Modeling sarcoplasmic reticulum Ca²⁺ in rat cardiomyocytes

Abstract

The sarcoplasmic reticulum (SR) primarily serves as the intracellular Ca²⁺ store in cardiac myocytes, mediating cellular function under cardiac physiology and diseases. However, the properties of cardiac SR Ca²⁺ have not yet been fully determined, particularly in rats and mice, which are the most commonly used experimental species in studies on cardiac physiology and diseases. Here, we developed a spatially detailed numerical model to deduce Ca²⁺ movements inside the junctional SR (jSR) cisternae of rat cardiomyocytes. Our model accurately reproduced the jSR Ca²⁺ kinetics of local and global SR Ca²⁺ releases reported in a recent experimental study. With this model, we revealed that jSR Ca²⁺ kinetics was mostly determined by the total release flux via type 2 ryanodine receptor (RyR2) channels but not by RyR2 positioning. Although Ca²⁺ diffusion in global SR was previously reported to be slow, our simulation demonstrated that Ca²⁺ diffused very quickly inside local jSR cisternae and the decrease in the diffusion coefficient resulted in a significant reduction of jSR Ca²⁺ depletion amplitude. Intracellular Ca²⁺ was typically experimentally detected with fluorescence dye. Our simulation revealed that when the dynamical characteristics of fluorescence dye exerted a minimal effect on actual Ca²⁺ mobility inside jSR, the reaction rate of the dye with Ca²⁺ could significantly affect apparent jSR Ca²⁺ kinetics. Therefore, loading a chemical fluorescence dye with fast kinetics, such as Fluo-5N, into SR is important for Ca²⁺ measurement inside SR. Overall, our model provides new insights into deciphering Ca²⁺ handling inside nanoscopic jSR cisternae in rat cardiomyocytes.

Graphical abstract

Keywords

Numerical model / Sarcoplasmic reticulum / Calcium / Rat cardiomyocytes / Fluorescence dye

INTRODUCTION

In cardiac myocytes, the sarcoplasmic reticulum (SR) primarily serves as the intracellular Ca²⁺ store that provides most contractile Ca²⁺ to myofilaments (Bers 2002; Eisner et al. 2017). Structurally, SR is a continuous membrane-bound organelle that extends across the cytosolic space with interconnected nanotubules, i.e., free SR (fSR), and flat cisterns, i.e., junctional SR (jSR), which form junctions with transverse tubules (TTs) at the level of the sarcomeric Z lines (Brochet et al. 2005). Ca²⁺ release from cardiac SR is gated by type 2 ryanodine receptor (RyR2), which is the main Ca²⁺ release channel located at the jSR membrane inside SR–TT junctions, via the Ca²⁺-induced Ca²⁺ release mechanism (Bers 2002). This mechanism generates multiscale and multimodal cytosolic Ca²⁺ signals, including quarky Ca²⁺ release, Ca²⁺ sparks, Ca²⁺ transients, and Ca²⁺ waves, in cardiomyocytes (Cheng et al. 2008; Brochet et al. 2011). SR Ca²⁺ dynamics is currently recognized to play a critical role in the regulation of RyR2 gating, controlling cytosolic Ca²⁺ pattern and cellular Ca²⁺ homeostasis (Eisner et al. 2017; Jones et al. 2017; Zhang et al. 2021). Therefore, further deciphering SR Ca²⁺ dynamics in cardiac physiology and diseases is informative.

With the development of a protocol that favors the SR retention of low-affinity Ca²⁺ indicators Fluo-5N in 2005, Ca²⁺ blinks, which are local SR Ca²⁺ events that accompany Ca²⁺ sparks, were first experimentally observed in rabbit cardiomyocytes (Brochet et al. 2005). Following this report, a few studies have revealed cardiac SR Ca²⁺ kinetics and its regulation of cellular Ca²⁺ homeostasis by interplaying with cytosolic Ca²⁺ events (Zima et al. 2008; Brochet et al. 2011, 2012; Domeier et al. 2012; Greensmith et al. 2014; Wang et al. 2014; Bovo et al. 2015). To date, however, such a strategy for imaging SR Ca²⁺ has failed to achieve widespread application in cardiomyocytes from species other than rabbit and sheep, limiting our knowledge about cardiac SR Ca²⁺ to these species. By expressing SR-targeted carboxylesterase via adenoviruses, Lu et al. successfully imaged SR Ca²⁺ in intact cardiomyocytes from rats and mice (Lu et al. 2020), small rodents that are most commonly used in cardiovascular research, providing most of our knowledge about cardiac Ca²⁺ signaling, particularly in heart diseases. Although quantitative measurements of cytosolic Ca²⁺ dynamics in cardiomyocytes have demonstrated considerable differences among species (Bers 2002; Eisner et al. 2017), further extending our knowledge about SR Ca²⁺ signals to murine cardiomyocytes is urgent.

Complementing experimental studies, computational modeling has further demonstrated nanoscale details for Ca²⁺ mobilization, which is experimentally limited by optical resolution. Although most models have been developed for cytosolic Ca²⁺ kinetics, several models have also simulated SR Ca²⁺ kinetics (Sobie et al. 2005; Zima et al. 2008; Cannell et al. 2013; Li et al. 2017). In particular, Cannell et al. developed a model with considerable details in the dyad and SR network; this model reproduced most of the spatiotemporal characteristics of Ca²⁺ sparks/blinks and their termination mechanism (Cannell et al. 2013). Li et al. developed a spatially detailed model to describe Ca²⁺ movements inside the jSR of cardiomyocytes (Li et al. 2017). However, on the basis of Ca²⁺ blinks in rabbit cardiomyocytes, these previous simulations of SR Ca²⁺ kinetics did not agree well with a recent experimental study on rat cardiomyocytes (Lu et al. 2020).

In the current work, we developed a spatially detailed numerical model to deduce Ca²⁺ movements inside the jSR cisternae of rat cardiomyocytes. Our model not only agreed well with the experimental Ca²⁺ kinetics inside jSR but also revealed the influences of jSR Ca²⁺ diffusion and fluorescence dye characteristics on apparent jSR Ca²⁺ kinetics.

RESULTS

In rat cardiomyocytes, a typical Ca²⁺ spark event corresponds to Ca²⁺ release with a peak flux of ~2.5 pA (Wang et al. 2004) from the jSR cisterna. This value is four times that of a single RyR current (~0.6 pA) under physiological conditions (Mejia-Alvarez et al. 1999). The average lasting time for SR Ca²⁺ release is ~20 ms during a Ca²⁺ spark (Lu et al. 2020). We then modeled the accompanying Ca²⁺ event inside jSR, i.e., Ca²⁺ blink, with an opening of 20 ms for four adjacent RyR2 channels located at (0, 0), (0, 30), (30, 30), and (30, 0) in the jSR cisterna (Fig. 1B, top). As shown in Fig. 1C, the modeling results of Ca²⁺ release through the four channels agree with the experimental Ca²⁺ blink kinetics of rat cardiomyocytes (Lu et al. 2020) with an amplitude (in ΔF/F₀) of 0.185 (model) versus 0.190 (experiment) and a full duration at half maximum (FDHM; in ms) of 34.1 (model) versus 32.8 (experiment). The depletion of free Ca²⁺ in jSR cisternae reaches up to 45%, which is ~2.4 times of the apparent depletion indicated by Fluo-5N fluorescence intensity in a Ca²⁺ spark/blink pair (Fig. 1C).

1 Simulations of Ca2+ kinetics inside the jSR of rat cardiomyocytes. A Schematic of jSR and the connected fSR network. Dots represent RyR2 channels. B The unstructured grids near the open RyR2 channels and fluorescence contour at the indicated time points. Top, four adjacent RyR2 channels that correspond to the red dots in panel A. Bottom, four random RyR2 channels that correspond to the blue dots in Panel A. C The simulated time course curves of Ca2+ concentration (left) and normalized Fluo-5N fluorescence (right) in the jSR of rat cardiomyocytes in response to the four adjacent (red) or random (blue) RyR2 channels. The curves represent the average Ca2+ or CaF concentration in the whole jSR. D The simulated curves of Fluo-5N fluorescence changes in response to the 20 ms opening of the indicated number of open RyR2 channels, or four open RyR2 channels with iRyR adding/reducing to 10 folds of the original value. E The modeled Ca2+ blink nadir with different opening times of four RyR2 channels. F,G The modeled Ca2+ blink curve in response to the 20 ms opening of four adjacent RyR2 channels with different numbers of refilling fSR tubules or CSQ concentrations. H The simulated curves for Ca2+ depletion transient inside the jSR of rat cardiomyocytes by overlaying 100 jSR CaF traces from 4–8 open RyR2 channels with 1/3 fSR refilling flux and 0–50 ms Gaussian-distributed latency

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Although several previous studies have reported the interplay between adjacent RyR2 channels in the same CRU (Xie et al. 2010), the locations of open RyR2 channels in a Ca²⁺ spark/blink pair remain unsolved (Cheng et al. 2008). We then assessed the effect of open RyR2 positioning on jSR Ca²⁺ kinetics by replacing the adjacent RyR2 opening with four randomly located channels (Fig. 1B, bottom). Such alteration exerted nearly no effect on the modeled Ca²⁺ blink kinetics (Fig. 1C). Meanwhile, the alteration of the total releasing flux, which can result from changing the number of open RyR2 channels, or i_RyR, or the open time of RyR2, evidently affect the nadir of the modeled Ca²⁺ blink (Figs. 1D and 1E). Previous studies have indicated that refilling flux from fSR tubules and the buffering capacity of CSQ are important in Ca²⁺ blink kinetics (Li et al. 2017). Similarly, our simulations demonstrated that changes in refilling fSR tubule number (referred to as the refilling flux hereafter) and CSQ concentrations could affect Ca²⁺ blink nadir and recovery time (Figs. 1F and 1G).

Ca²⁺ transient is the summation of Ca²⁺ spark/blink throughout a cell. It involves more RyR2 openings at each CRU (Cheng et al. 2008) and exhibits a triple recovery time for cytosolic and jSR [Ca²⁺] compared with a single spark/blink pair (Lu et al. 2020). We modeled jSR Ca²⁺ depletion transient kinetics by overlaying 100 modeled jSR CaF traces from 4–8 open RyR2 channels with 1/3 fSR refilling flux and 0–50 ms Gaussian-distributed latency (Song et al. 2001). As shown in Fig. 1H, the modeled jSR Ca²⁺ depletion transient exhibited 24.3% depletion of CaF fluorescence, time to nadir of 48.5 ms, and half recovery time of 69.5 ms, which are extremely close to the experimental characteristics of jSR Ca²⁺ depletion transients (Lu et al. 2020).

Previous experimental studies have reported a relatively slow mobility of Ca²⁺ inside global SR (with one or two orders of magnitude lower apparent diffusion coefficient than that in cytosolic space) (Swietach et al. 2008), which is largely limited by the extremely thin fSR network. The manner in which Ca²⁺ diffuses inside the relatively wider jSR space remains unknown. While reproducing the experiment on Ca²⁺ blink dynamics by using the same Ca²⁺ diffusion coefficient inside jSR as that in cytosolic space, we tested the effect of the reduced Ca²⁺ diffusion coefficient inside jSR on Ca²⁺ blink kinetics. The decrease in Ca²⁺ diffusion coefficient to 20%, 10%, or 1% resulted in decreases of the modeled Ca²⁺ blink amplitude by about 16%, 32%, or 80%, respectively (Fig. 2A). The contour displayed steeper gradients around the open RyR2 channels with a reduction in the Ca²⁺ diffusion coefficient (Fig. 2B).

2 Effect of the reduction of the Ca2+ diffusion coefficient inside jSR on modeled Ca2+ blink amplitude. A The simulated time course curves of Fluo-5N fluorescence in response to the 20 ms opening of four RyR2 channels with different Ca2+ diffusion coefficients. B The fluorescence contour of the indicated Ca2+ diffusion coefficients at a time point of 20 ms

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Experimental jSR Ca²⁺ was visually measured with a fluorescence indicator; hence, we also assessed its influences on Ca²⁺ and CaF kinetics. As displayed in Fig. 3A, the diffusion coefficient of the fluorescence indicator exerted no effect on Ca²⁺ and fluorescent signals. The association and dissociation constants determine the reaction rate of fluorescent dye with Ca²⁺. A reduction in the association and dissociation constants did not affect jSR Ca²⁺ kinetics, but considerably decreased the sensitivity of fluorescent signals (Fig. 3B). Notably, the total concentration of the Ca²⁺ indicator should be controlled to an appropriate range, because it also serves as a Ca²⁺ buffer and can considerably affect Ca²⁺ and fluorescent signals inside jSR (Fig. 3C).

3 Effect of the characteristics of fluorescence dye on the modeled Ca2+ blink amplitude. The simulated time course curves of Ca2+ concentration (left) and normalized Fluo-5N fluorescence (right) in the jSR of rat cardiomyocytes with different CaF diffusion coefficients (A), reaction rates between the dye and Ca2+ (B), or total Fluo-5N concentrations (C)

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DISCUSSION

SR functions as an intracellular Ca²⁺ store in cardiomyocytes (Bers 2002; Eisner et al. 2017). However, the properties of cardiac SR Ca²⁺ have not been fully determined, particularly in small rodents, such as rats and mice, which are the most commonly used experimental species in studies on cardiac physiology and diseases (Lu et al. 2020). Here, on the basis of a recent experimental study (Lu et al. 2020), we developed a spatially detailed numerical model to deduce Ca²⁺ movements inside the jSR cisternae of rat cardiomyocytes. With this model, we reproduced local SR Ca²⁺ event, Ca²⁺ blink, and global Ca²⁺ depletion transient in rat cardiomyocytes.

The number of RyR2 channels that open during the Ca²⁺ spark remains controversial. An early study revealed that Ca²⁺ sparks in rat ventricular myocytes exhibited quantized Ca²⁺ release flux with a quantal unit of 1.24 pA and a peak histogram of quantal number at 2 (Wang et al. 2004). Thus, a typical Ca²⁺ spark corresponds to a total SR releasing flux of ~2.5 pA. We modeled four RyR2 openings during a typical local SR Ca²⁺ release event, because a single RyR2 current was measured as ~0.6 pA in the bilayer lipid membrane (Mejia-Alvarez et al. 1999). Our simulated Ca²⁺ blink kinetics agreed with the recently reported experimental results (Lu et al. 2020). Considering that in vivo single RyR2 current might differ from this value (0.6 pA), our simulations further revealed that the total release flux, but not the number or positioning of open RyR channels, determined jSR Ca²⁺ kinetics in rat cardiomyocytes.

Compared with the open space of cytosol, the intraluminal space of thin fSR tubules limits Ca²⁺ mobilization in the SR network, and thus, a slow diffusion of Ca²⁺ in global SR is identified (Swietach et al. 2008). In the current study, we determined that a reduction in the jSR Ca²⁺ diffusion coefficient resulted in an evidently decreased amplitude of the simulated Ca²⁺ blink, while simulation with Ca²⁺ mobilization in jSR that was as fast as cytosol concurred with the experimental results. Such fast mobilization of Ca²⁺ inside jSR also accounts for the unimportance of open RyR2 positioning.

When the chemical fluorescence dye is extremely difficult to load into SR in myocytes, the genetically encoded Ca²⁺ indicators (GECIs) provide an alternative strategy. Several low-affinity GECIs located in SR lumen were developed previously (Kasai et al. 2004; Jimenez-Moreno et al. 2010). However, these GECIs can only detect global Ca²⁺ changes, but fail in detecting fast local SR Ca²⁺ events, such as blinks in cardiomyocytes. These GECIs typically have considerably slower kinetics than synthetic chemical Ca²⁺ indicators (Jimenez-Moreno et al. 2010). In the current study, our simulation suggested that the reaction rate of Ca²⁺ and dye remarkably affected the sensitivity of detecting apparent Ca²⁺ changes in jSR, while the real Ca²⁺ kinetics remained unaltered. Thus, the development of a straegy for loading a chemical Ca²⁺ dye into cardiac SR is crucial for research on SR Ca²⁺ signals (Lu et al. 2020). A prior simulation study described heavy underestimation of the real local SR Ca²⁺ depletion (~80%) by Fluo-5N signals (~0.2 ΔF/F₀) due to optical blurring and noise (Kong et al. 2013). However, this result disagreed with the recent experimental study on rat cardiomyocytes that displayed a considerably smaller apparent amplitude of SR Ca²⁺ during Ca²⁺ sparks (~0.19 ΔF/F₀) and transients (~0.26 ΔF/F₀) compared with caffeine-induced SR Ca²⁺ depletion (~0.67 ΔF/F₀) (Lu et al. 2020). Thus, determining the extent to which optical blurring and noise can affect Fluo-5N signals in the SR of rat cardiomyocytes calls for further investigation.

Our present model has several limitations. Previous experimental and modeling studies have revealed the importance of the dyad space between jSR and TTs. As a relatively closed space between jSR and open cytosol, dyad Ca²⁺ kinetics is highly distinct from them (Cannell et al. 2013; Shang et al. 2014). While most models of Ca²⁺ sparks could not reproduce experimental spatial characteristics, e.g., full width at half maximum (FWHM), modeling with detailed spatial geometry of dyad has solved the problem of FWHM (Cannell et al. 2013). Dyad Ca²⁺ concentration is also crucial for RyR2 gating, release flux, and the resultant jSR Ca²⁺ kinetics. For cytosolic modeling, our present model used a previous model without precisely describing the dyad compartment and RyR2 gating. During an SR Ca²⁺ release event, RyR2 channels open and close stochastically, and the diversity of the number and opening time of RyR2 produces SR Ca²⁺ releasing events with changed amplitude and mass (Brochet et al. 2011). In some cases, the random switch of RyR2 channels can lead to multiple releases of SR Ca²⁺, resulting in prolonged Ca²⁺ release events (Brochet et al. 2011). In the present study, we used a simple fixed open time but not a random switch mode for RyR2 channels. Therefore, while reproducing the average Ca²⁺ blink kinetics, our model is limited from further deciphering jSR and cytosolic Ca²⁺ movements.

The properties of cardiac sarcoplasmic reticulum (SR) Ca²⁺ have not yet been fully determined experimentally and theoretically in small rodents, such as rats and mice, which are the most commonly used experimental species in studies on cardiac physiology and diseases. In the present work, we have demonstrated a simple numerical model that provides an extremely useful investigative tool for understanding SR Ca²⁺ handling in rat cardiomyocytes, and our numerical model provides new insights into the understanding of Ca²⁺ dynamics in the SR of rat cardiomyocytes.

METHODS

Model geometry

The geometry of jSR cisternae in murine cardiomyocytes is morphologically and structurally similar to that of rabbits (Brochet et al. 2005, Rog-Zielinska et al. 2021). Thus, we simplified Ca²⁺ diffusion inside a flat pancake-shaped jSR with a diameter of 600 nm and an altitude 30 nm as 2D movements in a circle with four connecting fSR tubules of 30 nm diameter along its periphery (Fig. 1A). The Ca²⁺ release unit (CRU) in jSR is composed of a square RyR2 array with a size of 5 × 5 and an interval of 30 nm between adjacent channels (Fig. 1A).

Reaction/diffusion equations

When a few RyR2 channels in CRU suddenly open, considerable [Ca²⁺] gradients between both sides of the channels drive a rapid and substantial outflow of Ca²⁺ from jSR to the cytosol of cardiac myocytes, forming a local or global Ca²⁺ release event. Intra-jSR [Ca²⁺] is determined by the following fluxes: local diffusion that follows Fick’s law, binding of Ca²⁺ to buffers in jSR cisternae, efflux through RyR2 channels, and influx via connecting fSR tubules. To mimic experimental Ca²⁺ signals, a fluorescent dye (Fluo-5N) is also introduced into our model. It binds Ca²⁺ to form the fluorescence compound (CaF), indicating alterations in free [Ca²⁺]. Thus, the governing equations for jSR Ca²⁺ can be written as

1$$\text{Unknown environment 'document'}$$

2$$\text{Unknown environment 'document'}$$

where D_C and D_F denote the diffusion coefficients of Ca²⁺ and CaF with values of 350 µm²/s and 20 µm²/s, respectively (Smith et al. 1998).

The flux for calsequestrin (CSQ), the primary Ca²⁺ buffer in jSR, is given by

3$$\text{Unknown environment 'document'}$$

4$$\text{Unknown environment 'document'}$$

where [CaCSQ] represents the concentration of Ca²⁺ that binds to CSQ. The three constants, [CSQ]_T, $$\text{Unknown environment 'document'}$$, and $$\text{Unknown environment 'document'}$$, denote the total concentration of CSQ (14 mmol/L), and the association (100.0 (µnol/L)⁻¹·s⁻¹) and dissociation (60,000 s⁻¹) parameters in the reaction of CSQ and Ca²⁺, respectively (Li et al. 2017).

The fluxes for the indicator dye take the form of

5$$\text{Unknown environment 'document'}$$

where [F]_T, $$\text{Unknown environment 'document'}$$, and $$\text{Unknown environment 'document'}$$ represent the total concentration of the fluorescence dye Fluo-5N (0.1 mmol/L), and the association (48.8 (µmol/L)⁻¹·s⁻¹) and dissociation (19,520 s⁻¹) constants in the reaction of Fluo-5N and Ca²⁺, respectively (Li et al. 2017).

Ca²⁺ flux through the RyR2 array is proportional to channel permeability and the concentration gradient between both sides of the channel. Thus,

6$$\text{Unknown environment 'document'}$$

where i_RyR denotes the molar flux through a single open RyR2; Far is Faraday’s constant; V₀ denotes the volume elements around RyR2; $$\text{Unknown environment 'document'}$$ indicates the state of the ith RyR2 channel with 1 as open and 0 as close; and $$\text{Unknown environment 'document'}$$ represents the gradient of [Ca²⁺] at the two sides of this opening RyR2, for which [Ca²⁺] at the cytosolic side is calculated simultaneously using a previously reported numerical model (Smith et al. 1998). The calcium current through a single opening RyR2 is ~0.6 pA upon a 1 mmol/L gradient of [Ca²⁺] (Mejia-Alvarez et al. 1999), thus, i_RyR = 0.6 pA.

SERCA is located in fSR; hence, the refilling flux of jSR contributes mostly via influx by connecting fSR tubules. Therefore,

7$$\text{Unknown environment 'document'}$$

where $$\text{Unknown environment 'document'}$$ and $$\text{Unknown environment 'document'}$$ represent Ca²⁺ concentrations inside and near the ith connecting fSR tubule, respectively; and constant k_fSR = 10 µm²/s denotes molar flux through single connecting fSR tubules (Brochet et al. 2005).

Implementation of model

Our model is spatially detailed; that is, [Ca²⁺], [CaF], [CaCSQ], and all the fluxes are calculated with detailed spatial distribution. The jSR space is discretized into triangle grids through the Delaunay triangulation technique (Wu et al. 2009). Grid density is greater near fSR tubules and opening RyR2, where [Ca²⁺] gradient is larger. Equations 1–7 are numerically solved using the basic function method based on unstructured grids (Wu et al. 2009).

Initially, jSR space is under resting condition, and thus, intra-jSR [Ca²⁺] at every spatial grid node and [Ca²⁺]_fSR are 1.0 mmol/L, cytoplasmic [Ca²⁺] = 0.1 μmol/L, fluorescence compound [CaF] = 0.0714 μmol/L, and CSQ bound complex [CaCSQ] = 8.75 mmol/L.

The boundary of the computational domains is composed of the jSR circle and the circles of opening RyR2 channels. In accordance with Ca²⁺ movement at the boundary, it can be divided into three parts: the efflux boundary (RyR circle), influx boundary (sites of jSR that connect to fSR tubules), and wall boundary (jSR circle except influx boundaries).

In the influx and efflux boundaries, the fluxes J_ref and J_RyR should be calculated for the major control equation, i.e., Eq. 1, respectively. In the wall boundary, normal flux is prevented, i.e., $$\text{Unknown environment 'document'}$$, where n denotes the normal vector of the wall boundary.

The program was encoded in Python language.

Acknowledgements

This work was supported by grants from the National Natural Science Foundation of China (31971045).

RIGHTS & PERMISSIONS

2024 The Author(s)