Differential Regulation of ER Ca²⁺ Uptake and Release Rates Accounts for Multiple Modes of Ca²⁺-induced Ca²⁺ Release

The ER is an important component in Ca²⁺ signaling in virtually all nonmuscle cells (Pozzan et al., 1994; Clapham, 1995; Berridge, 1998; Meldolesi and Pozzan, 1998). Net Ca²⁺ transport by the ER is critical for regulating intraluminal Ca²⁺ concentration ([Ca²⁺]_ER), as well as for modulating the dynamics of cytoplasmic free Ca concentration ([Ca²⁺]_i) during and after stimulation. As a result, Ca²⁺ transport by this organelle is expected to influence the activity of Ca²⁺-sensitive processes within the ER and the cytoplasm, as well as in organelles such as mitochondria and the nucleus that undergo secondary changes in intraluminal Ca²⁺ concentration in response to evoked changes in [Ca²⁺]_i (Gerasimenko et al., 1996; Babcock and Hille, 1998).

In neurons, the role that the ER plays in modulating depolarization-induced [Ca²⁺]_i elevations is complicated, since this organelle may act as either a Ca²⁺ source or sink, in some cases even in the same cell type (Friel and Tsien, 1992a; Garaschuk et al., 1997; Toescu, 1998; for review see Simpson et al., 1995; Rose and Konnerth, 2001). These distinct forms of net ER Ca²⁺ transport are expected to have very different functional effects on the activity of intraluminal Ca²⁺ binding proteins (Corbett and Michalak, 2000). Nevertheless, the conditions of stimulation that determine which form of transport occurs are incompletely understood. The direction and rate of net ER Ca²⁺ transport depend on the relative rates of Ca²⁺ uptake and release via distinct transport pathways. Ca²⁺ uptake is regulated by sarco(endo)plasmic reticulum Ca ATPases (SERCAs;^*East, 2000), whereas passive Ca²⁺ release is regulated by Ca²⁺ release channels that open in response to elevations in [Ca²⁺]_i and contribute to Ca²⁺-induced Ca²⁺ release (CICR; Bezprozvanny et al., 1991; Ehrlich, 1995; for reviews see Kuba, 1994; Verkhratsky and Shmigol, 1996; Usachev and Thayer, 1999). If the rate of Ca²⁺ uptake exceeds the rate of release, the ER acts as a Ca²⁺ sink and slows depolarization-evoked [Ca²⁺]_i elevations. If release is faster than uptake, it acts as a Ca²⁺ source, speeding and potentially amplifying these responses.

The main goal of the present study was to understand how differential regulation of ER Ca²⁺ uptake and release rates by Ca²⁺ determines the direction and rate of net ER Ca²⁺ transport during stimulation. Our previous work in sympathetic neurons showed that as evoked [Ca²⁺]_i elevations become larger, the ER undergoes a transition from a Ca²⁺ sink to a Ca²⁺ source (Albrecht et al., 2001; Hongpaisan et al., 2001). Specifically, it was found that if [Ca²⁺]_i is raised to less than or equal to ∼350 nM by weak depolarization, the ER accumulates Ca²⁺, whereas if global [Ca²⁺]_i is raised to 600–800 nM by stronger depolarization, there is little or no net ER Ca²⁺ transport. However, if [Ca²⁺]_i rises to higher levels during depolarization, for example, in outer cytoplasmic regions near sites of Ca²⁺ entry, or during inhibition of mitochondrial Ca²⁺ uptake, the ER releases net Ca²⁺, presumably reflecting net CICR. We proposed a simple explanation for this transition: progressive [Ca²⁺]_i-dependent activation of a ryanodine-sensitive CICR pathway that operates in parallel with SERCAs to regulate net ER Ca²⁺ transport. According to this idea, small [Ca²⁺]_i elevations stimulate Ca²⁺ uptake more effectively than Ca²⁺ release, leading to Ca²⁺ accumulation, whereas large [Ca²⁺]_i elevations stimulate release more effectively than uptake, leading to net Ca²⁺ release. We also presented indirect evidence that activation of the CICR pathway is influential even when [Ca²⁺]_i is low and the ER acts as a Ca²⁺ sink, causing the rate of ER Ca²⁺ accumulation to be reduced so that the ER becomes a less powerful buffer.

A quantitative model was presented, which showed that this idea is plausible (Albrecht et al., 2001). In terms of the model, differential regulation of ER Ca²⁺ uptake and release rates by Ca²⁺ is the key factor in determining when the ER acts as a Ca²⁺ source or sink. Moreover, we proposed that the relative rates of net ER Ca²⁺ transport and Ca²⁺ clearance by other pathways determine whether net Ca²⁺ release, if it occurs, can be regenerative.

In the present study, we test some of these ideas by characterizing the Ca²⁺ transport pathways responsible for ER Ca²⁺ uptake and release in sympathetic neurons. We sought to determine how Ca²⁺ transport by each pathway is regulated by Ca²⁺ when [Ca²⁺]_i is low and the ER acts as a Ca²⁺ sink. It was asked if quantitative differences in the Ca²⁺-dependent regulation of Ca²⁺ uptake and release rates can account for Ca²⁺ accumulation at low [Ca²⁺]_i at a rate that is reduced by activation of a ryanodine-sensitive CICR pathway. We also sought to understand how [Ca²⁺]_i-dependent regulation of ER Ca²⁺ uptake and release rates determines when the ER is a Ca²⁺ source or sink over a wider [Ca²⁺]_i range, and how net ER Ca²⁺ transport contributes to multiple modes of CICR.

Bullfrog sympathetic neurons were dissociated and placed in culture for up to 1 wk, as described previously (Colegrove et al., 2000a). All procedures conform to guidelines established by our Institutional Animal Care and Use Committee.

To measure [Ca²⁺]_i, cells were incubated with 3 μM fura-2 AM in normal Ringer's solution for 40 min at room temperature with gentle agitation followed by rinsing. The composition of normal Ringer's solution was the following (in mM): 128 NaCl, 2 KCl, 2 CaCl₂, 10 HEPES, and 10 glucose, pH adjusted to 7.3 with NaOH. Fura-2 AM was dispensed from a 1-mM stock solution in DMSO containing 25% (wt/wt) pluronic F127 (BASF Corporation). Cells were washed with normal Ringer's solution and placed on the stage of an inverted microscope (Diaphot TMD; Nikon) and superfused continuously (∼5 ml/min). Recordings began ∼20 min after washing away fura-2 AM, permitting de-esterification of the Ca²⁺ indicator. With this loading procedure, there is little compartmentalization of fura-2 (Albrecht et al., 2001). Solution changes (∼200 ms) were made using a system of microcapillaries (20 μl; Drummond microcaps) mounted on a micromanipulator. Fluorescence measurements were performed as described in Colegrove et al. (2000a).

In this study, three different macroscopic Ca²⁺ fluxes were measured: (1) J_SERCA, the rate of Ca²⁺ uptake via SERCAs; (2) J_i, the total cytoplasmic Ca²⁺ flux when SERCAs are inhibited; and (3) J_pm, the rate of Ca²⁺ extrusion across the plasma membrane. One additional flux (J_Release) was calculated from the difference between two of the measured fluxes (J_i and J_pm). Finally, J_Release and its integral were used to obtain information about intraluminal Ca²⁺ concentration and the Ca²⁺ permeability of the ER (⁠

⁠).

Fluxes were measured using the following experimental protocols. To determine J_SERCA, cells were rapidly exposed to a saturating concentration (100 μM) of the SERCA inhibitor 2,5-Di-(t-butyl)-1,4-hydroquinone (t-BuBHQ), using the abrupt change in d[Ca²⁺]_i/dt after application of the inhibitor as a measure of the t-BuBHQ-sensitive component of the total cytoplasmic Ca²⁺ flux (see Fig. 2 A). To measure this change, lines were fit to the linear portions of the [Ca²⁺]_i record just before and after the perturbation, and J_SERCA was taken as the difference between the final and initial slopes. The total cytoplasmic Ca²⁺ flux (J_i) during t-BuBHQ-induced [Ca²⁺]_i transients (see Fig. 3, A and B) was calculated as the time derivative of [Ca²⁺]_i at each sample time t_i according to ([Ca²⁺]_i(t_i + Δt/2) − [Ca²⁺]_i(t_i − Δt/2))/Δt, where Δt (400–500 ms) is twice the sampling interval. For the first and last sample points, the flux was estimated by computing the slope of a fitted line over the first and last sets of three sample points, respectively. The rate of Ca²⁺ extrusion across the plasma membrane (J_pm) was determined by measuring the total cytoplasmic Ca²⁺ flux during the [Ca²⁺]_i recovery after brief high K⁺ depolarizations while cells were continuously exposed to t-BuBHQ, and to FCCP to inhibit mitochondrial Ca²⁺ uptake (see Fig. 3, A–C; Colegrove et al., 2000a). The rate of passive Ca²⁺ release from the ER (J_Release) during the t-BuBHQ-induced [Ca²⁺]_i transient was then taken as the difference between J_i and J_pm at corresponding times (Fig. 3 B). J_pm was determined at each point in time during the [Ca²⁺]_i transient based on the rate of Ca²⁺ extrusion during the recovery after depolarization at corresponding values of [Ca²⁺]_i. This is justified by our previous finding that, in sympathetic neurons, J_pm can be specified at each time by the magnitude of [Ca²⁺]_i at that time (Colegrove et al., 2000a). Before calculating d[Ca²⁺]_i/dt, [Ca²⁺]_i measurements were smoothed with a binomial filter. Since measurements were acquired with regular sample intervals, J_i and J_pm were not always measured at identical values of [Ca²⁺]_i, so to facilitate flux subtraction, linear interpolation was used to approximate each of the measured fluxes at equally spaced values of [Ca²⁺]_i.

As shown in appendix A, if Ca²⁺ binding to cytoplasmic buffers equilibrates rapidly compared with changes in [Ca²⁺]_i, each measured Ca²⁺ flux can be interpreted as the rate of Ca²⁺ transport by the respective system (e.g., J̅ in nmol/s) divided by the product of the cytoplasmic volume (v_i) and a buffering factor (κ_i) that gives the change in total cytoplasmic Ca concentration accompanying small changes in [Ca²⁺]_i (Neher and Augustine, 1992; Tse et al., 1994; Neher, 1995; Colegrove et al., 2000a). While it was assumed that v_i is constant, κ_i was treated as a function of [Ca²⁺]_i (see next section). Thus, the measured fluxes are expected to show a composite [Ca²⁺]_i dependence that reflects Ca²⁺-dependent regulation of the individual transport rates and the [Ca²⁺]_i dependence of κ_i.

To determine if the measured fluxes account for the time course of [Ca²⁺]_i after various experimental perturbations, quantitative descriptions of J_pm, J_SERCA,

⁠, and κ_i were used as the defining equations in the model described in appendix B. Quantitative descriptions of the fluxes were of the form J̅/(v_iκ_i), where J̅ is represented by a Hill-type equation, or in the case of J_pm, such an equation plus a leak, v_i is constant and κ_i is a known function of [Ca²⁺]_i (see next section). Parameters of these equations were estimated based on the flux versus [Ca²⁺]_i measurements. While mechanistically motivated, the equations used to describe the [Ca²⁺]_i dependence of transport by the different pathways should be regarded as empirical, since the [Ca²⁺]_i range over which measurements were made was not always broad enough to determine unique parameter sets. Nevertheless, as shown in results, given equations that accurately describe the [Ca²⁺]_i dependence of the measured fluxes, it is possible to account for [Ca²⁺]_i dynamics after various experimental perturbations. Given information about the [Ca²⁺]_i dependence of κ_i, it is also possible to make inferences about the [Ca²⁺]_i dependence of transport rates and [Ca²⁺]_i dynamics in cells without exogenous Ca²⁺ buffers, but this was not the focus of the present study.

To examine qualitative properties of CICR over a wider range of [Ca²⁺]_i, continuous extensions of the descriptions for J_pm, J_SERCA, and

⁠, were used. In this case, there is uncertainty regarding quantitative features of the simulations (e.g., precise values of [Ca²⁺]_i thresholds for net CICR), but the qualitative features (e.g., the existence of thresholds and their order relationship) are expected to be reliable. Nevertheless, experimental characterization of the transport systems at higher [Ca²⁺]_i levels is an important goal of future experiments.

To characterize the Ca²⁺ permeability of the ER, it was necessary to obtain information about the driving force favoring passive Ca²⁺ release during t-BuBHQ-induced [Ca²⁺]_i transients (appendix A). Information about changes in intraluminal Ca²⁺ concentration was obtained by integrating J_Release over time. However, since J_Release is a flux per unit (effective) cytoplasmic volume (in nmol/v_iκ_i/s), conversion to a flux per unit (effective) intraluminal volume (in nmol/v_ERκ_ER/s) was required before integration. The appropriate flux was obtained after multiplying J_Release by (v_iκ_i/v_ERκ_ER). It was assumed that (1) v_i/v_ER is constant, (2) κ_ER is constant, as would be expected if intraluminal Ca²⁺ buffers have low affinity for Ca²⁺, and (3) that κ_i adjusts instantaneously to changes in total Ca concentration. Evaluation of κ_i and its [Ca²⁺]_i dependence required consideration of fura-2, since this Ca²⁺ indicator must contribute to cytoplasmic Ca²⁺ buffering in our experiments and binds Ca²⁺ with moderately high affinity (K_d,Fura-2 ∼224 nM). To evaluate this potential contribution to the [Ca²⁺]_i dependence of κ_i, the experiments illustrated in Fig. 1 were performed.

Fig. 1 (A and B) shows a representative voltage-sensitive Ca²⁺ current and associated [Ca²⁺]_i response elicited from a fura-2 AM–loaded sympathetic neuron by weak depolarization under voltage clamp (perforated patch conditions). Using standard methods (Albrecht et al., 2001), we measured the cytoplasmic buffering strength κ_i,basal when [Ca²⁺]_i was at its resting level. By progressively reducing the fura-2 AM incubation time, it was possible to estimate the resting value of κ_i in native, unloaded cells, as well as the component of κ_i representing fura-2 in our experiments, where the incubation time was 40 min. As expected, κ_i is smaller if the incubation time is reduced (Fig. 1 C). The dependence of κ_i on loading time could be described empirically by a third-order polynomial function, and extrapolation to zero incubation time provides an estimate of the endogenous cytoplasmic Ca²⁺ buffering strength at rest (κ_i,Endog ∼ 25). The strength of buffering (κ_i,Fura-2) by fura-2 at the 40-min time point then was calculated as κ_i,basal − κ_i,Endog ∼ 238. Thus, under our experimental conditions, fura-2 represents the major cytoplasmic Ca²⁺ buffer at rest. This made it possible to describe explicitly the [Ca²⁺]_i dependence of κ_i in our experiments as follows (Fig. 1 D):

Given κ_i, κ_i,Endog, K_d,Fura2, and the mean resting [Ca²⁺]_i (Fig. 1, legend), Eq. 1 permits calculation of the average cytoplasmic fura-2 concentration ([Fura-2]) after a 40-min incubation, ∼80 μM. Thus, assuming that κ_i,Endog is constant, small elevations in [Ca²⁺]_i starting from initial values within the range 50–300 nM are associated with changes in total cytoplasmic Ca concentration between ∼250× and 100× as large, with most of the Ca²⁺ being bound by fura-2. Based on these measurements and assumptions 1–3 above, (v_iκ_i/v_ERκ_ER) was treated as the product of a constant (v_i/v_ERκ_ER) and a [Ca²⁺]_i-dependent term κ_i that could be described explicitly by the curve in Fig. 1 D. Note that this treats all cells as if they have identical cytoplasmic Ca²⁺ buffering properties; in the absence of single cell measurements of κ_i and its [Ca²⁺]_i dependence, this seems to be a reasonable simplifying assumption. As described in appendix A, information about the [Ca²⁺]_i dependence of κ_i was used to convert J_Release into a flux that could be integrated to give information about changes in intraluminal Ca²⁺ concentration during t-BuBHQ-induced [Ca²⁺]_i transients.

To inhibit CICR, cells were exposed to ryanodine (1 μM) and then transiently to caffeine (10 mM) in the continued presence of ryanodine. Under these conditions, caffeine elicits a transient rise in [Ca²⁺]_i like that observed in control cells, but unlike control cells, responsiveness to caffeine is not restored after caffeine is removed (Thayer et al., 1988). Caffeine opens RyRs by increasing their sensitivity to [Ca²⁺]_i (Rousseau et al., 1988), and ryanodine is thought to inhibit caffeine responsiveness by irreversibly modifying RyRs so that they are insensitive to Ca²⁺ (Rousseau et al., 1987) or have greatly increased Ca²⁺ sensitivity (Masumiya et al., 2001). Ryanodine was used in conjunction with caffeine because ryanodine preferentially interacts with the open channel, causing ryanodine-induced RyR modifications to be use-dependent.

Population results are expressed as mean ± SEM, and statistical significance was assessed using t test. Fura-2 AM was obtained from Molecular Probes, ryanodine was obtained from RBI, and t-BuBHQ was purchased from Calbiochem. All other compounds were obtained from Sigma-Aldrich.

Rate equations describing Ca²⁺ extrusion across the plasma membrane (Colegrove et al., 2000b) and Ca²⁺ uptake and release by the ER were incorporated into a system of differential equations (see appendix B) that was solved numerically using a fourth-order Runge-Kutta routine (Boyce and DiPrima, 1969) written in Igor Pro (Wavemetrics, Inc.). Step size was 50 ms; further reductions in step size did not noticeably alter the results.

In the following, we will describe measurements of the rate of ER Ca²⁺ uptake by SERCAs (J_SERCA), illustrating how it varies with [Ca²⁺]_i. We will describe measurements of the rate of passive Ca²⁺ release by the ER (J_Release), showing how it depends on a [Ca²⁺]_i-sensitive permeability (⁠

⁠) that is influenced by the activity of RyRs. We then show how these rate descriptions, when taken together with a description of Ca²⁺ extrusion across the plasma membrane, account for several interesting features of Ca²⁺ dynamics described previously, including [Ca²⁺]_i-dependent attenuation of ER Ca²⁺ accumulation during depolarization, caffeine-induced [Ca²⁺]_i oscillations, and multiple modes of CICR.

We begin by summarizing evidence that in sympathetic neurons, Ca²⁺ uptake by the ER is controlled by SERCAs. Three observations support this conclusion. First, specific SERCA inhibitors such as thapsigargin (Tg) and t-BuBHQ elicit transient [Ca²⁺]_i elevations in the absence of extracellular Ca²⁺ (no added Ca²⁺ + 0.2 mM EGTA), indicating that they release Ca²⁺ from an intracellular store (unpublished data), presumably by unmasking ongoing passive Ca²⁺ release that discharges the store. Second, when used at saturating concentrations, pretreatment with one inhibitor occludes responses to the others, arguing that they have a common site of action (unpublished data). Third, pretreatment with a SERCA inhibitor (e.g., Tg) at maximally effective concentrations abolishes responsiveness to other agents that stimulate passive Ca²⁺ release in naive cells by different means (e.g., caffeine; Friel, 1995), indicating that the inhibitors effectively dissipate the gradient favoring Ca²⁺ release, and that SERCAs represent the major, if not the only, pathway for energy-dependent Ca²⁺ uptake by the store. At the concentrations tested, neither of these inhibitors systematically influenced resting [Ca²⁺]_i, indicating that depletion of stores does not elicit capacitative Ca²⁺ entry, in contrast to many nonexcitable cells (Lewis, 1999). Direct measurement of changes in total Ca concentration within the ER and other cellular compartments accompanying Tg- and caffeine-induced [Ca²⁺]_i transients indicate that the Tg- and caffeine-sensitive store in these cells is the ER (Hongpaisan et al., 2001).

To characterize the rate of ER Ca²⁺ uptake and its regulation by [Ca²⁺]_i, the following protocol was used. Cells were exposed to t-BuBHQ to inhibit Ca²⁺ uptake, and the resulting change in [Ca²⁺]_i was observed (Fig. 2). The inhibitor was applied rapidly (within ∼200 ms) and at a high concentration (100 μM; see Fig. 2 C, inset) to minimize the delay between exposure and cessation of uptake. With this concentration, the delay to the first detectable [Ca²⁺]_i increase was within one sample interval (200–250 ms), indicating that t-BuBHQ reached its site of action within this time. Moreover, reducing [t-BuBHQ] from 100 to 50 μM, which would be expected to cause the intracellular concentration of the inhibitor to increase more slowly, did not reduce the size of evoked [Ca²⁺]_i transients (Fig. 2 C, inset), supporting the conclusion that SERCA activity is rapidly inhibited in these experiments.

When t-BuBHQ was applied to resting cells (Fig. 2 A), [Ca²⁺]_i rose at an initial rate of 6.0 ± 0.6 nM/s; resting [Ca²⁺]_i in this set of experiments was 43.6 ± 2.2 nM (28 responses in six cells). The initial rate of rise provides a measure of the rate of passive Ca²⁺ release just before the perturbation, and of the rate of Ca²⁺ uptake that balances release under basal conditions (Fig. 2 A, diagrams). The same idea applies under nonsteady-state conditions (e.g., during the recovery after a depolarization-evoked [Ca²⁺]_i elevation; Fig. 2 B), leading to the generalization that the rate of SERCA-dependent Ca²⁺ uptake is given by the change in slope after rapid SERCA inhibition.

Collected results showing how the rate of Ca²⁺ uptake (J_SERCA) varies with [Ca²⁺]_i are presented in Fig. 2 C. Over the range examined (up to ∼800 nM), J_SERCA increases monotonically with [Ca²⁺]_i. Although it is difficult to exclude a functional dependence of J_SERCA on intraluminal Ca²⁺ concentration, we found that after treatment with ryanodine, which reduces intraluminal total Ca concentration by ∼60% (Hongpaisan et al., 2001) and presumably causes a significant reduction in intraluminal free Ca concentration, the resting value of J_SERCA was unchanged. This suggests that [Ca²⁺]_i is the most important variable controlling J_SERCA in these experiments, at least under resting conditions. The smooth curve in Fig. 2 C, obtained as described in materials and methods, provides a description of the composite [Ca²⁺]_i dependence of J_SERCA from basal levels up to ∼800 nM.

Pathways that may contribute to passive, or energetically downhill, Ca²⁺ release include RyRs, inositol (1,4,5)-trisphosphate receptors (InsP₃Rs), as well as an independent leak pathway. To determine the rate of passive Ca²⁺ release via all such pathways (J_Release) and its dependence on Ca²⁺ concentration, the following experiment was performed (Fig. 3). Cells were exposed to carbonyl cyanide p-(trifluoromethoxy)phenylhydrazone (FCCP), and then were exposed rapidly to 100 μM t-BuBHQ to inhibit SERCA-mediated Ca²⁺ uptake. As before, this elicited a transient [Ca²⁺]_i rise (Fig. 3 A, left). Since the main, or only, Ca²⁺ fluxes responsible for the t-BuBHQ-induced [Ca²⁺]_i transient are passive Ca²⁺ release from the ER and Ca²⁺ extrusion across the plasma membrane, measurement of the total Ca²⁺ flux during the transient, along with a characterization of the rate of Ca²⁺ extrusion across the plasma membrane, permits calculation of the rate of passive Ca²⁺ release by subtraction at each point in time during the [Ca²⁺]_i transient. The rate of Ca²⁺ extrusion was determined from the recovery after a brief, high K⁺ depolarization elicited in the continued presence of t-BuBHQ and FCCP (Fig. 3 A, right). Under these conditions, Ca²⁺ extrusion is the primary, or only, mechanism of Ca²⁺ clearance.

Fig. 3 B shows the total cytoplasmic Ca²⁺ flux (J_i) during the t-BuBHQ-induced [Ca²⁺]_i transient, determined by calculating the derivative of [Ca²⁺]_i at each point in time (inward fluxes are negative, outward fluxes are positive). J_i was initially negative and increased in magnitude to a peak before declining and changing sign after [Ca²⁺]_i attained its peak value, to become an outward flux. It then increased to maximum before finally declining to zero.

To determine J_Release, it was necessary to dissect J_i into its component fluxes. The rate of Ca²⁺ extrusion across the plasma membrane (J_pm) was determined by measuring the total Ca²⁺ flux during the recovery after depolarization, and is plotted against [Ca²⁺]_i in Fig. 3 C; for comparison, J_i is also plotted throughout the t-BuBHQ-induced transient. In a previous study, it was shown that at each point in time, J_pm depends on the [Ca²⁺]_i level at that time (Colegrove et al., 2000a). This made it possible to determine the rate of Ca²⁺ extrusion at each time point during the t-BuBHQ-induced transient based on the magnitude of J_pm during the recovery after repolarization at the corresponding [Ca²⁺]_i level. The time course of J_pm determined in this way is shown in Fig. 3 B and parallels the [Ca²⁺]_i response. Subtracting J_pm from J_i at each point in time then gives the remaining Ca²⁺ flux (Fig. 3 B, shaded region). Since these measurements were performed in the presence of FCCP and a saturating concentration of t-BuBHQ, the remaining flux (J_Release) is expected to represent the rate of passive Ca²⁺ release from the ER (Fig. 3 B). If cytoplasmic and intraluminal buffers equilibrate rapidly with Ca²⁺ and the latter bind Ca²⁺ with low affinity, then at each instant in time, the product J_Releaseκ_i should be directly proportional to the net ER Ca²⁺ flux, and, therefore, to the rate at which [Ca²⁺]_ER changes with time (see appendix A). The properties of J_Release are revealing. During the entire t-BuBHQ-induced [Ca²⁺]_i transient, J_Release is negative, which is indicative of Ca²⁺ release. During the rising phase, the magnitude of J_Release increases to a peak. This increase occurs even though the driving force for passive Ca²⁺ release should be falling ([Ca²⁺]_i is rising and the intraluminal Ca²⁺ concentration is falling). As discussed in connection with Fig. 2, with our application protocol, t-BuBHQ appears to block SERCAs rapidly (within 200 ms) and completely, arguing that the initial increase in J_Release observed in control cells does not simply reflect the time required for the inhibitor to act. This is supported by the finding that, in ryanodine-treated cells, the magnitude of J_Release declines monotonically after t-BuBHQ application (see Fig. 4). This suggests that the pathway responsible for passive Ca²⁺ release includes a [Ca²⁺]_i-sensitive permeability.

Given measurements of J_Release, along with a description of the intraluminal Ca²⁺ concentration, it is possible to characterize the Ca²⁺ permeability of the ER and test the idea that it is sensitive to [Ca²⁺]. When ER Ca²⁺ uptake is inhibited, J_Release gives the net ER Ca²⁺ flux referred to the effective cytoplasmic volume, so multiplying by the ratio of effective cytoplasmic and intraluminal volumes (v_iκ_i/v_ERκ_ER) gives the rate at which [Ca²⁺]_ER changes with time. Integration of this quantity from the instant of t-BuBHQ application to the time t thus provides a measure of the change in [Ca²⁺]_ER relative to its initial value just before the perturbation. Subtracting the integral during the entire t-BuBHQ-induced [Ca²⁺]_i transient gives the change in concentration relative to its final basal value. As shown in appendix A, this latter quantity, which we call Δ[Ca²⁺]_ER(t), is given by Eq. 2:

where minus the integral (⁠

⁠) can be interpreted as the change in total cytoplasmic Ca concentration that would occur if from time t onward, J_Release were deposited into a closed compartment having the same volume as the cytoplasm. Accordingly, the initial value (⁠

\(\mathrm{{\Delta}}\left[\mathrm{Ca}^{2\mathrm{+}}\right]_{\mathrm{ER}}^{\left(\mathrm{i}\right)}\left(0\right)\)

⁠) provides information about the resting Ca²⁺ concentration within the ER. The relationship is (Eq. 3):

A similar approach to assessing changes in ER Ca²⁺ concentration in T cells was described previously by Bergling et al. (1998).

Before using J_Release and

to characterize the Ca²⁺ permeability of the ER, it is important to determine if these quantities have the expected properties. During the entire t-BuBHQ-induced [Ca²⁺]_i transient, the sign of J_Release is indicative of net Ca²⁺ release, and correspondingly

\(\mathrm{{\Delta}}\left[\mathrm{Ca}^{2\mathrm{+}}\right]_{\mathrm{ER}}^{\left(\mathrm{i}\right)}\left(\mathrm{t}\right)\)

declines monotonically from the point of t-BuBHQ addition (Fig. 3 D). Analysis of sympathetic neurons gives an estimate of 10–20 for v_i/v_ER (unpublished data); although measurements of κ_ER have not been made in these cells, values have been reported in other cells: ∼17 in AtT-20 cells (Wu et al., 2001) and ∼20 in pancreatic acinar cells (Mogami et al., 1999). Based on these values, v_i/(v_ERκ_ER) can be estimated to be ∼0.5–1.2. Thus, the ∼140-μM decline in

\(\mathrm{{\Delta}}\left[\mathrm{Ca}^{2\mathrm{+}}\right]_{\mathrm{ER}}^{\left(\mathrm{i}\right)}\)

shown in Fig. 3 C would correspond to a 70–168-μM decline in [Ca²⁺]_ER. Since the basal value of [Ca²⁺]_ER after treatment with t-BuBHQ ([Ca²⁺]_ER(∞)) would be expected to approximate the resting cytoplasmic Ca²⁺ concentration (∼50–100 nM), using Eq. 3 we arrive at an estimated initial value of [Ca²⁺]_ER ∼70.1–168.1 μM. This is consistent with the value obtained from the reduction in total ER Ca concentration induced by Tg, as determined from electron probe microanalysis in these cells (∼2 mM; Hongpaisan et al., 2001) using the same values for κ_ER: Δ[Ca²⁺]_ER ∼ 2 mM/20 = 100 μM. It should be noted that because slow net Ca²⁺ release is increasingly difficult to resolve as [Ca²⁺]_i approaches its resting level, it is difficult to determine when J_Release is truly zero and Ca²⁺ within the ER is in equilibrium with the cytoplasmic compartment. Therefore, it is possible that the initial value of

\(\mathrm{{\Delta}}\left[\mathrm{Ca}^{2\mathrm{+}}\right]_{\mathrm{ER}}^{\left(\mathrm{i}\right)}\)

⁠, and hence our estimations of basal [Ca²⁺]_ER, underestimate the actual values.

Measurements of J_Release and

⁠, along with the characterization of κ_i from Fig. 1, can now be used to provide information about the Ca²⁺ permeability of the ER (⁠

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

⁠).

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

is defined operationally by Eq. 4:

where P_ER is a lumped parameter giving the ratio of

to v_iκ_i, and [Ca²⁺]_ER(t) is the free Ca concentration within the ER at time t.

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

would be expected to depend on the number, open probability, and unitary Ca²⁺ permeability of ryanodine-sensitive Ca²⁺ release channels expressed in these cells, as well as other channels that are permeable to Ca²⁺ and influence the rate of passive Ca²⁺ release. In particular, the [Ca²⁺]_i dependence of

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

should provide information about how the activity of these channels varies with [Ca²⁺]_i. In general,

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

could be influenced by [Ca²⁺]_i, [Ca²⁺]_ER, and could show explicit time dependence (e.g., as a result of desensitization). Finally, P_ER would be expected to show a composite [Ca²⁺]_i dependence representing properties of both

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

and κ_i.

Given measurements of J_Release and ([Ca²⁺]_i − [Ca²⁺]_ER), P_ER could be determined from the ratio J_Release/([Ca²⁺]_i − [Ca²⁺]_ER) at each point in time during the t-BuBHQ-induced [Ca²⁺]_i transient; measurements of κ_i would then make possible to obtain information about

⁠. This approach requires information about [Ca²⁺]_ER(t). Although single cell measurements of [Ca²⁺]_ER(t) are not available, it is shown in appendix A that ([Ca²⁺]_i − [Ca²⁺]_ER) can be approximated by −(v_i/v_ERκ_ER)

\(\mathrm{{\Delta}}\left[\mathrm{Ca}^{2\mathrm{+}}\right]_{\mathrm{ER}}^{\left(\mathrm{i}\right)}\)

⁠, making it possible to rewrite Eq. 4 as Eq. 5:

and to obtain a quantity that is proportional to P_ER from measured values,

which is valid as long as [Ca²⁺]_ER is much larger than [Ca²⁺]_i (see appendix A). Fig. 3 E shows P_ER(v_i/v_ERκ_ER) plotted against [Ca²⁺]_i during the t-BuBHQ-induced [Ca²⁺]_i transient, calculated according to Eq. 6. The dark noisy trace shows P_ER(v_i/v_ERκ_ER) during the rising phase of the transient, and the light trace represents the recovery phase. Three features of these measurements should be noted. First, P_ER(v_i/v_ERκ_ER) is not constant, but increases monotonically with [Ca²⁺]_i over the range ∼50–250 nM. Second, the [Ca²⁺]_i dependence of P_ER(v_i/v_ERκ_ER) during the onset and recovery (dark and light traces, respectively) is very similar. In other words, for a given value of [Ca²⁺]_i, P_ER(v_i/v_ERκ_ER) has essentially the same magnitude during both the onset and the recovery. Since the intraluminal Ca²⁺ concentration is expected to be very different during these phases of the t-BuBHQ-induced [Ca²⁺]_i transient, it appears that P_ER(v_i/v_ERκ_ER) depends much more strongly on [Ca²⁺]_i than on [Ca²⁺]_ER. Moreover, if the underlying permeability undergoes desensitization, it must be very rapid, or very weak, compared with the [Ca²⁺]_i-dependent changes observed in these experiments. Finally, extrapolation of P_ER(v_i/v_ERκ_ER) to [Ca²⁺]_i = 0 gives an estimate of the basal Ca²⁺ permeability of the ER (Fig. 3 E, dotted trace); however, since this value is based on extrapolation, there is uncertainty about its precise value. Importantly, these properties are shared by the macroscopic Ca²⁺ permeability. Fig. 3 E (inset) shows

/v_ERκ_ER, obtained after scaling P_ER(v_i/v_ERκ_ER) by κ_i, indicating that the macroscopic Ca²⁺ permeability of the ER depends on [Ca²⁺]_i. Results presented in the next section provide evidence that this [Ca²⁺]_i-dependent permeability is dominated by ryanodine receptors.

A number of observations indicate that sympathetic neurons express functional RyRs (Kuba and Nishi, 1976; Lipscombe et al., 1988; Friel and Tsien, 1992a,b; Hua et al., 1993; Akita and Kuba, 2000) that would contribute to the macroscopic Ca²⁺ permeability of the ER, so we performed experiments to determine if

is sensitive to pharmacological modifiers of RyRs (Zucchi and Roncha-Testoni, 1997). Fig. 4 shows t-BuBHQ-induced [Ca²⁺]_i transients (Fig. 4 A) and the corresponding measurements of J_Release (Fig. 4 B) and

\(\mathrm{{\Delta}}\left[\mathrm{Ca}^{2\mathrm{+}}\right]_{\mathrm{ER}}^{\left(\mathrm{i}\right)}\)

(Fig. 4 C) under control conditions, during continuous exposure to caffeine (after the caffeine-induced [Ca²⁺]_i transient) and after treatment with ryanodine, which rendered cells unresponsive to caffeine. Fig. 4 D compares the [Ca²⁺]_i dependence of P_ER(v_i/v_ERκ_ER) for each cell whose responses are illustrated in Fig. 4, A–C; population results are shown in Fig. 4 E. In the presence of caffeine, t-BuBHQ-induced [Ca²⁺]_i transients are faster, and

\(\mathrm{{\Delta}}\left[\mathrm{Ca}^{2\mathrm{+}}\right]_{\mathrm{ER}}^{\left(\mathrm{i}\right)}\)

declines more rapidly, compared with controls, reflecting an approximately threefold increase in the peak magnitude of J_Release. In contrast, after treatment with ryanodine, the evoked [Ca²⁺]_i transients are slower, and

\(\mathrm{{\Delta}}\left[\mathrm{Ca}^{2\mathrm{+}}\right]_{\mathrm{ER}}^{\left(\mathrm{i}\right)}\)

declines more slowly than the control, reflecting a steady decline in J_Release that contrasts markedly with the initial increase seen both in the control case and in the presence of caffeine. Given that the magnitude of J_Release declines monotonically from the instant of t-BuBHQ application in ryanodine-treated cells, it is unlikely that the initial increase in J_Release observed in control and caffeine-treated cells occurs simply because the inhibitor acts slowly, or because of [Ca²⁺]_i-dependent changes in cytoplasmic Ca²⁺ buffering strength. It also was found that the initial value of

\(\mathrm{{\Delta}}\left[\mathrm{Ca}^{2\mathrm{+}}\right]_{\mathrm{ER}}^{\left(\mathrm{i}\right)}\)

followed the order: control (115 ± 12 μM, four cells) is greater than +caffeine (38 ± 4 μM, four cells) is greater than +ryanodine (20 ± 3 μM, three cells). Neither caffeine nor ryanodine had a systematic effect on J_pm (unpublished data). These actions of caffeine and ryanodine on t-BuBHQ-induced [Ca²⁺]_i transients are consistent with their effects on P_ER(v_i/v_ERκ_ER) and

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

/(v_ERκ_ER) (Fig. 4 D). In the presence of caffeine and ryanodine,

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

/(v_ERκ_ER) shows higher values at resting [Ca²⁺]_i than the control, accounting for the lower basal values of

\(\mathrm{{\Delta}}\left[\mathrm{Ca}^{2\mathrm{+}}\right]_{\mathrm{ER}}^{\left(\mathrm{i}\right)}\)

(Fig. 4 C). In the presence of caffeine,

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

/(v_ERκ_ER) also increases more steeply with [Ca²⁺]_i than in the control and shows a supralinear [Ca²⁺]_i dependence, which presumably contributes to the accelerated [Ca²⁺]_i rise (Fig. 4, A and B). After ryanodine treatment, the [Ca²⁺]_i dependence of P_ER(v_i/v_ERκ_ER) could be accounted for simply by the [Ca²⁺]_i dependence of κ_i, indicating that, under these conditions,

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

/(v_ERκ_ER) does not vary with [Ca²⁺]_i, accounting for the monotonic decline in the magnitude of J_Release (Fig. 4 B) and the slower [Ca²⁺]_i transient (Fig. 4 A). Each effect is consistent with known properties of RyRs and their modification by caffeine and ryanodine (Rousseau et al., 1987, 1988). Overall, the results illustrate how a caffeine- and ryanodine-sensitive Ca²⁺ permeability representing the activity of a population of RyRs contributes to passive Ca²⁺ release from the ER. Importantly, the properties of

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

in ryanodine-treated cells suggests that RyRs are responsible for most of the [Ca²⁺]_i dependence of ER Ca²⁺ permeability when [Ca²⁺]_i < 250 nM and InsP3-generating agonists are not present.

To determine if the rate descriptions presented above are sufficient to account for the dynamics of cytoplasmic and intraluminal Ca²⁺ concentration during t-BuBHQ-induced [Ca²⁺]_i transients, simulations were performed using the experimentally determined descriptions of J_SERCA, J_pm, P_ER(v_i/v_ERκ_ER), and κ_i, approximating v_i/v_ERκ_ER by unity. In displaying the results, simulated Ca²⁺ concentrations are designated by c_i and c_ER to distinguish them from measured quantities. To facilitate comparison with responses from cells in Fig. 4, simulations were performed using the transport descriptions and initial [Ca²⁺]_i values obtained from those same cells. It was found that the simulations reproduce the experimental observations quite well, including the relative values of basal c_ER and the time courses of c_i, J_Release, and c_ER (Fig. 5). This leads to three conclusions. First, J_pm, J_SERCA, and

describe the main Ca²⁺ transport pathways responsible for cytoplasmic and intraluminal Ca²⁺ dynamics after rapid SERCA inhibition. Second, the equations used to describe these pathways do not ignore variables that are important for the dynamics of [Ca²⁺]_i and

\(\mathrm{{\Delta}}\left[\mathrm{Ca}^{2\mathrm{+}}\right]_{\mathrm{ER}}^{\left(\mathrm{i}\right)}\)

⁠. Third, the functional dependence of the fluxes on [Ca²⁺]_i and [Ca²⁺]_ER is sufficiently accurate to reproduce the salient features of the time courses of [Ca²⁺]_i and

\(\mathrm{{\Delta}}\left[\mathrm{Ca}^{2\mathrm{+}}\right]_{\mathrm{ER}}^{\left(\mathrm{i}\right)}\)

⁠. Thus, when mitochondrial Ca²⁺ transport is suppressed, the initial distribution of intracellular Ca²⁺, as well as the dynamics of Ca²⁺ after inhibition of SERCAs, can be explained in terms of the properties of J_pm, J_SERCA,

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

⁠, and κ_i.

We have shown that when [Ca²⁺]_i is low (less than or equal to ∼350 nM) during weak depolarization, the ER normally accumulates Ca²⁺, and that after treatment with ryanodine, the same stimuli lead to enhanced ER Ca²⁺ accumulation (Albrecht et al., 2001). We asked if the properties of J_pm, J_SERCA P_ER(v_i/v_ERκ_ER) and κ_i described above account for these observations. Fig. 6 shows simulations of depolarization-induced changes in [Ca²⁺]_i and [Ca²⁺]_ER using a measured Ca²⁺ current (I_Ca) as the basis for calculating the rate of stimulated Ca²⁺ entry (Fig. 6 A). Mitochondrial Ca²⁺ uptake was taken into consideration as described in Colegrove et al. (2000b) to facilitate comparison with measurements performed under voltage clamp in the absence of FCCP (Albrecht et al., 2001). Using parameters for P_ER(v_i/v_ERκ_ER) obtained under control conditions, Ca²⁺ entry produces a c_i elevation that is accompanied by weak ER Ca²⁺ accumulation; consequently, the [Ca²⁺]_i response is slightly accelerated when uptake is inhibited with Tg, as observed experimentally (Albrecht et al., 2001). Using P_ER(v_i/v_ERκ_ER) parameters taken from ryanodine-treated cells, Ca²⁺ entry elicits a slower rise in c_i but a more robust increase in c_ER, also as observed experimentally (Albrecht et al., 2001). Finally, using P_ER(v_i/v_ERκ_ER) parameters from caffeine-treated cells, [Ca²⁺]_i rises more rapidly in response to the same stimulus in concert with net Ca²⁺ release. Net Ca²⁺ release occurs in this case because J_Release increases more steeply with c_i than does J_SERCA over this c_i range. Resting c_ER is lower in this and the +Ryan case because basal P_ER(v_i/v_ERκ_ER) is higher than it is under control conditions. These results validate the quantitative model presented in our previous study (Albrecht et al., 2001).

Comparing ER Ca²⁺ uptake and release rates shows how activation of the CICR pathway influences net ER Ca²⁺ transport and c_i and c_ER dynamics during such weak stimuli (Fig. 7). Before stimulation, ER Ca²⁺ uptake and release rates are in balance, accounting for the steady resting value of c_ER. The resting rate of release is not modified by ryanodine because while

is increased, the driving force is reduced, such that their product is unchanged. Under control conditions (Fig. 7 B), stimulation leads to Ca²⁺ accumulation by the ER (Fig. 7 B, dark trace) because J_SERCA increases more rapidly than J_Release. J_SERCA increases because of its intrinsic c_i dependence, whereas J_Release rises in magnitude because of two factors: an increase in driving force (since c_ER rises more rapidly than c_i) and an increase in

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

⁠. The c_i-dependent increase in

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

accelerates the increase in J_Release, reducing the imbalance between J_SERCA and J_Release, ultimately causing the ER to be a less powerful Ca²⁺ buffer. After inhibiting the c_i-dependent activation of

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

(Fig. 7 C), the magnitude of J_Release increases more slowly in response to an increase in driving force only, and this exaggerates the imbalance between J_SERCA and J_Release, leading to enhanced Ca²⁺ accumulation. As a result, the ER becomes a stronger buffer, as observed experimentally (Albrecht et al., 2001).

Previous work has shown that when caffeine-treated sympathetic neurons are depolarized to stimulate Ca²⁺ entry, [Ca²⁺]_i rises rapidly to produce a spike and then, in many cases, oscillates (Lipscombe et al., 1988; Nohmi et al., 1992; Friel and Tsien, 1992b). To determine if these [Ca²⁺]_i oscillations can be accounted for by the interplay between J_pm, J_SERCA, and P_ER(v_i/v_ERκ_ER), simulations were performed using descriptions of J_pm and J_SERCA from control cells and of P_ER(v_i/v_ERκ_ER) from caffeine-treated cells. Although Ca²⁺ entry led to a steady increase in c_i when Ca²⁺ uptake by the store was inhibited (Fig. 8, +Tg, dotted traces), oscillations were observed when both uptake and release pathways were enabled. The oscillations were much like those observed experimentally when caffeine-treated sympathetic neurons are depolarized by exposure to high K⁺ (Friel and Tsien, 1992b). Using descriptions of P_ER(v_i/v_ERκ_ER) from control and caffeine-treated cells contributing to the collected results in Fig. 4 E indicates that depolarization-evoked Ca²⁺ entry does not elicit c_i oscillations when control P_ER(v_i/v_ERκ_ER) descriptions are used (4/4 cells), whereas oscillations can be elicited when descriptions are taken from caffeine-treated cells (4/4 cells). Thus, the quantitative descriptions of ER Ca²⁺ uptake and release pathways obtained using t-BuBHQ-induced perturbations account for the observation that membrane depolarization typically elicits [Ca²⁺]_i oscillations in caffeine-treated cells, but not in untreated cells.

Measurements in sympathetic neurons implicate distinct modes of CICR that operate over different ranges of [Ca²⁺]_i (Albrecht et al., 2001, Hongpaisan et al., 2001). When [Ca²⁺]_i is low, the ER accumulates Ca²⁺ at a rate that is reduced by activation of the CICR pathway (Mode 1 CICR). At higher [Ca²⁺]_i levels, the ER releases Ca²⁺, either at a rate that is slower than Ca²⁺ clearance by other pathways (Mode 2 CICR), or faster, such that release overwhelms Ca²⁺ clearance, leading to regenerative release (Mode 3 CICR). Do the measurements of J_pm, J_SERCA, and P_ER(v_i/v_ERκ_ER) described above help explain these modes of CICR? Although we did not carry out rate measurements at high [Ca²⁺]_i, it is possible to investigate the qualitative properties of these modes using the measured rate descriptions extrapolated to higher [Ca²⁺]_i. J_pm, J_SERCA, and P_ER were represented by continuously extending the functions describing their [Ca²⁺]_i dependence at lower [Ca²⁺]_i levels. The resulting descriptions coincide with the measured values at low c_i and represent approximations at high c_i. Fig. 9 shows how in the steady state, c_ER varies with c_i. When c_i is below ∼200 nM, an increase in c_i leads to net Ca²⁺ uptake and a rise in c_ER. Increasing c_i further over the physiological range leads to net Ca²⁺-induced Ca²⁺ release and a decline in c_ER. Further (nonphysiological) increases in c_i lead to Ca²⁺ accumulation and a rise in c_ER. Thus, there are two major effects of the Ca²⁺ sensitive permeability on the relationship between c_i and c_ER under steady-state conditions. First, it leads to the definition of three distinct c_i ranges in which the ER plays qualitatively different roles in Ca²⁺ regulation: low c_i (ER is a Ca²⁺ sink), intermediate c_i (ER is a Ca²⁺ source), and high c_i (ER is a Ca²⁺ sink). Second, it would act as a safety valve to stabilize c_ER in the face of prolonged [Ca²⁺]_i elevations that would otherwise lead to large increases in intraluminal Ca²⁺ levels. With CICR in place, c_ER increases by less than a factor of two for a 10,000-fold change in c_i above resting levels.

To illustrate how the Ca²⁺-sensitive permeability is expected to influence evoked Ca²⁺ signals, Fig. 10 (B and C) shows instantaneous flux/c_i relations like those described in Albrecht et al. (2001), calculated using the same parameter values as in Fig. 9 (with CICR). Fig. 9 A shows the c_i dependence of P_ER and

/V_i, whereas Fig. 9 B shows how J_ER and its components J_SERCA and J_Release would be expected to change if c_i was suddenly raised without perturbing c_ER from its resting value, assuming a normal resting [Ca²⁺]_i level (50 nM). When c_i is increased up to ∼350 nM, the outward flux J_SERCA is larger in magnitude than the inward flux J_Release, so that the ER accumulates Ca²⁺. However, Ca²⁺ accumulation becomes gradually slower because of progressive Ca²⁺-dependent activation of P_ER, which we called Mode 1 CICR. When c_i exceeds the threshold for net CICR, J_Release is larger in magnitude than J_SERCA, causing J_ER to be an inward flux, leading to net Ca²⁺ release (Mode 2). The Ca²⁺ level at which this transition occurs, defined by a specific threshold (Fig. 10 B, arrow), depends on the quantitative relationship between the underlying fluxes and their c_i dependence. Similarly, the interplay between Ca²⁺ extrusion across the plasma membrane and net ER Ca²⁺ transport defines the total cytoplasmic Ca²⁺ flux (J_i,total; Fig. 10 C). When c_i is low, J_pm and J_ER are both outwardly directed, so that if c_i were increased rapidly to such a level and then allowed to relax, c_i would decline at a rate that is jointly influenced by Ca²⁺ extrusion and net uptake by the ER. If c_i were increased to higher levels where J_ER is negative, c_i would also decline, but at a rate that reflects the difference between Ca²⁺ extrusion and net release rates. Finally, if c_i is increased beyond ∼935 nM, the rate of net Ca²⁺ release exceeds the rate of Ca²⁺ clearance, leading regenerative release. Fig. 10 (right) illustrates simulated c_i and c_ER responses (Fig. 10, E and F) evoked by stimuli that raise c_i to levels below or above the threshold for net Ca²⁺ release, and above the threshold for regenerative net CICR. Simulations were performed using Ca²⁺ entry waveforms obtained from measured Ca²⁺ currents of 2-s duration (Fig. 10 D). As [Ca²⁺]_i rises during the first (subthreshold) stimulus (curve 1), the ER accumulates Ca²⁺ (Fig. 10 F, inset). After the stimulus ends, c_ER continues to rise and c_i declines under the joint influence of Ca²⁺ extrusion across the plasma membrane and Ca²⁺ accumulation by the store. During the second stimulus, which exceeds the threshold for net CICR (curve 2), the ER is transformed into a source, with c_ER eventually declining below the basal level (Fig. 10 F, inset). When the stimulus ends, c_i declines initially at a rate that depends on Ca²⁺ extrusion and net Ca²⁺ release, but the recovery is eventually accelerated when the ER once again becomes a Ca²⁺ sink, causing an overshoot of the basal level before c_ER finally approaches the resting value. The third stimulus (curve 3) is sufficiently strong to bring c_i above the threshold for regenerative CICR, such that when the stimulus ends, c_i continues to rise under the influence of continued net Ca²⁺ release at a rate that exceeds the rate of Ca²⁺ extrusion. Thus, the extrapolated rate descriptions for J_pm, J_SERCA, and P_ER provide an explanation for the observation that stimuli producing progressively larger [Ca²⁺]_i elevations cause the ER to undergo a transition from sink to source (Hongpaisan et al., 2001).

The main goal of this study was to determine how Ca²⁺-dependent activation of a ryanodine-sensitive CICR pathway contributes to [Ca²⁺] responses evoked by weak depolarization. Our previous study showed that under these conditions of stimulation, the ER accumulates Ca²⁺, but we also presented indirect evidence that the rate of Ca²⁺ accumulation is attenuated by activation of the CICR pathway, which, in effect, makes the ER a weaker Ca²⁺ buffer. Since the rate of net ER Ca²⁺ transport depends on the relative rates of Ca²⁺ uptake and release via different transport pathways, we characterized these rates and their regulation by Ca²⁺ to test the hypothesis that the direction and rate of net ER Ca²⁺ transport depends on a slight imbalance between uptake and release rates of much larger magnitude, each showing a distinct functional dependence on [Ca²⁺]. We found that Ca²⁺ uptake is regulated by SERCAs in a [Ca²⁺]_i-dependent manner, and that passive Ca²⁺ release is regulated by a [Ca²⁺]_i-sensitive permeability that is modified by caffeine and ryanodine in a way that indicates it is dominated by ryanodine-sensitive Ca²⁺ release channels. It was found that quantitative differences in the [Ca²⁺]_i sensitivity of Ca²⁺ uptake and release rates account for Mode 1 CICR. Although these rates are in balance under resting conditions, small [Ca²⁺]_i elevations stimulate Ca²⁺ uptake more strongly than Ca²⁺ release, accounting for Ca²⁺ accumulation. Moreover, increases in the rate of passive Ca²⁺ release by such small [Ca²⁺]_i elevations, reflecting a [Ca²⁺]_i-induced rise in ER Ca²⁺ permeability, reduces the imbalance between uptake and release rates, accounting for attenuated Ca²⁺ accumulation during stimulation. Taken together with the properties of Ca²⁺ extrusion across the plasma membrane, these same transport pathways account for caffeine-induced [Ca²⁺]_i oscillations. Finally, extending the rate descriptions of Ca²⁺ uptake and release to higher [Ca²⁺]_i levels provides an explanation for our finding that as depolarization-evoked [Ca²⁺]_i elevations become larger, the ER becomes a less effective Ca²⁺ buffer, and at high [Ca²⁺]_i, becomes a Ca²⁺ source.

The impact of SERCAs (J_SERCA) on Ca²⁺ dynamics was assessed by measuring the t-BuBHQ-sensitive component of the total cytoplasmic Ca²⁺ flux (J_i) just after exposing cells to a high concentration of t-BuBHQ. As it was measured, the [Ca²⁺]_i dependence of J_SERCA is expected to depend both on the rate of Ca²⁺ uptake via SERCAs at the instant of inhibition, and the properties of cytoplasmic Ca²⁺ buffering. The composite [Ca²⁺]_i dependence of J_SERCA could be described by Eq. B8 quite well, and along with the other transport characterizations it made it possible to reconstruct the observed t-BuBHQ-induced [Ca²⁺]_i transients. While the equations used to describe transport in this study were mechanistically motivated, they should be regarded as empirical descriptions of the transport rates and their [Ca²⁺]_i dependence. Nevertheless, it is noteworthy that the apparent [Ca²⁺]_i sensitivity of uptake (EC_50,SERCA < 100 nM) was higher than expected based on studies of SERCAs in isolation (Lytton et al., 1992). One possible explanation is that CICR raises local [Ca²⁺]_i beyond the level detected by bulk [Ca²⁺]_i measurements. Such an increase could partially saturate the uptake pathway, even though bulk [Ca²⁺]_i is considerably lower. As shown by Albrecht et al. (2001), ryanodine does not alter J_SERCA under resting conditions, arguing against such an effect when [Ca²⁺]_i is at its resting level. However, with stronger activation of the CICR pathway at higher [Ca²⁺]_i, it is possible that increases in local [Ca²⁺]_i near sites of ER Ca²⁺ uptake bring SERCAs close to saturation, so that at high [Ca²⁺]_i the [Ca²⁺]_i dependence of J_SERCA largely reflects the [Ca²⁺]_i dependence of κ_i. Assessment of this possibility will require additional information regarding the spatial distribution of Ca²⁺ near the ER and the specific SERCA isoforms that are expressed in sympathetic neurons.

It has been difficult to characterize CICR in intact cells because the rate of passive Ca²⁺ release depends on two factors that are difficult to distinguish experimentally in intact cells: driving force and permeability. It is expected that Ca²⁺ release channel activity influences J_Release primarily through its effect on P_ER, and secondarily through its effect on driving force; although the latter effect depends on other transport systems that influence ER Ca²⁺ loading, such as Ca²⁺ uptake and extrusion. We devised a way to distinguish between these contributions to J_Release. Integration of J_Releaseκ_i provided a measure of changes in intraluminal Ca²⁺ concentration, which in turn made it possible to estimate the driving force for Ca²⁺ release. Along with the definition of P_ER provided by Eq. 4, this made it possible to obtain a quantity that is expected to be proportional to the macroscopic permeability of the ER (⁠

⁠) from the ratio of two measured quantities.

Based on this procedure, we characterized

and its [Ca²⁺] dependence, as well as its sensitivity to pharmacological agents known to modify RyR gating in vitro. We found that (1)

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

/(v_ERκ_ER) increases with [Ca²⁺]_i over the range studied (up to ∼250 nM), which is consistent with regulation of RyR activity through low affinity Ca²⁺–channel interactions with little cooperativity. (2) Caffeine increased, and ryanodine reduced, the [Ca²⁺]_i sensitivity of

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

/(v_ERκ_ER), arguing that its [Ca²⁺]_i dependence is dominated by RyRs. The apparent loss of Ca²⁺ sensitivity after ryanodine treatment also provides a simple explanation for the previous finding that ryanodine enhances ER Ca²⁺ accumulation during depolarization. By preventing a Ca²⁺-dependent increase in ER Ca²⁺ permeability, ryanodine also prevents an increase in the rate of Ca²⁺ release that normally occurs in response to evoked elevations in [Ca²⁺]_i. This would exaggerate the imbalance between uptake and release rates under conditions where the ER is a Ca²⁺ sink, rendering the ER a more powerful Ca²⁺ buffer. (3) Ryanodine increased basal

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

/(v_ERκ_ER), which is consistent with its effects on RyR open probability at the concentration used (1 μM). This result provides an explanation for our finding that ryanodine at the same concentration reduces basal intraluminal total Ca concentration (and presumably free Ca concentration) without altering the basal rate of Ca²⁺ uptake or release (Albrecht et al., 2001). (4) The [Ca²⁺]_I dependence of

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

/(v_ERκ_ER) was not detectably different during the rising and falling phases of the t-BuBHQ-induced [Ca²⁺]_i transients.

This leads to two conclusions about RyR regulation during these responses. First,

is not very sensitive to reductions in intraluminal Ca²⁺ concentration that occur during these two phases of the transients. In other words, the major sites responsible for Ca²⁺-dependent regulation of

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

are directly accessible from the cytoplasmic solution. This agrees with the conclusions of Xu and Meissner (1998), who showed that intraluminal Ca levels influence gating of canine cardiac RyRs in a way that can be accounted for by Ca²⁺ release followed by interactions with cytoplasmic regulatory sites. Second,

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

does not show appreciable intrinsic time dependence. This finding is consistent with the results of Schiefer et al. (1995) who showed there is little inactivation of canine cardiac RyRs when cis [Ca²⁺] < 1 μM (our measurements of

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

were made below 250 nM). Thus, the effects of caffeine and ryanodine on

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

at low [Ca²⁺]_i are in general agreement with in vitro studies of RyRs derived from mammalian cardiac cells.

An important step in characterizing

was estimation of the driving force for passive Ca²⁺ release. Several approximations were made. First, it was assumed that the ER membrane potential is small enough that it has little or no effect on J_Release. Second, it was assumed that intraluminal Ca²⁺ buffers bind Ca²⁺ rapidly and with low affinity. Third, it was assumed that Δ[Ca²⁺]_i is small enough compared with Δ[Ca²⁺]_ER (the differences between [Ca²⁺]_i and [Ca²⁺]_ER and their basal levels during t-BuBHQ-induced [Ca²⁺]_i transients) that cytoplasmic Ca²⁺ has negligible effect on driving force (appendix A).

Our results describe the quantitative properties of ER Ca²⁺ transport in intact cells under conditions where the spatial distribution of Ca²⁺ within cellular compartments is likely to be nearly uniform. How relevant are the rate descriptions obtained under these conditions to the case where Ca²⁺ is distributed nonuniformly (e.g., during depolarization-evoked Ca²⁺ entry)? In this case, [Ca²⁺]_i is highest near sites of Ca²⁺ entry and falls off with distance from the plasma membrane (Sala and Hernandez-Cruz, 1990; Hua et al., 1993). As long as the transport descriptions refer to populations of Ca²⁺ transporters that are distributed uniformly within the membranes delimiting compartments, and these membranes have simple geometry, the results are also expected to predict the spatial distribution of [Ca²⁺] within compartments during periods of Ca²⁺ entry. Results that support this conclusion have been presented for the analogous problem of mitochondrial Ca²⁺ loading during depolarization (Pivovarova et al., 1999). Moreover, examination of the case where Ca²⁺ is spatially uniform provides an explanation for the basis of steady-state Ca²⁺ level within ER in terms of the quantitative properties of ER Ca²⁺ uptake and release rates, and shows how [Ca²⁺]_i levels help determine which modes of CICR can be recruited in response to stimulation. Nevertheless, if the distribution of the ER or of transporters within ER or plasma membranes is nonuniform, for example, such that the density or intrinsic properties of ER transporters vary appreciably from one somatic region to another (e.g., peripheral versus central regions), or if proximity between intracellular membranes permits the development of Ca²⁺ microdomains (Rizzuto et al., 1998), an accurate description of [Ca²⁺] dynamics during stimulation would require detailed specification of the distribution of transporters and membrane geometry. An example where spatial nonuniformity may introduce an error in the [Ca²⁺]_i dependence of transport presented in this study was mentioned in connection with J_SERCA.

To our knowledge, this is the first description of ER Ca²⁺ uptake and release fluxes and Ca²⁺ permeability in intact cells. Our study builds on previous work in skeletal (Baylor et al., 1983; Kovacs et al., 1983; Melzer et al., 1987) and cardiac muscle (Sipido and Wier, 1991) describing CICR from the SR after membrane depolarization. As in these studies, we used the basic idea that at each instant in time, [Ca²⁺]_i changes at a rate that depends on the rates of passive Ca²⁺ release and removal, and on the properties of intracellular Ca²⁺ buffering. Thus, with information about the rate of Ca²⁺ removal and buffering, the rate of Ca²⁺ release can be calculated from the total Ca²⁺ flux. In these earlier studies, the rate of Ca²⁺ uptake was not measured, and was either included in an overall description of Ca²⁺ removal (Melzer et al., 1987) or was calculated (Sipido and Wier, 1991). In the present study, we used t-BuBHQ as a tool to measure both the rates of ER Ca²⁺ uptake and release and their [Ca²⁺] dependence. As a result, it was possible to describe the relationship between Ca²⁺ uptake and release fluxes during and after stimulation, which was essential for understanding the direction and rate of net ER Ca²⁺ transport during depolarization and how it is regulated by [Ca²⁺]_i. With an understanding of the basis of net ER Ca²⁺ transport, it became possible to clarify how the interplay between net ER Ca²⁺ transport and Ca²⁺ extrusion across the plasma membrane sets the stage for multiple modes of CICR.

Previous studies have shown that when sympathetic neurons are exposed steadily to caffeine and then depolarized, [Ca²⁺]_i oscillates (Lipscombe et al., 1988; Friel and Tsien, 1992b; Kuba, 1994). Oscillations can be elicited by caffeine alone, but in our experiments, depolarization considerably increased the reliability with which they are evoked. In an earlier study (Friel, 1995), three independent components of the total Ca²⁺ flux underlying caffeine-induced Ca²⁺ oscillation were measured. These components represented caffeine-sensitive Ca²⁺ release, Ca²⁺ entry, and the remainder of the total cytoplasmic Ca²⁺ flux, interpreted as the sum of the rates of Ca²⁺ extrusion and Ca²⁺ uptake. A simple model was presented that accounted for small amplitude oscillations when [Ca²⁺]_i was low enough that mitochondrial Ca²⁺ transport was weak and linear approximations of the [Ca²⁺]_i dependence of Ca²⁺ extrusion and uptake are adequate. In this model, the rate of Ca²⁺ release was described as a product of a permeability factor and a driving force, as in the present study. The permeability was assumed to increase monotonically with [Ca²⁺]_i, was insensitive to intraluminal Ca²⁺ concentration and did not show inactivation.

In the present study, this permeability was directly characterized and the third component of the total cytoplasmic Ca²⁺ flux was explicitly represented by the sum of two fluxes J_SERCA and J_pm that were measured in the absence of caffeine under conditions where [Ca²⁺]_i is not oscillating. It is remarkable that simulations performed using descriptions of J_pm, J_SERCA, and κ_i from control cells, and of

from each of the four caffeine-treated cells, showed [Ca²⁺]_i oscillations in response to stimulated Ca²⁺ entry, whereas descriptions from the same number of control cells did not. It was possible to reproduce the basic properties of [Ca²⁺]_i oscillations evoked by stimulated Ca²⁺ entry, as well as the temporal properties of the three flux components measured in the earlier study (Fig. 7).

Studies from various in vitro preparations (e.g., vesicles, and isolated organelles) has provided information regarding the types of transporters that participate in Ca²⁺ signaling and their biophysical properties. However, since this information is derived from multiple tissues and species, it may not describe the particular collection of transporters that operate together in any one cell type. Such in vitro data have been invaluable in developing general concepts about Ca²⁺ regulation, but inferences drawn from them are limited. One reason is that the Ca²⁺ transport rates depend on [Ca²⁺] in a nonlinear manner. In a coupled system of nonlinear Ca²⁺ transporters, quantitative properties of the individual transport systems can influence qualitative properties of Ca²⁺ regulation. Therefore, to understand the Ca²⁺ signaling regimes that can exist in vivo, it is necessary to consider collections of transporters that are actually expressed together in living cells.

Our results show that the relative rates of ER Ca²⁺ uptake and release are critical in determining whether depolarization-evoked [Ca²⁺]_i elevations lead to ER Ca²⁺ accumulation or net Ca²⁺ release, and, therefore, whether intraluminal Ca²⁺ concentrations rise or fall in response to stimulation. The relative rates of transport are expected to depend on multiple factors, including transporter expression levels, sensitivity to Ca²⁺, and the state of modulation. Differences between the relative rates of Ca²⁺ uptake and release in vivo and those deduced from in vitro data could lead to completely different predictions regarding the direction in which ER Ca²⁺ concentrations change in response to particular stimuli. Certainly, from the standpoint of regulation of intraluminal Ca²⁺ sensors, this is an important difference.

Our results provide a picture of CICR in intact cells in terms of the interplay between multiple transport systems that can lead to qualitatively different modes of Ca²⁺ dynamics in response to different patterns of stimulated Ca²⁺ entry. One approach illustrating this was in terms of instantaneous flux/c_i relations analogous to the momentary current voltage relations used previously to illustrate the basis for initial responses to depolarizing stimuli in excitable cells (Jack et al., 1983). We described how [Ca²⁺]_i and [Ca²⁺]_ER would be expected to change after an increase in [Ca²⁺]_i that was so rapid that changes in [Ca²⁺]_ER would be negligible. Although useful for describing qualitative properties of Ca²⁺ dynamics, the instantaneous flux/c_i relations shown in Fig. 10 do not show how the properties of CICR change during stimulation in response to changes in intraluminal Ca²⁺ concentration. However, these changes can be predicted for arbitrary stimuli using the rate descriptions presented in this study. For example, one conclusion is that ER Ca²⁺ (accumulation/net release) should (lower/raise) the threshold for net CICR as a consequence of changes in driving force of passive Ca²⁺ release. As a result, which mode of CICR that is recruited during stimulation would depend critically on the history of stimulation.

Regarding the role of mitochondria, the rate descriptions of J_pm, J_SERCA, and

were obtained under conditions where mitochondrial Ca²⁺ uptake is weak, but also are expected to apply when mitochondrial Ca²⁺ transport is strong. Indeed, after including rate descriptions for mitochondrial Ca²⁺ uptake and release, obtained in cells where ER Ca²⁺ transport was inhibited, it was possible to reproduce most of the features of [Ca²⁺]_i elevations evoked under voltage clamp and of caffeine-induced [Ca²⁺]_i oscillations. As argued in Albrecht et al. (2001) and Hongpaisan et al. (2001), Ca²⁺ transport by mitochondria is also expected to influence the prevailing mode of CICR indirectly by modulating [Ca²⁺]_i.

In addition to establishing three different [Ca²⁺]_i ranges supporting different modes of CICR during stimulation, the presence of a CICR pathway also stabilizes intraluminal Ca²⁺ concentrations over a wide range of [Ca²⁺]_i. This may be important in maintaining processes that are sensitive to intraluminal Ca²⁺ levels (Meldolesi and Pozzan, 1998; Corbett and Michalak, 2000) in the face of large swings in [Ca²⁺]_i that might occur in response to excessive stimulation or injury.

The purpose of this appendix is to derive an equation that relates the macroscopic Ca²⁺ permeability of the ER (⁠

⁠) to measurements in intact cells presented in this study. Let J̅_ER be the rate of net Ca²⁺ transport between the ER and cytoplasm (e.g., in units of nmol/s). This flux would cause the total ER Ca concentration ([Ca]_ER) to change at a rate given by Eq. A1:

where v_ER is the ER volume and outward fluxes from the cytoplasm are positive and inward fluxes are negative. For simplicity, it is assumed that Ca²⁺ is uniformly distributed within the ER and cytoplasm at all times, which is a reasonable approximation as long as transport between compartments is slow compared with diffusion within compartments. If binding to intraluminal Ca²⁺ buffers reaches equilibrium rapidly, then this flux would cause the intraluminal free Ca²⁺ concentration ([Ca²⁺]_ER) to change at a rate of

where κ_ER is the ratio of change in total ER Ca concentration to the accompanying change in free Ca concentration. In the absence of other forms of net cytoplasmic Ca²⁺ transport, the same flux would cause the cytoplasmic free Ca²⁺ concentration to change at a rate given by Eq. A3:

where J_ER can be interpreted as the net flux (e.g., in units nmol/liter s) of Ca²⁺ between the ER and cytoplasm per unit effective cytoplasmic volume (v_iκ_i; Melzer et al., 1987). J_ER can be separated into two components:

where J_SERCA represents Ca²⁺ uptake via SERCAs, and J_Release represents passive Ca²⁺ release. Results presented in Fig. 2 provide information about J_SERCA, whereas Figs. 3 and 4 show measurements of J_Release. J_Release is expected to depend both on the Ca²⁺ permeability of ER and the driving force for Ca²⁺ movement across the ER membrane. If this driving force depends only on the difference between cytoplasmic and intraluminal Ca²⁺ concentrations, J_Release can be described at each point in time as follows:

where

is the permeability of the entire ER membrane (units cm³s⁻¹) and P_ER =

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

/v_iκ_i (in units s⁻¹).

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

is a macroscopic permeability that can be related to single-channel properties by

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

= Σ_uN_up_uπ_u, where N_u is the number of Ca²⁺-permeable channels of type u, p_u is their open probability, and π_u is the unitary Ca²⁺ permeability, if permeation through channels is the dominant form of passive ER Ca²⁺ transport. Note that if a channel contributing to

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

has a [Ca²⁺]_i-dependent open probability (e.g., RyRs), then

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

will depend on [Ca²⁺]_i. Eq. A5 can be rewritten as follows:

where Δ[Ca²⁺]_i(t) and Δ[Ca²⁺]_ER(t) are the differences between [Ca²⁺]_i and [Ca²⁺]_ER at time t and their basal values after inhibition of SERCAs (e.g., with t-BuBHQ). If in the continuous presence of t-BuBHQ, Ca²⁺ becomes passively distributed between the ER and cytoplasm, then [Ca²⁺]_ER,basal = [Ca²⁺]_i,basal and Eq. A6 reduces to

Now, if Δ[Ca²⁺]_i(t) ≪ Δ[Ca²⁺]_ER(t), Eq. A7 can be approximated by

To obtain Δ[Ca²⁺]_ER(t), Eq. A2 can be integrated from the instant of SERCA inhibition to the time t and then offset by the integral over the entire t-BuBHQ-induced [Ca²⁺]_i transient:

If inhibition of Ca²⁺ uptake is complete, J_SERCA = 0, and so from Eqs. A3 and A4 J_ER = J_Release,

= J_Release, so that Eq. A9 becomes:

If

and κ_ER do not change with time during the t-BuBHQ-induced [Ca²⁺]_i transients, then Eq. A10 can be written:

where

designates minus one times the integral and can be interpreted as the change in total Ca concentration that would occur if the net ER Ca²⁺ flux from t onward were deposited in a closed compartment having the same volume as the cytoplasm. κ_i is retained under the integral sign to allow for changes in cytoplasmic Ca²⁺ strength that occur as [Ca²⁺]_i changes with time (Fig. 1 D). However, it is assumed that κ_i adjusts instantaneously to changes in [Ca²⁺]_i, so that if it varies with time, it derives its time dependence exclusively from the time dependence of [Ca²⁺]_i. Substituting the expression for Δ[Ca²⁺]_ER(t) (Eq. A11) into Eq. A8 gives:

Eq. A12 makes it possible to define a function related to permeability in terms of measured quantities:

(See Shirokova et al., 1995, for an alternative approach to measuring SR Ca²⁺ permeability in skeletal muscle.) This can be related to the macroscopic permeability of the ER (⁠

⁠) by Eq. A14:

Therefore, if v_ERκ_ER is constant, P_ER(v_i/v_ERκ_ER) is expected to show a composite [Ca²⁺]_i dependence reflecting both the properties of κ_i and

⁠. In this study, we present measurements of P_ER(v_i/v_ERκ_ER) to avoid assumptions regarding (v_i/v_ERκ_ER). Multiplication by κ_i using results shown in Fig. 1 D then gives

\(\overline{\mathrm{P}}_{\mathrm{ER}}\)

/(v_ERκ_ER). If v_ERκ_ER is constant, this is proportional to the macroscopic Ca²⁺ permeability of the ER. Given measurements of

\(\mathrm{{\Delta}}\left[\mathrm{Ca}^{2\mathrm{+}}\right]_{\mathrm{ER}}^{\left(\mathrm{i}\right)}\left(\mathrm{t}\right)\)

⁠, estimates of Δ[Ca²⁺]_ER(t) are obtained after multiplying by (v_i/v_ERκ_ER).

The validity of Eq. A13 depends on the approximation Δ[Ca²⁺]_i(t) − Δ[Ca²⁺]_ER(t) ≈ −Δ[Ca²⁺]_ER(t) used in obtaining Eq. A8 from Eq. A7. If during evoked t-BuBHQ transients Δ[Ca²⁺]_i(t) < 250 nM and Δ[Ca²⁺]_ER(t) > 25 μM, the error in estimating P_ER(v_i/v_ERκ_ER) would be ∼1% and would be smaller when Δ[Ca²⁺]_ER(t) is higher. During the final phase of the recovery, −Δ[Ca²⁺]_ER(t) systematically overestimates (Δ[Ca²⁺]_i(t) − Δ[Ca²⁺]_ER(t)) in magnitude, leading to an underestimation of P_ER(v_i/v_ERκ_ER). However, such an underestimation was difficult to resolve (Fig. 3 E, light trace) possibly because in this case P_ER(v_i/v_ERκ_ER) is determined from the ratio of two small and noisy numbers.

The dynamics of the free Ca²⁺ concentration within the cytosol (c_i) and the ER (c_ER) were represented by the following differential equations (Eqs. B1 and B2):

where the total cytoplasmic Ca²⁺ flux is given by Eq. B3

and the intercompartmental fluxes J_pm and J_ER depend on the relative rates of transport via different pathways as follows:

and

where

and

where k_leak,pm, c_o, V_max,extru, EC_50,extru, n_extru, F, V_max,SERCA, EC_50,SERCA, n_SERCA, P̅_basal, P̅_max,RyR, EC_50,RyR, and n_RyR are constants. c_o is the extracellular Ca²⁺ concentration and F is the Faraday constant. Eqs. B4–B9 describe the rate of total Ca²⁺ transport by the respective pathways divided by the cytoplasmic volume (v_i) and the cytoplasmic buffering factor κ_i. According to the sign convention used, fluxes that raise c_i are negative while fluxes that lower c_i are positive. J_extru is the sum of plasma membrane pump and leak fluxes.

/v_i, a lumped quantity representing the total ER permeability per unit cytoplasmic volume, consists of a constant basal component (P̅_basal) and a c_i-dependent component that increases saturably with c_i (half-maximal activation when c_i = EC_50,RyR) and approaches P̅_max,RyR when is high c_i.

To obtain an analytical description of ER Ca²⁺ permeability for use in simulations, measurements of P_ER(v_i/v_ERκ_ER) were described by Eq. B11:

where κ_i was treated as a known function of [Ca²⁺]_i based on measurements shown in Fig. 1 D, (⁠

/v_i) was described by Eq. B10, v_ERκ_ER/v_i was estimated to be unity. The description of mitochondrial Ca²⁺ transport used in simulations (Figs. 6–8) is from Colegrove et al. (2000b).

In carrying out simulations, the resting value of c_i was determined as the solution of Eq. B6 when J_pm = 0. Alternatively, if simulations were to be compared at the same value of resting c_i, (Fig. 5, A and B, insets), Eq. B6 was solved determine the value of k_leak,pm yielding that value of c_i. The initial value of c_ER was determined as the particular level where Ca²⁺ uptake and release rates are equal at the prevailing basal c_i according to Eq. B12:

Therefore, at rest c_ER is defined by the properties of J_SERCA and

/v_i and basal c_i.

The authors thank Drs. Hillel Chiel and Steve Jones for their helpful comments on the manuscript.

This work was supported by a grant from the National Institutes of Health/National Institute of Neurological Disorders and Stroke (NS 33514) to D.D. Friel.