Nonlinear [Ca²⁺] Signaling in Dendrites and Spines Caused by Activity-Dependent Depression of Ca²⁺ Extrusion

Activity and Ca²⁺ accumulations slow the decay of [Ca²⁺] transients

Together with Ca²⁺ influx and buffering, Ca²⁺ extrusion is an important determinant of the time course of cytosolic Ca²⁺ signals, especially during the temporal integration resulting from repetitive activity. To study the kinetics of Ca²⁺ extrusion from dendritic spines, we evoked Ca²⁺ influx through VSCCs by firing single back-propagating APs or trains of APs and recorded the resulting [Ca²⁺] transients in spines and their parent dendrites using two-photon excitation laser-scanning microscopy (Fig. 1A,B). In contrast to activation of other sources of Ca²⁺, such as NMDARs, APs cause virtually an instantaneous, δ-function-like Ca²⁺ influx (Helmchen et al., 1996; Maravall et al., 2000; Sabatini et al., 2002). In the absence of continuing influx, the decay of AP-evoked [Ca²⁺] transients directly reflects the clearance of Ca²⁺ ions from the cytosol. Thus, the decay time constants of the [Ca²⁺] transients directly reflect the rate of Ca²⁺ extrusion.

Quantitative studies of the mechanisms shaping [Ca²⁺] signals using [Ca²⁺] imaging demand conditions that minimize the perturbation of [Ca²⁺] dynamics by addition of the Ca²⁺ indicator (Neher and Augustine, 1992; Tank et al., 1995; Yasuda et al., 2004). We thus loaded CA1 pyramidal neurons in acute hippocampal brain slices with the low-affinity Ca²⁺ indicator Fluo-4ff (K_D = 8.1 μm). To ensure a linear relationship between [Ca²⁺] and fluorescence, we included relatively high concentrations of the indicator (500 μm). Compared with the unbuffered case, the buffer capacity of the indicator is expected to reduce [Ca²⁺] transient amplitudes and prolong their durations by a factor of ∼4 (Eqs. 1, 2). To visualize neuronal morphology and improve the SNR in [Ca²⁺] imaging, we also included a red Ca²⁺-insensitive fluorophore (Alexa 594; 30 μm) (Fig. 1A) (Yasuda et al., 2004).

To quantify the rates of Ca²⁺ extrusion, we determined the decay time constants of the [Ca²⁺] transients (Eq. 2) (Fig. 1F) by fitting exponentials to their decay phase (Fig. 1C–E, blue lines) (for details, see Materials and Methods). The decay of [Ca²⁺] transients evoked by single APs was mono-exponential [τ_decay(AP); spines, 41 ± 4 ms; dendrites, 55 ± 5 ms; n = 17] (Figs. 1C,F, 2B). Taking into account the presence of the indicator, these time constants are consistent with reported values (Sabatini et al., 2002). AP trains evoked larger [Ca²⁺] transients that decayed with two time constants, a major fast component (<150 ms) followed by a minor slow component (in approximately seconds) (Fig. 1D). Surprisingly, the decay time constant of the fast component increased with AP frequency and [Ca²⁺] both in spines (80 Hz, factor of 3.0 ± 0.3; n = 17) and dendrites (2.4 ± 0.2) (Figs. 1E,F, 2B,G). The time constant of the slow component was independent of AP frequency. Because its amplitude was ∼10 times smaller than the fast component under all conditions (data not shown), we restricted further analysis to the fast time constant and refer to it simply as the time constant of decay, τ_decay.

The slowing of [Ca²⁺] transient decays enhanced the temporal summation of Ca²⁺ such that the peak [Ca²⁺] increased supralinearly with AP frequency (Figs. 1G, 2C). This effect could play an important role in [Ca²⁺] signaling by preferentially enhancing [Ca²⁺] signals evoked by high levels of activity. Under our conditions, the single AP-evoked [Ca²⁺] transient amplitudes are expected to be ∼0.25 μm in spines and ∼0.18 μm in dendrites (see Materials and Methods). The [Ca²⁺] levels at the end of 20, 50, and 80 Hz trains are expected to be ∼0.5, 1.1, and 2.0 μm in spines and ∼0.4, 0.9, and 1.6 μm in dendrites, respectively (Fig. 2C).

To test whether the activity-dependent increase in τ_decay is dependent on [Ca²⁺], we reduced [Ca²⁺] transient amplitudes by loading neurons with a high-affinity Ca²⁺ indicator [500 μm Fluo-4; K_D = 0.34 μm (Yasuda et al., 2004)] (Fig. 2D–F). Compared with our standard conditions (Fig. 2A-C), τ_decay was prolonged by ≈8-fold (Eq. 2) (Fig. 2E), and the amplitudes of [Ca²⁺] transients were reduced by about the same factor (Eq. 1). Under these conditions, τ_decay was independent of AP frequency (Fig. 2D,E,G, squares), suggesting that the increase in τ_decay requires high-intracellular Ca²⁺ accumulations (>0.3 μm).

Slowing of [Ca²⁺] transients is attributable to depression of Ca²⁺ extrusion pathways

Several mechanisms could contribute to slow the decay of [Ca²⁺] transients including the following: (1) Ca²⁺-dependent increases in Ca²⁺ buffer capacity; (2) continuing release of Ca²⁺ from Ca²⁺ sources activated during AP trains; (3) saturation of Ca²⁺ extrusion mechanisms; and/or (4) depression of Ca²⁺ extrusion mechanisms. We performed experiments to test each of these possibilities.

Because the rate of Ca²⁺ extrusion is inversely proportional to the total buffer capacity (Eq. 2), Ca²⁺-dependent increases in the endogenous Ca²⁺ buffer capacity would increase τ_decay. Buffers with nonlinear Ca²⁺ binding could produce activity-dependent increases in buffer capacity and prolong the [Ca²⁺] transient decay time constant. Such increase in buffer capacity would also reduce the amplitudes of [Ca²⁺] transients by the same factor (Eqs. 1, 2). Because the opposing effects of increasing buffer capacity on the amplitude and τ_decay cancel, the plateau level of [Ca²⁺] transients during AP trains is expected to be independent of buffer capacity (Eq. 4). Slow buffers (equilibration time > τ_decay) would progressively load with Ca²⁺ during a train. However, this would only affect the rate at which the plateau level of [Ca²⁺] transients is reached, not the plateau level itself. After the stimulus, τ_decay would be slowed because of unbinding from the buffer.

Therefore, if nonlinear or slow buffers would account for the slowing of τ_decay, then the plateau [Ca²⁺] levels for AP trains should be equal to the expected plateau [Ca²⁺] levels based on the [Ca²⁺] increment (Δ[Ca²⁺]_AP) and τ_decay produced by single APs (Regehr and Atluri, 1995; Helmchen et al., 1996). However, when recording with low-affinity buffer (Fluo-4FF), the measured plateau levels were larger than expected (Fig. 3A,B), implying that the increase in τ_decay leads to more effective summation of individual [Ca²⁺] increments per AP. This argues that activity-dependent changes in buffer capacity cannot explain the slowing of τ_decay.

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Figure 3.

The activity-dependent slowing of the decay of [Ca²⁺] transients is attributable to depression of Ca²⁺ extrusion mechanisms. A, Comparison of measured [Ca²⁺] transients (black) and simulated [Ca²⁺] transients (gray). Simulations were based on the amplitude and decay time of the [Ca²⁺] transient evoked by a single AP. B, Measured [Ca²⁺] transient amplitudes versus expected [Ca²⁺] transient amplitudes, based on the amplitude and decay time of the [Ca²⁺] transient evoked by a single AP (Eq. 4). The black line shows equality. C, Same as B, except the calculation (Eq. 4) used the decay time of the [Ca²⁺] transient at the end of AP trains. The black line shows equality. D, Top, The decay phase of a [Ca²⁺] transient evoked by an 80 Hz AP train in a spine (baseline subtracted). Bottom, Corresponding Γ_i versus time. Dotted lines indicate amplitude levels as a percentage of peak [Ca²⁺]. E, Γ_i versus [Ca²⁺] level (percentage of peak [Ca²⁺]). To facilitate comparison of the rate constants between cells, instantaneous rate constants were averaged over [Ca²⁺] level windows of ±10% (thin lines, individual cells; circles, averages; n = 17).

When the activity-dependent increase in τ_decay is prevented, [Ca²⁺] should accumulate linearly (Regehr and Atluri, 1995; Helmchen et al., 1996). Consistent with this prediction, in recordings with high-affinity buffer (Fluo-4), the expected and measured plateau [Ca²⁺] levels matched (supplemental Fig. 2A, available at www.jneurosci.org as supplemental material).

The activity-dependent increase in τ_decay could also be caused by sources of Ca²⁺, which continue to release Ca²⁺ after termination of the AP train, such as CICR (Jacobs and Meyer, 1997; Sandler and Barbara, 1999). In the absence of such sources, [Ca²⁺] plateau levels during AP trains would be determined by the balance between the [Ca²⁺] increment per AP and the amount of Ca²⁺ extruded during the interstimulus interval (Eq. 4). Calculating plateau [Ca²⁺] using the slowed τ_decay at the end of the train, we find that the measured and expected plateau levels match (n = 17) (Fig. 3C). Moreover, blocking CICR pharmacologically (1 μm thapsigargin and 20 μm ryanodine) (Garaschuk et al., 1997) did not prevent slowing of τ_decay after a 50 Hz train of depolarizations (see results of recordings in voltage clamp below and Fig. 6A). We conclude that continuing Ca²⁺ release from delayed Ca²⁺ sources does not contribute to the slowing of [Ca²⁺] transient decays.

Could a combination of an increase in buffer capacity, which would slow extrusion, together with Ca²⁺ release from internal stores, which would enhance [Ca²⁺] levels, explain the results? In this case, when internal stores were blocked with thapsigargin and ryanodine, the measured [Ca²⁺] plateau levels should be predicted by the plateau levels calculated with the fast τ_decay, derived from the [Ca²⁺] transient evoked by a single stimulus (Eq. 4; compare Fig. 3B). However, we found that plateau levels were unaffected by blocking stores and were still predicted best by the slow τ_decay after trains of stimuli (supplemental Fig. 2C, available at www.jneurosci.org as supplemental material). Thus, release from internal stores in combination with increased endogenous buffer capacity does not explain enhanced Ca²⁺ accumulation and slowing of extrusion.

These arguments make the assumption that Δ[Ca²⁺]_AP remains unchanged during trains of APs. This assumption is supported by the observation that the measured [Ca²⁺] plateau levels and those predicted based on unchanged Δ[Ca²⁺]_AP match (Fig. 3C, Fluo-4FF; supplemental Fig. 2A, Fluo-4, available at www.jneurosci.org as supplemental material).

The slowing of Ca²⁺ clearance at high [Ca²⁺] could also be caused by saturation of Ca²⁺ extrusion mechanisms. At saturation, extrusion mechanisms would operate close to their maximal rate and [Ca²⁺] transients would decay from their maxima linearly (i.e., with a constant rate). As [Ca²⁺] drops, the instantaneous rate constant Γ_i = −(d[Ca²⁺]/dt)/([Ca²⁺] − [Ca²⁺]₀) would increase with decreasing [Ca²⁺]. As [Ca²⁺] drops below the ∼K_D of the extrusion mechanism, the decay will become exponential. Arguing against saturation, we find that Γ_i remains unchanged over the entire range of Ca²⁺ concentrations during the decay of even the largest [Ca²⁺] transients (Fig. 3D,E). In addition, [Ca²⁺] transients of different amplitudes evoked by depolarizations in voltage clamp decayed with the same time constant (see results of recordings in voltage clamp below and Fig. 4A–C). Thus, saturation of extrusion cannot explain the slowing of [Ca²⁺] transient decays. Together, these observations argue that the Ca²⁺ accumulations during trains of APs cause a Ca²⁺-dependent change in the rate constant of extrusion (Eq. 2, Γ). In analogy with previous work on VSCCs (Yasuda et al., 2003), we call this phenomenon depression of Ca²⁺ extrusion.

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Figure 4.

Time constant of the recovery from depression of Ca²⁺ extrusion. A, [Ca²⁺] transients in a spine evoked by a weak (pulse width, 2–5 ms; left) and a strong (pulse width, 8–15 ms; right) depolarization in voltage clamp. B, Amplitudes of [Ca²⁺] transients produced by single APs (n = 5 cells; open bars) and depolarizations (3–15 ms; n = 18 cells; filled bars). C, τ_decay of [Ca²⁺] evoked by APs (open bars; n = 17) and depolarizations (filled bars; n = 18) (same data set as in B). D, Protocol for measuring the recovery of depression of Ca²⁺ extrusion in a spine. E, Time course of recovery from depression of Ca²⁺ extrusion (t = 0; decay time constant of train evoked [Ca²⁺] transient; n = 9). F, Same as E, except normalized with respect to the baseline extrusion time constant. Error bars indicate SEM.

Time constant of recovery from activity-dependent depression of Ca²⁺ extrusion

The activity-dependent slowing of τ_decay was not restricted to [Ca²⁺] transients produced by APs but could also be induced by trains of depolarizations in voltage clamp (Fig. 4). These depolarizations directly activate VSCCs, allowing better experimental control of Ca²⁺ influx and more extensive pharmacological manipulations (e.g., manipulations of ionic gradients that interfere with APs). We therefore used depolarizations produced in voltage clamp in the presence of TTX for a majority of the subsequent experiments while recording [Ca²⁺] transients with 500 μm Fluo-4FF.

We compared the [Ca²⁺] transients evoked by depolarizations (Fig. 4A–C) with those evoked by APs. Applying pulses from a holding potential of −70 to +50 mV induced Ca²⁺ tail currents after repolarization (Sabatini et al., 2002). Varying the pulse width allowed tuning of the fraction of activated channels and the amount of Ca²⁺ influx. Application of single 2–5 ms pulses (“weak” depolarization) mimicked single AP-evoked [Ca²⁺] transients regarding amplitude and decay time (unpaired t test) (Fig. 4B,C). Larger [Ca²⁺] transients of about twice the amplitude as obtained with weak depolarization could be evoked using 8–15 ms pulses (“strong” depolarization). τ_decay of the [Ca²⁺] transients evoked by single weak and strong depolarizations and APs were indistinguishable (Fig. 4C). Although the amplitude of [Ca²⁺] transients evoked by strong depolarizations were similar to the amplitude of transients evoked by trains of weak depolarizations (Fig. 4D), their duration was not sufficient to induce depression of extrusion. This represents additional evidence that slowing of extrusion is not attributable to saturation of extrusion mechanism. The induction of extrusion depression requires prolonged [Ca²⁺] elevations.

To analyze the recovery from depression of extrusion, we measured τ_decay of [Ca²⁺] transients evoked by strong depolarizations before and after a 50 Hz train of weak depolarizations and varied the recovery time between the train and the second strong depolarization (Fig. 4D). The depression of extrusion recovered with time constants of <1 s (spine, ∼500 ms; dendrite, ∼700 ms) (Fig. 4E,F).

Na⁺/Ca²⁺ exchangers and PMCAs extrude Ca²⁺ from spines and dendrites

We sought to determine the molecules responsible for Ca²⁺ extrusion in spines and dendrites (Markram et al., 1995; Mainen et al., 1999; Majewska et al., 2000b; Sabatini et al., 2002). In addition to SERCA pumps (Mainen et al., 1999; Majewska et al., 2000b; Sabatini et al., 2002), PMCAs and Na⁺/Ca²⁺ exchangers are likely to contribute to extrusion. Both PMCAs and Na⁺/Ca²⁺ exchangers derive from multiple genes and occur in multiple splice variants with potentially different properties (Blaustein and Lederer, 1999; Strehler and Zacharias, 2001). Available inhibitors have mostly been tested only on a subset of isoforms and often have nonspecific effects (Kaczorowski et al., 1989; Thayer et al., 2002). We therefore used methods that specifically reduce the activity of Na⁺/Ca²⁺ exchangers versus PMCAs, independent of the particular isoform.

PMCAs can be partially inhibited by blocking their activator calmodulin with calmidazolium (Markram et al., 1995; Werth et al., 1996). We recorded [Ca²⁺] transients evoked by depolarizations before and after wash-in of 20 μm calmidazolium (Fig. 5A). Because calmidazolium reduced Ca²⁺ influx (by ∼40%), we increased the widths of the depolarizations to keep [Ca²⁺] transient amplitudes constant (weak depolarizations to 5–10 ms; strong depolarizations to 15–20 ms). Calmidazolium had little effect on resting [Ca²⁺] in spines and dendrites compared with the amplitudes of depolarization-evoked [Ca²⁺] transients (relative change in baseline [Ca²⁺]: spine, 0.01 ± 6%; dendrite, 23 ± 4%; transient amplitude relative to baseline [Ca²⁺]: spine, ≈170%; dendrite, ≈90%; n = 6) (supplemental Fig. 3A,B, available at www.jneurosci.org as supplemental material). Because Ca²⁺ influx is effectively instantaneous, quantification of the decay time of [Ca²⁺] transients isolates the effect of calmidazolium on Ca²⁺ extrusion. Calmidazolium dramatically slowed extrusion for [Ca²⁺] transients evoked by both weak and strong depolarizations (Fig. 5B,C). Partial block of PMCA increased τ_decay by almost a factor of two in spines (weak depolarization, 1.85 ± 0.18; strong depolarization, 2.15 ± 0.46; n = 6) and dendrites (weak depolarization, 1.50 ± 0.12; strong depolarization, 1.73 ± 0.40). We obtained similar results when blocking PMCAs with 25–50 μm orthovanadate (supplemental Materials and Methods and supplemental Fig. 4, available at www.jneurosci.org as supplemental material) (Usachev et al., 2002).

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Figure 5.

Ca²⁺ extrusion is via PMCA and Na⁺/Ca²⁺ exchangers. A, Example of [Ca²⁺] transients evoked by a weak (left) and strong (right) depolarization in control conditions (black) and calmidazolium (gray). B, τ_decay in calmidazolium (Calm.) and control (Ctrl) (open circles, individual cells; filled circles, averages; n = 6). C, τ_decay in calmidazolium relative to control. D, Example of a [Ca²⁺] transient evoked by a weak (left) and strong (right) depolarization in control conditions (black) and with Li⁺ replacing Na⁺ (gray; scale bars as in A). E, [Ca²⁺] τ_decay in Li⁺ and control (Ctrl) (open circles, individual cells; filled circles, averages; n = 6). F, τ_decay in Li⁺ normalized to control. Error bars indicate SEM.

Na⁺/Ca²⁺ exchange can be inhibited by replacing extracellular Na⁺ with ions that are not transported by the exchanger. We recorded [Ca²⁺] transients evoked by depolarizations before and after replacing Na⁺ in the ACSF with Li⁺ (Fig. 5D) (Mulkey and Zucker, 1992; Koch and Barish, 1994; Fierro et al., 1998). Again, the depolarization pulse width was adjusted to maintain constant [Ca²⁺] transient amplitudes. Li⁺ increased τ_decay by almost a factor of 2 (Fig. 5E,F) (spine: weak depolarization, 1.76 ± 0.18; strong depolarization, 1.81 ± 0.35; dendrite: weak depolarization, 1.67 ± 0.07; strong depolarization, 1.85 ± 0.43; n = 6). Changes in resting [Ca²⁺] after replacing Li⁺ for Na⁺ were small compared with the amplitudes of depolarization-evoked [Ca²⁺] transients (relative change in baseline [Ca²⁺]: spine, 14 ± 4%; dendrite, 23 ± 4%; transient amplitude relative to baseline [Ca²⁺]: spine, ≈180%; dendrite, ≈110%; n = 6) (supplemental Fig. 3C,D, available at www.jneurosci.org as supplemental material).

Under our conditions, SERCA pumps do not contribute significantly to Ca²⁺ clearance. The average τ_decay in the presence of thapsigargin and ryanodine (spine: weak depolarization, 54.2 ± 7.5 ms; strong depolarization, 58.5 ± 14.5 ms; dendrite: weak depolarization, 58.8 ± 4.3 ms; strong depolarization, 41.5 ± 3.6 ms; n = 4; unpaired t test; data not shown) was not significantly different from control conditions.

Thus, Na⁺/Ca²⁺ exchangers and PMCAs contribute to Ca²⁺ extrusion through the plasma membrane. Because calmidazolium is only a partial blocker of PMCAs (Penniston and Enyedi, 1998), whereas Li⁺ completely abolishes Na⁺/Ca²⁺ exchanger activity, under our conditions PMCAs likely extrude slightly more than half of Ca²⁺ ions (spines, >46%; dendrites, >33%; n = 6) and Na⁺/Ca²⁺ exchangers are responsible for extruding most of the remainder (spines, 43%; dendrites, 40%; n = 6). Consistent with our physiological measurements, immunofluorescence images revealed that PMCA and Na⁺/Ca²⁺ exchangers (NCX2) were expressed in CA1 dendrites and spines (A. Burette and R. Weinberg, personal communication).

Ca²⁺ extrusion via both PMCA and Na⁺/Ca²⁺ exchangers depresses

To determine the substrates of Ca²⁺-dependent depression of Ca²⁺ extrusion, we compared [Ca²⁺] transients produced by single weak depolarizations and trains (50 Hz) of weak depolarizations, while manipulating Ca²⁺ extrusion mechanisms (Fig. 6). Trains of depolarizations evoked [Ca²⁺] transients that were similar to those evoked by AP trains. As for APs (Fig. 3C), the plateaus of depolarization-evoked transients matched the predicted plateaus calculated based on the [Ca²⁺] increment per stimulus, stimulus frequency, and τ_decay at the end of the train (Eq. 4; supplemental Fig. 2B, available at www.jneurosci.org as supplemental material).

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Figure 6.

Na⁺/Ca²⁺ exchangers and PMCAs are substrates for activity-dependent depression of extrusion. A, τ_decay after 50 Hz trains of APs (open bars) or weak depolarization (filled bars) normalized to single stimuli [AP, n = 17; depolarization (Depol.), n = 18; calmidazolium (Calm.), n = 6; Li⁺, n = 6; thapsigargin plus ryanodine (Thaps. + Ryanod.), n = 4; *statistically significant difference, unpaired t test; **statistically significant difference compared with internal control; NS, not significant compared with depolarization, unpaired t test]. B, [Ca²⁺] transients evoked by a single (left) and a 50 Hz (right) train of weak depolarizations in control conditions (black) and Li⁺ (gray). C, τ_decay of [Ca²⁺] transients (open circles, individual cells; filled circles, averages; n = 6). D, [Ca²⁺] transients evoked by a single (left) and a 50 Hz (right) train of weak depolarizations in control conditions (black) and in calmidazolium (gray; scale bars as in B). E, τ_decay of [Ca²⁺] transients (open circles, individual cells; filled circles, averages; n = 6). Error bars indicate SEM.

Because Na⁺/Ca²⁺ exchangers are present in spines and dendrites, depression of extrusion could be mediated in part by the accumulation of cytosolic Na⁺, which would reduce the [Na⁺] gradient across the plasma membrane and thus the driving force for the exchanger. Consistent with this possibility, in the presence of the Na⁺ channel blocker TTX, [Ca²⁺] transients displayed less pronounced extrusion depression than observed with AP-evoked transients (APs, n = 17; depolarization with TTX, n = 18) (Fig. 6A). This result is consistent with an estimate of the reduction in the forward Ca²⁺ transport rate of the Na⁺/Ca²⁺ exchanger based on the change of [Na⁺] per AP. An elevation of the internal Na⁺ concentration by ∼5 mm during a 500-ms-long train of APs at 50 Hz (0.2 mm per AP) (Rose et al., 1999) reduces the Na⁺/Ca²⁺ exchanger Ca²⁺ translocation rate by a factor of 0.77 [Regehr (1997), Eq. 2) (with internal [Ca²⁺]_i of 1 μm, [Na⁺]_i of 15 mm, external [Ca²⁺]_e of 2 mm, [Na⁺]_e of 153 mm, V_m = −70 mV, and kT = 26.9 mV at 35°C). Thus, depression of extrusion is partially attributable to diminished Ca²⁺ transport by Na⁺/Ca²⁺ exchangers caused by accumulation of cytosolic Na⁺ during trains of APs.

Why is depression of Ca²⁺ extrusion attributable to cytosolic Na⁺ accumulation not observed in the recordings with Fluo-4 (Fig. 2E)? Under these conditions, [Ca²⁺] transients are so small that the Na⁺/Ca²⁺ exchangers remain close to equilibrium, implying little net transport of Ca²⁺ ions (Regehr, 1997). When recorded with Fluo-4, the ratios of τ_decay for single depolarization-evoked [Ca²⁺] transients in Li ⁺ (Na⁺/Ca²⁺ exchangers blocked) versus Na⁺ were not significantly different from unity (spine, 1.06 ± 0.07; dendrite, 0.96 ± 0.04; n = 3; data not shown).

With Na⁺/Ca²⁺ exchangers blocked, which Ca²⁺ extrusion mechanism is responsible for the remainder of activity-dependent depression of extrusion? In the presence of extracellular Li⁺, [Ca²⁺] transient decays were slowed dramatically (factor of 4–5) after 50 Hz trains (Fig. 6B) compared with single depolarizations (Fig. 6A,C, right). Under control conditions (Na⁺/Ca²⁺ exchangers active), this factor was only ∼1.5 (Fig. 6A,C, left). With Na⁺/Ca²⁺ exchangers blocked, the slowing of extrusion caused a dramatic increase in peak [Ca²⁺] during the train (spine, factor of 3.2 ± 0.4; dendrite, 3.0 ± 0.4; n = 6) (Fig. 6B). Despite this increase, the enhanced slowing of extrusion was not attributable to saturation of PMCAs (supplemental Fig. 3E, available at www.jneurosci.org as supplemental material). Thus, we conclude that PMCAs inactivate in response to intracellular Ca²⁺ accumulations.

With Na⁺ accumulations blocked, inactivation of PMCAs seems to mediate the majority of Ca²⁺-dependent depression of extrusion (Fig. 6A,C). Partial block of PMCAs with calmidazolium increased τ_decay for single depolarizations and the 50 Hz train by a factor of 2 compared with control (spine: single, 1.85 ± 0.15; train, 2.34 ± 0.32; difference not significant; dendrite: single, 1.50 ± 0.12; train, 1.96 ± 0.17; difference significant; n = 6) (Fig. 6E). Ca²⁺-dependent depression of extrusion was slightly enhanced in the presence of calmidazolium (spine, 27 ± 15%; dendrite, 33 ± 12%) (Fig. 6A). If PMCAs mediate Ca²⁺-dependent depression of extrusion under these conditions, why is the amplitude of Ca²⁺-dependent depression of extrusion increased by partial block of PMCAs? By reducing Ca²⁺ extrusion, the presence of calmidazolium leads to larger [Ca²⁺] accumulations (Fig. 6D), which presumably causes stronger inactivation of the remaining PMCAs (for a formal analysis, see supplemental Materials and Methods, available at www.jneurosci.org as supplemental material). However, we cannot exclude an additional contribution of Ca²⁺-dependent inactivation of Na⁺/Ca²⁺ exchangers. Furthermore, this result suggests also that depression of extrusion is not mediated by Ca²⁺-dependent calmodulin binding to PMCA or one of its regulators, because calmidazolium interferes with calmodulin binding to its targets. However, it is possible that calmodulin is preassociated with PMCAs (Erickson et al., 2001) to control their activity.

In contrast, inhibiting stores with thapsigargin and ryanodine neither prevented nor dramatically increased depression of extrusion (Fig. 6A). Thus, uptake into the smooth endoplasmic reticulum did not contribute to depression of Ca²⁺ extrusion, consistent with the finding that it plays only a minor role in extruding Ca²⁺ under our conditions.

Interactions with NMDAR-mediated [Ca²⁺] signals

To determine whether depression of Ca²⁺ extrusion could play a role in [Ca²⁺] signals related to synaptic transmission, we combined stimulation of synaptic glutamate receptors by two-photon glutamate uncaging with two-photon [Ca²⁺] imaging (Carter and Sabatini, 2004; Sobczyk et al., 2005; Losonczy and Magee, 2006) (Fig. 7A) (see Materials and Methods). To evoke and isolate currents and Ca²⁺ influx through NMDARs (Fig. 7E), experiments were performed in voltage clamp with the Mg²⁺ block relieved (0.1 mm Mg²⁺), in the presence of the AMPA receptor blocker NBQX, drugs to reduce dendritic excitation and nonlinearities, and drugs to abolish Ca²⁺ release from intracellular stores (see Materials and Methods) (Sobczyk et al., 2005). Uncaging reliably induced NMDAR-mediated uEPSCs and [Ca²⁺] transients that were primarily restricted to the stimulated spine (Fig. 7B). To avoid membrane depolarization and possible activation of VSCCs, the uncaging intensity was limited to keep currents small (mean uEPSC, 9.4 ± 1.1 pA; 14 spines; seven cells).

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Figure 7.

Depression of Ca²⁺ extrusion and Ca²⁺ influx through NMDAR-timing-dependent plasticity of Ca²⁺ extrusion. A, Simultaneous [Ca²⁺] imaging and glutamate uncaging. The image of a spine is shown. The green line indicates the position of line scans performed for Ca²⁺ imaging. Caged glutamate was photolyzed next to the spine head (red line). B, Examples of [Ca²⁺] transients evoked by a strong depolarization alone (depol.; left) and glutamate uncaging (uncag.), followed by strong depolarization after 250 ms (right). C, τ_decay of [Ca²⁺] transients evoked by strong depolarization after glutamate uncaging (uncag.) compared with control (Ctrl.; open circles, individual cells; filled circles, averages; n = 15 spines, 5 cells). D, Averages and SEM (**statistically significant difference from unity). Dendr., Dendrite. E, [Ca²⁺] transients (red, spine; black, dendrite) and NMDAR currents (blue) evoked by single glutamate uncaging stimuli (left) and trains of six stimuli at 10 Hz (right) (n = 14 spines, 7 cells). F, Glutamate uncaging evoked Ca²⁺ accumulations produced by single stimuli compared with trains of stimuli. Ca²⁺ accumulations were quantified as the integral of [Ca²⁺] normalized to the integral of NMDAR currents (open circles, individual cells; filled circles, averages; n = 14 spines, 7 cells). G, Ca²⁺ accumulation produced by trains of uncaging stimuli normalized to single stimuli as a function of [Ca²⁺] transient amplitude of the single stimulus response (Δ[Ca²⁺]). Ca²⁺ accumulations were calculated as in F. H, Ca²⁺ accumulation produced by trains of uncaging stimuli normalized to single stimuli as a function of I_NMDA of the single response. Ca²⁺ accumulations were calculated as in F.

To test whether NMDAR-mediated Ca²⁺ and Na⁺ influx induces depression of Ca²⁺ extrusion, we followed glutamate uncaging with a strong depolarization (interstimulus interval, 250–300 ms). τ_decay was significantly larger than under control conditions (n = 15 spines) (Fig. 7C, red, left, D, red). Depression of extrusion was limited to the stimulated spine and did not occur in the parent dendrite (dendritic τ_decay; n = 15 spines) (Fig. 7C, black, right, D, black), most likely because the glutamate uncaging-evoked [Ca²⁺] transients were restricted to single spines (Fig. 7B) (Noguchi et al., 2005; Sobczyk et al., 2005). We conclude that NMDAR activation induces depression of extrusion restricted to stimulated spines.

Next we tested how depression of Ca²⁺ extrusion shapes NMDAR-mediated [Ca²⁺] transients during trains of uncaging stimuli. In the case of NMDAR-mediated [Ca²⁺] signals in spines, τ_decay does not simply reflect extrusion (Eq. 2) but, in addition, is shaped by the time course of the uEPSC and Ca²⁺ diffusion from the spine head into the dendrite. Therefore, to detect differences in the effectiveness of Ca²⁺ extrusion, we compared the integral of [Ca²⁺] transients normalized to the integral of the NMDAR current (Σ[Ca²⁺]/ΣI_NMDA; see Materials and Methods) (supplemental Eq. S11, available at www.jneurosci.org as supplemental material). The normalization accounts for potential desensitization of NMDAR currents and the resulting reduction in Ca²⁺ influx during trains of uncaging stimuli.

We compared the [Ca²⁺] transients evoked by a single uncaging stimulus and a train of six uncaging stimuli (10 Hz) (Fig. 7E). Surprisingly, on average the normalized [Ca²⁺] integrals were not significantly different for single uEPSCs and trains of uEPSCs (n = 14 spines) (Fig. 7F). Only a subset of spines displayed enhanced [Ca²⁺] accumulation during trains of uEPSCs. Similarly, trains of depolarization did not significantly change the time course of subsequent NMDAR-mediated [Ca²⁺] transients (n = 8 spines) (supplemental Fig. 5, available at www.jneurosci.org as supplemental material).

Spines have been shown to display heterogeneity in NMDAR-mediated Ca²⁺ signaling in response to glutamate uncaging (Noguchi et al., 2005; Sobczyk et al., 2005). Here we observed that spines also respond to trains of uncaging stimuli in diverse ways. Different spines yielded similar, enhanced, or reduced [Ca²⁺]/NMDAR current integral ratios for trains of uncaging stimuli compared with single stimuli, in which enhancement was preferentially observed if single stimulus-evoked [Ca²⁺] transients were small [<10% (G/R)_max] (Fig. 7G). A similar correlation was not apparent with respect to the size of the NMDAR-mediated currents (Fig. 7H), consistent with the absence of correlation between NMDAR-mediated [Ca²⁺] transients and currents (Noguchi et al., 2005; Sobczyk et al., 2005).

PMCAs and Na⁺/Ca²⁺ exchangers extrude Ca²⁺ from dendritic spines

We find that both PMCAs and Na⁺/Ca²⁺ exchangers contribute to Ca²⁺ extrusion from spines and dendrites (Fig. 5). PMCAs have been previously detected by immunolocalization in spines from cerebellar Purkinje cells (Stauffer et al., 1997) and hippocampal neurons (DeMarco and Strehler, 2001; Kip et al., 2006). b splice variants contain a C-terminal PDZ [postsynaptic density-95 (PSD-95)/Discs large/zona occludens-1]-binding motif, and several PMCA isoforms have been shown to interact with PSD-95 family members at the postsynaptic density (DeMarco and Strehler, 2001; Strehler and Zacharias, 2001).

There are two distinct groups of Na⁺/Ca²⁺ exchangers. Members of the NCX family exchange Na⁺ and Ca²⁺ ions in a stoichiometric ratio of 3:1, whereas NCKX also exchanges K⁺ ions [4 Na⁺:(1Ca²⁺ + 1K⁺)] (Blaustein and Lederer, 1999; Lytton et al., 2002). NCX2 labeling is found in apical dendrites and spines of CA1 pyramidal neurons (Burette and Weinberg, personal communication), a finding consistent with studies of NCX2 knock-out mice, which exhibit slowing of Ca²⁺ extrusion in the somato-dendritic compartment (Jeon et al., 2003). Other immunolocalization data suggest that NCX3 can also be found in CA1 dendrites (Canitano et al., 2002; Papa et al., 2003). NCKX can contribute to Ca²⁺ extrusion in the somata of CA1 neurons (Kiedrowski, 2004), but little is known about the subcellular distributions of NCKX.

We found that PMCA and Na⁺/Ca²⁺ exchanger together are responsible for the majority of Ca²⁺ clearance from the cytoplasm. Ca²⁺ clearance by uptake into internal stores (endoplasmic reticulum) via SERCA pumps (Mainen et al., 1999; Majewska et al., 2000b; Sabatini et al., 2002) plays only a minor role under our conditions. PMCAs have 10-fold higher affinity and a >10 times lower transport rate than NCX for Ca²⁺ (Blaustein and Lederer, 1999). For this reason, PMCAs have generally been associated with maintaining low resting [Ca²⁺] and NCX with rapid clearance of [Ca²⁺] transients (Thayer et al., 2002). In contrast with this view, under our experimental conditions, PMCA and Na⁺/Ca²⁺ exchanger contribute to extrusion of Ca²⁺ to similar extents. It is possible that Na⁺/Ca²⁺ exchanger dominates Ca²⁺ clearance for larger [Ca²⁺] transients than those probed in our study.

Activity- and Ca²⁺-dependent depression of Ca²⁺ extrusion

Large and prolonged [Ca²⁺] transients, for example those evoked by trains of APs relevant for hippocampal function (Czurko et al., 1999), decay more slowly than transients evoked by single APs. This positive feedback is attributable to Ca²⁺-dependent depression of extrusion. Previous measurements of AP-evoked [Ca²⁺] signals used high-affinity indicators with higher added buffer capacity, and thus much less (Helmchen et al., 1996) or no (Maravall et al., 2000) activity-dependent depression of extrusion was detected. Depression of extrusion after AP trains was reported in one study using high-affinity buffer (Callaway and Ross, 1995). However, because the indicator was loaded through a sharp electrode, it is possible that the indicator concentration in the dendrite was sufficiently low so that it corresponded to our standard low added buffer capacity condition.

We found that with Na⁺ channels blocked, activity-dependent depression of extrusion was reduced. The most straightforward interpretation of our data are that Na⁺ accumulation during trains of APs reduces the driving force for Na⁺/Ca²⁺ exchangers (Blaustein and Lederer, 1999; Thayer et al., 2002). A similar interplay between Na⁺ accumulation and Ca²⁺ extrusion has been studied in presynaptic terminals (Mulkey and Zucker, 1992; Regehr, 1997). The Na⁺-dependent depression was not observed under the condition of high Ca²⁺ buffering because for the tiny [Ca²⁺] levels achieved under these conditions, Na⁺/Ca²⁺ exchangers remained close to equilibrium and contributed effectively no net ion translocation to total extrusion.

With Na⁺/Ca²⁺ exchangers blocked, we observed very large [Ca²⁺] accumulations and a more pronounced activity-dependent depression of extrusion (Fig. 6), reflecting Ca²⁺-dependent inactivation of PMCAs. Although [Ca²⁺] reached up to 2 μm, we found no indication of PMCA saturation (supplemental Fig. 3E, available at www.jneurosci.org as supplemental material). In contrast, biochemical data reports Ca²⁺ affinities in the range ∼0.1–1.0 μm with calmodulin bound (∼20 μm without calmodulin) and affinities for calmodulin on the order of ∼1 nm (Carafoli, 1992; Caride et al., 2001). Because the concentration of calmodulin ranges from 10 to 100 μm (Xia and Storm, 2005), PMCAs would be expected to be predominantly in the high-affinity state and thus saturated under our conditions. Absence of saturation argues instead that PMCAs have surprisingly low affinity for Ca²⁺ in intact neurons, at least in their inactivated state (Strehler and Zacharias, 2001).

Ca²⁺-dependent inactivation of PMCAs resembles Ca²⁺-dependent inactivation of VSCCs (Budde et al., 2002). Although various signaling pathways have the potential to modulate PMCA activity (Strehler and Zacharias, 2001; Thayer et al., 2002), the mechanisms underlying the observed Ca²⁺-dependent inactivation remain uncertain.

Depression of Ca²⁺ extrusion and synaptic [Ca²⁺] signaling

Activation of synaptic NMDARs by glutamate uncaging produced depression of extrusion in the stimulated spine. This is not surprising, because under our experimental conditions, NMDAR activation produces larger accumulations of Na⁺ and Ca²⁺ in the stimulated spine than do trains of APs (Rose and Konnerth, 2001; Sabatini et al., 2002). We also expected to observe the reverse, an enhanced accumulation of Ca²⁺ attributable to slowing of extrusion during trains of NMDAR-mediated [Ca²⁺] transients. Surprisingly, [Ca²⁺] per stimulus was similar for single uncaging stimuli and trains. However, there was heterogeneity in the NMDAR-mediated [Ca²⁺] response of individual spines to trains of uncaging stimuli. Some spines showed an enhanced [Ca²⁺] per stimulus during trains as expected when depression of Ca²⁺ extrusion occurs, whereas other spines behaved in opposite ways (Fig. 7G). This heterogeneity in Ca²⁺ handling may be interesting with respect to the induction of synaptic plasticity. It could reflect input-specific Ca²⁺ handling in spines, or different functional states arising from metaplasticity.

In the spines that did not produce enhanced Ca²⁺ accumulations during trains of uncaging stimuli, depression of Ca²⁺ extrusion might be compensated for or obscured by one of the following mechanisms. (1) The activity of particular extrusion mechanisms could be selectively enhanced. Because, for example, PMCA b splice variants interact with PSD-95 family members at the postsynaptic density (DeMarco and Strehler, 2001; Strehler and Zacharias, 2001), different Na⁺/Ca²⁺ exchanger and PMCA isoforms are potentially regulated in diverse ways and associated with different postsynaptic signaling complexes. (2) The amount of Ca²⁺ influx could decrease without a change in the NMDAR current. NMDAR currents display short-term plasticity (Tong et al., 1995), which might extend to Ca²⁺ permeability, because there is evidence that the Ca²⁺ permeability of NMDAR can be selectively regulated (Sobczyk et al., 2005). (3) Ca²⁺ clearance could be dominated by diffusion into the dendrite across the spine neck (Majewska et al., 2000a; Bloodgood and Sabatini, 2005). Future experiments will have to address these possibilities.

Functional physiological role of depression of Ca²⁺ extrusion

[Ca²⁺] signals in dendritic spines play a key role in inducing diverse forms of neuronal plasticity, including long-term depression and potentiation. Stimuli that produce an enhancement of synaptic strength are associated with higher-amplitude [Ca²⁺] signals compared with stimuli that lead to a decrease in synaptic strength (Cummings et al., 1996; Yang et al., 1999; Froemke et al., 2005). Our results show that the rate of Ca²⁺ extrusion, which determines the temporal summation of [Ca²⁺] signals, is regulated in an activity- and Ca²⁺-dependent manner. This positive feedback mechanism causes nonlinear Ca²⁺ signaling. Therefore, it can contribute to translating differences in stimuli into differential activation of Ca²⁺-dependent signaling cascades to induce different forms of plasticity.

We show that the clearance of VSCC-mediated [Ca²⁺] transient is slowed subsequent to NMDAR activation, but not vice versa. The order of the stimuli can thus play an important role in determining the total integrated Ca²⁺ accumulation in individual dendritic spines. This is reminiscent of STDP, in which postsynaptic spiking before synaptic activation leads to synaptic depression, whereas postsynaptic spiking after synaptic activation results in synaptic potentiation (Sjostrom and Nelson, 2002). Depression of extrusion might play a role in the induction of plasticity by producing larger integrated Ca²⁺ accumulations if synaptic stimuli precede postsynaptic spiking. However, the recovery time constant of depression of extrusion is slower than the time window for STDP (500 ms vs 10–50 ms). It is possible that depression of extrusion plays a role in learning rules that involve longer time scales (Larson and Lynch, 1986).

The heterogeneity in Ca²⁺ handling after trains of NMDAR activations, where spines displayed either an unchanged or enhanced accumulation of [Ca²⁺] compared with a single stimulus, could be a mechanisms underlying synaptic metaplasticity (Fusi et al., 2005). For example, a potentiated spine might not express depression of extrusion and therefore would be less likely to be potentiated further. Conversely, depressed spines would express depression of extrusion and be more likely to be potentiated by generating enhanced [Ca²⁺] accumulations during trains of synaptic activation.