The ER is a central element in Ca2+ signaling, both as a modulator of cytoplasmic Ca2+ concentration ([Ca2+]i) and as a locus of Ca2+-regulated events. During surface membrane depolarization in excitable cells, the ER may either accumulate or release net Ca2+, but the conditions of stimulation that determine which form of net Ca2+ transport occurs are not well understood. The direction of net ER Ca2+ transport depends on the relative rates of Ca2+ uptake and release via distinct pathways that are differentially regulated by Ca2+, so we investigated these rates and their sensitivity to Ca2+ using sympathetic neurons as model cells. The rate of Ca2+ uptake by SERCAs (JSERCA), measured as the t-BuBHQ-sensitive component of the total cytoplasmic Ca2+ flux, increased monotonically with [Ca2+]i. Measurement of the rate of Ca2+ release (JRelease) during t-BuBHQ-induced [Ca2+]i transients made it possible to characterize the Ca2+ permeability of the ER (
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.
Materials And Methods
Cell Dissociation and Culture
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.
Cytoplasmic Calcium Measurements
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).
Ca2+ Flux Measurements
In this study, three different macroscopic Ca2+ fluxes were measured: (1) JSERCA, the rate of Ca2+ uptake via SERCAs; (2) Ji, the total cytoplasmic Ca2+ flux when SERCAs are inhibited; and (3) Jpm, the rate of Ca2+ extrusion across the plasma membrane. One additional flux (JRelease) was calculated from the difference between two of the measured fluxes (Ji and Jpm). Finally, JRelease 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 JSERCA, 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 JSERCA was taken as the difference between the final and initial slopes. The total cytoplasmic Ca2+ flux (Ji) 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 ti according to ([Ca2+]i(ti + Δt/2) − [Ca2+]i(ti − 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 (Jpm) 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 (JRelease) during the t-BuBHQ-induced [Ca2+]i transient was then taken as the difference between Ji and Jpm at corresponding times (Fig. 3 B). Jpm 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, Jpm 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, Ji and Jpm 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 (vi) and a buffering factor (κi) 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 vi is constant, κi 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 κi.
To determine if the measured fluxes account for the time course of [Ca2+]i after various experimental perturbations, quantitative descriptions of Jpm, JSERCA,
To examine qualitative properties of CICR over a wider range of [Ca2+]i, continuous extensions of the descriptions for Jpm, JSERCA, and
Cytoplasmic Ca2+ Buffering
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 JRelease over time. However, since JRelease is a flux per unit (effective) cytoplasmic volume (in nmol/viκi/s), conversion to a flux per unit (effective) intraluminal volume (in nmol/vERκER/s) was required before integration. The appropriate flux was obtained after multiplying JRelease by (viκi/vERκER). It was assumed that (1) vi/vER is constant, (2) κER is constant, as would be expected if intraluminal Ca2+ buffers have low affinity for Ca2+, and (3) that κi adjusts instantaneously to changes in total Ca concentration. Evaluation of κi 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 (Kd,Fura-2 ∼224 nM). To evaluate this potential contribution to the [Ca2+]i dependence of κi, 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 κi,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 κi in native, unloaded cells, as well as the component of κi representing fura-2 in our experiments, where the incubation time was 40 min. As expected, κi is smaller if the incubation time is reduced (Fig. 1 C). The dependence of κi 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 (κi,Endog ∼ 25). The strength of buffering (κi,Fura-2) by fura-2 at the 40-min time point then was calculated as κi,basal − κi,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 κi in our experiments as follows (Fig. 1 D):
Given κi, κi,Endog, Kd,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 κi,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, (viκi/vERκER) was treated as the product of a constant (vi/vERκER) and a [Ca2+]i-dependent term κi 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 κi 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 κi was used to convert JRelease into a flux that could be integrated to give information about changes in intraluminal Ca2+ concentration during t-BuBHQ-induced [Ca2+]i transients.
Inhibition of CICR
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.
Data Analysis and Reagents
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 (JSERCA), illustrating how it varies with [Ca2+]i. We will describe measurements of the rate of passive Ca2+ release by the ER (JRelease), showing how it depends on a [Ca2+]i-sensitive permeability (
Characterization of the ER Ca2+ Uptake Pathway
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 (JSERCA) varies with [Ca2+]i are presented in Fig. 2 C. Over the range examined (up to ∼800 nM), JSERCA increases monotonically with [Ca2+]i. Although it is difficult to exclude a functional dependence of JSERCA 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 JSERCA was unchanged. This suggests that [Ca2+]i is the most important variable controlling JSERCA 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 JSERCA from basal levels up to ∼800 nM.
Characterization of the ER Ca2+ Release Pathway
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 (JRelease) 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 (Ji) 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). Ji 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 JRelease, it was necessary to dissect Ji into its component fluxes. The rate of Ca2+ extrusion across the plasma membrane (Jpm) 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, Ji is also plotted throughout the t-BuBHQ-induced transient. In a previous study, it was shown that at each point in time, Jpm 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 Jpm during the recovery after repolarization at the corresponding [Ca2+]i level. The time course of Jpm determined in this way is shown in Fig. 3 B and parallels the [Ca2+]i response. Subtracting Jpm from Ji 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 (JRelease) 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 JReleaseκi 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 JRelease are revealing. During the entire t-BuBHQ-induced [Ca2+]i transient, JRelease is negative, which is indicative of Ca2+ release. During the rising phase, the magnitude of JRelease 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 JRelease 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 JRelease 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 JRelease, 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, JRelease gives the net ER Ca2+ flux referred to the effective cytoplasmic volume, so multiplying by the ratio of effective cytoplasmic and intraluminal volumes (viκi/vERκER) 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 (
A similar approach to assessing changes in ER Ca2+ concentration in T cells was described previously by Bergling et al. (1998).
Before using JRelease and
Measurements of JRelease and
where PER is a lumped parameter giving the ratio of
Given measurements of JRelease and ([Ca2+]i − [Ca2+]ER), PER could be determined from the ratio JRelease/([Ca2+]i − [Ca2+]ER) at each point in time during the t-BuBHQ-induced [Ca2+]i transient; measurements of κi would then make possible to obtain information about
and to obtain a quantity that is proportional to PER from measured values,
which is valid as long as [Ca2+]ER is much larger than [Ca2+]i (see appendix A). Fig. 3 E shows PER(vi/vERκER) plotted against [Ca2+]i during the t-BuBHQ-induced [Ca2+]i transient, calculated according to Eq. 6. The dark noisy trace shows PER(vi/vERκER) during the rising phase of the transient, and the light trace represents the recovery phase. Three features of these measurements should be noted. First, PER(vi/vERκER) is not constant, but increases monotonically with [Ca2+]i over the range ∼50–250 nM. Second, the [Ca2+]i dependence of PER(vi/vERκER) during the onset and recovery (dark and light traces, respectively) is very similar. In other words, for a given value of [Ca2+]i, PER(vi/vERκER) 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 PER(vi/vERκER) 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 PER(vi/vERκER) 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
Changes in ER Ca2+ Permeability Induced by Caffeine and Ryanodine
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
Reconstruction of t-BuBHQ-induced Ca2+ Responses and the Underlying Ca2+ Fluxes
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 JSERCA, Jpm, PER(vi/vERκER), and κi, approximating vi/vERκER by unity. In displaying the results, simulated Ca2+ concentrations are designated by ci and cER 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 cER and the time courses of ci, JRelease, and cER (Fig. 5). This leads to three conclusions. First, Jpm, JSERCA, and
The Properties of Jpm, JSERCA, PER(vi/vERκER), and κi Account for Ca2+ Dynamics during Depolarization-evoked Ca2+ Entry
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 Jpm, JSERCA PER(vi/vERκER) and κi 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 (ICa) 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 PER(vi/vERκER) obtained under control conditions, Ca2+ entry produces a ci 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 PER(vi/vERκER) parameters taken from ryanodine-treated cells, Ca2+ entry elicits a slower rise in ci but a more robust increase in cER, also as observed experimentally (Albrecht et al., 2001). Finally, using PER(vi/vERκER) 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 JRelease increases more steeply with ci than does JSERCA over this ci range. Resting cER is lower in this and the +Ryan case because basal PER(vi/vERκER) 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 ci and cER 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 cER. The resting rate of release is not modified by ryanodine because while
Properties of PER(vi/vERκER) Account for Caffeine-induced [Ca2+]i Oscillations
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 Jpm, JSERCA, and PER(vi/vERκER), simulations were performed using descriptions of Jpm and JSERCA from control cells and of PER(vi/vERκER) from caffeine-treated cells. Although Ca2+ entry led to a steady increase in ci 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 PER(vi/vERκER) from control and caffeine-treated cells contributing to the collected results in Fig. 4 E indicates that depolarization-evoked Ca2+ entry does not elicit ci oscillations when control PER(vi/vERκER) 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.
Quantitative Basis for Multiple Modes of CICR in Sympathetic Neurons
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 Jpm, JSERCA, and PER(vi/vERκER) 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. Jpm, JSERCA, and PER 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 ci and represent approximations at high ci. Fig. 9 shows how in the steady state, cER varies with ci. When ci is below ∼200 nM, an increase in ci leads to net Ca2+ uptake and a rise in cER. Increasing ci further over the physiological range leads to net Ca2+-induced Ca2+ release and a decline in cER. Further (nonphysiological) increases in ci lead to Ca2+ accumulation and a rise in cER. Thus, there are two major effects of the Ca2+ sensitive permeability on the relationship between ci and cER under steady-state conditions. First, it leads to the definition of three distinct ci ranges in which the ER plays qualitatively different roles in Ca2+ regulation: low ci (ER is a Ca2+ sink), intermediate ci (ER is a Ca2+ source), and high ci (ER is a Ca2+ sink). Second, it would act as a safety valve to stabilize cER in the face of prolonged [Ca2+]i elevations that would otherwise lead to large increases in intraluminal Ca2+ levels. With CICR in place, cER increases by less than a factor of two for a 10,000-fold change in ci 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/ci 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 ci dependence of PER and
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.
Properties of the ER Ca2+ Uptake Pathway
The impact of SERCAs (JSERCA) on Ca2+ dynamics was assessed by measuring the t-BuBHQ-sensitive component of the total cytoplasmic Ca2+ flux (Ji) just after exposing cells to a high concentration of t-BuBHQ. As it was measured, the [Ca2+]i dependence of JSERCA 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 JSERCA 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 (EC50,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 JSERCA 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 JSERCA largely reflects the [Ca2+]i dependence of κi. 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.
Characterization of the Ca2+ Permeability of the ER
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 JRelease primarily through its effect on PER, 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 JRelease. Integration of JReleaseκi 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 PER 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 (
Based on this procedure, we characterized
This leads to two conclusions about RyR regulation during these responses. First,
Assumptions Used in the Analysis
An important step in characterizing
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 JSERCA.
Comparison with Previous Work
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.
Caffeine-induced Ca2+ Oscillations
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 JSERCA and Jpm 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 Jpm, JSERCA, and κi from control cells, and of
Importance of Studying Ca2+ Regulation by the Collection of Transporters Expressed together in Intact Cells
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.
Implications for Studies of Ca2+ Signaling
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/ci 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/ci 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 Jpm, JSERCA, and
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.
Assessment of ER Ca2+ Permeability in Intact Cells
The purpose of this appendix is to derive an equation that relates the macroscopic Ca2+ permeability of the ER (
where vER 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 κER 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 JER 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 (viκi; Melzer et al., 1987). JER can be separated into two components:
where JSERCA represents Ca2+ uptake via SERCAs, and JRelease represents passive Ca2+ release. Results presented in Fig. 2 provide information about JSERCA, whereas Figs. 3 and 4 show measurements of JRelease. JRelease 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, JRelease can be described at each point in time 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, JSERCA = 0, and so from Eqs. A3 and A4 JER = JRelease,
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 (
Therefore, if vERκER is constant, PER(vi/vERκER) is expected to show a composite [Ca2+]i dependence reflecting both the properties of κi and
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 PER(vi/vERκER) 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 PER(vi/vERκER). However, such an underestimation was difficult to resolve (Fig. 3 E, light trace) possibly because in this case PER(vi/vERκER) is determined from the ratio of two small and noisy numbers.
Description of the Model
The dynamics of the free Ca2+ concentration within the cytosol (ci) and the ER (cER) 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 Jpm and JER depend on the relative rates of transport via different pathways as follows:
where kleak,pm, co, Vmax,extru, EC50,extru, nextru, F, Vmax,SERCA, EC50,SERCA, nSERCA, P̅basal, P̅max,RyR, EC50,RyR, and nRyR are constants. co 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 (vi) and the cytoplasmic buffering factor κi. According to the sign convention used, fluxes that raise ci are negative while fluxes that lower ci are positive. Jextru is the sum of plasma membrane pump and leak fluxes.
To obtain an analytical description of ER Ca2+ permeability for use in simulations, measurements of PER(vi/vERκER) were described by Eq. B11:
where κi was treated as a known function of [Ca2+]i based on measurements shown in Fig. 1 D, (
In carrying out simulations, the resting value of ci was determined as the solution of Eq. B6 when Jpm = 0. Alternatively, if simulations were to be compared at the same value of resting ci, (Fig. 5, A and B, insets), Eq. B6 was solved determine the value of kleak,pm yielding that value of ci. The initial value of cER was determined as the particular level where Ca2+ uptake and release rates are equal at the prevailing basal ci according to Eq. B12:
Therefore, at rest cER is defined by the properties of JSERCA and
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.
Abbreviations used in this paper: [Ca], total Ca concentration; FCCP, carbonyl cyanide p-(trifluoromethoxy)phenylhydrazone; InsP3R, d-myo-inositol 1,4,5-trisphosphate receptor; SERCA, sarco(endo)plasmic reticulum Ca ATPase; t-BuBHQ, 2,5-Di-(t-butyl)-1,4-hydroquinone; Tg, thapsigargin.