Correspondence to: David D. Friel, Department of Neuroscience, Case Western Reserve University, 10900 Euclid Ave. Cleveland, OH 44106. Fax:(216) 368-4650 E-mail:ddf2{at}po.cwru.edu.
Released online: 28 February 2000
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Abstract |
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Rate equations for mitochondrial Ca2+ uptake and release and plasma membrane Ca2+ transport were determined from the measured fluxes in the preceding study and incorporated into a model of Ca2+ dynamics. It was asked if the measured fluxes are sufficient to account for the [Ca2+]i recovery kinetics after depolarization-evoked [Ca2+]i elevations. Ca2+ transport across the plasma membrane was described by a parallel extrusion/leak system, while the rates of mitochondrial Ca2+ uptake and release were represented using equations like those describing Ca2+ transport by isolated mitochondria. Taken together, these rate descriptions account very well for the time course of recovery after [Ca2+]i elevations evoked by weak and strong depolarization and their differential sensitivity to FCCP, CGP 37157, and [Na+]i. The model also leads to three general conclusions about mitochondrial Ca2+ transport in intact cells: (1) mitochondria are expected to accumulate Ca2+ even in response to stimuli that raise [Ca2+]i only slightly above resting levels; (2) there are two qualitatively different stimulus regimes that parallel the buffering and non-buffering modes of Ca2+ transport by isolated mitochondria that have been described previously; (3) the impact of mitochondrial Ca2+ transport on intracellular calcium dynamics is strongly influenced by nonmitochondrial Ca2+ transport; in particular, the magnitude of the prolonged [Ca2+]i elevation that occurs during the plateau phase of recovery is related to the Ca2+ set-point described in studies of isolated mitochondria, but is a property of mitochondrial Ca2+ transport in a cellular context. Finally, the model resolves the paradoxical finding that stimulus-induced [Ca2+]i elevations as small as ~300 nM increase intramitochondrial total Ca2+ concentration, but the steady [Ca2+]i elevations evoked by such stimuli are not influenced by FCCP.
Key Words: mitochondria, calcium, neurons, Ca2+ uniporter, mitochondrial Na+/Ca2+ exchanger
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INTRODUCTION |
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Ionized free calcium (Ca2+) is an important signal that links a variety of extracellular stimuli to their intracellular effectors. Since Ca2+ accomplishes this function by interacting with Ca2+ binding proteins, the cellular effects of Ca2+ depend critically on the dynamics of Ca2+ concentration ([Ca2+]). One of the central goals in the study of calcium signaling is to understand the basis of [Ca2+] dynamics. This is complicated by several factors: (a) Ca2+ is present in multiple membrane-delimited intracellular compartments, each of which employs distinctive Ca2+ transport systems; (b) Ca2+ may be distributed in a spatially nonuniform manner within these compartments; (c) the rate of Ca2+ transport between compartments can exhibit a complex nonlinear dependence on free Ca concentration.
We have studied how mitochondrial Ca2+ transport contributes to the redistribution of intracellular Ca2+ during and after depolarization-evoked Ca2+ entry in sympathetic neurons. Here, the rise in cytosolic free Ca2+ concentration ([Ca2+]i) is initiated by Ca2+ entry but is strongly influenced by Ca2+ uptake and release by organelles such as mitochondria and the endoplasmic reticulum (ER).1 We simplified the analysis of [Ca2+] dynamics by inhibiting SERCA Ca2+ pumps to minimize Ca2+ accumulation by the ER, and by focusing on the slow recovery that follows repolarization, a period during which the spatial distribution of [Ca2+]i is approximately uniform. Analysis of this case is relevant to slow changes in [Ca2+] that occur in the aftermath of depolarizing stimuli, and is a logical step in understanding the more complex case where [Ca2+] undergoes rapid, spatially nonuniform changes within multiple intracellular compartments.
In the preceding study, the total Ca2+ flux during the recovery after depolarization was dissected into three components, one representing net Ca2+ extrusion across the plasma membrane, the others representing mitochondrial Ca2+ uptake and release via the uniporter and Na+/Ca2+ exchanger. In this study, these flux components are described analytically to determine if they are sufficient to account for the time course of the [Ca2+]i recovery after weak and strong stimuli, and the effects of mitochondrial Ca2+ transport inhibitors on these recoveries. It is found that they are. Moreover, the results are in general quantitative agreement with the dynamics of total mitochondrial Ca concentration deduced from x-ray microanalysis under the same conditions of stimulation. The results provide a conceptual framework for describing how mitochondrial Ca transport operates in the context of intact cells.
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MATERIALS AND METHODS |
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Preparation of cells and measurement of [Ca2+]i and Ca2+ fluxes follow the procedures described in the preceding paper. Empirical rate equations for net plasma membrane Ca2+ transport and for mitochondrial Ca2+ uptake and release were obtained by fitting equations to flux data obtained from [Ca2+]i recordings that were smoothed 12 times with a binomial filter. The rate equations were then incorporated into a system of differential equations that was solved numerically using a 4th-order Runge-Kutta routine (
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RESULTS |
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Quantitative Description of the Flux Components
We begin with analytical descriptions of the three components of the total Ca2+ flux. In each case, rate equations will be used that are motivated by known properties of plasma membrane and mitochondrial Ca2+ transport. It is then asked if the quantitative properties of the individual fluxes are sufficient to account for the kinetic properties of the [Ca2+]i recovery. For this purpose, the equations may be regarded as completely empirical. However, in the Discussion, the equations and parameters describing mitochondrial Ca2+ transport will be considered in light of information obtained from previous studies of isolated organelles.
The [Ca2+]i -dependent Fluxes: Jpm and Juni
Fig 1 A shows how the rate of net Ca2+ extrusion across the plasma membrane (Jpm) depends on [Ca2+]i during the recovery after high K+ depolarization, averaged over 10 cells (solid symbols). The smooth curve is a plot of Equation 1 (see Appendix) that describes the net flux generated by a linear leak operating in parallel with a saturable extrusion system. According to this equation, Jpm increases monotonically with [Ca2+]i, crossing zero at a (stable) resting level (50 nM). Equation 1 regards Jpm as an instantaneous function of [Ca2+]i, conforming with the observed properties of this flux (see Figure 2 B of preceding study). While there is evidence for distinct components of Jpm that are differentially sensitive to extracellular Na+ and La3+ (Friel, D.D., unpublished observations), Equation 1 lumps together all energetically uphill Ca2+ transport into a single equation and should therefore be regarded as an empirical description of the measured flux. Clearly, the [Ca2+]i dependence of Jpm is adequately described by Equation 1 for [Ca2+]i up to 800 nM. Similar results were obtained from three cells studied under voltage clamp (open symbols).
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Fig 1 B shows the [Ca2+]i dependence of Juni based on collected results from three cells studied under voltage clamp (open symbols). Juni increases steeply and monotonically with [Ca2+]i in a manner that can be described by a modified sigmoidal function of [Ca2+]i (Equation 2). According to this equation, Juni depends on [Ca2+]i but not [Ca2+]m, consistent with the finding that Juni exhibits the same [Ca2+]i dependence after stimuli that are expected to produce very different mitochondrial Ca2+ loads (see Figure 7, D and E, of preceding study). There is no indication that Juni saturates over this [Ca2+]i range, so no attempt was made to estimate a limiting slope (kmax,uni) or a [Ca2+]i level where activation is half-maximal (EC50,uni). However, Hill plot analysis provides an estimate of the Hill coefficient (nuni = 1.93 ± 0.18) that is quite insensitive to these parameters (
Ca2+ Release via the Mitochondrial Na+/Ca2+ Exchanger
In the preceding study, it was shown that JNa/Ca exhibits an apparent U-shaped dependence on [Ca2+]i. Although JNa/Ca varies with [Ca2+]i, it is not clear that JNa/Ca actually depends on [Ca2+]i (i.e., is a function of [Ca2+]i). Previous studies of isolated mitochondria have shown that with constant extramitochondrial Na+ and Ca2+ concentrations, the rate of Ca2+ release via the Na+/Ca2+ exchanger is a saturable function of the intramitochondrial free Ca concentration ([Ca2+]m;
Fig 2 A shows [Ca2+]i responses from an exemplar cell elicited by four 50 mM K+ depolarizations of different duration. While the rise in [Ca2+]i during the depolarizations and the initial recovery after repolarization were similar in each case (see inset), the subsequent phases of recovery depended strongly on stimulus duration. In particular, the slow plateau phase became longer as the duration of the preceding depolarization was increased, as described previously ([Ca2+]m(i)(t), D), and the Na+/Ca2+ exchanger flux (JNa/Ca, E). As discussed in the preceding study,
[Ca2+]m(i)(t) provides a measure of the mitochondrial Ca2+ concentration at time t relative to its basal value, referred to the effective cytosolic volume. For each stimulus duration, the initial rapid decline in [Ca2+]i is coincident with a large outward net mitochondrial Ca2+ flux (Fig 2 C), an increase in mitochondrial Ca concentration (D) and an increase in the magnitude of JNa/Ca (E). In contrast, the plateau phase of recovery is associated with net mitochondrial Ca2+ release, a decline in mitochondrial Ca concentration, and a nearly constant inward flux via the Na+/Ca2+ exchanger, each of which becomes more prolonged as the stimulus length is increased. Note that the initial value of
[Ca2+]m(i)(i.e., the value at the end of the depolarization) is proportional to stimulus duration when the stimulus lasts at least 7.5 s (Fig 2 D, inset). Using the measured ratio of mitochondrial and cytosolic volumes (0.1) and the estimated ratio of total and free cytosolic Ca concentration in sympathetic neurons (~200; Friel, D.D., and S.B. Andrews, unpublished observations), the proportionality constant (71 nM/s) converts to (71)(200/0.1) = 142 µM/s, in reasonable agreement with the rate at which total mitochondrial Ca concentration rises during 50 mM K+ depolarization in these cells as determined from electron probe microanalysis (184 µM/s;
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Importantly, Jmito and its inward component JNa/Ca are both limited as the stimulus duration increases. For example, increasing the stimulus length from 11.5 to 20.7 s nearly doubles the mitochondrial Ca load, but has relatively little effect on the peak magnitude of JNa/Ca (Fig 2, compare D with E). Saturation of JNa/Ca can be seen more clearly by plotting JNa/Ca versus [Ca2+]m(i)during the recovery for each stimulus duration (F). In each case, JNa/Ca increases saturably with
[Ca2+]m(i)in a manner that is described by Equation 7 over most of the
[Ca2+]m(i)range (see smooth curve). This equation, which assumes that JNa/Ca depends on intramitochondrial Ca2+ concentration but not [Ca2+]i, provides a simple description of the measured flux over all but the initial phase of recovery. Estimating the ratio of mitochondrial and cytoplasmic effective volumes (
) as 2 (see previous study) gives
[Ca2+]m =
[Ca2+]m(i)/2 (Equation 4), Vmax,Na/Ca = -34.8 nM/s, EC50,Na/Ca = 307.5 nM and [Ca2+]m(
) = 9.2 nM. Results from two other cells were similar except that Vmax,Na/Ca was somewhat larger (~ -75 nM/s).
While the rate of mitochondrial Ca2+ release is described quite well by Equation 7 during most of the recovery, it deviates systematically from this description during the initial phase when [Ca2+]i highest. During this phase, the rapid decline in [Ca2+]i is accompanied by a similarly rapid rise in JNa/Ca (Fig 2E and Fig F arrows). The basis for this deviation, which is relevant to the apparent U-shaped [Ca2+]i dependence of JNa/Ca (see preceding study, Fig 7 and Fig 8) is not certain. However, previous studies have shown that the mitochondrial Na+/Ca2+ exchanger is inhibited by extramitochondrial Ca2+ (
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Below, we examine the behavior of a model in which plasma membrane Ca2+ transport is described by Equation 1, mitochondrial Ca2+ uptake is described by Equation 2, and mitochondrial Ca2+ release is described by Equation 7 or Equation 8, with parameter values obtained directly from the experimental data presented above. It is found that the model accounts very well for most of the features of [Ca2+]i recovery kinetics in sympathetic neurons.
Simulated Changes in Intracellular Ca2+ Concentration Induced by Ca2+ Entry
To determine if the quantitative properties of Jpm, Juni, and JNa/Ca are sufficient to account for [Ca2+]i dynamics during the recovery, the rate equations described above were taken as the flux definitions in a previous model of Ca dynamics in sympathetic neurons (
In the model, Ca2+ extrusion across the plasma membrane occurs at rate Jextru and passive Ca2+ entry occurs at rate Jleak. These two fluxes define the net Ca2+ flux across the plasma membrane (Jpm). Mitochondrial Ca2+ uptake is described by Juni and Ca2+ release is described by JNa/Ca; these two fluxes define the net mitochondrial Ca2+ flux. Since Jpm and Juni are both defined by ci, they are plotted together against ci in B (left) along with their sum (thick trace). JNa/Ca is plotted both versus cm (Fig 3 C, left, shown as a positive flux for simplicity) and versus ci (D) for comparison with the results in the preceding study (e.g., Fig 7 and Fig 8); solid traces describe the case where JNa/Ca depends only on cm and dotted traces illustrate the case where this flux depends on both cm and ci.
Simulated changes in ci and cm after step increases in the rate constant of Ca2+ entry (Fig 3 A, right) are plotted in B and C (right); note that the ci- and cm-dependent fluxes can be read from the corresponding plots at left. During a small stimulus (s1) that elevates ci to a low level (~160 nM, Fig 3 B, right), Juni is only weakly activated (B, left) so that cm increases to a low level (<50 nM, C right). In this case, when the stimulus ends, the net mitochondrial Ca2+ flux is small compared with Jpm so the ci recovery is dominated by Ca2+ extrusion across the plasma membrane, accounting for the simple recovery kinetics. With a stronger stimulus (s2) that raises ci to a higher level, Juni is activated more strongly, causing robust Ca2+ accumulation and a rapid rise in cm. Due to its steep ci dependence, Juni is nearly four times larger than JNa/Ca at the highest ci levels achieved during stimulation, setting the stage for continuous mitochondrial Ca2+ accumulation. When this stimulus ends, continued Ca2+ accumulation contributes to a rapid rise in cm and decline in ci (Fig 3 E; see Fig 5 C from
If the rate description of JNa/Ca is modified to include inhibition by ci, JNa/Ca is no longer completely defined by cm and is depressed during the initial rapid phase of recovery when ci is high, showing an apparent U-shaped dependence on ci like the measured flux (dotted curves s2*, s3* in Fig 3C and Fig D). However, the time courses of ci and cm are nearly unchanged (see dotted curves in B and C right, insets). The explanation is simple: JNa/Ca constitutes only a small fraction of the total mitochondrial Ca2+ flux over the ci range where inhibition occurs, so that inhibition has little impact on the total flux. Since inhibition of JNa/Ca during the initial phase the recovery does not appreciably influence the dynamics of ci or cm, for simplicity, it will be ignored in the following, and it will be assumed that JNa/Ca depends only on cm.
Responses to Stimuli of Variable Magnitude and Duration
Fig 4 A illustrates responses to stimuli of fixed duration and increasing strength. Weak stimuli that raise ci to low levels barely activate the uniporter so that mitochondrial Ca2+ accumulation is slow. Thus, when the stimulus ends, Ca2+ uptake and release rates are low, so the recovery kinetics depend almost entirely on Ca2+ extrusion across the plasma membrane. Stronger stimuli that raise ci to higher levels increasingly activate the uniporter, causing Ca2+ accumulation at progressively higher rates (see Fig 4 A, bottom). During each stimulus, ci and the rate of mitochondrial Ca2+ accumulation both approach steady values, and when the stimulus ends, continued mitochondrial Ca accumulation speeds the initial ci decline. This leads to partial deactivation of the uniporter, causing Ca2+ accumulation to give way to net release, which then slows the ci recovery. As discussed in the next section, when the mitochondrial Ca2+ load is large, the rate of Ca2+ release via the Na+/Ca2+ exchanger, and the rate of net mitochondrial Ca2+ release, are both nearly constant, causing ci to hang up at an elevated plateau level until cm falls and saturation of the exchanger is relieved. The ci plateau level, defined as the ci level where the recovery rate reaches a minimum, increases with stimulus strength and appears to approach a limiting value where ci declines at a vanishingly slow rate (see below).
Fig 4 B illustrates responses to stimuli of fixed magnitude and variable duration. In this case, the briefest stimulus raises ci sufficiently to activate the uniporter, and increasing the stimulus duration increases the mitochondrial Ca2+ load. As the stimulus length increases, ci approaches a steady elevated level and cm rises linearly with time (compare with Fig 2 D, inset). When the stimulus ends, ci undergoes a rapid decline to a plateau level that depends on stimulus duration (compare with Fig 2 A) and eventually recovers to basal levels.
Comparison between Simulated Responses to Weak and Strong Stimulation: Analysis of the Underlying Fluxes
Mitochondrial Ca2+ uptake has often been viewed as a low-affinity process that is only important when [Ca2+]i rises to high levels, either in microdomains near mitochondria during physiological stimulation (
The changes in Jtotal can be understood by examining the component fluxes. With the onset of stimulation, the rate of Ca2+ entry suddenly increases, creating an imbalance between Ca2+ entry and extrusion which causes Jpm (dotted trace), and therefore Jtotal, to suddenly become inwardly directed (On arrow). As ci rises, the rate of Ca2+ extrusion increases, eventually equaling the rate of Ca2+ entry, so that Jpm declines to zero. The rise in ci also creates an imbalance between mitochondrial Ca2+ uptake and release, leading to net mitochondrial Ca2+ accumulation (Jmito positive, dashed trace) which slows the rise in ci. As cm rises, Ca2+ release eventually balances uptake and Jmito falls to zero. Termination of the stimulus creates a sudden imbalance between Ca2+ entry and extrusion which causes Jpm (and Jtotal) to become outward fluxes (Off arrow) so that ci declines. As the rate of Ca2+ extrusion approaches the rate of entry, Jpm approaches zero. The decline in ci also creates an imbalance between mitochondrial Ca2+ uptake and release, leading to net Ca2+ release (Jmito negative, dashed trace), which slows the ci recovery. As ci and cm return to their resting levels, the rates of Ca2+ uptake and release both decline and Jpm and Jmito approach zero. Thus, a weak stimulus leads to a reversible transition between two steady states in which all intercompartmental net fluxes are zero.
Strong stimuli produce qualitatively different responses (Fig 5C and Fig D). For clarity, the fluxes underlying the response onset and recovery are shown separately (Fig 5 D, left and right, respectively). When the stimulus begins, Jtotal instantly becomes a large inward flux (Fig 5 D left, thick trace, On arrow) and then declines to zero as ci stabilizes at a new elevated level. However, in this case, Jtotal approaches zero not because the component fluxes individually fall to zero, but because the outward flux Jmito eventually balances the inward flux Jpm. This occurs when ci is so high that Juni exceeds the maximal rate of Ca2+ release via the Na+/Ca2+ exchanger, setting the stage for continuous mitochondrial Ca2+ accumulation at a rate that equals the rate of net Ca2+ entry. When the stimulus ends, Jtotal suddenly becomes a large outward flux (Fig 5 D right, thick trace, Off arrow) which causes ci to fall rapidly. However, Jtotal does not decline continuously, but instead reaches a minimum and then rises again to reach a maximum before finally approaching zero. Jtotal is biphasic because it is the sum of Jpm, which increases montonically with ci, and Jmito, which is biphasic, representing an initial phase of Ca2+ accumulation and a late phase of net Ca2+ release. The similarity between the simulated and measured fluxes during the recovery is clear (compare with Fig 3 D in the preceding study).
The interplay between the components of the total flux explains the four phases of the ci recovery (Fig 5C and Fig D right). During phase i, both Jmito and Jpm are positive, accounting for the initial rapid ci decline. The reduction in ci causes partial deactivation of Juni and a reduction in the rate of mitochondrial Ca2+ accumulation. When the rates of Ca2+ uptake and release are equal, Jmito is zero, but the decline in ci continues because of ongoing net Ca2+ extrusion. Further deactivation of Juni causes mitochondrial Ca2+ accumulation to give way to net release (phase ii) which slows the recovery. However, as cm falls, the rate of Ca2+ release declines so that Jmito approaches zero. As a result, Jtotal rises, accounting for the accelerated recovery during phase iii. Finally, as Jmito approaches zero, the recovery is dominated by net Ca2+ extrusion across the plasma membrane (phase iv).
Simulated Effects of CGP on Responses to Weak Stimulation
In the preceding study, it was shown that despite being largely insensitive to FCCP, [Ca2+]i responses elicited by weak depolarization are strongly depressed by CGP. This makes sense in light of the preceding discussion. After inhibiting mitochondrial Ca2+ release, weak stimuli that would otherwise lead to transient mitochondrial Ca2+ accumulation are expected to cause continuous accumulation and depressed [Ca2+]i elevations, as in the strong stimulus regime described above. Fig 6 shows simulated responses to a long, weak stimulus that under control conditions raises ci to a steady state level of ~230 nM and cm to ~100 nM. To model the actions of CGP, Vmax,Na/Ca was set to zero. In this case (JNa/Ca = 0), the same stimulus elicited a smaller steady rise in ci that was accompanied by a continuous rise in cm. Vmax,uni was then set to zero to model the additional effects of FCCP (Juni = 0). This abolished the stimulus-evoked rise in cm and speeded the elevation in ci, reversing the simulated actions of CGP. Moreover, after inhibiting uptake, ci rose to the same steady state level during stimulation as it did in the control. These simulations reproduce the observed effects of CGP and FCCP on steady [Ca2+]i elevations elicited by weak depolarization (see Figure 9 D of the preceding study;
The Basis for the Plateau Level and Its Relationship to the Mitochondrial Ca2+ Set Point
Previous studies have identified the [Ca2+]i plateau level with the mitochondrial Ca2+ set point (
If the recovery begins with cm equal to zero (Fig 7 C, trace 1), cm never reaches a very high level and the rate of net mitochondrial Ca2+ release is low during the entire recovery (E). In this case, Jtotal does not exhibit a minimum (Fig 7 D) so there is no ci plateau (B). With larger initial values of cm (Fig 7 C, traces 25), Jtotal passes through a minimum that approaches zero (D) and the ci plateaus become increasingly flat (B). Another way to visualize how the Jtotal minimum is influenced by mitochondrial Ca2+ load is to plot this flux against ci during each of the recoveries (Fig 7 G). As shown in the inset, the magnitude of Jtotal at the minimum approaches zero, and the value of ci where the minimum occurs approaches a limiting value. In each case, the Jtotal minimum occurs near the ci level where Jmito is minimal (Fig 7, compare G with H) and the magnitude of JNa/Ca is maximal.
The basis for the plateau and its limiting level finally becomes clear when Jtotal for each of the five recoveries (Fig 7 I, thick traces 15) is separated into its ci-dependent component (Jpm + Juni) and the remaining (cm-dependent) component, JNa/Ca. During each recovery, (Jpm + Juni) (thin trace) declines montonically with a stereotyped ci dependence. In contrast, the rate of Ca2+ release ascends to a peak during phase i of the recovery as ci falls and cm rises, and then descends as cm declines, having an initial value that depends on cm (Fig 7, thin traces 15); the peak is sharper if the rate equation for JNa/Ca includes inhibition by cytosolic Ca2+ (see Fig 3 D). In terms of the model, it is the JNa/Ca peak that is responsible for the Jmito and Jtotal minima, and therefore the ci plateau. As the initial mitochondrial Ca2+ load increases, the release pathway nears saturation, the magnitude of JNa/Ca during the initial phase of recovery approaches Vmax,Na/Ca (horizontal dotted line) and the plateau level approaches a limiting value. This is the (stable) steady state value of ci that would be reached if cm were clamped at such a high value that the rate of Ca2+ release is maximal (JNa/Ca ~ Vmax,Na/Ca) and ci were allowed to relax from its initial value at the end of the stimulus. In this case, Jtotal would be described by Jtotal* = (Jpm + Juni) + Vmax,Na/Ca (dotted curve), which crosses the zero-net flux axis at the limiting plateau level (Fig 7 I, up arrow). Here, the outward flux (Jpm + Juni) and the inward flux Vmax,Na/Ca are in balance. Of course, if cm is free to change, the limiting plateau level is never attained because the mitochondrial pool is finite and cm and JNa/Ca ultimately decline.
Therefore, the limiting plateau level depends not only on the properties of mitochondrial Ca2+ release but also on uptake (
Graded Inhibition of JNa/Ca: Comparison with the Actions of CGP
It has been proposed that the [Ca2+]i plateau is caused by mitochondrial Ca2+ release via the Na+/Ca2+ exchanger (
Effect of Graded Changes in Vmax,uni: Comparison with the Effects of FCCP
It was shown above that disabling mitochondrial Ca2+ accumulation only slightly modifies responses to weak stimuli, in agreement with the observed effects of FCCP (see Fig 6). In that simulation, Ca2+ accumulation was inhibited by setting kmax,uni to zero. Fig 9 illustrates how graded changes in kmax,uni influence responses to strong stimuli. When uptake is completely inhibited (kmax,uni = 0) ci responses resemble those seen in the presence of FCCP. As kmax,uni is increased, mitochondrial Ca2+ accumulation proceeds at progressively higher rates so that cm rises more rapidly and reaches higher levels by the end of the stimulus. This is accompanied by a slower and smaller rise in ci during the stimulus, and a modified recovery marked by a faster phase i and a slower phase ii with lower plateau level. When kmax,uni = 80 s-1, ci responses resemble [Ca2+]i responses elicited by depolarization in the absence of FCCP.
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The effects of increasing kmax,uni can be explained as follows. The plateau level is lowered because the maximal rate of net mitochondrial Ca2+ release during the recovery is reduced owing to stronger Ca2+ uptake at each value of ci; the lower rate of net Ca2+ release also causes the recoveries to be more prolonged. Net mitochondrial Ca2+ release is slower in spite of increased mitochondrial Ca2+ loads, which by themselves would tend to increase JNa/Ca. This is because the release pathway is nearly saturated, and the rate of release is low compared with uptake over this range of concentrations.
Effect of Graded Changes in Ca2+ Extrusion Rate: Relationship between the Plateau Level and the Mitochondrial Ca2+ Set Point
The mitochondrial set point concept provides an elegant explanation of the ability of isolated mitochondria to maintain the extramitochondrial Ca concentration at a fixed value when the intramitochondrial Ca2+ concentration is high. As described previously, the basis of the set point lies in the relationship between mitochondrial Ca2+ uptake and release pathways: if intramitochondrial Ca2+ concentration is high enough that the rate of release is constant, then uptake by the uniporter will maintain the extramitochondrial steady state Ca2+ concentration at a fixed level (
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Simulated Responses to Brief and Long Periodic Stimulus Trains
It was shown previously that after brief trains of stimulated action potentials that elevate [Ca2+]i to ~300 nM, [Ca2+]i recovers with a kinetically simple time course, while after longer trains that raise [Ca2+]i to levels approaching ~500 nM, the recovery is kinetically complex, much like the recovery that follows a strong, steady depolarization (
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DISCUSSION |
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Summary of Main Findings
Mitochondrial Ca2+ uptake and release pathways have been characterized in isolated mitochondria, but to our knowledge, the activity and [Ca2+] dependence of these transporters has not been described in intact cells. Such information is important because transport by isolated mitochondria may differ from that in situ, and because mitochondrial Ca2+ transport occurs within a system of transporters that must be taken into consideration.
This study extends to intact cells several general conclusions that have been drawn from studies of isolated mitochondria (
Third, the [Ca2+]i plateau level cannot be equated with the mitochondrial set point observed in studies of isolated mitochondria, since it depends jointly on mitochondrial and nonmitochondrial Ca2+ transport. Only in the limiting case where the plasma membrane is an impenetrable barrier to net Ca2+ transport can the plateau level be identified with the set point: in this case the model describes mitochondrial Ca2+ transport in a closed system like those used in studies of isolated mitochondria.
Finally, since [Ca2+]i dynamics depends on a system of Ca2+ transport pathways, there are multiple sites for potential modulation of intracellular Ca2+ signals and the processes they control. For example, the simulations indicate that properties of the [Ca2+]i recovery are jointly regulated by the mitochondrial Na+/Ca2+ exchanger, Ca2+ uniporter and plasma membrane Ca2+ transport systems; they would also be influenced by ER Ca2+ transport if it were enabled (not shown).
Simplifications Used in the Analysis
Cells were studied under conditions that simplified the analysis of Ca2+ dynamics. Thapsigargin was used to inhibit Ca2+ transport by SERCA pumps, making it possible to study the interplay between Ca2+ transport across the plasma membrane and uptake and release by mitochondria in isolation from ER Ca2+ transport. Analysis was restricted to the recovery after depolarization-induced [Ca2+]i elevations, after spatial [Ca2+]i gradients are largely dissipated, so that the free Ca concentration within each cellular compartment is approximately uniform spatially. Extension of the analysis to include the ER will require quantitative information about its Ca2+ uptake and release pathways, while treating the initial period of stimulation, when Ca2+ is distributed non-uniformly, will require detailed information about the spatial distribution of mitochondria and its dynamics.
For the model simulations, Ca2+ entry was evoked by a step increase in plasma membrane Ca2+ permeability. This leads to an instantaneous increase in the rate of Ca2+ entry across the plasma membrane to a level that depends on both Ca2+ permeability and the difference between internal and external Ca2+ concentrations (see Appendix). During stimulation, Ca2+ permeability was assumed to be constant, so time-dependent Ca2+ channel activation and inactivation were not taken into consideration. As a result, the simulated time courses of ci and cm during a depolarizing stimulus are not expected to follow precisely the changes in [Ca2+]i and [Ca2+]m that occur in situ. Information about the rate of Ca2+ entry during the stimulus should facilitate extension of the analysis to the period of depolarization.
Properties of Mitochondrial Ca2+ Uptake and Release in Intact Neurons
The equations describing mitochondrial Ca2+ uptake and release were motivated by results from studies of isolated mitochondria, so it is logical to compare, where possible, parameters of the equations with those describing transport by the isolated organelles. For Juni, reliable estimates of kmax,uni and EC50,uni were not possible given the limited [Ca2+]i range over which our measurements were made. However, it was possible to estimate the Hill coefficient (nuni ~2) which agrees with measurements from isolated mitochondria (
During all but the initial rapid phase of recovery, JNa/Ca depends on [Ca2+]m(i)in way that is consistent with previous studies (
[Ca2+]m(i),suggesting that the rate of mitochondrial Ca2+ release depends on other factors as well. Since previous work shows that JNa/Ca can be inhibited by high [Ca2+]i, the rate equation for JNa/Ca was modified to include an inhibitory term, after which it described JNa/Ca during the entire recovery. However, the steep [Ca2+]i dependence of inhibition that was required seemed unrealistic (Hill coefficient ~6). This suggests that yet other variables may contribute to the depression of JNa/Ca under these conditions, for example, intramitochondrial Na concentration (
Saturation of JNa/Ca strongly influences the way ci and cm change during and after stimulation. It sets the stage for continuous mitochondrial Ca2+ accumulation when ci is high during stimulation, and it is responsible for a nearly constant rate of net Ca2+ release during phase ii of the recovery, which generates the ci plateau. Ca2+ release could also occur at constant rate even when the release pathway is not saturated if Ca phosphate (CaP) formation effectively clamps intramitochondrial free Ca2+ concentration at a constant level (
Mitochondrial Ca2+ Transport during Repetitive Electrical Activity
Based on the model simulations, the effect of repetitive stimulation on [Ca2+]i and [Ca2+]m would depend critically on stimulus frequency. If the interval between individual stimuli or bursts of stimuli is long enough to permit complete recovery, then [Ca2+]i and [Ca2+]m would change periodically. If the intervals are brief enough so that recovery is incomplete, both [Ca2+]i and [Ca2+]m would be expected to undergo temporal summation, ultimately oscillating about an elevated mean that increases with frequency. This could provide a mechanism by which fluctuations in [Ca2+]i are translated into more steady elevations in [Ca2+]m. Indeed, this has been argued for the heart (
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Footnotes |
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1 Abbreviations used in this paper: ER, endoplasmic reticulum; Tg, thapsigargin.
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Acknowledgements |
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This work was supported by grants from the American Heart Association (96011490) and from the National Institutes of Health (NS 33514-03).
Submitted: 23 September 1999
Revised: 30 December 1999
Accepted: 5 January 2000
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Appendix |
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Equations Used to Describe the Components of the Total Ca2+ Flux
Ca2+ extrusion across the plasma membrane
Jpm was described by the sum of a linear leak flux (Jleak) and a saturable extrusion flux:
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(1) |
where kleak describes the Ca2+ permeability of the plasma membrane, [Ca2+]o is the extracellular free Ca concentration, Vmax,extru is the maximal rate of Ca extrusion, EC50,extru is the [Ca2+]i concentration where the Ca2+ extrusion rate is half maximal, and nextru describes how steeply the extrusion rate increases with [Ca2+]i. Although the equation for the leak pathway does not explicitly include the voltage dependence of Ca2+ entry, it is consistent with the Goldman-Hodgkin-Katz flux equation if membrane potential is constant and the permeant ion is present at a much higher concentration in the extracellular solution than the intracellular solution. Note that according to this description, extrusion and leak fluxes are of opposite sign as long as [Ca2+]i < [Ca2+]o and that Jpm is zero when the magnitudes of the component fluxes are equal.
Mitochondrial Ca2+ uptake
Juni Mitochondrial Ca2+ uptake was described by:
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(2) |
where kuni,max is the limiting slope at high [Ca2+]i, EC50,uni is the value of [Ca2+]i where activation of uptake is half-maximal and nuni is a Hill coefficient. Equation 2 would describe the total Ca2+ flux carried by a population of channels whose open probability increases with [Ca2+]i and which, when open, permit Ca2+ to flow unidirectionally at a rate that depends on [Ca2+]i and the magnitude of a constant electric field. This conforms with expectations from the Goldman-Hodgkin-Katz flux equation under conditions where mitochondrial membrane potential is constant, intramitochondrial Ca2+ concentration is low compared with [Ca2+]i, and the permeation pathway is far from saturation. In this case, kuni,max would depend on mitochondrial membrane potential. Since there was no indication that Juni was limited over the range [Ca2+]i < 1 µM, parameters for Equation 2 were estimated as follows. nuni was determined as the slope of a line fitted to a plot of log(kuni,max [Ca2+]i/Juni - 1) vs log([Ca2+]i). This provided estimates of nuni that were quite insensitive to kuni,max over the range (10 - 1000 s-1). After determining nuni, kuni,max was determined by fitting Equation 2 to Juni data while holding nuni constant and setting EC50,uni to 10 µM (
Mitochondrial Ca2+ release: JNa/Ca
The rate of Ca release via the Na+/Ca2+ exchanger was described by a saturable function of [Ca2+]m:
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(3) |
where Vmax,Na/Ca is the maximal rate of Ca2+ release and EC50,Na/Ca is the value of [Ca2+]m at which release rate is half maximal. The Na+ concentration is not explicitly taken into consideration since changes in [Na+]i and [Na+]m induced by depolarizations up to ~20 s are small ([Ca2+]m(i):
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(4) |
This was done by writing [Ca2+]m in terms of [Ca2+]m(i)as follows (Equation 5):
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(5) |
where [Ca2+]m() is the resting value of [Ca2+]m and
is the ratio of effective mitochondrial and cytosolic volumes. Substituting into Equation 3 gives (Equation 6):
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(6) |
This equation can be written as a function of [Ca2+]m(i)and three parameters:
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(7) |
where A = Vmax,Na/Ca, B = EC50,Na/Ca, and C = [Ca2+]m(
)/EC50,Na/Ca. Equation 7 was fit to data shown in Fig 2 F during the plateau phase of the recovery to obtain estimates of Vmax,Na/Ca and the lumped parameters
EC50,Na/Ca and [Ca2+]m(
)/EC50,Na/Ca. The steep decline in JNa/Ca at high
[Ca2+]m(i)can be described by multiplying by an inhibitory factor to give JNa/Ca':
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(8) |
where (Equation 9)
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(9) |
where Kd,inhib is the concentration for half maximal inhibition by cytosolic Ca2+ and ninhib describes the steepness of inhibition by [Ca2+]i.
Description of the Model
The experimentally determined rate laws for Jpm, Juni, and JNa/Ca provided all the flux definitions for a one-pool model of Ca2+ dynamics (
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(10) |
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(11) |
where the concentration fluxes (nM/s, referred to cytosolic effective volume) are (Equation 12Equation 13Equation 14Equation 15 HREF="#FD16">Equation 16Equation 17Equation 18):
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(12) |
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(13) |
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(14) |
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(15) |
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(16) |
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(17) |
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(18) |
where kleak, Vmax,extru, EC50,extru, nextru, kmax,uni, EC50,uni, nuni, Vmax,Na/Ca, and EC50,Na/Ca are constants described above, and co is the (constant) extracellular Ca2+ concentration. Note that Equation 12Equation 13Equation 14Equation 15 HREF="#FD16">Equation 16Equation 17 describe concentration fluxes that can be interpreted as the rate of Ca2+ delivery by the individual transport systems (e.g., pm) divided by the effective cytoplasmic volume (e.g., Jpm=
) where vi is the cytoplasmic volume and
iTis the ratio of (infinitesimal) changes in total to free Ca concentration. This model does not explicitly include a description of mitochondrial membrane potential (
) dynamics and applies to the case where
is constant (see
To simulate the effects of membrane depolarization, kleak was increased by kleak. According to Equation 14, this would instantaneously increase the rate of Ca2+ entry by
kleak(ci - co). For example, this could describe rapid activation of non-inactivating Ca2+ channels in the case where permeation occurs at steady membrane potential and conforms with constant field theory with ci << co (
kleak would depend on membrane potential. To include inhibitory effects of cytosolic Ca2+ on JNa/Ca, Equation 17 was modified as follows:
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(19) |
where (ci) is given by Equation 20:
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(20) |
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