HEK-293 cells (ATCC CRL-1573) were cultivated in Minimal Essential Medium (MEM) supplemented with 10% (v/v) foetal bovine serum (FBS). We generated the cell line HEK-D1ER that stably expresses the FRET-based D1ER sensor in the ER lumen (Gamayun et al., 2019). D1ER was kindly provided by R. Y. Tsien (University of California San Diego, La Jolla, United States). HEK-D1ER cells were maintained in culture under selection with G418 (0.5 mg/mL) in MEM supplemented with 10% (v/v) FBS. Cell culture was carried out at 37°C in a humidified environment with 5% CO₂.

Thapsigargin and ionomycin (TG, IONO; Thermo Fisher Scientific) were dissolved in DMSO to obtain 1 mM and 10 mM stocks, respectively. TG and IONO stock solutions were maintained at −20°C in the dark and dilutions were made directly in the recording solution just before experiments. TG and IONO were applied “online” to the cells while the Ca²⁺ imaging was running. In order to avoid problems arising from slow mixing, we added 2× solutions of these substances to the bath at a ratio of 1:1. Typically, the end concentration of TG and IONO were 1 and 10 μM, respectively. The final DMSO concentration in the recording chamber was maximally 0.1% (v/v). Puromycin dihydrochloride (PURO; Sigma-Aldrich) was dissolved in a Ca²⁺-containing solution to obtain 10 mM stock and dissolved further as required. Just before Ca²⁺ imaging experiments, cells were incubated for 10 min in a 2 mM Ca²⁺ solution (140 mM NaCl, 4 mM KCl, 1 mM MgCl₂, 2 mM CaCl₂, 10 mM glucose, 10 mM HEPES-KOH, pH 7.3) that contained various PURO concentrations.

FURA-2 AM (Thermo Fisher Scientific) was dissolved in DMSO to obtain a 1 mM stock solution. Cells were loaded with FURA-2 prior to imaging experiments by incubation with a 1 mM Ca²⁺ solution containing 4 µM FURA-2 AM for 20 min, washed and subsequently exposed to the recording solution.

The initial Ca²⁺ imaging experiments were performed in the presence of external Ca²⁺ with recording solutions containing 1 or 10 mM Ca²⁺ (140 mM NaCl, 4 mM KCl, 1 mM MgCl₂, 1 or 10 mM CaCl₂, 10 mM glucose, 10 mM HEPES-KOH, pH 7.3–7.4). Subsequently, a Ca²⁺-free recording solution (140 mM NaCl, 4 mM KCl, 1 mM MgCl₂, 0.5 mM EGTA, 10 mM glucose and 10 mM HEPES-KOH, pH 7.3–7.4) was used in most experiments to abolish the Ca²⁺ entry from the extracellular space. In Ca²⁺ re-addition experiments, TG was applied to cells bathed in a nominal Ca²⁺-free solution (140 mM NaCl, 4 mM KCl, 1 mM MgCl₂, 10 mM glucose and 10 mM HEPES-KOH, pH 7.3–7.4) and subsequently, Ca²⁺-containing solutions were added to obtain 1 and 10 mM free Ca²⁺ after dilution in the recording chamber. The nominal Ca²⁺-free solution was also used in Ca²⁺ clearance experiments, in which cells were first exposed to TG for 8 min in this solution. The Ca²⁺ imaging was then started and a Ca²⁺-containing solution was added to raise the Ca²⁺ concentration in the recording chamber to 0.5 mM free Ca²⁺. Subsequently, Ca²⁺ was chelated in the recording chamber by adding further a EGTA-containing solution to attain a final concentration of 2 mM EGTA after dilution in the recording chamber.

The cytosolic Ca²⁺ ([Ca²⁺]_cyt) was imaged with FURA-2 as previously described (Lang et al., 2011a; Pick et al., 2021). FURA-2 was excited at 340 and 380 nm alternately. The emitted fluorescence light was captured at 510 nm to obtain FURA-2 images at 340 and 380 nm excitation. FURA-2 image pairs containing 30–50 cells/frame were obtained every 3 s at a magnification of 20×. FURA-2 signals were quantified in FURA-2 image pairs as F₃₄₀/F₃₈₀, where F₃₄₀ and F₃₈₀ correspond to the background-subtracted fluorescence intensity at 340 and 380 nm excitation wavelengths, respectively. [Ca²⁺]_cyt was calculated with the standard ratiometric equation [Ca²⁺]_cyt = K_FURA-2 ⋅ (R - R_min)/(R_max - R), in which R = F₃₄₀/F₃₈₀ and K_FURA-2 represents the system specific apparent Ca²⁺ dissociation constant for FURA-2 (Grynkiewicz et al., 1985; Pick et al., 2021). FURA-2 signals are given as [Ca²⁺]_cyt.

As previously described, ER and cytosolic Ca²⁺ concentrations ([Ca²⁺]_ER, [Ca²⁺]_cyt) were imaged simultaneously using the FRET-based D1ER sensor and FURA-2, respectively (Gamayun et al., 2019). Firstly, HEK-D1ER cells that stably express D1ER in the ER lumen were exposed to 433 nm and the emitted fluorescence light was split at 469/23 nm and 536/27 nm to obtain the CFP and citrine components, respectively (Palmer et al., 2004). The cell fluorescence light was additionally passed through a dichrotome and projected on the chip of the microscope camera to obtain simultaneously CFP and citrine images. Secondly, FURA-2 was excited by alternated excitation at 340 and 380 nm. The emitted fluorescence light was also passed through the dichrotome and captured at 510 nm to obtain FURA-2 images at 340 and 380 nm excitation. D1ER and FURA-2 image pairs containing 5–10 cells/frame were obtained at 60× magnification every 10 s. The FRET ratios were calculated from background-subtracted CFP and citrine image pairs as F_Citrine/F_CFP, where F_Citrine and F_CFP represent the citrine and CFP fluorescence intensities, respectively. [Ca²⁺]_ER was calculated with the standard ratiometric equation [Ca²⁺]_ER = K_D1ER ⋅ (R - R_min)/(R_max - R), in which R = F_Citrine/F_CFP and K_D1ER represents the system specific apparent Ca²⁺ dissociation constant for D1ER (Palmer et al., 2004; Gamayun et al., 2019). FURA-2 signals were quantified in the FURA-2 image pairs as F₃₄₀/F₃₈₀, which was used to calculate [Ca²⁺]_cyt, as previously described (Gamayun et al., 2019; Pick et al., 2021).

For visualization of the plasma membrane and the ER, HEK-293 cells were incubated with Cell Mask Green Plasma Membrane Stain (Thermo Fisher) with a dilution of 1:2000 and 1 µM ER-Tracker Red (BODIPY TR Glibenclamide) (Thermo Fisher), respectively, for 20 min at 37°C in HBSS containing Mg²⁺ and Ca²⁺. Images were acquired on a Zeiss LSM 880 (Zeiss, Germany) with a 63× oil objective (NA 1.4, Plan Apochromat) and 488 nm, 543 nm excitation light using Zen (Zeiss, Germany) software. Z-stack images were acquired every 500 nm throughout the entire cell to determine the cell, ER and nucleus area and the total RFP fluorescence. Subsequently, images were analyzed and processed with ImageJ (version 1.53t). Before analyzing the images, the background was subtracted using the rolling ball plugin with a radius of 50 pixels. To measure the area of the ER, a threshold was set at 20 times the mean background intensity, so that the outlines of the cells were not visible, allowing the ER area to be quantified.

Single cell data has been obtained in independent Ca²⁺ imaging recordings with 3–12 coverslips per experimental setting. Because of technical reasons, we imaged only 10–15 cells per coverslip in experiments with D1ER and FURA-2, while 30–50 cells per coverslip were imaged with FURA-2 alone. The total number of analysed cells in each experimental setting is given in the figure legends. Data is given as mean ± SEM. Statistical significance (p-values) was calculated using the non-parametric two sample Kolmogorov-Smirnov test.

Figure 1 illustrates the ER morphology in HEK-293 cells that we analysed using LSM microscopy. The cell membrane was stained with a GFP-based marker (Figure 1A, a-h) and the ER was visualised with an RFP-based marker (Figure 1A, a‵-h‵). As expected, HEK-293 cells displayed the typical flat morphology of adherent cells. For the quantitative analysis of the z-stacks, we used the cell membrane and ER staining to delimit the areas occupied by the cell and ER, respectively, while nuclei areas were defined as the non-stained enclosures within ER structures. In this way, we quantified the areas occupied by the cell as well as the ER and nuclei areas (Figures 1B–D). This analysis was performed with a homogeneously stained cell population, as it was substantiated by measurements of RFP intensities that showed an evenly ER staining in HEK-293 cells (Figures 1E, F). All in all, it appears that ER areas are larger than those of the nuclei. Furthermore, our quantification of ER areas suggested the presence of a prominent ER in HEK-293 cells, as illustrated by the merged images, where ER staining covers a considerable portion of the cytoplasm throughout all z-planes in the stack (Figure 1A, a‶-h‶). So far, little quantitative information is available on mammalian cell dimensions, but it is generally believed that the ER lumen generally occupies more than 10% of the total cell volume (e.g., Alberts et al., 2002). Hence, our measurements of cross-section areas strongly suggested that the ER of HEK-293 cells may be larger than previously assumed, although an optimal correlation between volumes and cross-sections in z-stacks will require a 3D reconstruction of the images.

Based on the measurements of cell and ER areas (Figures 1B, C), we calculated the ratio of ER to cell area and found that ER structures occupied approx. 61% of the cell cross-sections in the z-stacks of HEK-293 cells (Figure 1G). Furthermore, we observed a linear correlation between ER and cell area with a slope of 0.53 (Figure 1H). Thus, the average ratio of ER to cell area and the slope of the correlation between ER and cell area indicate that the ER area fraction of HEK-293 cells is in the range of 0.53–0.61. To obtain a rough estimate of the ER volume fraction in HEK-293 cells, we used for simplicity the following equation: volume fraction = (area fraction) ^3/2 (Bakunts et al., 2017). Following this calculation, our results indicate that the ER likely occupies in the range of 38%–48% of the volume of HEK-293 cells, supporting the suggestion that HEK-293 cells possess a prominent ER.

The signalling of G-protein-coupled receptors to intracellular effector proteins comprises various pathways, which in many cases involve the mobilisation of intracellular Ca²⁺ (Dhyani et al., 2020). Experimentally, Ca²⁺ mobilisation has been induced with TG in multiple cell types (Zima et al., 2010; Erdmann et al., 2011; Ikeya et al., 2014; Ferdek et al., 2017; Merino-Wong et al., 2021). Hence, we first tested the effects of 1 μM TG in HEK-293 cells in the absence and presence of external Ca²⁺ (Figure 2A). Cytosolic Ca²⁺ was imaged with FURA-2. As in other cell lines, the basal [Ca²⁺]_cyt (b[Ca²⁺]_cyt) increased in HEK-293 cells depending on the external Ca²⁺ concentration ([Ca²⁺]_ext), but it generally remained below 100 nM (Table 1). Shortly after TG application, a surge of cytosolic Ca²⁺ was observed independently of the presence of external Ca²⁺, indicating that the increase of [Ca²⁺]_cyt requires the release of Ca²⁺ from intracellular stores into the cytosol. Since TG is selective for SERCA pumps, it is generally accepted that TG unmasks specifically the Ca²⁺ leak from ER. Hence, the TG-induced surge of cytosolic Ca²⁺ reflects mainly the ER Ca²⁺ leak in the absence of external Ca²⁺. When Ca²⁺ was present in the external solution, the cytosolic Ca²⁺ transients were much higher than those in external free Ca²⁺ solutions, indicating that Ca²⁺ ions flowing from the extracellular space also contribute to the surges in [Ca²⁺]_cyt observed after TG application. This Ca²⁺ influx corresponds to SOCE, because it is activated upon depletion of internal stores (Putney, 2017; Lewis, 2020).

Quantification of TG-induced Ca²⁺ transients in HEK-293 cells reveals a remarkable proportionality between the amplitude of the Ca²⁺ transients (Δ[Ca²⁺]_cyt) and [Ca²⁺]_ext (Table 1). For instance, the peak amplitude of the Ca²⁺ transients (pΔ[Ca²⁺]_cyt) increased by approx. 0.5 µM by increasing external Ca²⁺ from zero to 1 mM and, again by approx. 0.5 µM from 1 to 10 mM external Ca²⁺. The area under the curve (AUC) also followed the increases of [Ca²⁺]_ext (Table 1). However, a precise measure of the AUC is hampered by the long Ca²⁺ plateaus observed with 1 and 10 mM external Ca²⁺ (Figure 2A). Hence, our results suggest that the entry of external Ca²⁺ adds to the Ca²⁺ release from intracellular stores to build up the TG-induced Ca²⁺ mobilisation in HEK-293 cells (Figure 2A), similarly as described previously for other cell types (Fierro et al., 1998; Chen et al., 2003; Baggaley et al., 2008). Additionally, we regularly observed that the TG-induced transients in HEK-293 cells decayed to basal levels within 350–550 s in the absence of external Ca²⁺ (Figure 2A), indicating that the plasma membrane of HEK-293 cells has definitely the capacity to remove cytosolic Ca²⁺, as described for other cell types (see Putney, 2017). The observations made in the experiments shown in Figure 2A allowed us, therefore, to formulate the balance equation describing the changes in cytosolic Ca²⁺ (d[Ca²⁺]_cyt/dt) induced by TG in HEK-293 cells: d C a 2 + c y t / d t = J e n t r y + J l e a k − J c l e a r (1) where J_entry, J_leak and J_clear denote the Ca²⁺ influx from the external space (SOCE), the Ca²⁺ efflux from internal stores (ER Ca²⁺ leak) and the Ca²⁺ efflux from cytosol due to clearance mechanisms, respectively. A similar approach has been used to model the Ca²⁺ dynamics in various cell types (Bergling et al., 1998; Perez-Rosas et al., 2015; Han et al., 2017).

Ca²⁺ is stored in the ER, mitochondria, and Golgi apparatus, whereby the ER is believed to be the main Ca²⁺ storage organelle in mammalian cells (Wang et al., 2019). Using [Ca²⁺]_cyt imaging, we next estimated the total amount of releasable Ca²⁺ that is stored in HEK-293 cells (Figure 2B). For this purpose, we took advantage of ionomycin (IONO), a Ca²⁺ ionophore that releases Ca²⁺ unselectively from ER, mitochondria, and other cell compartments (Mckenzie and Duchen, 2016; Pick et al., 2021). These experiments were performed in the absence of external Ca²⁺ to prevent contamination by the entry of external Ca²⁺. As shown in Figures 2A, B and Table 1, IONO mobilised in general more Ca²⁺ than TG in the absence of external Ca²⁺. In average the IONO-induced Ca²⁺ transients were approx. 4 times higher than those observed after TG-application in Ca²⁺-free recording solution. The IONO-induced Ca²⁺ transients were also short and, therefore, the AUC values were slightly lower than those of TG-induced transients. In order to precise the contribution of ER and non-ER Ca²⁺ stores to the total content of releasable Ca²⁺ in HEK-293 cells, we modified our protocol and applied TG followed by IONO (Figure 2C). In this protocol, the first Ca²⁺ surge induced by TG largely reflects the release of Ca²⁺ from the ER, i.e., from ER Ca²⁺ stores. The second Ca²⁺ surge induced by IONO arises from the release of Ca²⁺ sequestered in the remaining stores, which we termed non-ER Ca²⁺ stores. It is believed that Ca²⁺ released from mitochondria dominates during this IONO-induced Ca²⁺ surge (Mckenzie and Duchen, 2016; Pick et al., 2021). Comparing the amplitude and AUC of the TG- and IONO-induced Ca²⁺ transient shown in Figure 2C, it appears that the amount of Ca²⁺ released from ER is twice the amount of releasable Ca²⁺ present in non-ER stores of HEK-293 cells (Table 1).

The comparison of the Ca²⁺ mobilisation induced by TG in the presence and absence of external Ca²⁺ revealed SOCE in HEK-293 cells (Figure 2A). In order to measure SOCE separately, we used the standard Ca²⁺ re-addition protocol, which consisted in emptying Ca²⁺ stores with TG in nominally Ca²⁺-free solutions and raise external Ca²⁺ immediately after full Ca²⁺ depletion (see Prakriya and Lewis, 2015). In our experiments, we assessed SOCE as the amplitude of the cytosolic Ca²⁺ surges observed after re-addition of 1 and 10 mM external Ca²⁺ (Figure 2D). Such SOCE-induced transients were proportional to [Ca²⁺]_ext (Table 1). Compared with the Ca²⁺ transients shown in Figure 2A, the SOCE-induced Ca²⁺ transients were much higher. Using the Ca²⁺ re-addition data, we calculated that SOCE produced an increase of 29.25 ± 0.86 nM⋅s⁻¹ and 51.42 ± 1.29 nM⋅s⁻¹ in [Ca²⁺]_cyt when HEK-293 cells were abruptly exposed to 1 and 10 mM external Ca²⁺, respectively. Similar measurements with 0.5–2.0 mM external Ca²⁺ in other cell lines have revealed much smaller SOCE-induced Ca²⁺ transients (Feske et al., 2005; Li et al., 2018; Merino-Wong et al., 2021; Pick et al., 2021; Martínez-Martínez et al., 2022). Thus, it appears that our HEK-293 cells express a prominent SOCE. However, such high SOCE expression may be clone-specific because a high clone-to-clone variability of SOCE expression has been reported for the HEK-293 cell line (Zagranichnaya et al., 2005).

As illustrated by the cytosolic Ca²⁺ transients shown in Figures 2A–D, Ca²⁺ clearance mechanisms must exist to limit surges in [Ca²⁺]_cyt and, therefore, almost all Ca²⁺ transients in HEK-293 cells tended to decay quickly toward basal [Ca²⁺]_cyt levels. To measure the capacity of the plasma membrane to remove cytosolic Ca²⁺, we used the standard Ca²⁺ clearance assay (see Baggaley et al., 2008). As shown in Figure 2E, we first added Ca²⁺ to the external solution and initiated SOCE to raise [Ca²⁺]_cyt in cells that were previously treated with TG. At the peak of the SOCE-induced Ca²⁺ surge, we next chelated external Ca²⁺ with EGTA and interrupted the Ca²⁺ entry. As a consequence, [Ca²⁺]_cyt decayed rapidly reflecting the clearance of cytosolic Ca²⁺ (Figure 2E). As shown in Figure 2F, the decay of [Ca²⁺]_cyt after chelation of external Ca²⁺ is linear in the semi-log plot, suggesting that it follows an exponential time course. Accordingly, we assume that the Ca²⁺ clearance follows a first order kinetics in HEK-293 cells, and it can be described by the equation d C a 2 + c y t / d t = − k c l e a r ∙ C a 2 + c y t   t (2) where k_clear represents the Ca²⁺ clearance rate. By integration of Eq. 2, we obtained the equation that describes the time course of [Ca²⁺]_cyt after unmasking the Ca²⁺ clearance. C a 2 + c y t t = C a 2 + c y t 0 ∙ exp − k c l e a r ∙ t (3)

[Ca²⁺]_cyt (0) corresponds to the Ca²⁺ concentration at the time point when SOCE was abruptly interrupted. In order to facilitate the interpretation of our data, we also calculated τ_clear, the time constant for Ca²⁺ clearance that is defined as the inverse of k_clear. Figure 2F illustrates the fitting of Eq. 3 to the data. The average values of k_clear and τ_clear are presented in Table 1. Using Eq. 2 and the mean value of k_clear as given in Table 1, it can be calculated that the decay in [Ca²⁺]_cyt due to the Ca²⁺ clearance is around 10–13 nM⋅s⁻¹ for mid values of [Ca²⁺]_cyt (0.35–0.45 µM). This Ca²⁺ clearance rate is much lower than described for other cell types (Chen et al., 2003; Baggaley et al., 2008; Pick et al., 2021) and may be characteristic for HEK-293 cells. Since we obtained our data in the presence of TG, we have no information on the Ca²⁺ clearance mediated by SERCA pumps. The parameters given in Table 1 most likely reflect the Ca²⁺ clearance via the plasma membrane of HEK-293 cells.

As in almost every cell type that has been tested (Thastrup et al., 1990; Treiman et al., 1998), TG-induced cytosolic Ca²⁺ transients in HEK-293 cells (Figure 2A). Specifically, the release of Ca²⁺ from the ER was sufficient to generate cytosolic Ca²⁺ transients because such transients were readily recorded in the absence of external Ca²⁺. In order to understand the mechanism behind this phenomenon, we recorded [Ca²⁺]_cyt and [Ca²⁺]_ER simultaneously using FURA-2 and the genetically encoded ER Ca²⁺ sensor D1ER, respectively (Figure 3). For this purpose, we used the HEK-D1ER cell line that was generated by stable transfection of HEK-293 cells with D1ER (Gamayun et al., 2019). All experiments shown in Figure 3 were performed in the absence of external Ca²⁺. Under these conditions, basal ER Ca²⁺ levels of HEK-D1ER cells (b[Ca²⁺]_ER) scattered between 300 and 500 µM with a mean of approx. 370 μM (Table 1), which is slightly lower than previous measurements of basal ER Ca²⁺ in various cell lines (Suzuki et al., 2014). The b[Ca²⁺]_cyt of HEK-D1ER cells was within the range observed in HEK-293 cells. As expected, TG induced the typical surge in [Ca²⁺]_cyt in HEK-D1ER cells (Figure 3A). Although the simultaneous imaging of ER and cytosolic Ca²⁺ was performed in the absence of external Ca²⁺, the pΔ[Ca²⁺]_cyt was 0.91 ± 0.05 µM in the experiments with HEK-D1ER cells shown in Figure 3A. Generally, the pΔ[Ca²⁺]_cyt of HEK-D1ER cells scattered between 0.7 and 1.0 µM and, therefore, it was much higher than in the native HEK-293 cells (Table 1). We presume that this difference is associated with the inevitable cell cloning that we performed when the HEK-D1ER cell line was established.

In parallel to the cytosolic Ca²⁺ surge, we observed a decay in [Ca²⁺]_ER after TG application (Figure 3B), as previously reported for various cell types (Palmer et al., 2004; Zima et al., 2010; Suzuki et al., 2014; Bovo et al., 2017; Leon-Aparicio et al., 2017; Gamayun et al., 2019; Bhadra et al., 2021). When the time courses of [Ca²⁺]_cyt and [Ca²⁺]_ER were compared, it became clear that the cytosolic Ca²⁺ surge reached a peak before substantial ER Ca²⁺ depletion was detectable (Figure 3C). This apparent absence of correlation between [Ca²⁺]_cyt and [Ca²⁺]_ER has been previously reported (Leon-Aparicio et al., 2017; Gamayun et al., 2019). To understand the impact of ER Ca²⁺ release on [Ca²⁺]_cyt, we next compared the first time-derivatives of [Ca²⁺]_cyt and [Ca²⁺]_ER, whereby the first time-derivative of [Ca²⁺]_ER was expressed in terms of -d[Ca²⁺]_ER/dt for simplicity. As shown in Figure 3D, the first observation we made was that d[Ca²⁺]_cyt/dt increased and decreased rapidly while -d[Ca²⁺]_ER/dt still was in the rising phase. Approx. 90 s after application of TG, d[Ca²⁺]_cyt/dt became zero. During this 90 s time period, [Ca²⁺]_ER declined from an average b[Ca²⁺]_ER of 370 µM to approx. 348 μM, corresponding to about 6% Ca²⁺ depletion in the ER. Accordingly, a steep increase of [Ca²⁺]_cyt was detected at [Ca²⁺]_ER above 348 µM in correlation plots of [Ca²⁺]_cyt vs. [Ca²⁺]_ER (Figure 3E). Furthermore, plots of [Ca²⁺]_cyt as a function of -d[Ca²⁺]_ER/dt showed that the upstroke of the cytosolic Ca²⁺ surges took place before -d[Ca²⁺]_ER/dt reached its maximal value (Figure 3F). Thus, our results suggest that a 6% ER Ca²⁺ depletion is sufficient to generate the upstroke of cytosolic Ca²⁺ surges that generally reached peak values of 0.6–1.0 µM in native HEK-293 as well as in HEK-D1ER cells. A second important observation in the analysis of first time-derivatives was that the maximum of -d[Ca²⁺]_ER/dt almost coincided with the minimum of d[Ca²⁺]_cyt/dt (Figure 3D). After this time point, d[Ca²⁺]_cyt/dt followed a time course that mirrored that of -d[Ca²⁺]_ER/dt. Thus, the time point at which -d[Ca²⁺]_ER/dt reached the maximum represents an inflection point, which divides the TG-induced Ca²⁺ mobilisation in two phases. The cytosolic Ca²⁺ surge was built up in the early phase while the late phase was characterized by the decay of the Ca²⁺ surge. The corresponding average values of [Ca²⁺]_ER and [Ca²⁺]_cyt at this inflection point were 311 µM and 0.92 µM, respectively. When we analysed the relationship of -d[Ca²⁺]_ER/dt to [Ca²⁺]_ER (Figure 3G), we observed that there was a sharp increase of -d[Ca²⁺]_ER/dt at ER Ca²⁺ levels above 311 μM, corresponding to the early phase of the TG-induced Ca²⁺ mobilisation. We hypothesise that this early phase reflected the cumulating TG-inhibition of SERCA pumps that reached maximum at the maximum of -d[Ca²⁺]_ER/dt. Hence, the decaying phase of -d[Ca²⁺]_ER/dt shown in Figures 3D, G developed under a fully unmasked Ca²⁺ leak from ER. Since it has been suggested that changes in the SR Ca²⁺ concentration may not necessarily correspond to the amount of released Ca²⁺ (Perez-Rosas et al., 2015), however, we cautiously treated the process underlying the late phase of TG-induced Ca²⁺ mobilisation simply as ER Ca²⁺ depletion. In this late phase, there was a linear relationship between -d[Ca²⁺]_ER/dt and [Ca²⁺]_ER (Figure 3G), suggesting that the ER Ca²⁺ depletion followed a first order kinetic, which is expressed as d C a 2 + E R / d t = − k d e p l ∙ C a 2 + E R   t (4) where k_depl represents the Ca²⁺ depletion rate. A fit of Eq. 4 to the data revealed k_depl values around a mean of 6.12 e−3 s⁻¹ for HEK-D1ER cells (Figure 3G; Table 1). By integration of Eq. 4, we generated the equation describing the time course of [Ca²⁺]_ER in the late phase of the TG-induced Ca²⁺ mobilisation. C a 2 + E R t = b C a 2 + E R ∙ exp − k d e p l ∙ t (5) where b[Ca²⁺]_ER represents the basal [Ca²⁺]_ER. As shown in Figure 2H, Eq. 5 nicely fits the time course [Ca²⁺]_ER in the late phase, i.e., after the inflection point of Ca²⁺ mobilisation. To allow comparison to published data, we calculated the time constant of Ca²⁺ depletion (τ_depl) that is defined as the inverse of k_depl (Table 1). Although τ_depl is frequently used in models of Ca²⁺ dynamics as a correlate of the Ca²⁺ leak from ER (Bergling et al., 1998; Means et al., 2006), few reports provide quantitative data. Our τ_depl estimate of approx. 165 s for HEK-D1ER cells fits within the published data on ER Ca²⁺ depletion in various cell lines (Lomax et al., 2002; Gamayun et al., 2019; Bhadra et al., 2021).

Several studies have analysed the action of pharmacological active substances on the ER Ca²⁺ leak mediated by Sec61 translocons mostly by measuring the effects of these substances on TG-induced cytosolic Ca²⁺ transients (see Parys and van Coppenolle, 2022). Seminal work with tunicamycin, dithiothreitol (DTT), trifluoperazine and ophiobolin A has shown that these substances enhance TG-induced cytosolic Ca²⁺ transients by increasing specifically the Ca²⁺ leak through Sec61 translocons (Erdmann et al., 2011; Schäuble et al., 2012). In line with this body of evidence, emetine, cycloheximide and anisomycin, which stabilize Sec61 translocons in a closed state (e.g., Al-Mawla et al., 2020), reduced the amplitude of TG-induced cytosolic Ca²⁺ transients (van Coppenolle et al., 2004; Hammadi et al., 2013; Klein et al., 2018; Pick et al., 2021). However, PURO, which favours the open, Ca²⁺-permeable state of Sec61 translocons, surprisingly reduced the amplitude of TG-induced cytosolic Ca²⁺ transients (van Coppenolle et al., 2004; Lang et al., 2011b). Likely, the increase in ER Ca²⁺ leak leads inevitably to ER Ca²⁺ depletion, which in turn attenuates cytosolic Ca²⁺ transients. This concept has been tested with eeyarestatins and trifluoperazine, which favour the open, Ca²⁺-permeable state of Sec61 translocons (Gamayun et al., 2019; Bhadra et al., 2021). In the case of eeyarestatins, an increase of the concentration switched the effects on TG-induced cytosolic Ca²⁺ transients from amplification to attenuation (Gamayun et al., 2019). A similar switch was produced by prolonging the exposure time to trifluoperazine (Bhadra et al., 2021). Based on these observations, we hypothesised that the amplification-to-attenuation switch induced by Sec61 modulators on TG-induced cytosolic Ca²⁺ transients is both time and concentration dependent. In order to test this hypothesis for PURO, we next exposed HEK-D1ER cells to 500 μM and 1000 µM PURO and analysed the effects on Ca²⁺ mobilisation using our simultaneously image system for [Ca²⁺]_cyt and [Ca²⁺]_ER (Figure 4). Unlike previous reports (e.g., Lang et al., 2011b), HEK-D1ER cells were exposed to PURO for 10 min in a bath solution containing 2 mM Ca²⁺ before Ca²⁺ imaging in zero external Ca²⁺ solutions. In our hands, the presence of Ca²⁺ in the external solution protects against a fast ER Ca²⁺ loss. In these experiments, the most obvious effect was an increase in the amplitude of the cytosolic TG-induced Ca²⁺ transients to 110–135% in cells treated with 500 µM PURO, while Ca²⁺ transients were dramatically reduced to 15–38% after exposure to 1000 µM PURO, when compared to controls (Figure 4A). Additionally, it is remarkable that the Ca²⁺ transients in cells exposed to PURO were shorter than in control cells. PURO also decreased ER Ca²⁺ levels and accelerated the ER Ca²⁺ depletion in HEK-D1ER cells (Figure 4B). In cells exposed to 500 µM PURO, there was a mild decrease of b[Ca²⁺]_ER to 80–91% compared to controls probably because PURO exposures were performed in the presence of external Ca²⁺. However, b[Ca²⁺]_ER decreased dramatically to 37–45% in cells exposed to 1000 µM PURO. Thus, the simultaneous imaging of [Ca²⁺]_cyt and [Ca²⁺]_ER in HEK-D1ER cells showed that PURO enhances TG-induced cytosolic Ca²⁺ transients as long as ER Ca²⁺ levels are not strongly compromised. When ER Ca²⁺ levels are low, the cytosolic Ca²⁺ transients became understandably smaller. On this basis, we assume that previously reported low amplitudes of the cytosolic Ca²⁺ transients reflect a considerable loss of ER Ca²⁺ induced by PURO most likely due to the absence of external Ca²⁺ during the PURO exposure (e.g., Lang et al., 2011b; Al-Mawla et al., 2020).

As shown in the plot of [Ca²⁺]_cyt vs. [Ca²⁺]_ER (Figures 4C, F), the increase of cytosolic Ca²⁺ at basal ER Ca²⁺ levels was particularly steep, indicating that the Ca²⁺ efflux from ER was enhanced by the treatment with 500 µM PURO. Large Ca²⁺ effluxes were not expected after treatment with 1000 µM PURO because basal ER Ca²⁺ levels were reduced under these conditions. Hence, the changes induced by TG in [Ca²⁺]_cyt were relatively small at this high PURO concentration (Figure 4I). When we calculated k_depl in plots of -d[Ca²⁺]_ER/dt vs. [Ca²⁺]_ER (Figures 4D, G, J), the linear phases were generally much steeper in PURO-treated HEK-D1ER cells. Accordingly, k_depl increased from 6.51 e−3 ± 0.43 e−3 s⁻¹ in control cells to 9.89 e−3 ± 0.75 e−3 s⁻¹ and 22.46 e−3 ± 1.25 e−3 s⁻¹ in HEK-D1ER cells treated with 500 and 1000 µM PURO, respectively (p < 0.01; number of cells: 8–16). This changes in the k_leak translated into faster ER Ca²⁺ depletion in PURO-treated cells compared to controls (Figures 4E, H, K). The time constant τ_depl decreased from 157.21 ± 4.34 s in control cells to 92.62 ± 7.85 s and 41.36 ± 6.27 s in HEK-293 cells treated with 500 and 1000 µM PURO, respectively (p < 0.01; number of cells: 8–16). Thus, PURO likely enhanced the ER Ca²⁺ leak from ER, which produced a decrease of ER Ca²⁺ levels already during the exposure and then accelerated the Ca²⁺ depletion in ER when the Ca²⁺ leak was unmasked with TG. As a consequence, the effects on cytosolic TG-induced Ca²⁺ transients were sharply dependent on the PURO concentration. At the low PURO concentration of 500 μM, we observed an increase of the amplitude of the cytosolic Ca²⁺ transients, when the increase in k_depl was moderate. At the concentration of 1000 µM PURO, the loss of ER Ca²⁺ dominated and the cytosolic TG-induced Ca²⁺ transients became smaller than in control cells.

Most studies of the Ca²⁺ leak from ER have been performed in the absence of external Ca²⁺ to avoid SOCE (see Lomax et al., 2002; Lang et al., 2017; Parys and van Coppenolle, 2022). In this approach, the Ca²⁺ leak from ER is the only Ca²⁺ source underlying changes in [Ca²⁺]_cyt. Hence, J_entry has not been included in further analysis and we simplified Eq. 1 to obtain the following balance equation that describes the time course of cytosolic Ca²⁺ transients under blockade of SERCA pumps with TG in the absence of external Ca²⁺: d C a 2 + c y t / d t = J l e a k − J c l e a r (6)

This equation implies that J_leak and J_clear are the only Ca²⁺ fluxes involved in the generation of cytosolic Ca²⁺ transients. Accordingly, the cytosol is the central compartment in our model of the Ca²⁺ dynamics of HEK-293 cells and is flanked by the ER and the extracellular space, whereby the ER functions as Ca²⁺ source and the extracellular space behaves as a Ca²⁺ sink because EGTA was present in the external solution (Figure 5). Therefore, no changes in [Ca²⁺]_ext are expected during Ca²⁺ mobilisation.

Since the upstroke of the TG-induced cytosolic Ca²⁺ transients occurred with a marginal decrease of ER Ca²⁺ (Figures 3C–E), we assume that k_depl does not reflect the ER Ca²⁺ leak that generates cytosolic Ca²⁺ transients. Instead, we describe the ER Ca²⁺ leak as follows: J l e a k = − d C a 2 + l E R / d t (7) where [Ca²⁺]_lER represents the ER Ca²⁺ concentration that drives the Ca²⁺ leak and may correspond to a luminal Ca²⁺ concentration close to the ER membrane. Assuming a first order kinetics, the changes in [Ca²⁺]_lER can be then describes as: d C a 2 + l E R / d t = − k l e a k ∙ C a 2 + l E R   t (8) k_leak is the ER Ca²⁺ leak rate. By integrating Eq. 8, we obtained the following expression for the time course of [Ca²⁺]_lER: C a 2 + l E R t = b C a 2 + l E R ∙ exp − k l e a k ∙ t (9) and combining Eqs 7–9, the expression describing the ER Ca²⁺ leak can be written as: J l e a k = b C a 2 + l E R ∙ k l e a k ∙ exp − k l e a k ∙ t (10)

Following a similar rationale, we defined the clearance of cytosolic Ca²⁺ as: J c l e a r = − d C a 2 + c y t / d t (11) and using Eq. 2, the expression describing the Ca²⁺ clearance flux can be written as: J c l e a r = k c l e a r ∙ C a 2 + c y t   t (12)

In order to derive an expression that describes TG-induced cytosolic Ca²⁺ transients, we first substituted J_leak (Eq. 10) and J_clear (Eq. 12) in Eq. 6 and the balance equation became: d C a 2 + c y t / d t = b C a 2 + l E R ∙ k l e a k ∙ exp − k l e a k ∙ t − k c l e a r ∙ C a 2 + c y t   t (13)

Next, the following expression that models cytosolic Ca²⁺ transients was generated by integration of Eq. 13: C a 2 + c y t t = b C a 2 + l E R ∙ k l e a k / k c l e a r − k l e a k ∙ exp − k l e a k ∙ t − exp − k c l e a r ∙ t (14)

However, this equation predicts a zero value for b[Ca²⁺]_cyt. Therefore, we expressed Eq. 14 in terms of Δ[Ca²⁺]_cyt (t) that we calculated by subtracting b[Ca²⁺]_cyt from [Ca²⁺]_cyt (t). Accordingly, the general equation that models TG-induced cytosolic Ca²⁺ transients in the absence of external Ca²⁺ is: ∆ C a 2 + c y t t = b C a 2 + l E R ∙ k l e a k / k c l e a r − k l e a k ∙ exp − k l e a k ∙ t − exp − k c l e a r ∙ t (15)

This expression is the so-called “Bateman equation” that has been extensively used to model drug concentrations in blood plasma (Garrett, 1994; Macheras and Chryssafidis, 2020).

The Bateman formalism assumes a one-compartment model, in which the ER Ca²⁺ leak and the clearance of cytosolic Ca²⁺ follow first-order kinetics (Eqs 2, 8). As a proof-of-principle, we applied the Bateman equation (Eq. 15) to reconstruct the TG-induced cytosolic Ca²⁺ transients measured in the PURO experiments (Figure 4). In these simulations, we assumed the same k_clear of 28.34 e−3 s⁻¹ for all experimental conditions and the k_leak values were obtained by fitting Eq. 15 to the data (Figures 6A, C, E). As expected for an increase of ER Ca²⁺ leak, k_leak increased from 14.55 e−3 s⁻¹ in control cells to 21.03 e−3 s⁻¹ and 30.07 e−3 s⁻¹ in cells exposed to 500 μM and 1000 µM PURO, respectively. Similar control k_leak values were obtained by fitting Eq. 15 to TG-induced Ca²⁺ transients of HEK-293 cells (Table 1). Interestingly, these k_leak values are approx. two times higher than those obtained for k_depl (Figures 4D, G, J). For comparison, we constructed Ca²⁺ transients with k_depl values and found that they were 50–100 s longer than the experimental counterparts (not shown). Thus, the cytosolic Ca²⁺ transients of HEK-D1ER cells reflected k_leak rather than k_depl. On the other hand, the b[Ca²⁺]_lER values required to model the Ca²⁺ transients seem to mirror the PURO-induced changes in b[Ca²⁺]_ER (Figure 4B). The b[Ca²⁺]_lER values needed to fit cytosolic Ca²⁺ transients of control cells and of those treated with 500 µM PURO were very similar (2.38 µM vs. 2.40 µM, respectively), reflecting the minor loss of ER Ca²⁺ during the PURO treatment. The considerable loss of ER Ca²⁺ in cells treated with 1000 µM PURO (Figure 4B) was reflected in an b[Ca²⁺]_lER value that corresponded to approx. 25% of control (0.62 µM vs. 2.40 µM, respectively).

In general, it is expected that the shortest rate constant of the Bateman equation determines the decay of Ca²⁺ transients after its inflection point (see Garrett, 1994). Since k_leak < k_clear under control conditions (14.55 e−3 s⁻¹ vs. 28.34 e−3 s⁻¹), the term [exp (-k_leak ⋅ t) - exp (-k_clear ⋅ t)] of the Eq. 15 converges towards exp (-k_leak ⋅ t) in the tail of the Ca²⁺ transient, as shown in the breakdown of the Bateman equation (Figure 6B). A similar situation was found for the curves fitting the Ca²⁺ transient in the presence of 500 µM PURO (Figure 6D). In cells treated with 1000 µM PURO (Figure 6F), however, k_leak became slightly higher than k_clear (30.07 e−3 s⁻¹ vs. 28.34 e−3 s⁻¹). Therefore, it can be hardly distinguished whether the term [exp (-k_leak ⋅ t) - exp (-k_clear ⋅ t)] converge towards exp (-k_leak ⋅ t) or exp (-k_clear ⋅ t) in the tail of the Ca²⁺ transients (Figure 6F). Non-etheless, in general, the Bateman equation predicts that the decay of Ca²⁺ transient is dominated by k_clear if the relation of the constants reverses from k_leak < k_clear to k_leak > k_clear in the so-called flip-flop case (see Garrett, 1994). Thus, the decay of the TG-induced Ca²⁺ transients became faster in PURO-treated cells because k_leak increased compared to controls (Figures 6B, D, F) and consequently, the Ca²⁺ transients were shorter in PURO-treated cells (Figure 4A).

The peak amplitude of the Ca²⁺ transients increased by the treatment with 500 µM and decreased in the presence of 1000 µM PURO (Figure 4A), while the term [(k_leak/(k_clear - k_leak)) ⋅ (exp (-k_leak ⋅ t) - exp (-k_clear ⋅ t))] increased with the PURO treatment (Figures 6B, D, F). The latter is explained by the dependence of the term [k_leak/(k_clear - k_leak)] on k_leak. Since [k_leak/(k_clear - k_leak)] is not determined when k_leak = k_clear, the absolute value of [k_leak/(k_clear - k_leak)] increases asymptotically around k_leak = k_clear, as shown in Figure 6G for k_clear = 28.34 e−3 s⁻¹. Accordingly, the term [(k_leak/(k_clear - k_leak)) · (exp (-k_leak ⋅ t) - exp (-k_clear ⋅ t))] increases monotonically with k_leak, although the term [exp (-k_leak ⋅ t) - exp (-k_clear ⋅ t)] decreases (Figure 6H). Hence, the amplitudes of the TG-induced Ca²⁺ transients increase theoretically when the ER Ca²⁺ leak is enhanced. Experimentally, however, this prediction holds as long as the ER Ca²⁺ content remains constant during the treatment with Ca²⁺ leak enhancers. Yet, the increasing Ca²⁺ leak begins to deplete the ER already during the period of incubation with enhancers of Ca²⁺ leak (Van Coppenolle et al., 2004; Gamayun et al., 2019; Al-Mawla et al., 2020). When TG is then applied, the depleted ER generates Ca²⁺ transients with smaller amplitudes than those arising from a full ER. As shown in Figures 4A, B, this was the case in cells treated with 1000 µM PURO and b[Ca²⁺]_lER rather than [k_leak/(k_clear - k_leak)] determined the amplitude of the cytosolic Ca²⁺ transients in these cells. Conversely, the mild loss of ER Ca²⁺ in cells treated with 500 µM PURO was apparently compensated by the increase in k_leak and the term [k_leak/(k_clear - k_leak)] dominated over b[Ca²⁺]_lER in setting the amplitude of the cytosolic Ca²⁺ transients. Thus, the magnitude of ER Ca²⁺ loss produced by Ca²⁺ leak enhancers dictates whether b[Ca²⁺]_lER or [k_leak/(k_clear - k_leak)] determines the amplitude of TG-induced cytosolic Ca²⁺ transients.

As shown in Figure 6, increases in the ER Ca²⁺ leak can amplify or attenuate the TG-induced cytosolic Ca²⁺ transients. The reason for this switch from amplification to attenuation of cytosolic Ca²⁺ transients is that the Ca²⁺ leak induces a loss of ER Ca²⁺, which in turns reduces the amplitude of the cytosolic Ca²⁺ transients. To illustrate the general principle of this phenomenon, we modelled TG-induced cytosolic Ca²⁺ transients using Eq. 15 with increasing k_leak values between 8 e−3 and 35 e−3 s⁻¹ (Figures 7A–C). The clearance of cytosolic Ca²⁺ was assumed to be constant with a k_clear value of 28 e−3 s⁻¹. ER Ca²⁺ levels were either maintained constant (Figure 7A) or an ER Ca²⁺ loss was modelled by reducing b[Ca²⁺]_lER values from 100% to 15% (Figure 7B). As it can be predicted from Figure 6H, the amplitude of the calculated cytosolic Ca²⁺ transients increased monotonically, i.e., there was a continuous amplification of the cytosolic Ca²⁺ transients when the ER Ca²⁺ levels were maintained constant (Figure 7A). However, it is more likely that the ER Ca²⁺ levels decrease as an inevitable consequence of the increasing Ca²⁺ leak, for instance, when the ER Ca²⁺ leak exceeds the pumping capacity of SERCA. The result of a decrease in ER Ca²⁺ levels on the top of an increasing ER Ca²⁺ leak is shown in Figure 7B. The calculated cytosolic Ca²⁺ transients were amplified by the initial increase of k_leak as long as ER Ca²⁺ levels were not compromised. Further increase of k_leak to high levels accompanied by strong ER Ca²⁺ loss attenuated the calculated cytosolic Ca²⁺ transients. This switch from amplification to attenuation correlated with changes in the shape of cytosolic Ca²⁺ transients. As illustrated by the normalised Ca²⁺ transients in Figure 7C, the calculated Ca²⁺ transients became shorter, and the rising phase became faster as k_leak progressively increased. ER Ca²⁺ levels had no effects on the shape of the Ca²⁺ transients that was determined only by k_leak. Finally, we compared these calculated Ca²⁺ transients with the TG-induced cytosolic Ca²⁺ transients obtained in HEK-D1ER cells exposed to PURO (same experiments as in Figure 4). As illustrated in Figure 7B, the cytosolic Ca²⁺ transients of cells exposed to 500 µM PURO fit perfectly within the range of amplified Ca²⁺ transients, while those obtained after exposure to 1000 µM PURO correspond to attenuated Ca²⁺ transients. Compared to controls, the duration and rising phase of TG-induced cytosolic Ca²⁺ transients were shorter and faster, respectively, in HEK-D1ER cells exposed to PURO (Figure 7D). Thus, the experiments with HEK-D1ER cells exposed to PURO recapitulate the switch from amplification to attenuation of TG-induced cytosolic Ca²⁺ transients that results when the ER Ca²⁺ leak increases and ER Ca²⁺ levels decrease, as observed when Sec61 modulators enhance the ER Ca²⁺ leak through Sec61 translocons (Gamayun et al., 2019; Bhadra et al., 2021).

All in all, we described the cytosolic Ca²⁺ transients of HEK-293 cells using a simple one-compartment model, in which the ER Ca²⁺ leak and the cytosolic Ca²⁺ clearance followed first-order kinetics. Furthermore, we derived a Bateman equation that accounted for changes in the time course and amplitude of cytosolic Ca²⁺ transients that resulted when the ER Ca²⁺ leak was increased by PURO. In this model, the best indicators for an enhanced ER Ca²⁺ leak were the rise in amplitude accompanied by shortening of the duration of cytosolic Ca²⁺ transients, as long as the ER Ca²⁺ content was not compromised by the enhanced Ca²⁺ leak. In the case that the ER Ca²⁺ content was reduced by a strong Ca²⁺ leak, reduction of amplitude as well as shortening of cytosolic Ca²⁺ transients were the best indicators for an enhanced ER Ca²⁺ leak.