Neuron

ArticleCa2+ Requirements for Cerebellar
Long-Term Synaptic Depression:
Role for a Postsynaptic Leaky Integrator
Keiko Tanaka,1 Leonard Khiroug,1,2 Fidel Santamaria,1 Tomokazu Doi,4 Hideaki Ogasawara,4,5
Graham C.R. Ellis-Davies,3 Mitsuo Kawato,4 and George J. Augustine1,*
1

Department of Neurobiology, Duke University Medical Center, Box 3209, Durham, NC 27710, USA
Neuroscience Center, University of Helsinki, P.O. Box 65, Helsinki 00014, Finland3
Department of Pharmacology and Physiology, Drexel University College of Medicine, 245 North 15th Street, Philadelphia,
PA 19102, USA
4
Department of Computational Neurobiology, ATR Computational Neuroscience Laboratories, Kyoto 619-0288, Japan
5
National Institute of Information and Communications Technology, Kyoto 619-0288, Japan*Correspondence: georgea@neuro.duke.edu
DOI 10.1016/j.neuron.2007.05.014
2

SUMMARY

Photolysis of a caged Ca2+ compound wasused to characterize the dependence of cerebellar long-term synaptic depression (LTD) on
postsynaptic Ca2+ concentration ([Ca2+]i). Elevating [Ca2+]i was sufficient to induce LTD without requiring any of the other signals producedby synaptic activity. A sigmoidal relationshipbetween [Ca2+]i and LTD indicated a highly cooperative triggering of LTD by Ca2+. The duration of the rise in [Ca2+]i influenced the apparent
Ca2+ affinity of LTD, and this time-dependent
behavior could be described by a leaky integrator process with a time constant of 0.6 s. A computational model, based on a positive-feedback
cycle that includes protein kinase C and MAP
kinase, was capable of simulating these properties of Ca2+-triggered LTD. Disrupting this cycle
experimentally also produced the predictedchanges in the Ca2+ dependence of LTD. We
conclude that LTD arises from a mechanismthat integrates postsynaptic Ca2+ signals andthat this integration may be produced by the
positive-feedback cycle.
INTRODUCTION
Although many forms of long-lasting synaptic plasticity
arise from the actions of Ca2+ within the postsynaptic neuron, in no case have the Ca2+ requirements for long-term
plasticity been defined precisely (Augustine et al., 2003;
Malenka and Bear, 2004). This question is of importancefor understanding the mechanisms involved in synaptic
plasticity, specifically how a postsynaptic Ca2+ signal istransduced into a long-lasting change in synaptic trans-mission. An understanding of the Ca2+ signals for longterm plasticity also is needed to explain how opposing
forms of plasticity, such as long-term potentiation (LTP)
and long-term depression (LTD), can both result from
Ca2+ signals in the same postsynaptic neuron (Neveu
and Zucker, 1996; Malenka and Bear, 2004; Coesmans
et al., 2004; Nevian and Sakmann, 2006). This was first
proposed to reflect a difference in postsynaptic Ca2+ requirements, with LTD induced by lower Ca2+ levels than
LTP (Lisman, 1989; Artola and Singer, 1993), consistent
with the Bienenstock-Cooper-Munro (BCM) rule of synaptic plasticity (Bienenstock et al., 1982). However, it is now
thought that LTP and LTD result from different temporal
patterns of [Ca2+]i elevation (Yang et al., 1999) and/or
different requirements for other signals generated bysynaptic activity (Nevian and Sakmann, 2006).
Here we have examined the Ca2+ requirements for cerebellar LTD. This form of long-term synaptic plasticity
arises when excitatory parallel fiber (PF) and climbing fiber(CF) inputs of Purkinje cells are activated concurrently(Linden, 1994; Ito, 2001). Many lines of evidence indicatethat LTD arises from a transient rise in [Ca2+]i in the postsynaptic Purkinje cell (Sakurai, 1990; Linden et al., 1991;
Crépel and Jaillard, 1991; Konnerth et al., 1992; Shibuki
and Okada, 1992; Kasono and Hirano, 1994; Lev-Ram
et al., 1997; Miyata et al., 2000; Wang et al., 2000a). However the precise magnitude and duration of the Ca2+ signals required for LTD induction are not yet clear andmay even follow a reversed BCM rule (Coesmans et al.,2004). To define these fundamental characteristics ofLTD, we have used local uncaging to precisely control
the amount and duration of Ca2+ elevation. With this approach, we found that the magnitude of LTD is determinedby the level of [Ca2+]i, with LTD being triggered by Ca2+ ina highly cooperative manner. Further, the level of [Ca2+]i
required to induce LTD is dynamically regulated according
to the duration of [Ca2+]i elevation, indicating leaky integrator behavior. These properties are important for explaining how LTD is selectively induced by specific

Neuron 54, 787–800, June 7, 2007 ª2007 Elsevier Inc. 787

NeuronCalcium Triggering of LTD

patterns of synaptic activity. A computational model
based on a positive-feedback signal transduction cycle(Kuroda et al., 2001) is capable of reproducing theseemergent properties of LTD, suggesting that such interactions between signal transduction molecules underlie thetriggering of LTD by postsynaptic Ca2+.
RESULTSDMNPE-4 Photolysis Locally Elevates [Ca2+]i
The goal of our experiments was to raise postsynaptic[Ca2+]i and observe the resulting changes in PF synaptictransmission. [Ca2+]i was elevated by using UV light tophotolyze the caged Ca2+ compound, DMNPE-4 (EllisDavies, 1998). Upon photolysis, this compound undergoes a large drop in Ca2+ affinity that yields a rise infree [Ca2+]i (Ellis-Davies and Barsotti, 2006). DMNPE-4(10 mM) was dialyzed into voltage-clamped Purkinje cells
for at least 30 min to allow time for dendritic diffusion. In
our initial paradigm, DMNPE-4 was uncaged with brief(5 ms duration) UV light pulses, and the resultant rises infree [Ca2+]i were monitored with the high-affinity indicatordye, Oregon Green 488 BAPTA-1 (Kd of 0.17 mM). The
DMNPE-4 was photolyzed with a spot of UV light 5–
10 mm in diameter (Wang and Augustine, 1995). When
this light spot was focused on a distal region of a Purkinje
cell, over fine dendrites, a localized rise in [Ca2+]i was produced (Figure 1A). Three lines of evidence indicate that
this increase in the fluorescence of the Ca2+ indicator
dye arose specifically from light-induced release of Ca2+
from photolyzed DMNPE-4. First, including the Ca2+ chelator, BAPTA, in the intracellular solution along with the
DMNPE-4 prevented the light-induced signal (data notshown), indicating that it was a genuine rise in [Ca2+]i. Second, UV illumination of Purkinje cells that were not dialyzed
with DMNPE-4 did not cause any changes in [Ca2+]i.
Third, UV illumination also had no effect on cell input resistance or holding current. This indicates that the rise in[Ca2+]i was genuine and not caused by phototoxicity.
The rise in [Ca2+]i produced by uncaging DMNPE-4 wastransient (Figure 1B). [Ca2+]i was maximal immediately after UV exposure (within the 33 ms image acquisition time)
and then rapidly returned to the resting level. The time
constant for decay of the rise in [Ca2+]i was 90 ± 17 ms(n = 3). This rapid decline in [Ca2+]i presumably was due
to removal of Ca2+ from the site of photolysis, such as
by the action of Ca2+ pumps on plasma membrane andendoplasmic reticulum, although sequestration by Ca2+binding proteins and Ca2+-free DMNPE-4 may also contribute (Fierro et al., 1998; Maeda et al., 1999; Schmidt
et al., 2003; Sepúlveda et al., 2004). We next quantified
the size of this region of elevated [Ca2+]i by measuring[Ca2+]i along the length of a dendrite (Figure 1C). The spatial range of [Ca2+]i elevation could be described by
a Gaussian function with a peak at the center of uncaging
spot and a half-width of 7.9 ± 2.0 mm (n = 4). This range
was similar to the size of the UV light spot, consistent
with a previous report that Ca2+ does not spread far

788 Neuron 54, 787–800, June 7, 2007 ª2007 Elsevier Inc.

Figure 1. Temporal and Spatial Dynamics of [Ca2+]i Changes
Produced by Uncaging DMNPE-4 in Purkinje Cells(A) Fluorescence image of a Purkinje cell dendrite. Pseudocolor overlay indicates changes in [Ca2+]i following DMNPE-4 uncaging.
(B) Time course of [Ca2+]i signal in (A). [Ca2+]i changes were integrated
over a length of 3 mm centered at the uncaging spot. V indicates time of
uncaging.
(C) Spatial profile of [Ca2+]i along the dendrite in (A) at t = 66 ms; 0
indicates center of the uncaging spot, and numbers correspond to
the direction of arrow in (A).

from the site of uncaging in Purkinje cell dendrites (Santamaria et al., 2006).
When the brief light pulses were repeatedly applied at 1
Hz, to emulate the trains of synaptic activity traditionallyused to induce LTD (Crépel and Jaillard, 1991; Konnerth
et al., 1992; Karachot et al., 1994; Chen and Thompson,
1995), transient increases in [Ca2+]i occurred in responseto each pulse (see Figure 2A and Figure S1A in the Supplemental Data available with this article online). In addition,
there was a slow increase in baseline [Ca2+]i that accumulated during the train. The increase in [Ca2+]i remained very
localized, spreading only 53% ± 18% (n = 3) more at the
fifth pulse than at the first pulse and spreading no further
during the remaining 25 pulses in the train, again presumably due to Ca2+ removal mechanisms.

NeuronCalcium Triggering of LTD

Figure 2. Induction of LTD by Trains of [Ca2+]i Increases(A) Time course of [Ca2+]i changes produced in a Purkinje cell by two
trains of UV light pulses. Light energies are indicated above the traces,
and timing of the light pulses is indicated below.
(B) PF-EPSCs recorded before and after each of the light trains shownin (A). Numbers indicate times (in [C]) when each trace was recorded.
(C) Time course of changes in PF-EPSC amplitude resulting from thelight trains shown in (A).
(D) LTD induced by uncaging DMNPE-4 (10 mM; filled circles) isblocked by including the Ca2+ chelator, BAPTA (20 mM), in the intracellular solution (open circles). PF-EPSC amplitudes are normalized to themean pretrain level for each condition, and error bars indicate SEM.
(E) Persistence of Ca2+-induced LTD for 90 min after Ca2+ uncaging.

Elevated [Ca2+]i Is Sufficient to Induce LTD
It has been postulated that the ultimate signal for LTD isa local rise in [Ca2+]i, produced by IP3-mediated releaseof Ca2+ from endoplasmic reticulum within spines of PF
synapses (Berridge, 1993; Finch and Augustine, 1998;
Miyata et al., 2000; Wang et al., 2000a). To determine
whether such a rise in [Ca2+]i is sufficient to induce LTD,
we elevated [Ca2+]i at the same sites where an extracellular electrode was placed to stimulate PF axons and evoke
excitatory postsynaptic currents (PF-EPSCs). A representative experiment is shown in Figures 2A–2C. In this experiment, a 1 Hz train of low-intensity light pulses for 30 s
(5 ms duration, 6.5 mJ per pulse, 195 mJ total) was used
to elevate [Ca2+]i (Figure 2A, left). During the time that
[Ca2+]i was elevated, PF stimulation was halted to prevent
generation of other signals produced by PF activity.
Resumption of PF stimulation indicated that this rise in[Ca2+]i did not change PF-EPSC amplitude (Figures 2Band 2C). Higher-intensity light pulses (12.5 mJ per pulse,
375 mJ total) elevated [Ca2+]i faster and to higher levels,
particularly during the baseline between pulses (Figure 2A,
right). Such elevation of [Ca2+]i produced an LTD-like depression of the amplitude of PF-EPSCs (Figures 2B and
2C). Similar results were obtained in eight independent experiments, with uncaging Ca2+ producing on average
a 52% ± 4% reduction in PF-EPSC amplitude that developed with a time constant of 6.5 ± 1.1 min.
To determine whether the depression of PF-EPSCs wasdue directly to Ca2+, we repeated the experiments whilechelating intracellular Ca2+ by including BAPTA (20 mM) in
the intracellular solution. In the presence of BAPTA, there
was no measurable decline in PF-EPSCs for more than
30 min after illuminating three different Purkinje cells with
UV light (Figure 2D, open symbols, 375 mJ total). However,when BAPTA was not added to the intracellular solution,
the same illumination paradigm caused PF-EPSCs to be depressed to 46% ± 1% (n = 5) of their initial amplitudes (Figure 2D, filled symbols). This result demonstrates that the depression of PF synaptic transmission is caused by Ca2+
rather than by UV illumination or by the other by-productsof the photolysis reaction, such as free DMNPE-4 cage.
Further experiments, described in the Supplemental
Data, establish that the Ca2+-induced depression of PF
synaptic transmission shares many properties with the
LTD that results from pairing PF synaptic activity with Purkinje cell depolarization. First, like the Ca2+ signals resulting from CF activity, uncaged Ca2+ can be paired with PF
activity to depress PF-EPSCs (Figure S1). Second, theCa2+-induced depression of PF-EPSCs requires clathrindependent internalization of postsynaptic AMPA receptors (Figure S2A), as does LTD (Wang and Linden, 2000).
Third, Ca2+-induced depression of PF transmission andsynaptically induced LTD can occlude each other (Figure S2B), indicating that these two long-lasting forms ofsynaptic modification share common signal transduction
pathways. Because of these similarities, we conclude
that Ca2+ is sufficient to cause LTD in the absence of PF
or CF activity. By varying the distance between the sitesof Ca2+ uncaging and PF stimulation, we also could conclude that Ca2+-dependent LTD was limited to sites where[Ca2+]i was elevated (Figure S3).
Neuron 54, 787–800, June 7, 2007 ª2007 Elsevier Inc. 789

NeuronCalcium Triggering of LTD

LTD apparently consists of early and late phases, withthe early phase resulting from posttranslational regulationof AMPA receptor trafficking (Wang and Linden, 2000;
Matsuda et al., 2000; Chung et al., 2003) and the latephase caused by changes in gene expression (Linden,
1996). Studies with protein synthesis inhibitors indicatethat the early phase develops over a few minutes, while
the late phase begins 60 min after inducing LTD in cultured Purkinje cells (Linden, 1996) as well as in cerebellar
slices (K.T. and G.J.A., unpublished data). The LTD induced by uncaged Ca2+ persisted for as long as therecording lasted, with no evidence of recovery even
80–100 min after elevating [Ca2+]i (Figure 2E). On average,
PF-EPSCs were depressed by 45% ± 5% (n = 3) at 80–
100 min after elevating [Ca2+]i. Thus, uncaging Ca2+ locallyin PF dendrites apparently is sufficient to produce both theearly and late phases of LTD.
Ca2+ Requirements for LTD Induction
Our results indicate that raising [Ca2+]i to a sufficient level,via photolysis of DMNPE-4, can induce LTD without requiring any additional signals that may be generated by
the activity of PF or CF synapses. This greatly simplifies
analysis of the signaling events involved in LTD. Photolysis
of DMNPE-4 also simplifies analysis of the amount of intracellular Ca2+ required to induce LTD by avoiding thecomplex spatial dynamics of [Ca2+]i changes associatedwith entry of Ca2+ into the Purkinje cell cytoplasm via
membrane ion channels (Ross and Werman, 1987; Konnerth et al., 1992; Eilers et al., 1996). However, photolysis
by trains of brief light pulses still produced temporally
complex changes in [Ca2+]i (e.g., Figure 2A and Figure S1A). Therefore, to quantify the relationship between[Ca2+]i and LTD, we simplified the kinetics of [Ca2+]i elevation by using a single, prolonged pulse of very dim UV lightand varied the amount of [Ca2+]i by changing the peak intensity of this pulse.
The prolonged light pulses elevated [Ca2+]i monotonically and were capable of eliciting LTD. The experimentshown in Figures 3A and 3B illustrates a case where theUV light pulses were 1 s in duration. In this example, raising [Ca2+]i to 0.5 mM (150 mJ) or to 1 mM (250 mJ) failed toinduce LTD, as indicated by a lack of change in PFEPSC amplitude. However, elevating [Ca2+]i to a higher
level, with a 400 mJ pulse that raised [Ca2+]i to 1.4 mM, elicited LTD. In contrast, elevating [Ca2+]i to 0.8 mM (200 mJ)
twice was insufficient to induce LTD (Figure S4). Thus,
there appears to be a sharp threshold level of [Ca2+]i
required to induce LTD.
By using 1 s duration light pulses to vary [Ca2+]i in 17 different experiments, it was possible to define the quantitative relationship between the peak value of [Ca2+]i and theamount of LTD (Figure 3C). In these experiments, [Ca2+]i
sometimes was raised to several mM, so we used a lowaffinity indicator, Oregon Green 488 BAPTA-6F (Kd =3.4 mM), to measure [Ca2+]i. The relationship between[Ca2+]i and LTD was sigmoidal, with no LTD produced
at [Ca2+]i levels of 1 mM or lower and full LTD elicited at
790 Neuron 54, 787–800, June 7, 2007 ª2007 Elsevier Inc.

Figure 3. Ca2+ Requirements for LTD(A) Time course of [Ca2+]i increases evoked in a Purkinje cell by three
UV pulses (horizontal bars; 1 s duration) of different intensities.
(B) Time course of changes in PF-EPSC amplitude resulting from the[Ca2+]i increases shown in (A).
(C) Relationship between peak [Ca2+]i changes and amount of LTD.
Curve indicates fit of the Hill equation.
(D) Intermediate rise in [Ca2+]i (left) caused an intermediate amount of
LTD (right).

[Ca2+]i of 2.5 mM or greater. Intermediate amounts of
LTD sometimes were observed at intermediate [Ca2+]i(Figure 3D). The relationship shown in Figure 3C could
be described by the Hill equation:n½Ca2+ i
LTD = LTDmax nn
KCa + ½Ca2+ iwhere the Hill coefficient (n) was 3.8 ± 1.3, indicatinga highly cooperative triggering of LTD by Ca2+. The calculated maximal depression of PF-EPSCs (LTDmax) was
37.2% ± 7.9% and the concentration of Ca2+ requiredfor half-maximal LTD (KCa) was 1.8 ± 0.3 mM.

NeuronCalcium Triggering of LTD

Figure 4. Examples of LTD Induced by Rises in [Ca2+]i of Different Durations
Rises in [Ca2+]i (left) and changes in PF-EPSCs (right) induced by 0.5 s(A), 15 s (B), or 30 s (C) long light pulses. LTD developed with time constants of 11 (A), 9 (B), and 8.4 min (C). Light energy is indicated above
each plot.

Dynamic Ca2+ Requirements for LTD
Induction of LTD depends upon the duration of synaptic
activity (Karachot et al., 1994). Because this relationshipmay arise from the properties of Ca2+ triggering of LTD,
we next determined how LTD depends upon the amountof time that [Ca2+]i is elevated. This was done by varying
the duration of the UV light pulses from 0.5 to 30 s, yielding
ramp-like rises in [Ca2+]i of variable duration (Figure 4, left).
Sufficient elevation of [Ca2+]i was capable of producing
LTD at each duration (Figure 4, right). The relationship between [Ca2+]i and the amount of LTD was sigmoidal foreach duration and could be described by the Hill equation(Figure 5A). Prolonged elevation of [Ca2+]i caused a leftward shift in this relationship. This shift arose because
the KCa value was lower with longer durations of light(Figure 5B). Thus, the duration of [Ca2+]i elevation influences the Ca2+ requirements for LTD induction. In contrast, the maximal amount of LTD was independent of
the duration of [Ca2+]i elevation (Figure 5C). The Hill coefficient was also comparable for all durations and was 5(Figure 5D). These results indicate that the Ca2+ sensitivityof LTD is a dynamic process that depends on how long
[Ca2+]i is elevated in the postsynaptic Purkinje cell.
The time-dependent increase in the apparent Ca2+ sensitivity of LTD shown in Figure 5 suggests that the LTD induction mechanism can integrate Ca2+ signals over time.
To evaluate the integrative properties of LTD induction, we
examined the relationship between LTD and the time integral of [Ca2+]i for different durations of elevated [Ca2+]i.

Figure 5. Ca2+ Dependence of LTD Depends on Duration of[Ca2+]i Rise(A) Relationship between peak [Ca2+]i and LTD for different durations of[Ca2+]i elevation. Smooth curves indicate fits of the Hill equation; notethat the data are plotted on linear coordinates. 1 s data are from same
experiments shown in Figure 3C. Error bars indicate SEM. Total number of experiments ranged from 5 to 17 for different durations; eachpoint represents 1 to 3 experiments.
(B–D) Influence of duration of [Ca2+]i elevation on KCa values (B), maximum amount of LTD (C), and Hill coefficient (D). Error bars indicate twostandard deviations of parameter estimates.

These relationships were sigmoidal, saturating at highlevels of integrated Ca2+ (Figure 6A). The curves obtainedwith 0.5 and 1 s duration pulses virtually superimposed, indicating precise integration of Ca2+ over this time frame.
However, at longer durations the relationships diverged
and shifted to the right (red and green points in Figure 6A).
As a result, the half-maximal amount of integrated [Ca2+]i
required for LTD (KCa-integ; Figure 6B) increased overtime, a time dependence that was opposite that observed
for the relationship between LTD and peak [Ca2+]i (Figure 5B). The maximal amount of LTD and the Hill coefficient remained virtually independent of the duration of[Ca2+]i elevation (Figures 6C and 6D). We therefore conclude that the amount of Ca2+ within the dendrites of Purkinje cells is integrated during LTD, but this integration

Neuron 54, 787–800, June 7, 2007 ª2007 Elsevier Inc. 791

NeuronCalcium Triggering of LTD

nal electrical signaling (Knight, 1972; Fohlmeister et al.,1977). For the case of Ca2+ triggering of LTD, such a leaky
integrator can be described mathematically as
t



dx
=  x + a Ca2+ i ðtÞ
dt(1)

where t is the time constant of the integration, x is theamount of a downstream signal that transduces Ca2+
into LTD, and a is a scaling factor representing the efficiency of the integrator in converting Ca2+ into x. As detailed in the Supplemental Data, when [Ca2+]i is elevatedin a ramp-like fashion, as in our experiments (Figures 3A
and 4), the solution of Equation 1 is
 
t
(2)
xðtÞ = ak t exp  + akðt  tÞtwhere k is the rate of increasing [Ca2+]i, i.e., peak [Ca2+]i
divided by the light pulse duration, t. We used this function
to fit the dependence of KCa on light pulse duration; a good
fit was obtained (smooth curve in Figure 5B) when t was
0.56 s and a was 18.7%/mM. With these values, Equation 2
also provided a reasonable description of the dependenceof KCa-integ on light pulse duration (line in Figure 6B). The
ability of Equation 2 to describe the time dependence of
KCa and KCa-integ indicates that Ca2+ induction of LTD
can be described as a leaky integrator process.
To further test the leaky integrator proposal, we used
Equation 2 to transform the relationship between peak[Ca2+]i and amount of LTD (Figure 5A). When peak[Ca2+]i at the end of the UV pulse was converted into thecorresponding value of x, the curves obtained at all lightpulse durations superimposed (Figure 6E). This loss of duration dependence indicates that the dynamic properties
observed experimentally arise from the leaky integrator
behavior, supporting the idea that LTD results from Ca2+
activating signaling processes that behave as a leaky integrator with a time constant of 0.6 s.

Figure 6. Integration of Ca2+ during LTD(A) Relationship between integrated amount of Ca2+ and LTD; datafrom same experiments shown in Figure 5. Error bars indicate SEM.
(B–D) Influence of duration of [Ca2+]i elevation on KCa-integ (B), maximum amount of LTD (C), and Hill coefficient (D). Error bars indicate
two standard deviations of parameter estimates.
(E) Data from Figure 5A transformed by calculating x from Equation 2.

mechanism is imperfect and becomes less efficient during
prolonged elevation of [Ca2+]i.
Our results indicate that LTD induction can be considered as a ‘‘leaky integrator’’ process, similar to the ‘‘leaky
integrate and fire’’ concept often used in models of neuro-

792 Neuron 54, 787–800, June 7, 2007 ª2007 Elsevier Inc.

Computational Simulation of Ca2+ Requirementsfor LTD
To consider the mechanisms underlying the leaky integrator properties of LTD, we employed the computationalmodel of LTD signaling, which was developed by Kuroda
et al. (2001) from the signal transduction schemes first described by Bhalla and Iyengar (1999). Although this model(Figure 7A) was not originally designed to simulate the results of experiments that directly manipulated [Ca2+]i, infact with only four minor modifications (see Supplemental
Data) this model reproduced the major features of ourexperimental data very well. For example, the model predicted the threshold behavior of LTD and also reproduced
the experimental observation that the relationship between LTD and peak [Ca2+]i shifts leftward as [Ca2+]i is elevated for longer times (Figure 7B).
However, the model predicted that LTD was essentiallyan all-or-none function of [Ca2+]i, abruptly going fromnearly no LTD to maximal LTD over a very narrow range

NeuronCalcium Triggering of LTD

of [Ca2+]i. Because such bistable behavior was not observed in our experimental measurements, we next refined the model by taking into account the experimental
conditions. In particular, we transformed the model predictions (as described in Supplemental Data) by considering the spatial gradients in [Ca2+]i that occurred duringlocal uncaging (see Figures 1A and 1C) and the noise associated with experimental measurements of [Ca2+]i and
PF-EPSCs. After including these two factors, the model
very accurately simulated experimental measurementsof the relationship between peak [Ca2+]i and LTD (Figure 7C). Fits of the Hill equation to the simulation results
indicated that KCa was sensitive to the duration of [Ca2+]ielevation (Figure 7D), while the maximum amount of LTD(Figure 7E) and the Hill coefficient (Figure 7F) were duration independent. In all of these regards, the simulations
closely paralleled the experimental measurements shownin Figure 5. Further, the values of KCa, maximum amount ofLTD, and Hill coefficient determined for the simulation results were very similar to those measured experimentally,
as can be seen in Figures 7D–7F by comparing simulation
values (colored symbols) to the experimental measurements (gray symbols). Thus, the model emulated the dynamic properties of LTD induction by Ca2+.
To further compare the model predictions to the experimental measurements, we also plotted the predicted relationship between integrated [Ca2+]i and the amount ofLTD. Consistent with the leaky integrator properties observed in the experiments, the model reproduced therightward shift caused by prolonging the duration of[Ca2+]i elevation (Figure 8A). The KCa-integ value also increased with longer durations (Figure 8B), while the maximal amount of LTD and Hill coefficient were duration independent (Figures 8C and 8D). The predicted values for
KCa-integ, maximum amount of LTD, and Hill coefficientalso were very similar to those measured experimentally(compare colored and gray symbols in Figures 8B–8D), although the KCa-integ values for longer durations wereslightly smaller than those observed in the experimental
measurements. As was the case for the experimental
data, the mathematical description of a leaky integrator(Equation 2) could be fit to the simulation data (lines in Figures 7D and 8B). The best-fitting value of t was 1.52 s, anda was 20.4%/mM, which are in the same range as thevalues obtained from the experimental measurements.
As was the case for the experimental measurements, theinfluence of duration was greatly reduced when Equation
2 was used to transform the data in Figure 7C by

Figure 7. A Computational Model of LTD(A) Diagram of the signaling components proposed to be activated by
Ca2+ during LTD. [Ca2+]i elevation results in AMPA receptor phosphorylation by activating PKC, both directly and indirectly via a positivefeedback loop. Molecules involved in the positive-feedback loop areshown in blue.

(B) Simulated relationships between peak [Ca2+]i and LTD for different
durations of [Ca2+]i elevation.
(C) Results of simulation, after taking into account nonuniform spatial
distribution of [Ca2+]i and noise in experimental measurements.
(D–F) KCa value (D), maximum amount of LTD (E), and Hill coefficient (F)determined from fits of the Hill equation to the relationships shownin (C). For comparison, experimental data shown in Figures 5B–5D
are also plotted as gray circles. Smooth curve in (D) is derived from
Equation 2.

Neuron 54, 787–800, June 7, 2007 ª2007 Elsevier Inc. 793

NeuronCalcium Triggering of LTD

Figure 8. Integration of Ca2+ in the Computational Model(A) Relationship between integrated [Ca2+]i and LTD predicted by thecomputational simulation.
(B–D) Values for KCa-integ (B), maximum amount of LTD (C), and Hill coefficient (D) derived from fits of the Hill equation to the simulation datain (A). For comparison, experimental data shown in Figures 6B–6D arealso plotted as gray circles.
(E) Transformation of data of Figure 7C by using Equation 2 to
calculate x.

converting peak [Ca2+]i into x (Figure 8E). We therefore
conclude that the simulation was capable of reproducing
many significant features of Ca2+ triggering of LTD, including threshold behavior, cooperativity, saturation, andleaky integration.

794 Neuron 54, 787–800, June 7, 2007 ª2007 Elsevier Inc.

We next used the predictive power of the model toaddress the origins of these properties of LTD. The mainfeature of the model is the positive-feedback loop that includes protein kinases and several other signal transduction molecules (Figure 7A). To determine whether this positive-feedback mechanism underlies the Ca2+-dependent
triggering of LTD, we disrupted the feedback loop computationally by preventing activation of protein kinase C(PKC) by arachidonic acid (AA), while leaving unchanged
the activity of all other enzymes. The model predictedthat the relationships between LTD and both peak[Ca2+]i (Figure 9A and Figure S8A) and integrated [Ca2+]i(Figure 9B) will change in the absence of the positive-feedback loop.
To quantify the effects of loop disruption, we focused on
the relationship between integrated [Ca2+]i and LTD (Figures 9C–9E). A similar analysis for the relationship between peak [Ca2+]i and LTD is provided in the Supplemental Data (Figures S8B–S8D). Loss of the positive-feedback
loop increased KCa values, specifically at intermediate durations of [Ca2+]i elevation, and increased KCa-integ values
at longer durations of [Ca2+]i elevation (Figure 9C). Disrupting the positive-feedback loop also was predicted toaffect the maximum of LTD, which was predicted to vary
according to the duration of [Ca2+]i elevation (Figure 9D).
This indicates a loss of the all-or-none character of LTD
and is also predicted by the model before taking into account the experimental conditions (Figure S8E). Further,loss of the loop greatly reduced the Hill coefficient forCa2+ triggering of LTD (Figure 9E). Fits of Equation 2 tothese data (assuming a fixed threshold for LTD eventhough LTD was no longer predicted to be all-or-none)yielded estimates of 0.32 s for t and 5.0%/mM for a,Thus, loss of the positive-feedback loop reduces thestrength of integration (smaller a) and increases leakiness(faster t). In summary, the model predicted that disrupting
the positive-feedback loop will affect Ca2+ induction ofLTD, in particular causing a loss of the all-or-none character of LTD, reducing the cooperative triggering of
LTD by Ca2+, and lowering the effectiveness of the leaky
integrator.
To test these predictions, we returned to experimental
measurements and asked whether disruption of the proposed positive-feedback loop affects the Ca2+ dependence of LTD induction. For this purpose, we treated slices with OBAA, a potent and selective inhibitor ofphospholipase A2 (PLA2; Köhler et al., 1992; Bastianetto
et al., 2000) that prevents LTD induction in response tosynaptic activity (Reynolds and Hartell, 2001). We considered two extreme durations of [Ca2+]i elevation: 1 and 30 s.
In the presence of OBAA (5 mM), 1 s long rises in [Ca2+]i
had very little ability to trigger LTD (Figures 9F and 9G
and Figure S8F). Even when peak [Ca2+]i was high (3–4 mM), the magnitude of LTD was only half of the maximum
value of LTD observed in the absence of OBAA. With 30 s
light pulses, high [Ca2+]i (2–3 mM) produced LTD that was
similar in magnitude to what was observed in control conditions (Figures 9F and 9G and Figure S8F). Analysis ofNeuronCalcium Triggering of LTD

Figure 9. Effects of Disrupting the
Postulated Positive-Feedback Loop
Results of the computational simulation (A–E)
are compared to experimental results (F–J).
(A) Relationship between peak [Ca2+]i and LTD
predicted by simulation in the absence of activation of PKC by AA. Simulation data were corrected for the effects of nonuniform distributionof [Ca2+]i and noise, as in Figure 7.
(B) Relationship between integrated [Ca2+]i andLTD predicted by simulation in the absence ofactivation of PKC by AA.
(C–E) Values of KCa-integ (C), maximum amountof LTD (D), and Hill coefficient (E) obtained from
Hill equation fits of the data shown in (B). For
comparison, control data obtained by computational simulation with positive-feedback loop
intact (Figures 8B–8D) are also plotted as graysquares.
(F) Relationship between peak [Ca2+]i and LTD
measured experimentally in the presence ofa PLA2 inhibitor. Points represent means ofbinned results from individual experiments;
black symbols indicate results for 1 s pulses(n = 11) and green indicates 30 s pulses (n = 9).
(G) Experimentally measured relationship between integrated [Ca2+]i and LTD, derived
from the experiments shown in (F). Error bars
indicate SEM.
(H–J) Values of KCa-ingteg (H), maximum amountof LTD (I), and Hill coefficient (J) derived from
Hill equation fits to the experimental data in(G). For comparison, gray circles replot control
experimental data (Figures 6B–6D). Error bars
indicate two standard deviations of parameter
estimates.

these relationships indicated that application of OBAA
somewhat increased the KCa-integ value at 30 s (Figure 9H)
and greatly reduced the Hill coefficient for both durations(Figure 9J). Further, OBAA significantly (p < 0.05) reduced
the maximum amount of LTD elicited by elevating [Ca2+]i
for 1 s but not for 30 s (Figure 9I). In all these regards,
the experimental data closely resembled the predictionsof the computational model. The close correspondence
between computational and experimental results suggests that the steep, cooperative triggering of LTD by
Ca2+—attributed to a leaky integrator—arises, at least inpart, from the positive-feedback mechanism incorporated
into the model.
DISCUSSION
We have used photolysis of caged Ca2+ (Ellis-Davies,
2003) to quantify the ability of postsynaptic Ca2+ to trigger
LTD at the PF-Purkinje cell synapse. Elevation of Ca2+ topeak levels of a few micromolar or less was sufficient to
induce LTD without requiring any of the additional signalsthat normally are associated with activity at PF or CF synapses. Ca2+ triggering of LTD was dynamic: the durationof Ca2+ elevation influenced the Ca2+ sensitivity of LTD,
with higher sensitivity to peak [Ca2+]i and lower sensitivity

to integrated [Ca2+]i at longer duration. This dynamic behavior could be described quantitatively as a leaky integrator process with a time constant of 0.6 s. These properties of Ca2+ triggering of LTD could be reproduced by
a computational model based on a positive-feedback relationship between several protein kinases. Disrupting
this loop was predicted to affect Ca2+ triggering of LTD,and experimental perturbation of this feedback loop produced the predicted effects on Ca2+ induction of LTD.
This work illustrates new properties of Ca2+ triggering ofa form of long-term synaptic plasticity and implicates the
positive-feedback loop in Ca2+ action during LTD.
Calcium Requirements for LTD
Cerebellar LTD has long been known to depend on elevation of Ca2+ concentration within the postsynaptic Purkinjecell. The earliest evidence for this came from experiments
showing that postsynaptic introduction of the Ca2+ chelators EGTA (Sakurai, 1990; Shibuki and Okada, 1992) and
BAPTA (Konnerth et al., 1992) blocks LTD and that stimuli
which induce LTD also elevate [Ca2+]i in Purkinje cells(Konnerth et al., 1992). Moreover, several treatmentsthat elevate postsynaptic [Ca2+]i—such as depolarization(Linden et al., 1991; Crépel and Jaillard, 1991; Konnerth
et al., 1992), strong PF activity (Hartell, 1996; Eilers

Neuron 54, 787–800, June 7, 2007 ª2007 Elsevier Inc. 795

NeuronCalcium Triggering of LTD

et al., 1997), and photolysis of caged Ca2+ compounds(Kasono and Hirano, 1994; Lev-Ram et al., 1997)—canbe paired with PF activity or glutamate application to induce LTD. Our results have extended these observations
by showing that elevated postsynaptic Ca2+ alone cansuffice to induce LTD as long as [Ca2+]i exceeds a threshold level. Photolysis of caged Ca2+ compounds did not induce LTD in previous studies (Kasono and Hirano, 1994;
Lev-Ram et al., 1997); although [Ca2+]i was not determined in these studies, we presume that [Ca2+]i was below
the threshold for inducing LTD in these experiments. The
presence of a threshold can also explain why CF activity
alone is insufficient to induce LTD (Ito and Kano, 1982;
Chen and Thompson, 1995): activation of CF synapses elevates [Ca2+]i by a few hundred nM for 0.5 s (Konnerth
et al., 1992; Eilers et al., 1995; Wang et al., 2000a), which
is below the threshold for inducing LTD during such brief
rises in [Ca2+]i (Figure 5A).
During trains of brief pulses of light, we often observeda sustained rise in basal [Ca2+]i (Figure 2A and Figure S1A).
These sustained rises in [Ca2+]i appeared to be more effective in triggering LTD than were the larger transient
rises in [Ca2+]i. For example, while the peak levels of[Ca2+]i are very similar for the two trains of [Ca2+]i responses shown in Figure 2A, only the right response,
which also had a sustained rise in [Ca2+]i, was capableof inducing LTD (Figures 2B and 2C). Such behavior
emerges from the leaky integrator property of LTD, whichmakes LTD more sensitive to prolonged elevation of[Ca2+]i (Figure 5A). The leaky integrator property of LTD
may also account for the observation that LTD induction
requires prolonged trains of paired PF and CF activity(Karachot et al., 1994). Pairing of single PF and CF stimuli
induces only transient [Ca2+]i increases, lasting for 0.2 s(Wang et al., 2000a; Doi et al., 2005; Hernjak et al., 2005).
Because such responses cannot induce LTD, it is likelythat only repeated pairing of PF and CF activity causesa sustained increase in [Ca2+]i that can be integrated tocause LTD. Paradoxically, it has been reported that prolonging the duration of paired synaptic activity, from 300
to 500 s, causes a reduction in LTD expression (Karachot
et al., 1994). Such behavior could be explained by theleakiness of the integrator, which causes the effectivenessof Ca2+ to decline over time.
It has been proposed that cerebellar LTD results froma local, suprathreshold Ca2+ signal produced when IP3 receptors are synergistically activated by subthreshold IP3
signals, produced by active PFs, and subthreshold Ca2+
signals produced by CF activity (Berridge, 1993; Finchand Augustine, 1998; Miyata et al., 2000; Wang et al.,2000a; Doi et al., 2005; Hernjak et al., 2005). Two of our results provide additional support for this model. First, wefound that LTD was induced by pairing a subthreshold
amount of [Ca2+]i with PF stimulation (Figure S1). Second,
we found that a rise in [Ca2+]i alone is sufficient to cause
LTD as long as [Ca2+]i exceeds a threshold. Thus, our results are consistent with the idea that IP3 receptors serve
as a coincidence detector for LTD.

796 Neuron 54, 787–800, June 7, 2007 ª2007 Elsevier Inc.

Our definition of the [Ca2+]i requirements for cerebellar
LTD is one of the only efforts to quantify the relationshipbetween postsynaptic [Ca2+]i and induction of long-lasting synaptic plasticity. Coesmans et al. (2004) have proposed that cerebellar LTD is induced by relatively high(but unspecified) levels of [Ca2+]i and that LTP is induced
by lower [Ca2+]i levels. While we could confirm that micromolar amounts of postsynaptic Ca2+ could induce
LTD, in fact we did not observe LTP in response to elevation of [Ca2+]i to lower levels (e.g., Figures 3C and 5A).
This discrepancy could arise because LTP requires not
only an increase in [Ca2+]i but also another signal that is
produced by synaptic activity, such as NO (Lev-Ram
et al., 2002; Namiki et al., 2005). Our observation thatelevating [Ca2+]i in Purkinje cells to 0.9 mM for 30 s
yielded LTD (Figure 5A) is in line with a report thatelevating [Ca2+]i in hippocampal CA1 pyramidal cells
to 0.8 mM for 60 s caused LTD (Yang et al., 1999).
Thus, in terms of the BCM rule, cerebellar LTD can betriggered by the same ‘‘low’’ Ca2+ signal that produces
hippocampal LTD. This similarity is remarkable, giventhat these two forms of LTD are known to differ substantially in their signal transduction mechanisms (Malenka
and Bear, 2004). These differences in mechanism could
explain why hippocampal LTD apparently does notexhibit a well-defined [Ca2+]i threshold (Neveu andZucker, 1996). Differences in signal transduction mechanisms presumably also account for our observation that
cerebellar LTD could also be induced by relatively large
and brief rises in [Ca2+]i (e.g., 5 mM for 0.5 s), eventhough brief elevation of [Ca2+]i in hippocampal neurons,
to levels on the order of 10 mM, induces LTP rather thanLTD (Yang et al., 1999).
Because we uncaged Ca2+ in highly localized (5–10 mmdiameter) regions of distal dendrites of Purkinje cells, ourresults provide information about the spatial range of signaling during LTD. First, we found that the late phase of
LTD can be elicited by local elevation of [Ca2+]i in dendrites (Figure 2E). Given that the late phase of LTD apparently requires changes in nuclear gene expression (Linden, 1996), this suggests that localized rises in dendritic[Ca2+]i are capable of producing other, mobile signal(s)that can reach the nucleus to regulate gene expression.
The nature of such dendrite-to-nucleus signaling is not
yet clear (Deisseroth et al., 1998). Second, while the early
component of LTD is known to spread 50 mm from active
PF synapses to inactive ones (Wang et al., 2000b; Reynolds and Hartell, 2000), we found that Ca2+-induced
LTD does not spread beyond the site of Ca2+ uncaging(Figure S3). CF activity and/or depolarization elevate[Ca2+]i throughout the Purkinje cell (Ross and Werman,
1987; Konnerth et al., 1992; Miyakawa et al., 1992). This
subthreshold rise in Ca2+ can be viewed as being permissive for the spread of early LTD, although some other signal produced by PF activity—such as NO (Reynolds andHartell, 2001; Ogasawara et al., 2007) or glutamate (Marcaggi et al., 2003)—must mediate and spatially limit the
spread of LTD (Hartell, 2002).

NeuronCalcium Triggering of LTD

The relationships between postsynaptic [Ca2+]i and LTD
induction (Figures 5A and 6A) were sigmoidal with Hill coefficients of 5, indicating that LTD is cooperatively triggered by Ca2+. Our computational model was capable ofproducing very similar values of Hill coefficient, suggesting that the signaling reactions included in the model areresponsible for the cooperative behavior. The model predicted that the Hill coefficient should be reduced by loss ofthe positive-feedback loop (Figure 9E), and this was observed experimentally when we disrupted the loop (Figure 9J). These results indicate that the loop is involved in
the cooperative triggering of LTD and are consistent withprevious proposals that such positive-feedback mechanisms are a source of biochemical cooperativity (Ferrell
and Machleder, 1998). In the absence of the positive-feedback loop, the Hill coefficient was still 2. This residual
cooperativity may arise from direct activation of PKC;
this enzyme is known to be cooperatively activated by 2
Ca2+ (Sutton and Sprang, 1998; Verdaguer et al., 1999).
Thus, it appears that the highly cooperative triggering of
LTD by Ca2+ arises from the concerted actions of Ca2+
on the positive-feedback loop and on PKC directly.
All-or-None Behavior of LTD
The sigmoidal Ca2+ dependence of LTD confers threshold
behavior, in the sense that small rises in [Ca2+]i are insufficient to trigger LTD. Our computational model predicted
such behavior and, in fact, predicted even more extreme,bistable behavior at the level of individual synapses(Figure 7B). Thus, the model predicts that LTD has allor-none properties, as has been proposed for hippocampal LTP (Petersen et al., 1998). Our analysis indicated thatspatial nonuniformities in [Ca2+]i and noise largely blurs
this behavior, so that LTD appeared to be a graded function of [Ca2+]i in our experimental measurements. Experimental analysis of LTD at the level of individual synapses(Casado et al., 2002) will be required to evaluate allor-none behavior critically. However, all-or-none behavior
was evident in our experimental observation that the maximum amount of LTD produced by saturating [Ca2+]i wasconstant for all durations of [Ca2+]i elevation (Figures 5C
and 6C), even though the amount of [Ca2+]i required for
LTD varied. The model predicts that the all-or-none behavior of LTD results from the positive-feedback loop, sothat disrupting this loop will cause the maximum amountof LTD to depend upon how long [Ca2+]i is elevated(Figure 9D). This prediction was confirmed by our experimental measurements in the presence of a PLA2 inhibitor(Figure 9I), providing further support for the idea that LTD
is an all-or-none process and that this is due to the positive-feedback loop.
Dynamic Ca2+ Triggering of LTD
by a Leaky Integrator
We have discovered that the amount of [Ca2+]i required toinitiate LTD is a time-dependent variable. To our knowledge, such behavior has not been described previously
for cerebellar LTD, even though a dynamic threshold isa central tenet of the BCM theory of cortical plasticity(Bienenstock et al., 1982) and has been proposed as a requirement for encoding the history of synaptic activity(Bear, 1995). Mathematically, the dynamics of Ca2+ triggering of LTD could be described as a leaky integrator
with a time constant of 0.6 s. We view LTD in the same
way that neuronal electrical signaling is described asa ‘‘leaky integrate and fire’’ mechanism, with the ‘‘firing’’
being an all-or-none activation of the signal transduction
network that yields LTD.
Although our computational model of LTD signaling
consists of a single chemical compartment, the model
was able to reproduce the leaky integrator behavior accurately (Figures 7D and 8B). Further, integration was greatly
reduced in the absence of the positive-feedback loop (Figures S8B and S8G), demonstrating that this loop is part ofthe integration mechanism. Integration was still present at
a low level in the absence of this loop, indicating that integration does not depend entirely upon the loop. A simple
hypothesis is that integration arises both from the kinetics
of direct activation of PKC by Ca2+ (Oancea and Meyer,1998), as well as from the ability of the positive-feedback
loop to prolong activation of PKC (Kuroda et al., 2001). The‘‘leakiness’’ indicates the presence of reactions that oppose Ca2+ triggering of LTD. Loss of the positive-feedback
loop amplified the leakiness (Figures 9C and 9H), indicating that this loop counteracts the leakiness. Leakinesscould arise from a phosphatase reversing the effect of
PKC (Shenolikar, 1986). One specific candidate for theleak is protein phosphatase 2A, which is constitutively active in Purkinje cells and limits LTD induction (Launey et al.,2004).
The key feature of our computational model, as first proposed by Kuroda et al. (2001), is the positive-feedback
signal transduction loop (Bhalla and Iyengar, 1999). Thismodel is consistent with previous demonstrations that
LTD requires several enzymes proposed to participate
in the loop, such as PKC, MAP kinase, and PLA2 (Ito,2001). The concordance between our experiments andthe emergent predictions of this model provides an experimental indication that the positive-feedback loop is important for LTD; several more experimental tests in progress provide stronger support for this model (K.T. and
G.J.A., 2006, Soc. Neurosci., abstract). Although loss ofthe positive-feedback loop altered the relationship between [Ca2+]i and LTD induction, LTD could still be induced without this loop. This residual LTD, which wasgraded in amplitude and less sensitive to Ca2+, probably
arises because Ca2+ can still activate PKC directly in theabsence of the feedback loop.
Conclusions
We have found that a rise in postsynaptic Ca2+ concentration is sufficient to induce cerebellar LTD. Because of thecooperative triggering of LTD by Ca2+, LTD is induced only
when [Ca2+]i exceeds a certain level. The amount of Ca2+
required for LTD is relatively low, in the micromolar range,
but depends upon the amount of time that Ca2+

Neuron 54, 787–800, June 7, 2007 ª2007 Elsevier Inc. 797

NeuronCalcium Triggering of LTD

concentration is elevated. This time dependence arises
from the leaky integrator properties of the LTD induction
process. These characteristics of Ca2+ activation can explain many of the features of LTD induction following synaptic activity and are predicted by a computational modelthat postulates a central role for a positive-feedback loopof signal transduction enzymes.

EXPERIMENTAL PROCEDURES
Patch-Clamp Recordings
Whole-cell patch-clamp recordings were made from Purkinje cells as
described previously (Miyata et al., 2000; Wang et al., 2000b). Sagittal
slices (200–250 mm thick) were prepared from cerebella of 14- to
21-day-old rats or mice. Consistent with a previous study (Miyata
et al., 2000), the time course and spatial distribution of [Ca2+]i elevation
after uncaging Ca2+ and the properties of Ca2+-induced LTD weresimilar in slices from rats and mice. Slices were bathed in extracellularsolution containing (in mM) 119 NaCl, 2.5 KCl, 1.3 Mg2SO4, 2.5 CaCl2,
1.0 NaH2PO4, 26.2 NaHCO3, 10 glucose, and 0.01 bicuculline methiodide (all from Sigma). A PLA2 inhibitor, OBAA (5 mM; Tocris), wasadded into the extracellular solution as indicated. Patch electrodes(2–4 MU) were filled with a pipette solutions containing (in mM) 130
potassium gluconate, 2 NaCl, 4 MgCl2, 4 Na2-ATP, 0.4 Na-GTP, 20
HEPES (pH 7.3), 0.25 Ca2+ indicator (Oregon Green 488 BAPTA-1 or
6F; Molecular Probes), 10 caged Ca2+ compound (DMNPE-4; synthesized by G. Ellis-Davies), and 6 CaCl2 (pH adjusted to 7.2 with KOH). In
some experiments, BAPTA (20 mM; Molecular Probes) or AP2 and AP2
DDLL peptides (1.6 mM; Morgan et al., 2000) were included in the intracellular solution. EPSCs were evoked in Purkinje cells (clamped
at –60 mV) by activating parallel fibers with a glass stimulating electrode (5–10 mm tip diameter) filled with extracellular solution andplaced on the surface of the molecular layer. Details of our proceduresfor stimulating parallel fibers can be found in Wang et al. (2000b). PFEPSCs were acquired and analyzed using LTP software (W.W. Anderson, University of Bristol, UK) (Anderson and Collingridge, 2001). Data
were accepted if series resistance changed less than 20%, input resistance was between 100 to 150 MU, holding current changed less than
5%, and [Ca2+]i returned to baseline following photolysis of caged
Ca2+. Statistical comparisons between experimental groups were performed with the Student’s t test (Figure S2A) or a Z test (Figure 9I). LTD
was calculated as the change in PF-EPSC amplitude averaged over
10 min period 40 min after [Ca2+]i elevation, or in the last 10 min incases where the recording did not last for 40 min.

Optical Techniques
Procedures described previously (Miyata et al., 2000) were used to examine the response of Purkinje cells to uncaged Ca2+. In brief, cells
were dialyzed with a solution containing a fluorescent indicator and
DMNPE-4, and the set-up described in Wang and Augustine (1995)
was used to uncage Ca2+. UV light (351–364 nm) from an argon ion laser (Coherent model 305) was delivered to the slice, via an optical fiberand an Olympus 403 water-immersion objective, to make a light spotwith a half-width of 5–10 mm that was focused on the primary or secondary dendrites of a Purkinje cell. The duration of UV exposure wascontrolled by an electronic shutter. When UV light pulses of 1 s or
longer in duration were delivered, neutral density filters were used toreduce light intensity by 90%. UV energy was measured at the opticalplane, so that reported values reflect the amount of light delivered tothe slice.
Oregon Green fluorescence was imaged using a high-speed confocal microscope (Noran Odyssey XL), and [Ca2+]i values were calculated from the ratio of increased fluorescence to basal fluorescence(R = DF/F0) using the following equation (Swandulla et al., 1991):

798 Neuron 54, 787–800, June 7, 2007 ª2007 Elsevier Inc.


Ca2+ i = ðFd 3 Kd 3 ðR + 1Þ  Kd 3 Fmin Þ=ðFmax  Fd 3 ðR + 1ÞÞ


 


Kd + Ca2+ rest
Fd = Fmax 3 Ca2+ rest + Kd 3 Fmin

where Kd is the Ca2+ dissociation constant of the indicator and Fmin andFmax were the minimum and maximum amounts of fluorescence emission in the absence and presence of Ca2+, respectively. Resting [Ca2+]i([Ca2+]rest) was calculated as 72 nM (Augustine et al., 1991). In experiments with long light pulses (0.5–30 s), some bleaching occurred (e.g.,
Figure 3A) and was corrected for by separately measuring the rate of
bleaching of Oregon Green 488 BAPTA-6F in acrylamide gel. Because[Ca2+]i increased in a ramp-like manner during the time that Ca2+ waselevated (Figures 3A and 4), the integrated amount of Ca2+ was calculated by multiplying peak [Ca2+]i by pulse duration and then dividing by
2. Statistical analysis was performed using Origin 7.0 (Microcal). Averaged data are presented as mean ± SEM.
Computational Simulation
To simulate the relationship between Ca2+ and LTD, we used the mathematical model of signal transduction pathways for cerebellar LTD
described by Kuroda et al. (2001). A detailed description of our implementation of this model is described in the Supplemental Data
(Figure S6).
Supplemental Data
The Supplemental Data for this article can be found online at http://
www.neuron.org/cgi/content/full/54/5/787/DC1/.
ACKNOWLEDGMENTS
We thank Ken Berglund and Ryohei Yasuda for reading our manuscript. This work was supported by HFSP grant RGP0074/2003; NIH
grants NS-34045, GM-65473, and GM-53395; a Uehara Memorial
Foundation research grant; and a postdoctoral fellowship from theJapan Society for the Promotion of Science.
Received: December 15, 2006
Revised: March 30, 2007
Accepted: May 16, 2007
Published: June 6, 2007
REFERENCES
Anderson, W.W., and Collingridge, G.L. (2001). The LTP program:a data acquisition program for on-line analysis of long-term potentiation and other synaptic events. J. Neurosci. Methods 108, 71–83.
Artola, A., and Singer, W. (1993). Long-term depression of excitatory
synaptic transmission and its relationship to long-term potentiation.
Trends Neurosci. 16, 480–487.
Augustine, G.J., Adler, E.M., and Charlton, M.P. (1991). The calcium
signal for transmitter secretion from presynaptic nerve terminals.
Ann. N Y Acad. Sci. 635, 365–381.
Augustine, G.J., Santamaria, F., and Tanaka, K. (2003). Local calcium
signaling in neurons. Neuron 40, 331–346.
Bastianetto, S., Zheng, W.H., and Quirion, R. (2000). The Ginkgo biloba
extract (EGb 761) protects and rescues hippocampal cells against
nitric oxide-induced toxicity: involvement of its flavonoid constituentsand protein kinase C. J. Neurochem. 74, 2268–2277.
Bear, M.F. (1995). Mechanism for a sliding synaptic modificationthreshold. Neuron 15, 1–4.
Berridge, M.J. (1993). Cell signalling. A tale of two messengers. Nature
365, 388–389.
Bhalla, U.S., and Iyengar, R. (1999). Emergent properties of networksof biological signaling pathways. Science 283, 381–387.

NeuronCalcium Triggering of LTD

Bienenstock, E.L., Cooper, L.N., and Munro, P.W. (1982). Theory forthe development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. J. Neurosci. 2, 32–48.

Ito, M. (2001). Cerebellar long-term depression: characterization, signal transduction, and functional roles. Physiol. Rev. 81, 1143–1195.

Casado, M., Isope, P., and Ascher, P. (2002). Involvement of presynaptic N-methyl-D-aspartate receptors in cerebellar long-term depression. Neuron 33, 123–130.

Ito, M., and Kano, M. (1982). Long-lasting depression of parallel fiberPurkinje cell transmission induced by conjunctive stimulation of parallel fibers and climbing fibers in the cerebellar cortex. Neurosci. Lett. 33,
253–258.

Chen, C., and Thompson, R.F. (1995). Temporal specificity of longterm depression in parallel fiber–Purkinje synapses in rat cerebellar
slice. Learn. Mem. 2, 185–198.

Karachot, L., Kado, R.T., and Ito, M. (1994). Stimulus parameters for
induction of long-term depression in in vitro rat Purkinje cells. Neurosci. Res. 21, 161–168.

Chung, H.J., Steinberg, J.P., Huganir, R.L., and Linden, D.J. (2003).
Requirement of AMPA receptor GluR2 phosphorylation for cerebellar
long-term depression. Science 300, 1751–1755.

Kasono, K., and Hirano, T. (1994). Critical role of postsynaptic calcium
in cerebellar long-term depression. Neuroreport 6, 17–20.

Coesmans, M., Weber, J.T., De Zeeuw, C.I., and Hansel, C. (2004).
Bidirectional parallel fiber plasticity in the cerebellum under climbing
fiber control. Neuron 44, 691–700.
Crépel, F., and Jaillard, D. (1991). Pairing of pre- and postsynaptic activities in cerebellar Purkinje cells induces long-term changes in synaptic efficacy in vitro. J. Physiol. 432, 123–141.
Deisseroth, K., Heist, E.K., and Tsien, R.W. (1998). Translocation of
calmodulin to the nucleus supports CREB phosphorylation in hippocampal neurons. Nature 392, 198–202.
Doi, T., Kuroda, S., Michikawa, T., and Kawato, M. (2005). Inositol
1,4,5-trisphosphate-dependent Ca2+ threshold dynamics detect spiketiming in cerebellar Purkinje cells. J. Neurosci. 25, 950–961.
Eilers, J., Callewaert, G., Armstrong, C., and Konnerth, A. (1995). Calcium signaling in a narrow somatic submembrane shell during synaptic
activity in cerebellar Purkinje neurons. Proc. Natl. Acad. Sci. USA 92,
10272–10276.
Eilers, J., Plant, T., and Konnerth, A. (1996). Localized calcium signalling and neuronal integration in cerebellar Purkinje neurones. Cell Calcium 20, 215–226.

Knight, B.W. (1972). Dynamics of encoding in a population of neurons.
J. Gen. Physiol. 59, 734–766.
Köhler, T., Heinisch, M., Kirchner, M., Peinhardt, G., Hirschelmann, R.,
and Nuhn, P. (1992). Phospholipase A2 inhibition by alkylbenzoylacrylic acids. Biochem. Pharmacol. 44, 805–813.
Konnerth, A., Dreessen, J., and Augustine, G.J. (1992). Brief dendritic
calcium signals initiate long-lasting synaptic depression in cerebellar
Purkinje cells. Proc. Natl. Acad. Sci. USA 89, 7051–7055.
Kuroda, S., Schweighofer, N., and Kawato, M. (2001). Exploration of
signal transduction pathways in cerebellar long-term depression bykinetic simulation. J. Neurosci. 21, 5693–5702.
Launey, T., Endo, S., Sakai, R., Harano, J., and Ito, M. (2004). Protein
phosphatase 2A inhibition induces cerebellar long-term depression
and declustering of synaptic AMPA receptor. Proc. Natl. Acad. Sci.
USA 101, 676–681.
Lev-Ram, V., Jiang, T., Wood, J., Lawrence, D.S., and Tsien, R.Y.
(1997). Synergies and coincidence requirements between NO,
cGMP, and Ca2+ in the induction of cerebellar long-term depression.
Neuron 18, 1025–1038.

Eilers, J., Takechi, H., Finch, E.A., Augustine, G.J., and Konnerth, A.
(1997). Local dendritic Ca2+ signaling induces cerebellar long-term depression. Learn. Mem. 4, 159–168.

Lev-Ram, V., Wong, S.T., Storm, D.R., and Tsien, R.Y. (2002). A newform of cerebellar long-term potentiation is postsynaptic and depends
on nitric oxide but not cAMP. Proc. Natl. Acad. Sci. USA 99, 8389–
8393.

Ellis-Davies, G.C.R. (1998). Synthesis of photosensitive EGTA derivatives. Tetrahedron Lett. 39, 953–956.

Linden, D.J. (1994). Long-term synaptic depression in the mammalianbrain. Neuron 12, 457–472.

Ellis-Davies, G.C.R. (2003). Development and application of caged calcium. Methods Enzymol. 360, 226–238.

Linden, D.J. (1996). A protein synthesis-dependent late phase of cerebellar long-term depression. Neuron 17, 483–490.

Ellis-Davies, G.C.R., and Barsotti, R.J. (2006). Tuning caged calcium:
photolabile analogues of EGTA with improved optical and chelation
properties. Cell Calcium 39, 75–83.

Linden, D.J., Dickinson, M.H., Smeyne, M., and Connor, J.A. (1991). A
long-term depression of AMPA currents in cultured cerebellar Purkinje
neurons. Neuron 7, 81–89.

Ferrell, J.E., Jr., and Machleder, E.M. (1998). The biochemical basis ofan all-or-none cell fate switch in Xenopus oocytes. Science 280, 895–
898.

Lisman, J. (1989). A mechanism for the Hebb and the anti-Hebb processes underlying learning and memory. Proc. Natl. Acad. Sci. USA
86, 9574–9578.

Fierro, L., DiPolo, R., and Llano, I. (1998). Intracellular calcium clearance in Purkinje cell somata from rat cerebellar slices. J. Physiol.
510, 499–512.

Maeda, H., Ellis-Davies, G.C., Ito, K., Miyashita, Y., and Kasai, H.
(1999). Supralinear Ca2+ signaling by cooperative and mobile Ca2+
buffering in Purkinje neurons. Neuron 24, 989–1002.

Finch, E.A., and Augustine, G.J. (1998). Local calcium signalling by inositol-1,4,5-trisphosphate in Purkinje cell dendrites. Nature 396, 753–
756.

Malenka, R.C., and Bear, M.F. (2004). LTP and LTD: an embarrassment of riches. Neuron 44, 5–21.

Fohlmeister, J.F., Poppele, R.E., and Purple, R.L. (1977). Repetitive firing: a quantitative study of feedback in model encoders. J. Gen. Physiol. 69, 815–848.
Hartell, N.A. (1996). Strong activation of parallel fibers produces localized calcium transients and a form of LTD that spreads to distant synapses. Neuron 16, 601–610.
Hartell, N.A. (2002). Parallel fiber plasticity. Cerebellum 1, 3–18.
Hernjak, N., Slepchenko, B.M., Fernald, K., Fink, C.C., Fortin, D.,
Moraru, I.I., Watras, J., and Loew, L.M. (2005). Modeling and analysis
of calcium signaling events leading to long-term depression in cerebellar Purkinje cells. Biophys. J. 89, 3790–3806.

Marcaggi, P., Billups, D., and Attwell, D. (2003). The role of glial glutamate transporters in maintaining the independent operation of juvenile
mouse cerebellar parallel fibre synapses. J. Physiol. 552, 89–107.
Matsuda, S., Launey, T., Mikawa, S., and Hirai, H. (2000). Disruption of
AMPA receptor GluR2 clusters following long-term depression induction in cerebellar Purkinje neurons. EMBO J. 19, 2765–2774.
Miyakawa, H., Lev-Ram, V., Lasser-Ross, N., and Ross, W.N. (1992).
Calcium transients evoked by climbing fiber and parallel fiber synaptic
inputs in guinea pig cerebellar Purkinje neurons. J. Neurophysiol. 68,
1178–1189.
Miyata, M., Finch, E.A., Khiroug, L., Hashimoto, K., Hayasaka, S., Oda,
S.I., Inouye, M., Takagishi, Y., Augustine, G.J., and Kano, M. (2000).

Neuron 54, 787–800, June 7, 2007 ª2007 Elsevier Inc. 799

NeuronCalcium Triggering of LTD

Local calcium release in dendritic spines required for long-term synaptic depression. Neuron 28, 233–244.
Morgan, J.R., Prasad, K., Hao, W., Augustine, G.J., and Lafer, E.M.
(2000). A conserved clathrin assembly motif essential for synaptic vesicle endocytosis. J. Neurosci. 20, 8667–8676.
Namiki, S., Kakizawa, S., Hirose, K., and Iino, M. (2005). NO signalling
decodes frequency of neuronal activity and generates synapsespecific plasticity in mouse cerebellum. J. Physiol. 566, 849–863.

Schmidt, H., Stiefel, K.M., Racay, P., Schwaller, B., and Eilers, J.
(2003). Mutational analysis of dendritic Ca2+ kinetics in rodent Purkinjecells: role of parvalbumin and calbindin D28k. J. Physiol. 551, 13–32.
Sepúlveda, M.R., Hidalgo-Sánchez, M., and Mata, A.M. (2004). Localization of endoplasmic reticulum and plasma membrane Ca2+ATPases in subcellular fractions and sections of pig cerebellum. Eur.
J. Neurosci. 19, 542–551.

Neveu, D., and Zucker, R.S. (1996). Postsynaptic levels of [Ca2+]i
needed to trigger LTD and LTP. Neuron 16, 619–629.

Shenolikar, S. (1986). Control of cell function by reversible protein
phosphorylation. J. Cyclic Nucleotide Protein Phosphor. Res. 11,
531–541.

Nevian, T., and Sakmann, B. (2006). Spine Ca2+ signaling in spiketiming-dependent plasticity. J. Neurosci. 26, 11001–11013.

Shibuki, K., and Okada, D. (1992). Cerebellar long-term potentiation
under suppressed postsynaptic Ca2+ activity. Neuroreport 3, 231–234.

Oancea, E., and Meyer, T. (1998). Protein kinase C as a molecular machine for decoding calcium and diacylglycerol signals. Cell 95, 307–
318.

Sutton, R.B., and Sprang, S.R. (1998). Structure of the protein kinase
Cbeta phospholipid-binding C2 domain complexed with Ca2+. Structure 6, 1395–1405.

Ogasawara, H., Doi, T., Doya, K., and Kawato, M. (2007). Nitric oxide
regulates input specificity of long-term depression and context dependence of cerebellar learning. PLoS Comput. Biol. 3, e179. 10.1371/
journal.pcbi.0020179.

Swandulla, D., Hans, M., Zipser, K., and Augustine, G.J. (1991). Role ofresidual calcium in synaptic depression and posttetanic potentiation:
fast and slow calcium signaling in nerve terminals. Neuron 7, 915–926.

Petersen, C.C., Malenka, R.C., Nicoll, R.A., and Hopfield, J.J. (1998).
All-or-none potentiation at CA3-CA1 synapses. Proc. Natl. Acad.
Sci. USA 95, 4732–4737.

Verdaguer, N., Corbalán-Garcı́a, S., Ochoa, W.F., Fita, I., and GomézFernandéz, J.C. (1999). Ca2+ bridges the C2 membrane-binding domain of protein kinase Calpha directly to phosphatidylserine. EMBO
J. 18, 6329–6338.

Reynolds, T., and Hartell, N.A. (2000). An evaluation of the synapse
specificity of long-term depression induced in rat cerebellar slices.
J. Physiol. 527, 563–577.

Wang, S.S., and Augustine, G.J. (1995). Confocal imaging and local
photolysis of caged compounds: dual probes of synaptic function.
Neuron 15, 755–760.

Reynolds, T., and Hartell, N.A. (2001). Roles for nitric oxide and arachidonic acid in the induction of heterosynaptic cerebellar LTD. Neuroreport 12, 133–136.

Wang, Y.T., and Linden, D.J. (2000). Expression of cerebellar longterm depression requires postsynaptic clathrin-mediated endocytosis.
Neuron 25, 635–647.

Ross, W.N., and Werman, R. (1987). Mapping calcium transients in thedendrites of Purkinje cells from the guinea-pig cerebellum in vitro.
J. Physiol. 389, 319–336.

Wang, S.S., Denk, W., and Häusser, M. (2000a). Coincidence detection in single dendritic spines mediated by calcium release. Nat. Neurosci. 3, 1266–1273.

Sakurai, M. (1990). Calcium is an intracellular mediator of the climbing
fiber in induction of cerebellar long-term depression. Proc. Natl. Acad.
Sci. USA 87, 3383–3385.

Wang, S.S., Khiroug, L., and Augustine, G.J. (2000b). Quantification of
spread of cerebellar long-term depression with chemical two-photon
uncaging of glutamate. Proc. Natl. Acad. Sci. USA 97, 8635–8640.

Santamaria, F., Wils, S., De Schutter, E., and Augustine, G.J. (2006).
Anomalous diffusion in dendrites caused by dendritic spines. Neuron
52, 635–648.

Yang, S.N., Tang, Y.G., and Zucker, R.S. (1999). Selective induction of
LTP and LTD by postsynaptic [Ca2+]i elevation. J. Neurophysiol. 81,
781–787.

800 Neuron 54, 787–800, June 7, 2007 ª2007 Elsevier Inc.