Ca²⁺-Mobility in the Sarcoplasmic Reticulum of Ventricular Myocytes Is Low

Solutions

Normal Tyrode (NT) contained 130 mM NaCl, 4.5 mM KCl, 20 mM Hepes, 2 mM CaCl₂, 1 mM MgCl₂, 11 mM glucose. 0Na0Ca Tyrode contained 120 mM N-methyl-D-glucamine (NMDG), 4.5 mM KCl, 20 mM Hepes, 1 mM MgCl₂, 0.5 mM EGTA, 11 mM glucose. 0Na10Ca Tyrode was as for 0Na0Ca, but with 10 mM CaCl₂ and 110 mM NMDG and no EGTA. Solution pH was adjusted to 7.4 with 5 M HCl (0Na0Ca/0Na10Ca) or 4 M NaOH (NT). Cyclopiazonic acid (CPA), caffeine, and tetracaine (Tet) were obtained from Sigma (Dorset, UK).

Cell preparation

Rat and guinea pig ventricular myocytes were isolated by a combination of enzymatic (Roche Blendzyme III for rat (Roche, Basle, Switzerland); Sigma collagenase for guinea pig) and mechanical dispersion (16,17). Cells in Dulbecco's modified Eagle's medium were loaded (10 min) with the AM-ester of Fluo-3 (stock in DMSO; final concentration 10 μM) or, in one experimental series, carboxy-SNARF-1 (10 μM). Cells were superfused at 37°C in a chamber mounted on a DM-IRBE microscope (Leica, Wetzlar, Germany). Cell adhesion was improved by pretreating the chamber with poly-L-lysine (0.01%). Pacing (to load SR) was achieved by field stimulation through two platinum wires in the chamber.

Confocal imaging and analysis

Cells were imaged confocally (Leica TCS-NT). Fluo-3 was excited (488 nm argon laser), and fluorescence emission (>515 nm) was collected by a photomultiplier tube (for dye calibration, see Fig. S1 in Supplementary Material, Data S1). Images in xyt-mode were acquired at 256 × 256 pixels every 1.1 s. Line scans along the long axis of a myocyte were acquired at 256 pixels every 2.5 ms. In-house ImageJ (National Institutes of Health, Bethesda, MD) macros were used for background-subtraction and myocyte-edge detection. Fluorescence was averaged in regions of interest (ROIs) and then normalized to diastolic fluorescence (F₀). Data are presented as mean ± SE.

Protocol for Ca²⁺-loading and stabilizing SR

Before experiments, myocytes were initially paced electrically (2 Hz) for up to 2 min to load the SR with Ca²⁺. Sarcolemmal Ca²⁺-flux (through L-type channels and Na⁺/Ca²⁺ exchange) was then eliminated by halting stimulation and superfusing myocytes with Na⁺-free Ca²⁺-free solution (0Na0Ca) (9,18,19). This did not alter resting [Ca²⁺]_i, but it initially triggered Ca²⁺-waves (Fig. 1 A). These suggested fluctuations in [Ca²⁺]_SR, which would complicate our analysis. We therefore blocked SERCA by including 10 μM CPA in 0Na0Ca (“stabilizing solution”, SS), and we attenuated SR Ca²⁺-leak (which blocked the occurrence of Ca²⁺-waves) with 0.3 mM or 2 mM Tet. In the presence of SS + Tet, steady-state F/F₀ decreased by 25%, within 2 min, following a similar time course in both doses of Tet (Fig. 1 B). This fall in fluorescence was not due to quenching of Fluo-3 fluorescence by Tet or CPA, as it was absent in cells AM-loaded with 100 μM BAPTA, an intracellular Ca²⁺-buffer that clamps [Ca²⁺]_i (Fig. 1 C). Cells stabilized in SS + Tet were used for the main experimental work. Once experiments performed in SS were completed, cells were superfused in NT again. This was used to correct for dye leakage by fixing F/F₀ at 1.0 in NT at steady state ([Ca²⁺]_i = 100 nM).

Measuring total SR Ca²⁺-content

Total SR Ca²⁺ ([Ca²⁺]_SRT; free + buffered) was estimated by superfusing Tet-free SS containing 10 mM caffeine (to activate maximally RyR channel opening) (20) and then measuring the peak rise of [Ca²⁺]_i (with Fluo-3; Fig. 2 A). Superfusion details are given in the next section. Although the fluorescence rise was transient, further caffeine challenges induced no additional Ca²⁺-release (even after six consecutive caffeine episodes), confirming that the caffeine-sensitive store had been discharged completely and that SERCAs were fully inhibited by CPA. The recovery of [Ca²⁺]_i observed in caffeine (Fig. 2 A) is most likely caused by Ca²⁺-extrusion from the cell on PMCA (plasmalemmal Ca²⁺-ATPase) (19), as recovery was reversibly inhibited by raising superfusate [Ca²⁺] to 10 mM (Fig. 2 B), a maneuver known to inhibit the pump (19,21).

Some experiments required estimating [Ca²⁺]_SRT with a caffeine challenge immediately after a period of Tet superfusion. This was possible, as the inhibitory effects of Tet on RyR channels and the SR Ca²⁺ leak are fast (<3 s) and reversible (22,23). This was confirmed in this work from measurements of in the absence of CPA, showing that resting F/F₀ reversibly decreased by 19.5% ± 1.7% with a half-time of 2.7 ± 0.3 s on 0.3 mM Tet application and removal (n = 5; data not illustrated), consistent with rapid and reversible attenuation of SR Ca²⁺ leak. A slow Tet washout might be expected to reduce subsequent RyR activation by caffeine, and thus the mobilization of SR Ca²⁺. It is notable, therefore, that pretreating cells with 0.3 mM or 2 mM Tet for 2 min did not attenuate the caffeine-induced rise of (measured in Tet-free SS), again consistent with rapid Tet washout. After 2 min pretreatment with SS + 0.3 mM Tet, the caffeine-evoked peak F/F₀ was 5.0 ± 0.4 (fluorescence-rise normalized to resting fluorescence in NT solution; n = 8); after 2 min pretreatment with SS + 2 mM Tet, F/F₀ = 5.6 ± 0.2 (n = 7); after 2 min pretreatment with SS + zero Tet, F/F₀ = 4.9 ± 0.7 (n = 6).

Localizing the caffeine exposure

Rapid caffeine exposure was performed using a dual-microperfusion apparatus (16,17,24,25), which can switch between solutions in <1 s. The device releases two microstreams from a double-barreled square-bore pipette, maintaining a sharp interstream boundary (<10 μm) due to high flow (1–2 mL/min) (16,25). The width of a single microstream (∼300 μm) is sufficient to ensure that a whole myocyte, oriented at right angles to the flow, can be exposed uniformly to a solution held in one of the barrels. In this way, a myocyte could be uniformly exposed to a caffeine-containing solution. When required, a myocyte was regionally exposed to the drug by positioning the interstream boundary such that ∼25% of the cell length was enveloped by the caffeine microstream, whereas the rest of the cell was exposed to a caffeine-free microstream. To visualize the boundary optically, one microstream also contained 10 mM sucrose, which itself had no effect on Ca²⁺-signaling (16).

During partial exposure of a myocyte to caffeine, the drug's high membrane permeability (20 μm/s (26)) will ensure that its intracellular compartmentalization is similar to that imposed extracellularly. Caffeine, as a solute of molecular mass 200 Da, is expected to diffuse at ∼50 μm²/s (estimated from Swietach and Vaughan-Jones (17)). For a 120-μm-long myocyte exposed proximally along 25% of its length to 10 mM caffeine, steady-state [caffeine]_i at the distal end of the cell is expected to be <20 nM. [caffeine]_i will fall to 1% (0.1 mM) within 6 μm of the midpoint of the microstream boundary (see Fig. S2 in Data S1 for the solution to a mathematical model of intracellular caffeine diffusion during partial extracellular exposure). Since the half-maximal caffeine dose for RyR channel opening in intact cells is 2–3 mM (27), the sharp compartmentalization of [caffeine]_i will translate into a sharp compartmentalization of caffeine-induced RyR channel opening. Due to low cytosolic Ca²⁺-mobility, the spread of will exceed the [caffeine]_i profile by only 7% of cell length (see Appendix 1).

Estimating SR Ca²⁺-leak

When SERCA is inhibited (for example, with CPA), SR-membrane leakage slowly depletes the SR (18). As described later, the leakage must be known when estimating D_CaSR. Leakage was assessed by assaying [Ca²⁺]_SRT with caffeine at various times after switching a cell into SS. Fig. 3, A and B, shows specimen confocal longitudinal line scan recordings of [Ca²⁺]_i (rat myocytes), indicating that caffeine-induced Ca²⁺-release was smaller after 4 min than after 1 min, consistent with SR leakage depleting [Ca²⁺]_SRT. Data pooled in Fig. 3 C indicate a time constant of ∼200 s for the decline with 0.3 mM Tet but a much slower decline with 2 mM Tet. Fig. 3 Cii shows that the decline was paralleled by a similar fall in the peak contracture (Fig. 3, A and B) that coincided with SR Ca²⁺-release. A comparable rate of rundown of [Ca²⁺]_SRT in 2 mM Tet was also observed in guinea pig myocytes (Fig. 3 Ci). We conclude that Tet dose-dependently reduces SR-membrane leakage.

Experimental protocol for measuring D_CaSR

A rat myocyte was positioned within a stream of SS plus 0.3 mM Tet, emerging from one barrel of a dual-microstream apparatus (Fig. 4 A; configuration 0). The other stream contained 10 mM caffeine in Tet-free SS. The interstream boundary was quickly (<1 s) moved (Fig. 4 A; configuration 1), exposing one end of the cell (proximal end) to caffeine (24.0% ± 1.3% and 23.0% ± 3.0% of the length in rat and guinea pig, respectively; n = 87 and 24). This resulted in proximal SR Ca²⁺-release which was measured (as F/F₀) over the proximal 20% of the line scan (ROI-P, Fig. 4 A). After 30 s (Fig. 4 Bi), the solution boundary was readjusted, exposing the whole cell to caffeine (Fig. 4 A; configuration 2). There was now a local SR Ca²⁺-release from the remainder of the cell (Fig. 4 Bi), which was measured (as F/F₀) over the distal 20% of the line scan (distal ROIs; ROI-D; Fig. 4 A). This distal Ca²⁺ rise was frequently accompanied by a smaller, slower rise in the proximal region, caused by back diffusion of cytoplasmic Ca²⁺. Ca²⁺-release events from the SR were associated with cell contractures.

Thus localizing a cell's exposure to caffeine allows one to assess local [Ca²⁺]_SRT. Fig. 4 Bii shows that, in a different cell, increasing the time period (to 4 min) before readjusting the interstream boundary resulted in a considerably smaller caffeine-induced Ca²⁺-release from the distal end of the cell. Thus prolonged exposure of a proximal SR region to caffeine also empties the unexposed distal region. Although some of this emptying may be caused by Ca²⁺-leakage across the distal SR-membrane (the dashed line indicates the predicted leakage), there may also be emptying via luminal Ca²⁺-diffusion from distal to proximal SR regions, where Ca²⁺ escapes through caffeine-opened RyRs. This luminal diffusion was examined further by repeating the experimental protocol, but with 2.0 mM rather than 0.3 mM Tet, to inhibit most of the SR-membrane leak (Fig. 4 C). After a 2 min exposure of proximal SR to caffeine, the Ca²⁺-content of the distal SR region again became depleted, but this was now clearly more than expected from SR-membrane leakage alone (dashed line). Reducing the SR leak with 2 mM Tet, therefore, reveals that exposure of proximal SR to caffeine can drain distal areas via luminal Ca²⁺-diffusion.

Fig. 4 D plots the time course of decline of the distal SR Ca²⁺-content during proximal caffeine exposure in the presence of 0, 0.3, and 2 mM Tet (from a total of 87 rat myocytes and 24 guinea pig myocytes). In all cases, the Ca²⁺-content decreased, but more slowly at higher Tet concentrations, reflecting the reduced SR-membrane leak. In 2 mM Tet, SR-membrane leak is minimal, and the decline will be caused largely by spatial SR Ca²⁺-diffusion from distal to proximal areas. Note that this rate of decline (in 2 mM Tet) was similar in both guinea pig and rat myocytes.

As shown in Fig. 5, local [Ca²⁺]_SRT can be assessed from the contracture during a local caffeine challenge. To check that Ca²⁺-binding by Fluo-3, used in this work, did not affect the rate of local SR depletion, we monitored the decline of the distal contracture with caffeine after increasing periods of proximal caffeine exposure. It declined at the same rate irrespective of whether a cell was AM-loaded with Fluo-3 or with carboxy-SNARF-1, a fluorescent dye that does not bind Ca²⁺ (Fig. 5 B). Thus the presence of the Ca²⁺-fluorophore does not affect the rate at which luminal Ca²⁺-diffusion and Ca²⁺-leak drains the SR.

Calculating D_CaSR: simple diffusion model

Rates of local SR-depletion were used to quantify D_CaSR by applying a simple one-dimensional (1-D) diffusion model of the SR, featuring both longitudinal Ca²⁺-diffusion and lateral membrane Ca²⁺-leak (Fig. 6 Ai):

The model makes no assumptions about the cause of any deviation of Ca²⁺-mobility from its high value in water (D_Ca ≈ 1000 μm²/s) (28). SR-membrane leak is defined as the product of rate constant λ (estimated from Fig. 3 Ci for different Tet doses) and total SR Ca²⁺ content.

This definition of SR-membrane leak is in agreement with the monoexponential decline in SR content (Fig. 3 Ci and Bassani and Bers (18)) and allows for local variation in SR leak that can arise from SR depletion, driven by intra-SR Ca²⁺-diffusion. The caffeine-induced rise in Fluo-3 fluorescence was converted to [Ca²⁺]_i and, after accounting for cytoplasmic (intrinsic + Fluo-3) buffering (29), to [Ca²⁺]_SRT (for full details, see Appendix 1). The time course of depletion of distal [Ca²⁺]_SRT by proximal caffeine (Fig. 4 D) was solved by best-fitting a single D_CaSR value in the diffusion model. Depletion can be fitted in this way because [Ca²⁺]_SR equilibrates relatively rapidly (∼10 ms) with [Ca²⁺]_SRT (30), and the two parameters will be linearly related, given that the binding constant (3,30,31) of the principal luminal buffer, calsequestrin, is greater than or similar to [Ca²⁺]_SR. Fitting results are shown in Fig. 6 Aii. The least-squares best-fit value for D_CaSR is low, 8–9 μm²/s and is similar in both rat and guinea pig myocytes. The same best-fit value is obtained for conditions of high or low SR leak (0.3 and 2.0 mM Tet, respectively), suggesting that the model makes adequate correction for this. Interestingly, when the influence of the leak is ignored (λ forced to equal 0), the predicted D_CaSR value is not unique. It increases with leak size and appears to be 42 μm²/s in the absence of Tet. Thus accurate measurement of global D_CaSR requires a full correction for the effects of SR-membrane leak.

Calculating D_CaSR: mechanistic diffusion-reaction model

D_CaSR was quantified a second way, this time using a mechanistic, 1-D diffusion-reaction model (Fig. 6 Bi). This approach attempts to account for elements affecting both luminal and cytoplasmic Ca²⁺, such as RyR-permeability, luminal and myoplasmic Ca²⁺-buffers (including Fluo-3), and, where appropriate, the membrane transporters SERCA and PMCA. Parameters for these elements were derived either from the literature or from this work (see Appendix 1 and Table 1). The model best fits experimental data with a single Ca²⁺-diffusion coefficient This value is lower than its free aqueous value D_Ca because of SR tortuosity. The effective Ca²⁺-diffusion coefficient (D_CaSR) in the SR is, however, reduced further because of luminal buffering by calsequestrin (3,31):

(1)

C_csq and K_csq are the total concentration and Ca²⁺-binding constant for calsequestrin, respectively. The least-squares best-fits of the model to the experimental data are shown in Fig. 6 Bii. These fits are very similar to those achieved using the simple diffusion model (Fig. 6 Aii). In both cases, the goodness of fit was high (sum of squares < 0.01). Because of luminal buffering, the effective D_CaSR in the model will vary with [Ca²⁺]_SR, and so the value quoted for each curve in Fig. 6 Bii has been time-averaged over the whole period of local SR depletion to produce a mean for the experiment. This value is again low (7.9–9.1 μm²/s) and is independent of the size of prevailing SR-membrane leak. The value is also similar in both rat and guinea pig cells. The confidence interval for our D_CaSR estimate can be approximated by best fitting data within their mean ± SE. This interval was ±4.4 and ±3.6 μm²/s for rat and guinea pig myocytes, respectively.

TABLE 1.

Model parameters

Symbol	Definition	Value	Reference
[Ca2+]i,0	Diastolic myoplasmic Ca2+ in NT	100 nM (75 nM in Tet)	(39,40,43,46)
[Ca2+]SR,0	Diastolic fully loaded SR Ca2+ in NT	520 μM (700 μM in Tet)	(3,31,46)
vcell	Total cell volume	33 pL	(43,47)
vSR	Total SR volume	3.5% of Vcell	(1,48)
vmyo	Total nonmitochondrial volume	65% of Vcell	(1,43,48)
ρSL	SL surface area/volume ratio	0.89 μm−1	(47,49)
ρSR	SR surface area/volume ratio	1.19 μm−1	(1,48)
L	Cell length	120 μm (rat); 113 μm (g-p)	Measured
E	% SR mobilized during partial caffeine exposure	24% (rat); 23% (g-p)	Measured
kleak	SR leak rate constant	See text	Fig. 2
krel	Caffeine-evoked Ca2+-release rate constant	9 s−1	(50)
	Maximum rate of SERCA	100 μM s−1	Estimated*
	affinity of SERCA (forward)	0.246 μM	(43)
	affinity of SERCA (reverse)	1.7 μM	(43)
nS	Hill cooperativity of SERCA	1.787	(43)
	Maximum rate of PMCA in 0Na0Ca media (estimated from relaxation time constant)	30.0 μM s−1 (rat); 25.4 μM s−1 (g-p)	e.g., Fig. 1 A
KP	affinity of PMCA	0.5 μM	(43)
Jbal	SL Backflux to balance PMCA and stabilize [Ca2+]i	Adjustable
Cbuf	Cytoplasmic (fast) buffer concentration	175 μM	(29)
Kbuf	Cytoplasmic (fast) buffer equilibrium constant	0.59 μM	(29)
CCSQ	Calsequestrin buffer concentration (estimated from rise in total cytosolic Ca2+ during caffeine exposure)	4.4 mM (rat); 2.3 mM (g-p)	Estimated*
	Calsequestrin Ca2+ off-rate	109 s−1	(30)
KCSQ	Calsequestrin Ca2+ binding constant	0.63 mM	(3,31)
CFluo	Fluo-3 buffer concentration	25 μM	Data S1
KFluo	Fluo-3 buffer Ca2+ affinity	832 nM	Data S1
	Fluo-3 buffer Ca2+ off-rate	100 s−1	Assumed
DCai	Cytosolic effective Ca2+ mobility (absence of Fluo-3)	15 μm2/s	(7,39–41)
DFluo	Fluo-3 diffusion coefficient	25 μm2/s	(39,40)
DCaff	Caffeine diffusion coefficient	50 μm2/s	Data S1
PCaff	Caffeine permeability constant	9 μm/s	(26)

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SL, sarcolemma; SR, sarcoplasmic reticulum; r, rat; g-p, guinea pig.

^*

P. Swietach, K. W. Spitzer, and R. D. Vaughan-Jones, unpublished.

A final cross-check was made for the experimental estimates of D_CaSR. If the Ca²⁺-diffusion models used in the analysis are reliable, D_CaSR estimated during longitudinal SR-depletion with proximal caffeine should be the same, irrespective of where the depletion in the distal SR is estimated. We therefore positioned two ROI-Ds at different known distances downstream from the initial proximal area of caffeine exposure (where ROI-P was positioned). When the whole SR was eventually exposed to caffeine (configuration 2 of Fig. 4 A), the rise of in each ROI-D could be used to estimate D_CaSR, as described previously. ROI-D1 was positioned near the middle of the cell, such that its near border was at the cell's center, whereas ROI-D2 was positioned at the extreme distal end of the cell (this was the default position for ROI-D used in all other experiments). When best-fitted by our diffusion-reaction model, mean D_CaSR estimated using ROI-P in combination with ROI-D1 was 7.2 μm²/s (n = 87), which is similar to the estimate obtained using ROI-P in combination with ROI-D2 (8.6 μm²/s; n = 87), confirming the validity of the analytical technique. We preferred to use the more extreme ROI-D measurements for general analysis, as these exhibited the better signal/noise ratio for SR Ca²⁺-release (a larger Fluo-3 fluorescence increase), thus providing a more accurate estimate of SR Ca²⁺-mobility.

Fig. 6 C shows a model simulation of an experiment on a rat ventricular myocyte, demonstrating that proximal caffeine application is predicted to deplete distal SR regions by an amount very similar to that assessed experimentally (Fig. 4 D). We conclude that the low D_CaSR detected in our experiments here is consistent with the expected effects on Ca²⁺-diffusion of SR tortuosity and luminal Ca²⁺-buffering.

SR is continuous, and global D_CaSR is low

We find that, in both rat and guinea pig ventricular myocytes, locally opening RyRs at one end of the SR can drain it slowly of Ca²⁺, indicating a low SR Ca²⁺-mobility of 8–9 μm²/s. This remains true, even after natural Ca²⁺-leakage across the SR membrane has been minimized with 2 mM Tet. Diffusion of Ca²⁺ down the SR, a distance of ∼60 sarcomeres, is consistent with previous observations that, when Fluo-5N is loaded into the SR, both Ca²⁺-ions and the fluorophore can, over minutes, access all luminal regions, including the nuclear envelope (9). SR lumen therefore appears to be continuous and to extend beyond individual sarcomeres, as also suggested from anatomical observations of nSR breaching the Z-line region (2).

Our low value for D_CaSR is a global average, which includes both jSR and nSR Ca²⁺-mobility. It also refers to a partially mobilized SR ([Ca²⁺]_SR ≈ 0.25 mM). By extrapolation, D_CaSR in loaded SR ([Ca²⁺]_SR ≈ 0.5 mM) of guinea pig and rat would be 11–13 μm²/s (up to [Ca²⁺]_SR ≈ 1 mM, the [Ca²⁺]_SR-dependence of D_CaSR is near linear; Eq. 1). It is of interest to compare it with global cytoplasmic Ca²⁺-mobility, D_Cai. This latter parameter is difficult to quantify using Ca²⁺-fluorophores because they act as mobile buffers, enhancing Ca²⁺-mobility. However, a value for skeletal myoplasm (7), measured using radiotracers rather than Ca²⁺-fluorophores, is 14 μm²/s at 21°C. At 37°C this will be higher, ∼20 μm²/s (28). The value is similar to estimates of D_Cai in neurons (16 μm²/s; fluorophore corrected) (32) and similar to the value predicted in the absence of fluorophore by our cardiomyocyte diffusion-reaction model (16 μm²/s at 37°C). Global D_CaSR is therefore likely to be even lower than D_Cai.

Ca²⁺-mobility in water, D_Ca, is 1000 μm²/s at 37°C (7,28). Mobility in luminal SR is therefore reduced by about two orders of magnitude. Diffusion-reaction modeling of our experimental data (Fig. 6 D) suggests that one order of magnitude reduction is likely to be due to SR tortuosity (see Appendix 1), whereas the other can be attributed to luminal Ca²⁺-buffering. Assuming a similar total nSR and jSR volume (2), the jSR concentration of calsequestrin, the principal luminal buffer, is between 6 mM (3) and 28 mM (31), and K_csq for Ca²⁺ is ∼0.6 mM (3,31), a value close to [Ca²⁺]_SR in loaded SR, thus ensuring a maximal Ca²⁺-buffering capacity. As calsequestrin is poorly mobile (molecular mass of 45 kDa), it will significantly attenuate luminal Ca²⁺-mobility.

Our estimate of D_CaSR (8–9 μm²/s) is nearly 10-fold lower than a previous measurement (9) (60 μm²/s at 20°C approximates to 84 μm²/s at 37°C (28)), obtained using luminal Fluo-5 N to measure SR Ca²⁺-movement directly. It is not immediately apparent why the two estimates would differ so dramatically. Species differences (rabbit versus the guinea pig and rat here) are an unlikely explanation as, among the three cells, SR volume, and Ca²⁺-content are believed to be similar (18). Furthermore, revising the earlier mobility measurement to the higher temperature of 37°C only accentuates the discrepancy (28). As mentioned already, the previous use of Fluo-5N for direct measurement of [Ca²⁺]_SR may have enhanced D_CaSR, but running our diffusion-reaction model suggests the effect would be by <2%, given the dye's low luminal concentration (50–100 μM (9)) compared with calsequestrin and [Ca²⁺]_SR. Thus although Ca²⁺-fluorophores like Fluo-3 and Fura-2 significantly affect cytoplasmic Ca²⁺-mobility, the same is unlikely to be true for the effect of Fluo-5N on luminal Ca²⁺-mobility (providing [Ca²⁺]_SR ≫ [Fluo-5N]).

Unlike the previous work, we did not measure [Ca²⁺]_SR directly, but inferred it from local Ca²⁺-release with caffeine. Indeed, direct [Ca²⁺]_SR measurements in rat and guinea pig ventricular myocytes were not an option, as reliable SR-loading of Fluo-5N in these cells has not so far been achieved (15). There is, therefore, the possibility of errors in our own work. The use of rapid caffeine application to assess [Ca²⁺]_SRT has, however, been well validated (18,29,31), as has the use of dual microperfusion to localize extracellular solutes with high precision (16,24,25). Due to caffeine's high membrane permeability (26), intracellular caffeine compartmentalization will also be similar to the extracellular compartmentalization imposed by dual microperfusion (see Methods and Data S1). Although caffeine-application gauges [Ca²⁺]_SRT rather than [Ca²⁺]_SR, the two levels equilibrate in ∼0.01 s (calsequestrin unloading rate constant = 109 s⁻¹ (30)) and will thus decline in synchrony during local drainage, as jSR and nSR are interconnected throughout the cell.

One possible source for the discrepancy is the correction for SR membrane leakage. Our estimates of the time constant of Ca²⁺-leakage (in low or zero Tet) are in agreement with previous estimates (18) and would produce 45% SR depletion during the time required to measure luminal Ca²⁺-diffusion (∼2 min). Although SR leakage was accounted for in this work, no leakage was apparent in the earlier determination of D_CaSR (see Fig. 7 of Wu and Bers (9)). Given that SR leakage is known to occur, this may indicate some residual SERCA activity in the earlier work (9), despite a 90 s exposure to 5 μM thapsigargin. It is notable that failure to account for leakage in this work results in artifactually high values for D_CaSR (up to ∼42 μm²/s; Fig. 6 Aiii). We show, in Fig. S3 in Data S1, that it may also lead to an overestimate of D_CaSR using the experimental protocol adopted in the earlier work. If so, D_CaSR may be low in all three species. Alternatively, rabbit ventricular myocytes may be unusual in exhibiting a high luminal Ca²⁺-mobility.

Functional consequences of low D_CaSR: microscopic localization of SR Ca²⁺-signaling

Although the SR lumen appears continuous throughout the ventricular myocyte, this need not imply functional continuity. A low global value for D_CaSR means that local displacements of [Ca²⁺]_SR will not necessarily be transmitted to other regions, particularly if they are rapid and transient. This can be illustrated in our diffusion-reaction model (Fig. 7) by locally increasing RyR permeability to release Ca²⁺ along a 2 μm stretch of SR (roughly equivalent to Ca²⁺-release from a single sarcomere) and computing [Ca²⁺]_SR after 250 ms. If global D_CaSR in the model is set to a high value (>60 μm²/s), Ca²⁺-release (in the presence of local reuptake by SERCA) is associated with only a modest local fall of [Ca²⁺]_SR, as Ca²⁺ drawn diffusively from adjacent SR regions (and hence from adjacent sarcomeres) limits the local depletion. As a result, an extended length of lumen becomes significantly depleted (9 μm of lumen, at 5% depletion threshold, with D_CaSR = 300 μm²/s and 7 μm with D_CaSR = 60 μm²/s; Fig. 7). Thus a localized Ca²⁺-release is predicted to produce a more generalized SR depletion.

In contrast, when global D_CaSR is set to the value measured experimentally (9 μm²/s), Ca²⁺-release is associated with a considerably larger fall of [Ca²⁺]_SR but one that is more localized spatially (5% depletion in <4 μm of lumen; Fig. 7). Ca²⁺ is no longer drawn so extensively from adjacent regions (i.e., from adjacent sarcomeres), thereby preserving their integrity. Under these circumstances, local control of SR Ca²⁺-release is complemented by a local control of [Ca²⁺]_SR. Although the above modeling is simplistic (it does not, for example, reproduce the real geometry within an SR release site), it nevertheless implies that a low global value for both luminal and cytoplasmic Ca²⁺-mobility may result in local cytoplasmic Ca²⁺-microdomains being mirrored spatially by inverse luminal Ca²⁺-microdomains—as indeed appears to happen for a Ca²⁺-spark and its corresponding Ca²⁺-blink (2,13), and for a cytoplasmic Ca²⁺-wave and its corresponding wave of SR Ca²⁺-depletion (13,33). Indeed, given that [Ca²⁺]_SR is suggested to be an important regulator of RyR channel gating (34), a low D_CaSR, by optimizing the amplitude and minimizing the spatial extent of local [Ca²⁺]_SR depletion, may play an important role in the luminal regulation of the Ca²⁺-release process itself.

Changes in luminal Ca²⁺-mobility may be relevant to recent reports of abnormal Ca²⁺-signaling in ventricular myocytes. In one (34), increasing intra-SR Ca²⁺ buffering capacity with citrate or maleate was found to increase Ca²⁺ spark amplitude and duration. One possible explanation is an increase of D_CaSR, as these low molecular weight molecules will function as mobile Ca²⁺-buffers within the SR lumen. An increased D_CaSR will finance a greater and more spatially diffuse Ca²⁺-release, as illustrated in Fig. 7, and this may account for enhancement of the local Ca²⁺ spark. In a second report, the absence of calsequestrin from jSR in Casq2-null mice was found to be accompanied by an increased incidence of electrical arrhythmia (35). Results of this work predict that calsequestrin deletion, by reducing fixed luminal Ca²⁺-buffers, would increase the effective D_CaSR (Eq. 1), again enhancing local Ca²⁺-release. Such abnormal release may then contribute to the arrhythmic phenotype of Casq2-null mice (35). Conversely, calsequestrin overexpression would be expected to decrease D_CaSR (Eq. 1), which may play a role in the reduced spark frequency and Ca²⁺-release observed recently in transgenic mice (36).

The low D_CaSR measured in this work has implications for models of Ca²⁺-wave propagation during pathological conditions of -overload. Current hypotheses conflict, in that some assume a wave of [Ca²⁺]_SR depletion is coincident with the cytosolic Ca²⁺-wave (13,33), whereas a recent hypothesis suggests an SR wave of luminal Ca²⁺-loading that travels ahead of the cytosolic Ca²⁺-wave (12). As discussed earlier, Eq. 1 predicts that, even when [Ca²⁺]_SR is as high as 1 mM, as may occur during the incidence of Ca²⁺-waves, D_CaSR would still not be significantly greater than D_Cai, which tends to argue against the latter proposal. Finally, a low D_CaSR implies that conditions associated with spatially nonuniform Ca²⁺-release within the cell, such as regional alternans, will, at times, be associated with significant spatial nonuniformity of [Ca²⁺]_SR (15,37).

Possible causes of low D_CaSR: local heterogeneity of SR Ca²⁺-mobility

Although global D_CaSR is low, it is unlikely that Ca²⁺-mobility is uniform throughout the SR, given its complex geometry and the heterogeneous distribution of luminal Ca²⁺-buffers. It is therefore appropriate to ask which regional elements within the SR may limit the global movement of Ca²⁺. One such element is likely to be jSR, which will have implications for SR Ca²⁺-cycling within the sarcomere. The other may be the intersarcomeric portion of the nSR.

We deal first with jSR. During excitation-contraction coupling, after Ca²⁺-release from jSR cisternae, Ca²⁺-ion movement from nSR (the main site of Ca²⁺-reuptake by SERCA) refills jSR within each cardiac cycle. In rabbit and canine myocytes, this refilling appears to occur with a time constant (τ) of 29 ms (2) and 98 ms (13), respectively, as derived from the recovery time course of a Ca²⁺-blink (Fig. 8 Aii, inset for τ = 29 ms). Such recovery will be a more direct measure of local jSR refilling than, for example, Ca²⁺ spark restitution, as the latter appears to depend on factors other than SR load, such as RyR refractoriness (38). If local cisternal refilling is by passive Ca²⁺-diffusion, local [Ca²⁺]_SR recovery during a blink suggests that Ca²⁺-mobility into or within jSR is low. Within each rabbit sarcomere, one jSR cisterna (diameter ≈ 0.6 μm) is supplied, on average, by four nSR elements (2) (Fig. 8 Ai; see Appendix 2 for derivation of geometry), with volume being distributed equally between jSR and nSR (2).

If one makes the simplifying assumption that, during an isolated Ca²⁺-blink, the distal ends of the nSR elements are coupled to an infinite source of Ca²⁺ (because of diffusive coupling to quiescent elements of the SR and because of Ca²⁺-uptake on SERCA), then local jSR refilling can be simulated by setting effective jSR Ca²⁺-mobility to 1.8 μm²/s (for recovery τ = 29 ms; Fig. 8 Aii and iii; see Appendix 2 for details). This is a very low value, consistent with restricted access to jSR from nSR and also consistent with the known high expression in jSR of calsequestrin (2,11). Thus, a very low, local D_CaSR may underpin the local luminal Ca²⁺-flux required to refill jSR cisternae. But a predicted jSR Ca²⁺-mobility of 1.8 μm²/s is significantly lower than the global value of D_CaSR measured in guinea pig and rat myocytes (8–9 μm²/s) here. This may reflect a relatively high Ca²⁺-mobility in non-jSR elements (i.e., in nSR), as implied in the SR-unit model (Fig. 8 Ai and Appendix 2). Indeed such an arrangement has already been proposed (2), as nSR is believed to be devoid of known Ca²⁺-buffers, which would permit faster Ca²⁺-diffusion (2,11).

A two-dimensional (2-D) model network of jSR-nSR elements (Fig. 8 Bi) with unbuffered Ca²⁺-mobility in nSR and low, buffered Ca²⁺-mobility in jSR (1.8 μm²/s) can be used to predict the global value for D_CaSR (see Appendix 2 for details). Imposing zero-[Ca²⁺] at one end of the 2-D network (equivalent to tonically exposing one end of the SR to caffeine) predicts universal depletion, with an average D_CaSR of 8 μm²/s (Fig. 8 Bii), which is in agreement with the global value measured experimentally. Thus, if we assume heterogeneity of Ca²⁺-mobility between jSR and nSR, as proposed previously, our experimentally determined value for D_CaSR would be sufficient to support local SR Ca²⁺-signaling, as well as global luminal Ca²⁺ movement within the cardiac cell. The modeling implies that, at the nanoscopic level, luminal Ca²⁺-diffusion will vary, being very slow in jSR but faster in nSR. The global Ca²⁺ diffusion rate through the combined SR elements will tend toward the lower of the two individual limits, as shown in Fig. 8 Bii.

What about intersarcomeric SR? The above modeling of luminal Ca²⁺-diffusion takes no account of possible heterogeneity of Ca²⁺-mobility within nSR itself. For example, it is possible that SR Ca²⁺-diffusion is severely limited between adjacent sarcomeres (2), i.e., via intersarcomeric network SR (we call this inSR). Local Ca²⁺-mobility for inSR may be significantly lower than for intrasarcomeric nSR, i.e., the part of the nSR that ramifies within each sarcomere and makes connection with jSR cisternae (we call this intrasarcomeric network snSR). Low Ca²⁺-mobility for inSR would be consistent with the apparently sparse nature of inSR elements compared with the more densely arranged snSR elements (2). Subdividing nSR into inSR and snSR in our 2-D model network (Fig. 8 Biii) would have no effect on the predicted value for global D_CaSR, as the influence of the combined inSR-snSR would need to be identical to the original lumped nSR. In the simplest case, the subelements may be arranged in series, as shown in Fig. 8 Biii.

Analysis of the 2-D network indicates that the effective Ca²⁺-mobility for a lumped nSR would be 110 μm²/s for a D_jSR of 1.8 μm²/s and a global D_CaSR of 8 μm²/s (see Appendix 2). Ascribing specific values to Ca²⁺-mobility in the inSR or snSR subelements must await an anatomical description of their volume and tortuosity. But if Ca²⁺-mobility for inSR were as low as for jSR (i.e., 1.8 μm²/s), then the total nSR could be represented by a short inSR element with low Ca²⁺-mobility coupled to a longer snSR element with high Ca²⁺-mobility, where inSR is ∼1.5% of total nSR length (see Appendix 2). Thus, in effect, the inSR would occupy only a tiny fraction of total nSR volume, and so its limiting influence on global Ca²⁺-mobility would not be large. In this way, effective Ca²⁺-mobility in the whole nSR would still be 110 μm²/s. At this time, subdividing local Ca²⁺-mobility within the nSR is purely speculative. Furthermore, it takes no account of other regions of the SR/ER system, such as the nuclear envelope. As all these regions are interconnected (9), a comprehensive model of local Ca²⁺-mobility will require detailed characterization of all these noncisternal elements.

We can now attempt to answer the question of which regional elements within the SR may limit the global diffusion of luminal Ca²⁺. Assuming that the published recovery time for a Ca²⁺-blink represents diffusive refilling of jSR, it seems likely that the effective Ca²⁺-mobility in jSR is much lower than that averaged throughout the rest of the SR/ER. Because jSR occupies around half of total SR volume (2), its limiting effect on global Ca²⁺-mobility will be large. Effects of intersarcomeric nSR are more difficult to quantify, but, when lumped with the rest of the nSR, they probably limit global Ca²⁺-mobility far less than does jSR.

Low D_CaSR and SR Ca²⁺-scraps

The spatial uniformity of [Ca²⁺]_SR during Ca²⁺-scraps, where global SR Ca²⁺-release during an action potential appears to deplete both jSR and nSR elements, has led to suggestions for a high global value for D_CaSR (8). In contrast, the recovery time course of a Ca²⁺-blink, with little or no Ca²⁺ depletion in adjacent nSR, suggests D_CaSR is low (2). Observations on Ca²⁺-scraps and Ca²⁺-blinks are not necessarily contradictory. The Ca²⁺-blink is measured as an isolated, low-probability event (2,14). Thus fast Ca²⁺ movement from neighboring, quiescent SR elements may minimize local nSR depletion, as observed experimentally ((2) and Fig. 8 Aii, inset). But during an action potential, the high spatial density of Ca²⁺-blinks may prevent this from happening, leading to global nSR depletion accompanying the global Ca²⁺-discharge from jSR. As suggested previously (2,13), the recoveries of [Ca]_jSR during an isolated Ca²⁺-blink and a global Ca²⁺-scrap (8) are likely to occur via different mechanisms, the former being via simple Ca²⁺-diffusion and the latter via active Ca²⁺-reuptake on SERCA pumps. A low global D_CaSR need not, therefore, be inconsistent with spatially uniform Ca²⁺-scraps. In contrast, a high rather than low global D_CaSR of, say, 60 μm²/s would, from Fig. 8, Aii and 8 Bii, predict ultrafast diffusive jSR refilling after an isolated Ca²⁺-blink, with a time constant of <1 ms, which could not be resolved experimentally. The fact that localized Ca²⁺-blinks recover with a much longer time constant of 29–98 ms (2,13) thus reinforces our own proposal for a low D_CaSR.