Abstract
Calcium plays critical roles in cardiac cells, coupling electrical excitation to mechanical contraction with each heartbeat, while simultaneously mediating biochemical signals that regulate cell growth. While ryanodine receptors (RyRs) are fundamental to generation of elementary calcium release events (sparks) and global calcium elevations that underlie excitation-contraction coupling (ECC), calcium release via inositol 1,4,5-trisphosphate receptors (IP3Rs) is also reported in cardiomyocytes. IP3R calcium release modifies ECC as well as contributing to downstream regulation of hypertrophic gene expression. Recent studies suggest that proximal localisation of IP3Rs with RyRs contributes to their ability to modify Ca2+ handling during ECC. Here we aim to determine the mechanism by which IP3Rs modify Ca2+ handling in cardiomyocytes. We develop a mathematical model incorporating the stochastic behaviour of receptor opening that allows for the parametric tuning of the system to reveal the impact of IP3Rs on spark activation. By testing multiple spark initiation mechanisms, we find that Ca2+ release via IP3Rs result in increased propensity for spark initiation within the cardiac dyad. Our simulations suggest that opening of IP3Rs elevates Ca2+ within the dyad, which increase the probability of spark initiation. Finally, we find that while increasing the number of IP3Rs increases the probability of spark formation, it has little effect on spark amplitude, duration, or overall shape. Our study therefore suggests that IP3R play a critical role in modulating Ca2+ signaling for excitation contraction coupling
Author summary While Ca2+ release through ryanodine receptors (RyRs) initiates contraction in cardiomyocytes, the role of inositol 1,4,5-trisphosphate receptors (IP3Rs) in cardiomyocytes is less clear with Ca2+ release through these channels being invoked in regulating ECC and hypertrophic signalling. RyRs generate cytosolic Ca2+ signals through elemental Ca2+ release events called sparks. The mechanisms by which IP3Rs influence cytosolic Ca2+ are not well understood. We created a 1D model of calcium spark formation in a cardiomyocyte dyad—the primary site of elemental RyR-based calcium release. We investigated possible behaviours of IP3Rs and their interaction with RyRs in generating Ca2+ sparks. We show that for high IP3 concentration, a large number of IP3Rs and high IP3R affinity are required to noticeably affect spark shape. At lower IP3 concentration IP3Rs can increase Ca2+ spark activity, but do not significantly alter the spark shape. Finally our simulations suggest that spark frequency can be reliably increased when IP3Rs activity is such that a small continuous Ca2+ flux is introduced to the dyad to elevate Ca2+, and not via brief but high Ca2+ release from these receptors.
Introduction
Calcium plays a fundamentally important role in the regulation of each heartbeat. Ca2+ flux through L-type Ca2+ channels (LTCC) couples electrical activation to muscle contraction through excitation-contraction coupling (ECC) [1, 2]. Membrane depolarisation triggers a small influx of calcium through voltage-gated LTCCs (Fig. 1A) into 10-15 nm wide calcium microdomains [3, 4] called dyads. In these regions, LTCC channels are juxtaposed with a set of Ca2+ channels called ryanodine receptors (RyRs) on the intracellular sarcoplasmic reticulum (SR) compartment. RyRs are sensitised by the Ca2+ influx and release a larger amount of Ca2+ from the SR. This local Ca2+ release event at the dyad is known as a calcium spark (Fig. 1B) and cardiac contraction is determined by the sum of these elementary local Ca2+ release events at the many dyads regularly distributed through the cardiomyocyte volume.
In a majority of cell types, neurohormonal stimulation of intracellular Ca2+ is mediated by inositol 1,4,5-trisphosphate (IP3) and IP3 receptors (IP3Rs) located on the endoplasmic reticulum (ER) [5]. In cardiomyocytes, activation of G-protein coupled receptors (GPCR) for neurotransmitters such as endothelin-1 (ET-1) and angiotensin-II (AngII) leads to elevation of IP3 and Ca2+ release via IP3Rs [6–9]. Crosstalk between IP3Rs and RyRs, in which activation of IP3Rs via elevated IP3 leads to recruitment of neighbouring RyRs receptors, leading to larger Ca2+ release, was first suggested in smooth muscle cells [10]. Similar interaction between IP3Rs and RyRs has also been proposed in embryonic myocytes [11, 12], atrial cardiac myocytes [13–15], spontaneously hypertensive rat (SHR) myocytes [8], and rabbit ventricular myocytes [16]. Given the lower abundance and Ca2+ flux of IP3Rs relative to RyRs, how they can affect ECC remains poorly understood. In particular, the characteristics of IP3R gating that may lead to recruitment of RyR receptors also remains to be determined.
Experimental investigations [17] and computational models [18, 19] of Ca2+ sparks have elucidated the role of the spatial distribution and density of RyR channels, and their stochastic interactions, in determining the spatio-temporal characteristics of Ca2+ sparks in health and disease [20]. IP3Rs are proposed to collocate with RyRs [8,16, 21–23] and are also known to exhibit increased expression in pathological conditions [24], here we use computational modelling to test a hypothesis that IP3R Ca2+ release modulates Ca2+ spark activity, and thereby affects cytosolic Ca2+ and ECC.
Previously, stochastic and deterministic models have been developed which investigate the properties of RyRs in generating Ca2+ sparks [18, 25–30]. Computational models of IP3Rs have also been developed primarily for various cell types where IP3Rs are the predominant intracellular Ca2+ release channel [31–35]. Deterministic temporal models have been proposed that include both IP3Rs and RyRs, but do not provide information about sparks or spatial interactions between these two SR Ca2+ release channels [36, 37]. To date, the role of IP3Rs in Ca2+ spark formation, including both RyR and IP3Rs in a stochastic computational model, has not been investigated.
In this study, we investigate the influence that IP3R activation may have in the shape and temporal behavior of Ca2+ sparks through stochastic interaction between IP3Rs and RyRs. We creates a 1D spatial model of cardiomyocyte dyads containing stochastically opening RyR and IP3Rs. Using this model, we examine how Ca2+-mediated interaction (crosstalk) between IP3 R and RyR channels impacts the spatio-temporal profile of the Ca2+ spark. We investigate the sensitivity of spark initiation and shape to a range of IP3R gating parameters and IP3 concentration. Our findings suggest that for low IP3 concentrations, Ca2+ release via IP3Rs is insufficient to initiate sparks but they increase the probability of spark events without changing spark shape. The model also suggests that a small sustained Ca2+ flux from active IP3Rs diffusing to neighbouring RyRs can trigger spark formation.
Materials and methods
Model formulation
We model the transport of Ca2+ as a reaction-diffusion system that describes the movement of Ca2+ in three compartments: cytosolic (Cac); junctional sarcoplasmic reticulum (CaJSR); and network sarcoplasmic reticulum (CaNSR): where Dc and DNSR represent the Ca2+ diffusivities in the cytosol and the network SR respectively (the junctional SR is assumed to be a small and hence well-mixed volume). βJSR represents the calsequestrin buffer, which is modelled following the approach of Keizer et al. [38]. JSERCA represents the flux of Ca2+ from the cytosol into the NSR through the sarco-endoplasmic reticular Ca2+-ATPase (SERCA) pumps. Jrefill represents the flux of Ca2+ refilling the JSR compartment from the NSR. Jbuff is the flux of Ca2+ as it binds and unbinds to buffers in the cytosol. Jrelease represents the flux of Ca2+ from the JSR into the cytosol through RyRs and IP3Rs, and is defined such that where RyRopen and IP3Ropen represent the number of open RyRs and IP3Rs, respectively. RyRopen is calculated using a re-scaled stochastic model as proposed by Cannell et al. [18]. IP3Ropen is calculated based on the stochastic two-state ‘park-drive’ model proposed by Siekmann et al. [34] based on fitting single channel data [39, 40], as implemented by Cao et al. [35]. gRyR, gIP3R represent RyR and IP3R flux coefficients. A schematic illustration of these compartments and fluxes is provided in Fig. 2A. For simplicity, the effect of LTCCs in triggering receptor opening in the dyad was implemented by directly opening 30 RyRs, rather than introducing additional Ca2+ via LTCCs in each cycle. Jbuff is the Ca2+ flux on binding to mobile and immobile cytosolic Ca2+ buffers. The transport of Ca2+ bound to mobile buffers (Bm) including adenosine trisphosphate (ATP), the calcium indicator Fluo4, and calmodulin, and Ca2+ binding to the immobile buffer Troponin C, (Bim), are included as: where and represent the on and off rates for mobile buffers (ATP, CaM or Fluo4), and and are the on and off rate for the immobile buffer (TnC). Further expressions and model details may be found in the Supplementary Text S1.
Numerical implementation
We simulated the reaction-diffusion system and stochastic interactions between RyR and IP3Rs within a single dyad on a 1D geometry to reflect the experimental line-scan recording of calcium sparks and transients. This reduced-order representation enabled an investigation into the influence of IP3Rs on Ca2+ spark generation in the dyad. This choice of representation was further justified by previous detailed 3D simulations of Ca2+ spark generation, which showed that the spatial distribution of RyRs on the dyad was not critical to the spark profile when the number of RyRs in the cluster was greater than 9 [41].
The spatial settings for each cell compartment and receptors along this 1D geometry are illustrated in Fig. 2B. The 0.2 μm-wide dyad has 45 RyRs positioned on either side of the midline, separated by 0.04 μm, with a variable number of IP3Rs placed another 0.04 μm from the centre at both ends of the dyad.
The partial differential equations (PDEs) were discretized in space using a finite difference scheme. The resulting system of ODEs was solved using a first-order Runge-Kutta method with a maximum time step dt =1 × 10-4 ms and a spatial step dx = 0.04 μm. Stochastic IP3R and RyR gating states were solved using a hybrid Gillespie method. All software was written using Matlab2017b (The MathWorks Inc., Natick, Massachusetts).
Results
We tested the sensitivity of the Ca2+ spark profile to interactions between IP3Rs and RyRs by comparing sparks with no IP3Rs to sparks generated with different numbers of IP3Rs and varying parameter settings. Specifically, we investigated the dependence of amplitude, duration and frequency of spark events to: number of IP3Rs; IP3Rs Ca2+-sensitivity; and IP3 concentration.
Number of IP3Rs per dyad does not affect the shape of LTCC-initiated Ca2+ sparks
To determine the effects of IP3R-mediated Ca2+ release on the shape of the Ca2+ spark, single spark events were initiated within a dyad by opening 30 RyRs per cluster at t = 0 ms, with different numbers of IP3Rs: 0, 5, 10, or 20 per cluster (yellow box, Fig. 2B). Simulations were run for Tobs = 80 ms, and each simulation was repeated 108 times. Example simulation outputs are given in Supplementary Figures 1 and 2. Representative fluorescence trace, and means and 95% confidence intervals for Ca2+ concentration in the JSR at the RyR locations, and IP3Rs and RyR receptor open populations, are provided in Fig. 3. These simulation results show that LTCC-triggered sparks (Fig. 3, first column) are similar in shape and duration irrespective of the number of IP3Rs.
Additionally, in all simulations, minimum [Ca2+]JSR was ≈ 200 μM at ≈ 50 ms, which coincides with the time RyRs start to close. This is consistent with the hypothesis that spark termination is related to [Ca2+]JSR depletion, as suggested previously [42, 43]. IP3Rs were active primarily at the start of simulations (Fig. 3, third column) when only ≈ 20% of IP3Rs were open. However, RyRs fluctuated to ≈ 45% of RyRs for ≈ 50 ms and closed at ≈ 60 ms (Fig. 3, fourth column). This suggests that RyRs, but not IP3Rs, primarily determine spark shape. Since IP3Rs are mostly active at the beginning of simulations, they may however play a role in spark initiation.
IP3Rs can facilitate spark initiation
To test the role that IP3Rs play in spark activation, we next considered which dyad trigger settings were sufficient to generate a spark. Experiments on cardiac and smooth muscle cells suggested that IP3Rs may not create a spark by themselves, but can facilitate neighbouring RyR opening [10, 12, 13]. Therefore we tested how one dyad will behave when: (a) no initiation is applied; (b) 5 IP3Rs are opened at t = 0 ms; (c) 5 RyRs are opened at t = 0 ms; (d) 5 IP3Rs and 2 RyRs are opened at t = 0 ms; and (e) consistently open IP3Rs (IP3R “leakage”).
Simulation results shown in Fig. 3 do not show significant variability in spark shape with different number of IP3Rs, therefore we fixed the number of IP3Rs to 20. Simulations were run for Tobs = 80 ms and repeated 108 times, for each of these 5 triggering mechanisms. We calculated the percentage of simulations which showed sparks (we assumed a spark to have occured if max(ΔF/F0) > 1), and spark initiation times (when the maximum value of the fluorescence trace occurred) within each simulation. Results shown in Fig. 4 indicate that both the percentage of simulations that depict spark initiation (Fig. 4A) and the spark initiation times within a simulation (Fig. 4B) depend on the trigger mechanism. Simulations with (a) no trigger, (b) 5 opened IP3Rs, and (d) mixture of opened receptors, showed sparks in only ≈ 12%, ≈ 23% and ≈ 32% of runs, respectively (Fig. 4A). Furthermore, the small number of sparks and the broad distribution of their time to peak (Fig. 4B) suggests that in each of these cases spark initiation occurred at a random time following channel opening. Nevertheless spark amplitudes were approximately the same in these simulations (shown in Supplementary Figure 3). These results indicate that intermittently opening IP3Rs increases the probability of spark initiation but may not reliably initiate a spark under fixed IP3 concentration (0.15 μM).
Simulations with (c) 5 opened RyRs and (e) leaking IP3Rs showed spark initiation in almost all simulation runs. However, there was a difference in the distributions of spark initiation times (Fig. 4B): (c) 5 opened RyRs resulted in almost instantaneous spark initiation, while IP3R “leakage” increased the frequency of sparks, but spark initiation times were distributed more widely. Fig. 4B suggests that opening RyRs (c) instantaneously initiates sparks, while highly active IP3Rs facilitate spark formation by priming RyRs for activation thereby increasing their liklihood for spontaneous opening (e).
“Leaking” IP3Rs showed more broadly distributed spark initiation times, indicated in the much wider confidence intervals in bottom plots of Fig. 4C. Furthermore, the time to initiation was longer compared to the opened RyR case (Fig. 4C, first column). Decay but not recovery of [Ca2+]JSR can be seen in averaged results (second column, Fig. 4C). These observations again indicate that Ca2+ sparks were initiated spontaneously with IP3R activated slow Ca2+ release.
IP3R open probability influences spark shape
Cardiomyocytes express three isoforms of IP3R: IP3R1, IP3R2 and IP3R3 [21, 44, 45]. Type 2 isoform is predominant [21] and has the highest IP3 binding affinity, followed by type 1 and type 3 being the least sensitive to IP3. As mathematical models using the type 1 isoform are more developed, in simulations upto this point we used parameter values in the IP3R model that had previously been fitted to single channel recordings on type 1 IP3 receptors [46]. To explore the influence of the Ca2+-sensitivity of different IP3R isoforms we shifted the Ca2+-sensitivity curve (supplementary Figure 7) to give qualitative estimates of the different isoforms provided in the experimental literature [34, 47].
Simulations with type 2 receptor parameters and varying number of IP3Rs are shown in Fig. 5 for [IP3] = 0.15 μM. Sparks were initiated by opening 5 RyRs at t = 0 ms. It can be seen that, as for type 1 parameters, spark amplitudes were not affected by the number of receptors (Fig. 5A). However, unlike type 1 simulations, type 2 parameters showed an increase in spark duration under higher number of IP3Rs (Fig. 5B). This difference may be due to type 1 parameter simulations showing the number of opened IP3Rs to be highest at t = 0 ms and decreasing subsequently throughout the simulation (Fig. 3), while for type 2 parameters IP3Rs are initially closed over the first t = 5 ms, and may open again subsequently during the simulation (Fig. 5C). This difference is in particular evident for simulations with 20 IP3Rs, when type 2 parameters showed on average 1 opened IP3R after t = 10 ms, while for type 1 parameters all IP3Rs are on average closed by this point (Fig. 5D).
High [IP3] increases robustness of spark initiation
IP3R behaviour depends on cytosolic Ca2+ and IP3 concentrations [47]. Increased [IP3] overcomes Ca2+ dependent inhibition, which could be a factor in the dyadic environment. Therefore we next investigated spark triggering mechanisms and spark shape with 20 IP3Rs at 6 different IP3 concentrations ranging from 0.05 μM to 3 μM. As in previous simulations, we calculate the percentage of simulations in which a spark was initiated, as well as the spark initiation time (time to maximum of the fluorescence trace) and spark shape.
Table 1 shows the percentage of simulation runs in which a spark was initiated, for [IP3] = 0.05; 0.15; 0.5; 1; 2; 3 μM. In these simulations IP3R type 1 parameters were used, and different triggering mechanisms were considered, as in previous simulations. For “leaking” IP3Rs as well as simulations triggered with opened RyRs, reliable spark initiation occurred for all IP3 concentrations. For simulations triggered with IP3R opening, the probability of succesful spark generation increased with increasing IP3 concentration.
Summaries of spark shape and spark initiation times for these triggering mechanisms under different IP3 concentrations are shown in Fig. 6. Full simulation summaries are provided in Supplementary Figures 4-6. For simulations triggered by opened RyRs, spark times are not strongly affected by IP3 alterations, however for opened IP3Rs and “leaking” IP3Rs, more robust spark initiation times are observed under higher IP3 concentration (Fig. 6A). Spark amplitudes remained similar under all IP3 concentrations (Fig. 6B), showing only modest increase with increasing [IP3]. These observations confirm that for IP3R type 1 parameters, spark properties are determined predominantly by RyR activity.
Finally, we compared simulations for type 1 and type 2 parameter sets at different [IP3], shown in Fig. 7. A more detailed summary of effect of different [IP3] on spark shape and initiation times in simulations with type 2 parameter set are provided in Supplementary Figure 8. As illustrated by the third column of Fig. 7, IP3R activity increases with higher [IP3] under both parameter sets. For type 1 parameters, IP3Rs showed highest activity at t ≈ 5 ms after which receptors within the cluster started to close, while for type 2 parameters IP3Rs were continuously open under higher [IP3]. This difference influences RyR behaviour and hence spark duration (red boxes in Fig. 7).
Discussion
IP3Rs are expressed in cardiomyocytes, where they colocalise with RyRs in dyads, yet a functional role in Ca2+ spark formation – elementary Ca2+ events underlying cardiac ECC – is unclear, in part because of the dominance of RyR Ca2+ release. In this study, we have sought to determine the potential for IP3R Ca2+ release to contribute to spark formation in the cardiomyocyte dyad. We developed a 1D spatial model accounting for stochastic RyR and IP3R gating and examined spark initiation in a single dyad. Specifically, we investigated whether IP3Rs in a dyad can affect spark initiation and shape and how this changes depending on modelled IP3R gating behaviour.
Model assumptions and their implications
In our model we made two major assumptions: 1) SR receptors are in close proximity to each other, but they do not overlap, and 2) there is no Ca2+ diffusion in the JSR compartment. If receptors overlap, then Ca2+ depletion in the JSR could occur more quickly due to the larger Ca2+ flux through the SR receptors. This overlap could subsequently cause spark termination and reduce spark duration. Ca2+ diffusion in the JSR may also change spark duration by affecting Ca2+ depletion in the SR. However Cannell et al. [18] showed that the physical distribution of RyRs within the dyad will not greatly affect the spark profile in clusters greater than 9 RyRs. Walker et al. [48] also showed that the propensity of spark formation from stochastic release of Ca2+ from ion channels increased with larger and denser clusters of RyRs. Furthermore, our study shows that IP3R activation also does not alter spark profile.
Our simulations support the idea that Ca2+ via IP3R prime RyRs for ECC in disease
Our results indicate that for type 1 IP3R, the number of IP3Rs in a cluster does not significantly affect spark shape when triggered by the L-type channel Ca2+ flux. This implies that, in healthy cardiac cells, sparks are insensitive to the relatively small perturbations caused by IP3R opening. However, IP3R expression increases significantly in diseased cardiomyocytes [8, 44]. Increasing numbers of IP3Rs and in particular ‘leaky’ IP3Rs, as would result from increased diastolic Ca2+ concentration, lead to increased spark initiation frequency. This suggests that the increase in IP3R expression could be a compensatory mechanism to dyad uncoupling from electrical activity in disease [49].
In the absence of Ca2+ influx through the LTCC, however, our analysis indicated that prolonged IP3R “leakage” was able to initiate a spontaneous spark, while intermittently opening IP3Rs were not sufficient to reliably trigger a spark (figure 4A). These results agree with a range of experiments in cardiac cells [10, 12, 13] reporting that opened IP3Rs do not provide sufficient Ca2+ to trigger an event, however their activation can sensitize neighbouring RyR clusters. In hypertrophic rat cardiomyocytes and in atrial cells, IP3R channels have been been shown to increase diastolic [Ca2+] [50]. Our simulations imply that this rise in diastolic [Ca2+] can directly cause the increase in spontaneous calcium transients that is also observed in hypertrophic cells [50, 51].
“Leaky” IP3R in our simulations represented a type of spark trigger where IP3R channels were constitutively open. While ion channels do not physiologically remain constiutively open it is plausible that the “leak” may represent the elevation in Ca2+ arising from several intermittently opening and closing IP3Rs during ECC.
Our simulations indicate that increasing [IP3] can make spark initiation more robust and also slightly increase spark duration (Fig. 6). However, spark amplitudes remained similar under investigated [IP3] (Fig. 6B). Specifically, our simulations agree with previous findings in mouse and rabbit ventricular myocytes [16, 51] which found no significant changes in amplitude immediately after addition of 10 μM IP3. However, Domeier et al. [16] indicated that the amplitude of the sparks may change in longer duration experiments (after ≈ 7min following IP3 application). The authors also suggested that IP3 application did not affect spark duration, while our simulations generated slightly longer sparks under 2 μM IP3 compared to 0.05 μM IP3 concentration. It should be noted that Domeier et al. [16] used imaging resolution of 3 ms per scan, while in our simulations the time resolution was set to 0.0001 ms.
The potential roles of different isoforms of IP3R
We based our IP3R model on the Siekmann et al. stochastic two-state park-drive model [35, 46] to simulate IP3R induced calcium release. This model was parametrised for type 1 IP3Rs with the Ca2+ sensitivity ranging between 0.1 μ.M and 10 μM (see Supplementary Figure 7). This sensitivity was measured in type I IP3 R channels expressed in COS cells [?]. To investigate type 2 IP3R behaviour, we altered model parameters to qualitatively represent Ca2+-sensitivity curve as provided in [34, 47]. The type 2 IP3Rs are sensitive to Ca2+ in the range 0.01 μM to 1 μM (see Supplementary Figure 7).
Our simulations suggest that type-2 IP3Rs would alter the shape of the Ca2+ spark by releasing Ca2+ at the early rise phase as well as the late decay phase of the spark timeline. While this is surprising, given the wide range of Ca2+ sensitivities reported [?] even for one IP3R isoform type in experiments, it is unclear what the specific parameters for IP3Rs for Ca2+ sensitivity should be. In addition, the 1D dyadic simulations here do not include structural details that have been shown to produce Ca2+ concentrations within the dyad of 6 - 10 μM [52, 53]. Therefore, both types of IP3Rs may actually be inhibited by a high concentration of calcium within the dyad during Ca2+ spark events. This would mean that neither IP3R isoform would affect spark shape but the sensitising effect would remain. Additionally, IP3 sensitivity is suggested to vary between isoforms [?]. Further work needs to be done to incorporate more spatial detail of the collocation of IP3Rs and RyRs as well as the isoform differences to further test the validity of our type 2 isoform predictions in this study.
Conclusion
IP3Rs may not affect spark initiation or shape in healthy cells with coupled RyRs and LTCC. In the absence of LTCC trigger, however, we tested 5 different initiation cases and showed that Ca2+ release via IP3 R can trigger sparks by sensitizing neighbouring RyR clusters.
Further work is needed in order to link these findings on IP3Rs-influenced spark formation to models of IP3 signalling in cardiomyocytes [54, 55], and multi-scale integration of stochastic spark formation to understand how this impacts on global cytosolic Ca2+ transient dynamics and excitation-contraction coupling under normal and disease conditions [56, 57].
Supporting information
S1 Text: Model equations, parameters and references.
S2 Figures: Supplementary figures for single dyad simulations.
Acknowledgments
This research was supported in part by the Australian Government through the Australian Research Council Discovery Projects funding scheme (project DP170101358) to EJC and VR, and the Australian Research Council Centre of Excellence in Convergent Bio-Nano Science and Technology (project CE140100036) to EJC. HLR wishes to acknowledge financial support from the Research Foundation Flanders (FWO) through Project Grant G08861N and Odysseus programme Grant 90663.