes such as exchange with the extracellular environment through the sodium-calcium exchanger I_NCX, sarcolemmal Ca²⁺-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 are defined in the Supporting Materials and Methods.

When the simulation is run with IP₃ present, there is additionally a flux through the IP₃Rs:

$$I_{{\text{IP}}_3\text{R}}=k_{\text{f}}\times N_{{\text{IP}}_3\text{R}}\times P_{{\text{IP}}_3\text{R}}\times \left({\left[{\text{Ca}}^{2+}\right]}_{\text{SR}}-{\left[{\text{Ca}}^{2+}\right]}_{\text{cyt}}\right)/V_{\text{myo}}.$$ (3)

Here, V_myo is the volume of the cell. k_f is the maximal total flux through each IP₃R channel; this was chosen to be 0.45 μm³ ms⁻¹ unless otherwise stated to create a measurable effect on IP₃R channel activation while maintaining plausible total flux. $N_{{\text{IP}}_3\text{R}}$ is the number of IP₃R channels in the cell; this was set to 1/50th of the number of RyR channels (45). We studied the effect of varying k_f on IP₃-induced changes to the cytosolic Ca²⁺ transient in normal cardiomyocytes. Evidently, varying $N_{{\text{IP}}_3\text{R}}$ and varying k_f have the same effect on simulated calcium dynamics. Although $N_{{\text{IP}}_3\text{R}}$ is known to increase significantly in disease conditions, we have not emphasized it in this study because of our focus on normal cardiomyocytes. [Ca²⁺]_cyt and [Ca²⁺]_SR are the Ca²⁺ concentrations in the cytosol and SR, respectively.

$P_{{\text{IP}}_3\text{R}}$ is the [Ca²⁺]- and [IP₃]-dependent open probability of the IP₃R channels and is determined using the Siekmann-Cao-Sneyd model (31,32,46), which has a built-in delay in response to changing Ca²⁺ concentration, along with several parameters governing channel activation and inactivation. This model describes $P_{{\text{IP}}_3\text{R}}$ as

$$P_{{\text{IP}}_3\text{R}}=\beta /\left(\beta +k_{\beta }\times \left(\beta +\alpha \right)\right),$$ (4)

where k_β is a transition term derived from single-channel Siekmann et al. (46) and β describes the rate of activation and α the rate of inactivation:

$$\beta =B\times m\times h,$$ (5)

$$\alpha =\left(1-B\right)\times \left(1-m\times h_{\infty }\right),$$ (6)

where h is time dependent and B, m, and h and h_∞ describe the dependence on IP₃, the dependence on Ca²⁺, and the Ca²⁺-dependent delay in IP₃R gating, respectively. Expressions for these variables are as follows:

$$B={\left[{\text{IP}}_3\right]}^2/\left(K_p^2+{\left[{\text{IP}}_3\right]}^2\right),$$ (7)

$$m={\left[{\text{Ca}}^{2+}\right]}^4/\left(K_c^4+{\left[{\text{Ca}}^{2+}\right]}^4\right),$$ (8)

$$\frac{dh}{dt}=\left(\left(h_{\infty }-h\right)\times \left(K_t^4+{\left[{\text{Ca}}^{2+}\right]}^4\right)\right)/\left(t_{max}\times K_t^4\right),$$ (9)

$$h_{\infty }=K_h^4/\left(K_h^4+{\left[{\text{Ca}}^{2+}\right]}^4\right).$$ (10)

Here, K_c and K_h are parameters that determine the Ca²⁺-dependence of IP₃R channel open probability, whereas K_t and t_max are parameters that affect the delay in IP₃R response to cytosolic changes. K_t determines the influence of [Ca²⁺] on the delay, whereas 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 IP₃R Ca²⁺ release at normal IP₃ levels because that model did not explicitly include IP₃R. However, in the presence of IP₃, IP₃R Ca²⁺ flux during diastole is several orders of magnitude greater than I_SRl, which is largely dependent on [Ca²⁺]_SR, and hence, any discrepancy caused by this will have a negligible effect on overall Ca²⁺ dynamics within the cell (see also Fig. S4).

Several experimental studies have investigated IP₃R activity across a range of Ca²⁺ concentrations with 1 μM IP₃ (27,47). These studies suggest that IP₃R channels would be open, with almost constant $P_{{\text{IP}}_3\text{R}}$ over the full range of cytosolic Ca²⁺ concentrations experienced during ECC in the cardiomyocyte. An IP₃R-facilitated SR-Ca²⁺ leak has been reported to amplify systolic concentrations (48,49), as seen in most published experiments of IP₃-enhanced Ca²⁺ transients tabulated in Table 1. Through parameter sensitivity analysis of this model, we show that to be consistent with these observations, $P_{{\text{IP}}_3\text{R}}$ must be significantly smaller at resting Ca²⁺ concentrations than at higher concentrations.

Coupling cytosolic Ca²⁺ and NFAT activation

We coupled the calcium model to the NFAT model developed by Cooling et al. (50), which determines the proportion of total cellular NFAT that is dephosphorylated and translocated to the nucleus for a given cytosolic Ca²⁺ signal. In this study, we have used the model parameters estimated from the data in Tomida et al. (37), who measured activation of NFAT4 in BHK cells. Full details of the Cooling et al. (50) model are given in the Supporting Materials and Methods.

Results

An example of the model output when run with the original IP₃R channel parameter values determined by Sneyd et al. (32) for type I IP₃R channels is shown in Fig. 2 C. Measurements of the properties of IP₃R channel activity and their dependence on Ca²⁺ within cardiomyocytes are sparse in the literature. Therefore, we performed a parameter sensitivity analysis by running model simulations over a variety of parameter ranges to explore the dependence of features of the cytosolic calcium transient to IP₃R channel parameters.

Parameter sensitivity analysis

We conducted a parameter sensitivity analysis to determine the critical parameters related to IP₃R activation that affect the shape of beat-to-beat cytosolic Ca²⁺ transients. We used the Jansen method (51) as described in Saltelli et al. (52) (and summarized in the Supporting Materials and Methods) to calculate the “main effect” and “total effect” coefficients of each of the parameters associated with IP₃R channel gating in relation to changes in transient amplitude, full duration at half maximum (FDHM), diastolic Ca²⁺, and duty cycle (see Table 2). Saltelli et al. (52) describe the main effect coefficient as “the expected reduction in variance that would be obtained if [the parameter] could be fixed” and the total effect coefficient as “the expected variance that would be left if all factors but [the parameter] could be fixed,” both normalized by the total variance. Both coefficients are included here to provide a complete picture of the impact of each parameter. Simulation parameter values were generated using the MATLAB (The MathWorks) sobolset function with leap 1 × 10³ and skip 1 × 10².

Table 2.

Main and Total Effects of the IP₃R Gating Parameters on Ca²⁺ Transient Amplitude, Duration, Diastolic Ca²⁺, and Duty Cycle

Main Effect Coefficients	[IP3]	tmax	Kc	Kh	Kt	kf
Amplitude	027a	0.00	0.03	0.19a	0.00	0.03
Duration (FDHM)	0.17a	0.00	0.01	0.12a	0.00	0.50a
Diastolic Ca2+	0.44a	0.00	0.09	0.03	0.00	0.04
Duty cycle	0.23a	0.00	0.01	0.16a	0.00	0.33a
Total Effect Coefficients	[IP3]	tmax	Kc	Kh	Kt	kf
Amplitude	0.63a	0.04	0.43a	0.46a	0.02	0.13a
Duration (FDHM)	0.33a	0.00	0.19a	0.19a	0.00	0.54a
Diastolic Ca2+	0.79a	0.00	0.45a	0.06	0.00	0.18a
Duty cycle	0.45a	0.00	0.25a	0.24a	0.00	0.38a

Duration measured in FDHM.

^aSignificant values.

Variance-based parameter sensitivity analysis

Table 2 shows that the delay parameters t_max and K_t do not have a large effect on the cytosolic Ca²⁺ transient. Although they are necessary to describe the effect of IP₃R-dominated Ca² dynamics (32), 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 Ca²⁺ dynamics during ECC are most highly sensitive to IP₃ concentration ([IP₃]) and the maximal flux through each IP₃R (k_f). The maximal flux k_f has little effect on transient amplitude but large influence on duration and duty cycle, whereas [IP₃] has the greatest effect on the change in amplitude and diastolic Ca²⁺ concentration.

The gating parameters K_c and K_h also influence the cytosolic Ca²⁺ transient. K_h affects the [Ca²⁺] at which IP₃R channels are inhibited, and K_c affects the [Ca²⁺] at which IP₃R channels open. We illustrate how these two parameters affect IP₃R open probability, $P_{{\text{IP}}_3\text{R}}$, in Fig. 3. Fig. 3 also shows how [IP₃] affects the relationship between K_c, K_h, [Ca²⁺], and $P_{{\text{IP}}_3\text{R}}$. It can be seen that with K_h = 80 nM, $P_{{\text{IP}}_3\text{R}}$ will be close to zero regardless of the values of Ca²⁺ or [IP₃] or K_c. At K_h = 1.6 μM and [IP₃] ≥ 5 μM, $P_{{\text{IP}}_3\text{R}}$ dependence on K_c and Ca²⁺ becomes apparent. Finally, at K_h = 3.2 μM, $P_{{\text{IP}}_3\text{R}}$ is still dependent on K_c- and Ca²⁺-values, but [IP₃] does not change $P_{{\text{IP}}_3\text{R}}$ significantly.

Figure 3.

The effect of [Ca²⁺], [IP₃], K_c, and K_h on $P_{{\text{IP}}_3\text{R}}$ in the Siekmann-Cao-Sneyd IP₃R model (31,32,46). The colored bars on the side of each plot show the proportion of IP₃R channels that will open for each set of parameters at steady state. Note that IP₃Rs do not open at physiological Ca²⁺ concentrations when K_h is low (i.e., 80 nM or less). In subsequent simulations, we used the value K_h = 2.2 μM unless otherwise stated. To see this figure in color, go online.

From this analysis, we determine that for IP₃R channels to be active during ECC, K_h must be sufficiently high that IP₃Rs are not inhibited at diastolic [Ca²⁺]. Conversely, K_c must be low enough that IP₃R channels are active at Ca²⁺ concentrations below the systolic Ca²⁺ peak. Therefore, in the remainder of this study, we fix K_h at 2.2 μM: high enough to fulfill this condition but low enough that IP₃R channels are still affected by [IP₃]. We report simulation results only within the range of K_c that exhibits experimentally plausible Ca²⁺ transient properties.

With the plausible range of K_h and K_c established, we next show the effect of K_c, k_f, and [IP₃] on the ECC transient.

IP₃ concentration and IP₃R opening behavior have the greatest impact on the Ca²⁺ transient

As summarized in Table 1, different experimental studies suggest different effects of IP₃R activation on the ECC cytosolic Ca²⁺ transient. Fig. 4, A–C show quantitative predictions of how much Ca²⁺ transient properties could be affected by IP₃R activation across a range of [IP₃]- and Ca²⁺-dependent IP₃R gating parameter K_c-values. k_f was fixed at 0.45 μm³ ms⁻¹, and K_h was fixed at 2.2 μM.

Figure 4.

Effect of IP₃ concentration and the parameter K_c on the Ca²⁺ transient with pacing frequency 1 Hz. These two parameters, along with maximal IP₃R flux k_f, have the greatest impact when considering the effect of IP₃R activation on the Ca²⁺ transient. To better resolve the range in which FDHM changes, all FDHM increases of 45% and over are shown in the same color. See Fig. 5 for simulated transients at parameters indicated by crosses. We note that for ease of comparison between figures, in this and in subsequent figures, the maximal increase from baseline is cropped at 160%. Changes greater than this threshold are shown in the same color. To see this figure in color, go online.

The red region in Fig. 4 A corresponds to IP₃R activation parameters that produce the greatest increase in Ca²⁺ amplitude. Noteworthy is that the red region depicts moderate changes in amplitude of ∼15%. This region corresponds to K_c-values greater than 4 μM and [IP₃] greater than 2 μM. With K_h set at 2.2 μM, this corresponds to the middle and far-right plots of $P_{{\text{IP}}_3\text{R}}$ in Fig. 3. The middle subfigure shows that with K_c greater than 4 μM, IP₃R channels would open only at Ca²⁺ concentrations greater than the diastolic concentration of ∼0.1 μM. The plot also shows that IP₃Rs would remain active at Ca²⁺ greater than the systolic peak concentration of ∼1 μM (53). Fig. 4 B further indicates that the increase in peak amplitude is accompanied by an increase in transient duration (FDHM). However, this change may be small, particularly at IP₃ concentrations lower than 1 μM. In Fig. 4 C, it can be seen that the diastolic Ca²⁺ concentration decreases moderately (∼10%) in the parameter range in which the amplitude is maximized (Fig. 4 A).

Fig. 4 B shows that FDHM of the Ca²⁺ transient increases whenever IP₃Rs are active. This increase is greater with greater concentrations of IP₃ and with lower values of K_c. Fig. 4 C indicates that K_c and [IP₃] have a similar effect on the diastolic Ca²⁺ concentration except that the location of the red and orange cross predicts a small (∼10%) drop in diastolic Ca²⁺. In Fig. 4, A–C, there is little change when [IP₃] is low and K_c is high (bottom right corner of each image). This is a regime in which the IP₃R channels barely open in response to ECC transients. For comparison, Fig. S2 shows the same simulations as Fig. 4 at a commonly used experimental pacing frequency of 0.3 Hz, showing similar trends.

To compare our simulation results with the experimental observations summarized in Table 1, we divided the parameter space shown in Fig. 4, A–C into four regions, shown in Fig. 4 D. In the red region, amplitude and FDHM increase. In the orange region, only FDHM increases. In the green region, FDHM and diastolic [Ca²⁺] increase, but amplitude decreases. Comparing to the experimental observation of amplitude increase summarized in Table 1, the red region appears to describe the most plausible parameter range. Fig. 4 D also shows that there is no parameter set in which both amplitude and diastolic Ca²⁺ concentration increase. Furthermore, there is no region in which transients with increased amplitude and decreased duration are observed, as has been reported in ET-1-treated rat ventricular myocyte experiments (54). Finally, with the exception of the blue region in which there is no change, we observe that the FDHM increases in all parameter regimes.

To examine these results further, we investigated model behavior in different regions of Fig. 4 D, shown in Fig. 5 and marked as green, red, and orange crosses in Fig. 4, A–C. Comparing the green cytosolic profiles (corresponding to the green region in Fig. 4 D) and blue cytosolic Ca²⁺ profiles (corresponding to no IP₃R activation) in Fig. 5, we find that IP₃R opening at diastolic Ca²⁺ levels and IP₃R inhibition at Ca²⁺ levels below peak transient concentrations generates a flatter Ca²⁺ transient. This is the result of a gradual depletion of SR Ca²⁺ stores from IP₃Rs opening. This subsequently leads to lower Ca²⁺ release through RyR and IP₃R channels.

Figure 5.

Simulated ECC transient and fluxes in the absence (blue) and presence of IP₃, corresponding to low (green), medium (orange), and high (red) values of K_c. With K_c = 8 μM (orange), IP₃R channels open only at Ca²⁺ concentrations greater than 0.1 μM. This results in increased peak in cytosolic Ca²⁺ transients and depleted SR Ca²⁺ stores. Parameters here were selected to show absence of IP₃R channels (blue), increased transient amplitude (orange, red), and IP₃Rs parameterized as described in the original Siekmann-Cao-Sneyd model (green). IP₃ concentration is 10 μM and pacing frequency 1 Hz in all simulations. The sign of I_NCX indicates whether Ca²⁺ is moving into (positive) or out of (negative) the cell. To see this figure in color, go online.

Interestingly, a delayed time to peak is observed with IP₃R activation in all regimes selected. With the reduction in SR load due to IP₃R activation, we find reduced Ca²⁺ flux through RyRs. To maintain or increase Ca²⁺ transient amplitude after activation, the IP₃R channels must compensate for the drop in RyR flux. Because the spike in IP₃R flux is in response to Ca²⁺ release from RyR channels and initial RyR-mediated Ca²⁺ release is slower with lower SR Ca²⁺ stores, it delays the time between cell stimulation and Ca²⁺ transient peak.

The increase in FDHM of the transient from IP₃R activation apparent in Fig. 4 B can be explained by continued release of Ca²⁺ through IP₃R channels after RyRs have closed in Fig. 5. The slower release through IP₃R channels after RyRs close is a result of a smaller proportion of the channels opening and a decrease in SR Ca²⁺ store load.

Maximal flux through IP₃Rs can increase signal duration

The parameter sensitivity analysis in Table 2 indicates that maximal flux through IP₃Rs (k_f) has the greatest effect on Ca²⁺ transient duration. Therefore, we next examined how increased k_f-values in our model affect the Ca²⁺ transient. Fig. 6, A–C show that for K_c < 2 μM, increasing k_f above 0.45 μm³ ms⁻¹ mostly increases transient duration but has only marginal effects on amplitude and baseline. However, for large K_c, the role of k_f in modifying transient shape becomes more noticeable. There is a clear region in which amplitude increases (red region); however, this is more dependent on K_c than k_f. At 1 Hz, there is no value of k_f that reduces transient duration. With IP₃R activation, the transient duration increases, and k_f merely determines by how much. However it is of note that, as shown in Fig. 7, at a lower frequency of 0.3 Hz, when k_f > 1.2 μm³ ms⁻¹ and K_c > 8 μM, there is a decrease in duration of the transient.

Figure 6.

Effect of maximal IP₃R flux k_f and the Ca²⁺ sensitivity parameter K_c on the Ca²⁺ transient at 1 Hz. Maximal IP₃R flux has the greatest impact on transient duration. In these simulations, [IP₃] = 10 μM. See Fig. 5 for simulated transients at parameters indicated by crosses. To see this figure in color, go online.

Figure 7.

Effect of maximal IP₃R flux k_f and the Ca²⁺ sensitivity parameter K_c on the Ca²⁺ transient at 0.3 Hz. Maximal IP₃R flux has the greatest impact on transient duration. In these simulations, [IP₃] = 10 μM. See Fig. S3 for simulated transients at parameter values indicated by crosses. To see this figure in color, go online.

To compare simulation results to experimental observations in Table 1, we divided the parameter space shown in Fig. 6, A–C into three regions, shown in Fig. 6 D. The regions in this figure are consistent with the regions labeled in Fig. 4 D. Fig. 7 D shows similar regions corresponding to simulations at 0.3 Hz. It can be seen that at 0.3 Hz, K_c > 8 μM and k_f > 1.2 μm³ ms⁻¹ provide transients with increased amplitude and decreased duration, consistent with the rat ET-1 experiments summarized in Table 1. However, this value of k_f results in an unrealistic flux through IP₃R channels. Additionally, in vivo, the cell would be paced at a faster frequency, and this result is unlikely without the cell being able to return to resting Ca²⁺. We have not been able to identify a parameter set that would provide a simultaneous increase in both amplitude and diastolic Ca²⁺.

RyR and IP₃R interaction increases the intracellular Ca²⁺ duty cycle

Having established reasonable parameter ranges for IP₃R activation based on the influence on ECC Ca²⁺ transient properties (amplitude, FDHM, and diastolic Ca²⁺), we investigated the possibility that cytosolic Ca²⁺ plays a role in hypertrophic remodeling through changing the duty cycle. Given the timescale involved in hypertrophic remodeling and the signal integration properties of NFAT, the IP₃R -modified cytosolic Ca²⁺ transient could cumulatively encode hypertrophic signaling. Using optogenetic encoding of cytosolic Ca²⁺ transients in HeLa cells, Hannanta-anan and Chow (8) demonstrated that the transcriptional activity of NFAT4 can be upregulated by increasing the cytosolic Ca²⁺ duty cycle. This is a plausible mechanism of signal encoding that is likely to be less susceptible to noise than either amplitude or frequency encoding. Therefore, we examined the cytosolic Ca²⁺ duty cycle as a hypertrophic signaling mechanism.

We calculated the duty cycle for the Ca²⁺ transients in the plausible parameter ranges for IP₃R activation as the ratio between the area under the Ca²⁺ transient curve and the area of the bounded box defined by the amplitude and period of the Ca²⁺ transient (shown in Fig. 2). Fig. 8 shows the effects of [IP₃], k_f, and K_c on the duty cycle of the cytosolic Ca²⁺ transient. The figure shows that the Ca²⁺ duty cycle increases with IP₃R activation across the broad parameter range shown.

Figure 8.

Effects on the Ca²⁺ transient duty cycle of (A) IP₃ concentration and the Ca²⁺ sensitivity parameter K_c with pacing frequency 1 Hz, (B) maximal IP₃R flux k_f and K_c with pacing frequency 1 Hz, (C) IP₃ concentration and K_c with pacing frequency 0.3 Hz, and (D) maximal IP₃R flux k_f and K_c at pacing frequency 0.3 Hz. The color bar indicates the percent change from a simulation run with identical parameters but no IP₃R channels. The colored crosses indicate the parameters used for the corresponding plots in Fig. 5. Hannanta-anan and Chow (8) report a transcription rate increase of ∼30% with a duty cycle increase of 50% in Fig. 2 of their work. The duty cycle of the Ca²⁺ transient when IP₃Rs are inactive is 0.127. To see this figure in color, go online.

NFAT activation increases with an increase in calcium duty cycle

Having established that IP₃R activation results in increased calcium transient duty cycle, we coupled the model of cytosolic ARVM calcium dynamics to the model of NFAT activation developed by Cooling et al. (50). We then tested the effect of varying IP₃ concentration over a range of IP₃R parameter values on the proportion of dephosphorylated nuclear NFAT compared with that in the phosphorylated inactive state in the cytosol (Fig. 9). These simulation data clearly show that increased IP₃ and alteration in the Ca²⁺ transient duty cycle positively influence NFAT activation and thus provides a mechanism to couple IP₃-induced Ca²⁺ release and activation of hypertrophic gene expression.

Figure 9.

Effect of [IP₃] and K_c on the concentration of dephosphorylated nuclear NFAT (NFAT_n). Simulations were paced at 1 Hz. The color bar indicates the percent change from a simulation run with identical parameters but no IP₃. To see this figure in color, go online.

Discussion

Here, we have presented what is, to our knowledge, the first modeling study to investigate the effect of IP₃R channel activity on the cardiac ECC Ca²⁺ transient and possible information encoding mechanisms. We extended a well-established model of the ECC Ca²⁺ transient by Hinch et al. (14) to include a model of IP₃R activation and Ca²⁺ release. The model, upon IP₃R activation, simulates the influence of IP₃R activation on Ca²⁺ transients in nonhypertrophic adult rat left ventricular cardiac myocytes.

Parameter sensitivity analysis (Table 2) showed the maximal IP₃-induced Ca²⁺ release through individual IP₃R (k_f) had the greatest influence on the Ca²⁺ transient duration and duty cycle. [IP₃] had the biggest influence on the Ca²⁺ amplitude and diastolic Ca²⁺ concentration. We found that under fixed maximal IP₃R flux, k_f = 0.45 μm³ ms⁻¹, IP₃R activation increases the duration of the Ca²⁺ transient, but Ca²⁺ amplitude is IP₃ dependent. The Ca²⁺ transient duration can be reduced only by increasing k_f to physiologically unrealistic values.

The finding that the Ca²⁺ transient duty cycle increases with [IP₃] (see Fig. 8) provides a plausible explanation for the mechanism by which IP₃-dependent Ca²⁺ release from IP₃Rs can enhance pro-hypertrophic NFAT activity.

Does IP₃-induced Ca²⁺ release modify the ECC transient?

Figs. 4, 6 and 7 show that IP₃Rs can influence the ECC Ca²⁺ transient and that the effect is dependent on the IP₃R properties and IP₃ concentration. Our model simulations predict that Ca²⁺ transient amplitude increases ∼15% when IP₃R properties are such that IP₃Rs remain inhibited from opening at diastolic Ca²⁺ but release Ca²⁺ once RyRs are activated and remain open when Ca²⁺ concentration is above 1 μM. The IP₃R parameter combination marked by a red cross in the contour plots is a representative example of this type of effect of IP₃Rs. There is also a narrow parameter range at [IP₃] of 10 μM (K_h = 2.2 μM, K_c = 6 μM) in which the amplitude does not change more than 5% (see Fig. 4). The orange cross marks an example of IP₃R effects in this parameter range. These simulation predictions are consistent with the experimental studies that either show increased amplitude or no change in amplitude (Table 1).

Model simulations predict that IP₃R activation only increases diastolic [Ca²⁺] when IP₃Rs are open at resting [Ca²⁺] of ∼0.1 μM (see Fig. 4 D). Harzheim et al. (17) reported no measurable differences in diastolic [Ca²⁺] between ARVMs stimulated with an agonist known to induce hypertrophy in healthy ARVMs and those treated with a saline buffer (although effects have been observe in disease ventricular cardiomyocytes and atrial cardiomyocytes). Examination of simulated Ca²⁺ transients within a regime that results in diastolic [Ca²⁺] increase (green traces in Fig. 5) shows that the transients do not resemble any of the observed experimental measurements in the literature. Therefore, the comparison of model simulations and experimental measurements of diastolic [Ca²⁺] and Ca²⁺ transient amplitude suggest that the most likely regime of IP₃R activation lies between the orange and red regions in Fig. 4 D. Using these comparisons, we propose that IP₃R activation makes modest changes to the ECC Ca²⁺ transient that are often hidden within the measurement variability in experiments.

The biological significance of the duty cycle

We showed that although amplitude, duration, and diastolic Ca²⁺ can increase or decrease depending on IP₃R parameter values and pacing frequency, the duty cycle, as defined by Hannanta-anan and Chow (8), always increases with IP₃, consistent with effects seen in (21). The implication of this observation is that IP₃R activation is sufficient to provide a signal to drive NFAT nuclear translocation and hence hypertrophic gene expression in the manner described by Hannanta-anan and Chow (8).

Hannanta-anan and Chow (8) found that when comparing Ca²⁺ oscillations of the same amplitude, oscillations with greater duty cycle had a greater effect on NFAT dephosphorylation and translocation to the nucleus. In their study, duty cycle, γ, was calculated as the area under the curve, U, divided by the maximal area under the curve (for Ca²⁺ oscillations of the same amplitude, A, and period of oscillation, T), i.e., γ = U/AT (see Fig. 2 A). An alternative definition is γ = Δ/T, where Δ is the transient duration and T the period of oscillation. This alternate formulation is used by Tomida et al. (37) and Salazar et al. (55) but is less well defined for analog signals. The duty cycle in Fig. 8 was calculated using the former definition. This can be compared with the latter definition when remembering that duty cycle will now vary with FDHM (Figs. 4 C and 6 C).

The duty cycle in this system essentially reflects the fraction of each period of the Ca²⁺ cycle for which cytosolic Ca²⁺ is sufficiently elevated to affect the downstream proteins in the CnA/NFAT signaling pathway. The greater sensitivity of NFAT to Ca²⁺ oscillations with sustained elevation in intracellular Ca²⁺ is well established (19,38,56). Although it is difficult to determine where this threshold is, NFAT is a Ca²⁺ integrator, and a clear correlation has been found between Ca²⁺ duty cycle and NFAT activation (8). Increasing duty cycle increases the time NFAT spends in the dephosphorylated state, which is required to both enter and maintain it in the nucleus and hence affects transcription (57); NFAT responds to changes in duty cycle while being insensitive to both amplitude and frequency changes. We see in simulations too that the proportion of NFAT that is in the dephosphorylated nuclear state is highest when the duty cycle of the Ca²⁺ transient is high (Figs. 8 and 9).

In experiments, IP₃ stimulation has been shown to lead to an increase in systolic Ca²⁺ in cardiac cells, but a significant change in duration has not been reported (although as in Harzheim et al. (17) and Proven et al. (21), increased spontaneous calcium transients are observed that could function to prolong the duration of the Ca²⁺ transient). Based on the definition of the duty cycle presented in Hannanta-anan and Chow (8), there is a negative effect on duty cycle, and hence NFAT activation, when Ca²⁺ transient amplitude is increased. However, within the physiologically plausible parameter range, we find that simulations with increased Ca²⁺ transient amplitude also have increased transient duration. We postulate that NFAT may be responsive to the Ca²⁺ transient through the latter definition of the duty cycle—i.e., the duration of time that Ca²⁺ is elevated over a threshold divided by the period. This is more consistent with both the biological mechanism and the potential increase in peak Ca²⁺ concentration in the hypertrophic pathway, which may be a side effect of a corresponding increase in duration over this threshold. Further research, both theoretical and experimental, is required to determine the validity of this assumption.

Fig. 9 shows a strong correlation between [Ca²⁺]-dependent NFAT activation and Ca²⁺ transient duty cycle in the Cooling et al. (50) model; the correspondence between Figs. 8 A and 9 is striking. A caveat, however, is that the original Cooling et al. (50) study showed that the NFAT model is also sensitive to any average increase in cytosolic calcium. Therefore, although increasing Ca²⁺ transient duty cycle is shown to be sufficient for NFAT activation in this model, further experimental validation is required to confirm this mechanism in cardiomyocytes.

Experimental evidence of an IP₃-induced increase in calcium duty cycle?

An increase in duty cycle without an increase in frequency requires an increase in transient duration. Although this increase is observed in our simulations for a broad range of parameter values, it has not, however, been reported in experiments involving IP₃ stimulation. The possible reasons for this are many and varied; however, as discussed earlier, using different IP₃ concentrations to those that occur in vivo may result in different effects on the shape of the Ca²⁺ oscillations, leading to inconsistent observations. Furthermore, small variations in Ca²⁺ concentrations may not be experimentally discernible or may be hidden by the effect of Ca²⁺-sensitive dyes (58). A small but prolonged variation in transient duration can produce a comparatively large change in duty cycle. Hence, it remains to be confirmed experimentally whether IP₃R-dependent Ca²⁺ flux does indeed lead to an increased Ca²⁺ duty cycle in cardiomyocytes.

Limitations of study

In this study, we have considered generation of voltage-driven cytosolic Ca²⁺ transients using deterministic models of each ion channel in a compartmental model. There are several physiological features of cardiomyocyte Ca²⁺ dynamics that are not represented and hence not considered in this approach. In particular, our model does not represent any of the stochastic events associated with IP₃R channels. Further modeling of combined stochastic channel gating may be necessary to elucidate the entire impact of IP₃R interaction with the cytosolic Ca²⁺ machinery. Although cell structure is known to play a role in cardiac Ca²⁺ dynamics (59, 60, 61), effects beyond the synchronizing function of the dyad are not considered in this compartmental study. Furthermore, we have not considered the spatial IP₃R distribution. Our model is developed primarily using parameters fitted by (14) and (32) and makes no distinction between IP₃R channels located within or outside the dyad (62,63). These and other structural features of the cell could alter the Ca²⁺ available to regulate IP₃R channels and may be detected in the Ca²⁺ transient. Distinct effects of IP₃ signaling in the cytosol and the nucleus are also not considered. Cytosolic Ca²⁺ is thought to promote translocation of NFAT into the nucleus, whereas nuclear Ca²⁺ maintains it there (16). We have only investigated the former role for Ca²⁺ signaling within the CnA/NFAT pathway.

We have explored model behavior at pacing frequencies of 1 and 0.3 Hz rather than higher, more physiological frequencies, primarily because the majority of parameters were derived from in vitro experiments conducted at room temperature. Extrapolation of parameters, and hence model behavior, to in vivo temperature and correspondingly higher pacing frequency remains challenging. Therefore, model predictions must be interpreted cautiously in relation to higher pacing frequencies.

Additionally, not all components of this signaling pathway have been considered in this study. Ca²⁺/calmodulin-dependent kinases II and Class IIa histone deacetylases, for example, are both known Ca²⁺-mediated components of the hypertrophic pathway that are activated by IP₃ signaling (64) but are not included. Here, we have focused only on the impact of IP₃R activation on the cytosolic Ca²⁺ dynamics and how this relates to the mechanism of NFAT activation. To explore broader context for IP₃-mediated hypertrophic signaling, it remains to couple this model to upstream events, including models of IP₃ production through activation of cell membrane receptors (65,66). This would allow the profile and extent of the rise in IP₃ concentration due to the activation of the hypertrophic pathway in cardiomyocytes to be determined. We have focused on the effect of an elevated IP₃ concentration of 10 μM because many experimental studies on the effect of IP₃ on Ca²⁺ dynamics use saturating [IP₃]. However, Remus et al. (67) found stimulation of adult cat ventricular myocytes with 100 nM ET-1 induced a cell-averaged increase in IP₃ concentration of only 10 nM, indicating a much lower concentration than used in experiments. This, together with known differences between species, suggests the IP₃ concentration detected by IP₃R receptors in ARVMs in vivo could be lower than the simulated 10 μM. However, we note qualitatively similar effects on the Ca²⁺ transient in parameter regimes with lower [IP₃] in our model (Figs. 4 and S2), albeit with more modest effects on the transient shape. Additionally, ET-1 receptors are localized to t-tubule membranes (68), so IP₃ may be generated very close to IP₃R channels (63,69), increasing the concentration they detect.

Finally, IP₃R-induced Ca²⁺ release is a part of a larger hypertrophic signaling network. It remains to couple this model to other signaling pathways involved in bringing about hypertrophic remodeling (70). How cytosolic Ca²⁺ interacts with nuclear Ca²⁺ in regulation of NFAT nuclear residence and activity also remains to be determined.

Conclusions

The sensitivity of NFAT translocation to the Ca²⁺ duty cycle demonstrated by Hannanta-anan and Chow (8) raises the question as to whether IP₃R flux can increase the Ca²⁺ duty cycle in cardiomyocytes during hypertrophic signaling. Here, we have shown, using mathematical modeling, that an increase in cytosolic Ca²⁺ transient duration can occur after addition of IP₃, and furthermore, that this increase is sufficient to increase NFAT activation. Together, these results suggest a plausible mechanism for hypertrophic signaling via IP₃R activation in cardiomyocytes. Although it cannot be ruled out that a significant role is played by components of this pathway that are not considered here, the computational evidence provided in this study, along with the previous experimental findings, suggests encoding of the hypertrophic signal through alteration of the duration of cytosolic Ca²⁺ oscillations to be a feasible mechanism for IP₃-dependent hypertrophic signaling.

Author Contributions

E.J.C., V.R., H.L.R., C.S., and G.B. conceived of the study. E.J.C. and V.R. supervised the project. H.H., A.T., V.R., and E.J.C. developed the modeling approach. H.H. implemented the simulations. H.L.R., C.S., and G.B. provided critical feedback. All authors contributed to writing the manuscript.

Editor: Eric Sobie.

Supporting Citations

References (71,72) appear in the Supporting Material.