Neuron, Volume 54

Supplemental Data
Ca2+ Requirements for Cerebellar
Long-Term Synaptic Depression:
Role for a Postsynaptic Leaky Integrator
Keiko Tanaka, Leonard Khiroug, Fidel Santamaria, Tomokazu Doi,
Hideaki Ogasawara, Graham Ellis-Davies, Mitsuo Kawato,
and George J. Augustine

Coincidence of Ca2+ with PF activity induces LTD
When coupled with PF stimulation, the rise in [Ca2+]i resulting from CF activity
can cause LTD (Sakurai, 1990; Konnerth et al., 1992). We asked whether theelevation of [Ca2+]i by uncaging DMNPE-4 could substitute for CF activity to
induce LTD, as previously observed with a different caged Ca2+ compound by
Lev-Ram et al. (1997).
At the frequency and intensity employed in our experiments, PF
stimulation alone did not elevate [Ca2+]i measurably (Figure S1A, left) and wasincapable of inducing LTD (Figure S1B). (More robust PF activity can elevate[Ca2+]i and produce LTD: Eilers et al., 1995; Hartell, 1996; Eilers et al., 1997.)
Likewise, uncaging DMNPE-4 with a 1 Hz train of UV light pulses for 30 s (6.5 µJ
per pulse, 195 µJ total), which produced transient increases in [Ca2+]i similar to
those described in Figure 2 (Figure S1A, middle), was not sufficient to depress
PF synaptic transmission in the experiment shown in Figure S1B. However,activating PF synapses while elevating [Ca2+]i, by uncaging DMNPE-4, caused a
gradual decline in the amplitude of PF-EPSCs. This depression of PF synaptictransmission reached a new steady level that was 47% of control EPSC
amplitude in the example shown in Figure S1B. During the pairing of PF activity
with uncaged Ca2+, the peak level of [Ca2+]i measured during the UV light pulses
was very similar to that produced by the UV light pulses alone (Figure S1A, right).
But the activity of PF synapses caused baseline [Ca2+]i to rise more rapidly (redlines in Figure S1A). This may be due to a synergistic action of uncaged Ca2+
and the IP3 that is produced by PF activity (Finch and Augustine, 1998; Takechi
et al., 1998) upon IP3 receptors (Iino, 1990; Bezprozvanny et al., 1991; Finch etal., 1991).
We performed 3 experiments where PF activity was paired with [Ca2+]ielevation. In each case, LTD was induced and the mean level of depression was
49±3% of the initial control PF-EPSC amplitude. These reductions in PF synaptic
response occurred without any changes in pipette series resistance, or in the
input resistance and holding current of the Purkinje cell, indicating that theyreflect changes in PF synaptic efficacy rather than a recording artifact. The
depression had an exponential time course, with a time constant of 4.9±0.5 min.
The magnitude and kinetics of the LTD produced by pairing PF activity with
[Ca2+]i elevation were comparable to those observed when LTD is induced by
combining PF activity with CF activity or Purkinje cell depolarization (Konnerth etal., 1992; Karachot et al., 1994; Leitges et al., 2004). These results demonstratethat [Ca2+]i elevation and PF activity can act synergistically to induce LTD.

2

Ca2+-induced LTD shares signaling pathways with conventional LTD
It is known that LTD results from the clathrin-dependent internalization of
postsynaptic AMPA receptors (Wang and Linden, 2000). To determine whether
Ca2+-induced LTD is due to the same mechanism, we asked whether a peptide
inhibitor of clathrin assembly prevents the LTD induced by repetitive uncaging of
Ca2+. This peptide, termed AP2pep, acts by preventing assembly of clathrin into
membrane coats (Morgan et al., 2000). When AP2pep was introduced into
Purkinje cells through the patch pipette, increasing [Ca2+]i caused little or no LTD(Figure S2A, open symbols). On average, PF-EPECs were reduced by only
2.8±2.7% following DMNPE-4 photolysis in the presence of AP2pep (n=6). As acontrol, we also examined the action of a mutant peptide, AP2∆DLL peptide,which has a disrupted clathrin binding site and is less able to inhibit assembly ofclathrin (Morgan et al., 2000). In the presence of AP2∆DLL, Ca2+-induced LTD
was still observed (Figure S2A, filled symbols). The reduction in PF-EPSC
amplitude produced by uncaging Ca2+ was 27.1±2.7% (n=4) in the presence of
AP2∆DLL, which is significantly larger (p<0.001) than the amount of LTD
observed in the presence of AP2pep. However, AP2∆DLL did reduce the amountof LTD somewhat, perhaps due to the reported weak ability of AP2 ∆DLL peptide
to block clathrin assembly at high concentrations (Morgan et al., 2000). The
preferential ability of AP2pep to prevent Ca2+-induced LTD indicates that thisform of LTD depends on clathrin-dependent membrane traffic, as is the case forconventional LTD induced by synaptic activity.

3

In its magnitude and time course, as well as its requirements for Ca2+ andfor clathrin-dependent membrane trafficking, Ca2+-induced LTD resembles the
LTD induced by pairing PF synaptic activity with CF activity and/or depolarization.
To determine the relationship between these two forms of LTD more directly, we
asked whether they share the same downstream signaling pathway. Specifically,
we asked whether induction of one form of LTD prevents any further depressionof synaptic transmission by the other form of LTD. This type of occlusion
experiment frequently has been used to determine whether forms of hippocampal
synaptic plasticity share common pathways (Gustafsson et al., 1987; Kauer et al.,
1988; Muller et al., 1990; Cormier et al., 1993; Oliet et al., 1997).
In our experiments, stimuli that evoked Ca2+-induced LTD andsynaptically-evoked LTD were sequentially presented to single Purkinje cells.
When LTD was first elicited by pairing PF activity with depolarization of the
Purkinje cell membrane potential (∆V+PF in Figure S2B), subsequent elevationof [Ca2+]i via DMNPE-4 photolysis (Ca in the Figure S2B) produced no further
depression of PF-EPSCs (upper part of Figure S2B; n=3). The average reduction
in PF-EPSC amplitude caused by pairing PF activity with depolarization was
44±3%, while PF-EPSCs were reduced subsequently by only 4±5% following[Ca2+]i elevation (n=3). Likewise, initially inducing LTD by elevating [Ca2+]i
prevented any further depression of PF-EPSC amplitude by later pairing of PF
activity with depolarization (lower part of Figure S2B; n=3). On average, [Ca2+]ielevation reduced PF-EPSCs by 55±1%, while subsequent paired stimulation
reduced PF-EPSCs by only 5±3% (n=3). In summary, induction of one form of4LTD prevented subsequent induction of the other form. This mutual occlusionindicates that LTD and Ca2+-induced LTD share a final common signaling
pathway.

Spatial range of Ca2+-induced LTD
LTD induced by pairing localized PF synaptic activity with depolarization spreads
approximately 50 µm beyond active PF synapses to neighboring PF synapses(Wang et al., 2000; Reynolds and Hartell, 2000). Similar observations have been
made for LTD induced by high amounts of PF activity alone (Hartell, 1996; Eilers
et al., 1997). Because the signals responsible for such spread of LTD are notclear, we next asked whether the LTD induced by local elevation of [Ca2+]i wascapable of spreading.
Our first approach to this question involved locally stimulating two beams
of PF axons: one at the site of Ca2+ uncaging, which monitored the induction of
LTD at this site, and another at variable distances away from the site of [Ca2+]ielevation. Figure S3A illustrates an experiment where two stimulating pipettes
were placed 43 µm apart to activate two non-overlapping PF beams. Previous
work has established that such stimuli activate PF synapses within an area
approximately 5 µm in radius from the position of the pipette (Wang et al., 2000).
A train of UV light pulses (1 Hz, 30 s) was applied only at the location of the firststimulation pipette. During the time that Ca2+ was photoreleased, neither set of
PFs were activated; after [Ca2+]i returned to the resting level, PF stimulation was
resumed at both sites. With this protocol, only the PF synapses at the first PF

5input underwent LTD, while transmission at the second PF input remained
unchanged (Figure S3A). This result indicates that LTD induced by local
elevation of [Ca2+]i does not spread as far as LTD induced by synaptic activation.
To more precisely determine the spatial range of LTD induction, we
performed a second set of experiments where the UV spot was positioned at a
variable distance from a single site of PF activation. Data from 24 such
experiments are summarized in Figure S3B, where the degree of depression of
PF-EPSC amplitude is plotted as a function of the separation between the PF
stimulating electrode and the site of [Ca2+]i elevation. Again, it is apparent that
the LTD induced by [Ca2+]i elevation is restricted in its spread. These data could
be described by a Gaussian function with a half-width of 10.2±1.5 µm (solid line
in Figure S3B). This value is virtually identical to the dimensions of the region of[Ca2+]i elevation (Figure 1), indicating that LTD induced by local elevation of[Ca2+]i does not spread beyond locations where [Ca2+]i is elevated.

Lack of LTD following repeated subthreshold rises in [Ca2+]iExperiments such as the one illustrated in Figure 3A and 3B show that elevating[Ca2+]i to different levels three times causes LTD only after the third UV lightpulse, which raised [Ca2+]i to the highest level. One interpretation of this result isthat [Ca2+]i must exceed a threshold level to induce LTD. However, a reviewer
suggested that this depression might be due to the fact that the third light pulse
was preceded by two prior pulses of UV light, which could have damaged the
Purkinje cell sufficiently to depress PF transmission. To determine whether

6depression was due to suprathreshold [Ca2+]i elevation, or to repeatedillumination, we applied two UV light pulses (200 µJ) that caused subthreshold
rises in [Ca2+]i (Figure S4A) and monitored PF-EPSC (Figure S4B). While boththe first and second pulses elevated [Ca2+]i to 0.8 µM, PF-EPSC amplitude
remained unchanged. This indicates that subthreshold elevation of [Ca2+]i wasincapable of inducing LTD even though UV light was applied twice. Thus, weconclude that the depression occurring in Figure 3B after the third light pulse isdue to [Ca2+]i exceeding the threshold level, thereby inducing LTD.

“Leaky integrator” description of LTD
We propose that [Ca2+]i is integrated to produce a downstream signal, termed X.
X could correspond to any number of elements in the signal transduction
pathway downstream of Ca2+, such as one or more activated proteins (e.g.,protein kinase C, PKC) or other signals. If integrated Ca2+ exceeds somethreshold, then LTD occurs in an all-or-none manner. The integration of [Ca2+]i is
not perfect but is associated with some leak. Production of X can then be
described by the following differential equation:τdx= − x + a[Ca 2 + ]i (t )
dt

(S1)

where x denotes the concentration of the signal X, ‫ ז‬is the time constant of theleaky integrator, and a represents the efficiency of converting [Ca2+]i to x.
In our experiments, a prolonged pulse of UV light produced a ramp-likerise in [Ca2+]i. In this case, the time-dependent rise in [Ca2+]i can be described as:[Ca 2 + ]i (t ) = kt

7

(S2)

where k is the slope of [Ca2+]i increase. Substituting Eqn. (S2) into Eq. (S1)yields:τdx= −x + akt
dt

(S3)

With an initial condition of [Ca2+]i = 0, the solution of Eqn. (S3) is:⎛ t⎞
x (t ) = akτ exp⎜ − ⎟ + ak (t − τ )
⎝ τ⎠

(S4)

Because we do not know the level of x required to produce LTD, we assume that
LTD is produced when x reaches a threshold level. At saturating [Ca2+]i, themaximum amount of LTD is a 36% reduction in PF-EPSC amplitude, irrespectiveof the duration of [Ca2+]i elevation (Figure 5C). We therefore assumed that thethreshold value of x is reached when LTD is half of the maximum, that is an 18%
reduction in PF-EPSCs. This amount of LTD is achieved when [Ca2+]i = KCa, sothat the threshold (θ ) is:

⎛ t⎞
⎛K ⎞
⎛ KCa ⎞
⎟τ exp⎜ − ⎟ + a ⎜ Ca ⎟(t − τ )
⎝ t ⎠
⎝ τ⎠
⎝ t ⎠

θ = a⎜(S5)

We used this relationship to determine the values of a and ‫ ז‬that best describedthe dependence of KCa on the duration of [Ca2+]i elevation (Figure 5B). For thispurpose, a and ‫ ז‬were varied and eqn. S5 was used to determine the resulting
value of KCa. The error in the derived value of KCa, defined as the sum of squares
difference between the solution of eqn. S5 and the data points shown in Figure
5B, is shown for a range of values of a and ‫ ז‬in Figure S5A. The minimum error
occurred at a single point (red peak in Figure S5A) when a = 18.7 and τ = 0.56.
These values provided a good description of the duration-dependence of KCa, as8can be seen from the smooth curve in Figure S5B and the comparison to theexperimental data shown in Figure 5B. Further, because [Ca2+]i was elevated in a
ramp-like fashion, where the integral of [Ca2+]i is one-half the product of [Ca2+]iand the duration of the UV light pulse, KCa-integ values could also be predictedfrom the following relationship:⎞⎛ 2 K Ca −integ ⎞⎛ t ⎞ ⎛ 2K⎟⎟τ exp⎜ − ⎟ + a⎜⎜ Ca2−integ ⎟⎟(t − τ ) (S6)2tt⎝ τ⎠ ⎝⎠⎠⎝

θ = a⎜⎜As shown by the line in Figure S5C, the predicted values showed a durationdependence that emulated the relationship observed in the experimental
measurements (Figure 6B).
If LTD occurs when x reaches a threshold level, the relationship between
LTD and x should be independent of the duration of the Ca2+ signal thatgenerated x. To assess this, we plotted the amount of LTD, measured
experimentally for different durations of [Ca2+]i elevation, as a function of x
produced by a given rise in peak [Ca2+]i. The relative value of x was determinedfrom the following relationship, obtained by combining eqn. S2 and eqn. S4:⎛ [Ca 2 + ]i ⎞⎛ [Ca 2 + ]i ⎞⎛ t⎞⎟⎟(t − τ )⎟⎟τ exp⎜ − ⎟ + a ⎜⎜x = a ⎜⎜
⎝ τ⎠
⎠
⎝ t
⎠
⎝ t

(S7)

The relationship between LTD and the relative value of x was indeed found to be
independent of duration (Figure 6E), providing support for our conclusion that the
dynamic behavior of LTD arises from a leaky integrator.

9

Positive feedback loop model
The Kuroda et al. (2001) mathematical model of signal transduction pathways for
cerebellar LTD was used to simulate the relationship between Ca2+ and LTD. Asa measure of LTD, we used the calculated percentage of phosphorylated AMPA
receptors at 100 min after increasing [Ca2+]i. This model (Figure 7A) included thebiochemical and enzymatic reactions shown in Figure S6. Reversible biochemical
reactions can be described by the following formula:
k

f
⎯⎯→
A+ B
AB
←⎯⎯
kb

(S8)

where kf and kb are the forward and backward rate constants. Enzymatic
reactions were defined from the standard Michaelis-Menten scheme:
k1
⎯⎯→
cat
E+S
ES ⎯k⎯→
E+P
←⎯⎯
k −1

(S9)

In this formula, enzyme E first binds to its substrate S and then catalyzes areaction that produces P. k1 and k-1 are the forward and backward rate constantsfor the binding reaction, and kcat is the rate constant for the catalytic reaction. The
values used for each of these reaction kinetic parameters are listed in Table S1and the concentrations of each reactant are listed in Table S2. These values
were determined based on the previous reports indicated in the right-mostcolumns of Tables S1 and S2.
Because the present study focuses on LTD triggered by Ca2+, we used
only the part of the Kuroda et al. (2001) model that is downstream of Ca2+. Thismodel is available on-line (http://www.cns.atr.jp/neuroinfo/). To take into accountthe conditions of our Ca2+ uncaging experiments and recent insights into signal
10

transduction reactions, the following two modifications were first made: (1) In theoriginal model, the activity of phosphatase (PP2A) was decreased in response tosynaptic activity. In our experiments, synapses were not activated during LTD
induction; for this reason, the concentration of active PP2A was assumed to beconstant at 0.045 µM. (2) In the original model, PKC was assumed to be
degraded after activation, thus resulting in deactivation of the positive feedback
loop. Because there is no evidence for such a PKC degradation reaction, thisstep was eliminated from the present version of the model and the degradation
rate of arachidonic acid (AA) was increased from 0.001 to 0.4/s, as was done in
another study (Bhalla and Iyengar, 1999). Two other small modifications werenecessary to accurately reproduce our experimental results: (3) To obtain thecorrect value for KCa, the Ca2+ dissociation constant of PKC was reduced from 10
to 2 µM. The Hill coefficient for activation of PKC by Ca2+ also was increased
from 1 to 2, to reflect the actual number of Ca2+ ions that bind to a single PKC
molecule (Sutton and Sprang, 1998; Verdaguer et al., 1999). (4) After themodifications described above, the model predicted that almost 100% of the
AMPA receptors would be phosphorylated, so that the amplitude of PF-EPSCs
would be reduced to zero. To obtain a percentage of LTD similar to what wasobserved experimentally (~36%), the rate of phosphorylation of AMPA receptors
by PKC was reduced to 0.05/s.
We examined how varying these values or concentrations affects the Ca2+
triggering of LTD by repeating the simulation while systematically varying each of
the 64 parameters. These parameters included the time constant of biochemical

11

reactions (‫)ז‬, kcat, Kd, Keq, or Km in reactions shown in Table S1 (a1-d2) and theconcentrations of molecules shown in Table S2. For each parameter, we varied
the values over a 10,000-fold range, using 6 values lower than the original values(1/100, 2/100, 5/100, 1/10, 2/10, and 5/10 of the original value) and 6 higher
values (2, 5, 10, 20, 50, or 100 times the original value). In total, we collected 768
relationships between [Ca2+]i and LTD, all based on elevating [Ca2+]i for 1 s.
A graphic representation of the outcome of this exploration of parameter
space is shown in Figure S7. This figure illustrates the influence of changing
each parameter, indicated at the bottom of the figure, on several aspects of thepredicted relationship between [Ca2+]i and LTD, such as the KCa value (Figure
S7A), maximum amount of LTD (Figure S7B), and Hill coefficient (Figure S7C). In
many cases, depression occurred even in the absence of elevated [Ca2+]i; such
effects were quantified by determining the basal amount of depression at 0 µM
[Ca2+]i (Figure S7D). In these plots, the dashed horizontal lines indicate theoutcome produced by the parameter values used in the final model, while thecolored symbols indicate results obtained when the parameters were set to othervalues. In 175 out of the 768 relationships, basal depression was 10% or more
and the sigmoidal Ca2+-dependence of LTD was absent. We therefore fit the Hillequation to the remaining 593 relationships. Varying parameters had little or noeffect on KCa in 72% of the cases and on the maximum amount of LTD in 51% of
the cases. In contrast, the Hill coefficient was very parameter-sensitive, so thatthe Hill coefficient was unchanged in only 16% of the 593 relationships. The
spatial gradients in [Ca2+]i and the noise associated with experimental

12

measurements were not considered here, so that the Hill coefficient was verylarge (dashed line). In fact, in our deterministic simulation, the Hill coefficient
theoretically should become infinitely large because of the bistable dynamics ofthe system, as indicated in Figure 7B. The finite values of Hill coefficient
observed were due to finite intervals between simulated points and/or to poor fitsof the Hill equation. We believe that Hill coefficients of 5 or greater for a given
parameter set indicates that the system is highly cooperative and bistable. From
this point of view, the high cooperativity property was preserved in 53% of the
593 relationships.
To quantify the parameter-sensitivity of these predictions, we calculated
the standard deviations (SD) of KCa, maximum LTD, and Hill coefficient values
obtained when each parameter was varied over the 10,000-fold range (Table S3and S4). In addition to describing the robustness of the simulation, theseanalyses reveal some biologically interesting trends. In particular, the simulation
was particularly sensitive to the parameters that control Ca2+-dependent
activation of PKC - such as the reactions included in Figure S6A and PKC
concentration – as well as the parameters that regulate AMPA receptor
phosphorylation. These results suggest that the reactions which determine PKC
activity or AMPA receptor phosphorylation are biochemical control points that
may be precisely regulated at synapses to control LTD induction.
The nonlinear and bistable nature of the model, which is evident as the allor-none behavior shown in Figure 7B, was greatly affected by variations inparameter values. To quantify such effects, we calculated the difference (max-13basal) between the maximal (at 10 µM [Ca2+]i) and basal (Figure S7D) values for
LTD, as shown in Figure S7E. For the case of Figure 7B, max-basal was 35%
and this value is indicated by the dotted line in Figure S7E. In most cases,
bistability was associated with max-basal values of 30% or more. Variations inreactions d1 and d2 were exceptional, because they yielded bistability
independent of the max-basal values. As shown in Figure S7E, bistability wasparticularly sensitive to variations in parameters related to activation of mitogenactivated protein kinase (MAPK, b reactions). The loss of bistability in thesereactions was also associated with a low Hill coefficient (Figure S7C), consistent
with our conclusion that cooperativity requires the positive feedback loop.
Because MAPK is in the positive feedback loop, these results are consistent withour conclusion that bistability arises from this loop. Further, these results suggestthat regulating MAPK activity may be a control point for regulating the positive
feedback loop and LTD induction.

Refining the simulation by taking into account experimental conditions
The simulation described above is not spatially resolved, meaning that it
considers a situation where [Ca2+]i (and indeed all components of the signalingcascade) is spatially homogeneous. While such a situation is appropriate forconsidering LTD at the level of single synapses, it does not fully replicate theconditions of our experiments, where the Gaussian distribution of UV light
produced a similar gradient in [Ca2+]i (Figure 1).

14

To take into account this gradient of [Ca2+]i, we described the spatial
profile (S) of [Ca2+]i with a Gaussian function (equation S10):
S (a k , w j , xi ) = (a k + w j )e

x2
− i

2
2σ uv

(S10)

where ak is the maximum amplitude of the uncaged Ca2+ and xi is the distancefrom the center of the uncaging spot. We incorporated a homegenously
distributed random variable (wj) to introduce a noise term comparable to thefluctuations in laser intensity and Ca2+ uncaging efficiency over time during
illumination. The maximum amplitude, ak, was varied from 0 to 10 µM, the rangeof [Ca2+]i.covered by the simulation. Our experimental measurements (eg. Figure1) show that σuv = 5 µm and suggest that the range of values for wj is close to
25% of the maximum amplitude.
In addition to spatial variations in [Ca2+]i, it is also necessary to take into
account reductions in the number of active PFs with increasing distance from thestimulating electrode. This is necessary because any effect of elevated [Ca2+]ithat is outside of the area of activated PF synapses will not be reported in our
measurements of LTD, which are based on responses of activated PF synapses.
Therefore, we used equation S10 to calculate the spatially averaged value of S
over the dendritic region occupied by activated PFs. The measurements of Wanget al. (2000) indicated that this area has a radius, r, of 3 µm. In all of ourexperiments we were careful to align the stimulating electrode with the center ofthe uncaging spot, so the two Gaussian functions were concentric.

S x (a k , w j ) =1 xn = r∑ S (ak , w j , xi )2r x1 = − r

15

(S11)

We then used the Hill equation to determine the values of LTD produced
at each point within this area of active PFs:

LTD (ak , w j ) =S x (ak , w j )

n

(S12)

n
K Ca
+ S x (ak , w j )nwhere KCa and n are the values for [Ca2+]i required for half-maximal LTD and theHill coefficient, respectively. Both KCa and n were extracted from fitting the Hillequation to the simulation results shown in Figure 7B. Finally, because ourmeasurements of LTD were integrated over all activated PF synapses, weestimated the average value of LTD produced by a given ak. This was done bytaking into account laser power fluctuations and changes in uncaging efficiency
by taking N = 50 samples of the randomly distributed variable w.
w =w
S (a k , w j )1 j N
LTD (a k ) =∑nn
N w j = w1 K Ca
+ S (a k , w j )
n

(S13)

This average LTD calculation yielded a very good approximation of theexperimental measurements of the [Ca2+]i dependence of LTD, as shown in
Figure 7C. This concordance between the modeling results and experimental
measurements suggest that LTD is an all-or-none event at the single spine levelthat is blurred in experimental measurements due to spatial variations in [Ca2+]iand to noise.

16

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23

Supplementary Figures

Figure S1
LTD is induced by pairing of PF activation and Ca2+ uncaging(A) Time course of [Ca2+]i increase evoked in the same cell by each of the three
trains. Note lack of [Ca2+]i increase in response to PF stimulation alone. The
exponential fitting curves for the baseline Ca2+ during a train of pulse are shownby red line and the tau for uncaging Ca2+ alone and for paring PF stimulation with
uncaging Ca2+ is 15 and 3.3 s, respectively. (B) PF-EPSC amplitude (circles) is ata stable level (dashed line) prior to and after the 30 s 1 Hz train of PF stimuli(vertical bar, PF) and after the Ca2+ uncaging train (Ca). However, when the two
stimuli are paired (PF+Ca), a rapid, LTD-like decrease in EPSC amplitude
occurs.

24

Figure S2
Intracellular signaling pathways of Ca2+-induced LTD(A) Ca2+-induced LTD is dependent on clathrin-mediated endocytosis. When acontrol AP2 peptide (AP2 ∆DLL, 1.56 mM) was applied intracellularly (filled
circles), PF-EPSC amplitude undergoes LTD after 1 Hz train of Ca2+ uncaging(vertical bar; Ca).

In contrast, when AP2 peptide was applied intracellularly25

(open circles), Ca2+-induced LTD was blocked. Current amplitudes arenormalized to the mean of pre-train level for each cell (dashed line). Data areshown as mean + SEM from 4 experiments for each peptide. (B) Ca2+-induced
LTD and conventional LTD mutually occlude each other. Upper panel: Averaged
normalized PF-EPSC amplitude undergoes LTD upon a 30 s 1 Hz train of
depolarizing steps (to 0 mV for 100 ms) paired with PF stimuli. Twenty minutes
later, when LTD has reached its maximal level, a similar train of Ca2+ uncaging
fails to cause further depression of PF-EPSC amplitude. Dashed line indicatesthe pre-treatment level to which current amplitude is normalized. Lower panel:
After LTD is induced by a train of Ca2+ uncaging, pairing of depolarization with PF
stimulation did not produce any change in PF-EPSC amplitude.

26

Figure S3
Spatial range of Ca2+-induced LTD(A) An example of experiment with two stimulation pipettes activating two
separate inputs 43 µm apart. A train of Ca2+ uncaging produces LTD of the first27

input (at UV spot) but causes no change on the second input (43 µm away). (B)Pooled data from the experiments with varied distance between the activated PF
synapses and the uncaging spot. The amount of depression upon a Ca2+
uncaging train which would normally cause LTD, is plotted as a function of the
distance. The smooth line is a Gaussian function.

28

Figure S4
LTD is not induced by subthreshold level of rise in [Ca2+]i applied twice in a single
Purkinje cell.
(A) Time course of [Ca2+]i increases evoked in a Purkinje cell by two UV pulses(horizontal bars) of same intensities. (B) Time course of PF-EPSC amplitude. No
depression was observed after either first (1) or second (2) increase in [Ca2+]ishown in A.

29

Figure S5(A) Plot of the error of the theoretically predicted KCa values for experimental data
points from Figure 5B as a function of the two parameter values; a and ‫ז‬. The
error is defined as the sum of squared difference of the theoretical prediction anddata points. The landscape has a unique local maxima, corresponding tominimum prediction error, at a=18.7 and tau=0.56. (B and C) The theoretically
predicted KCa values (B) and KCa-area values (C) are plotted against duration of[Ca2+]i elevation. These values were calculated from eqn. S5 and S6. For
comparison, experimental data shown in Figures 5B and 6B are also plotted asgray circles.

30

Figure S6
Pathways of molecular signaling applied in the computational simulation
PKC activation by Ca2+ and AA (A), regulation of MAPK pathway by activated
PKC and phosphatases (B), PLA2 activation by Ca2+, MAPK, and PIP2 (C), AA
production by activated PLA2 (D), and regulation of AMPA receptor
phosphorylation by activated PKC and PP2A (E). Values for each parameter (a1d2) are shown in Table S1. Full name of molecules and their concentrations areshown in Table S2.

31

Figure S7Parameter sensitivity analysis of the computational simulation

32

KCa value (A), maximum amount of LTD (B), Hill coefficient (C), basal level ofdepression (D), and max-basal value (E), obtained in the parameter sensitivity
analysis. Parameters varied in this analysis were time constant (‫)ז‬, Kd, or Keq inthe biochemical reactions, kcat or Km in the enzymatic reactions, or concentrationsof each reactant. Different symbols show different scaling factors that original
parameter values were multiplied with (1/100 – 100). KCa value, maximum LTD,
and Hill coefficient were determined only when the relationship could be
described by Hill equation. Dashed lines show outcome produced by theparameter values used in the final model (Figure 7B). Note that the experimental
conditions were not incorporated into these results.

33

Figure S8
Cooperative triggering of LTD arises from the positive feedback loop(A) Relationships between peak [Ca2+]i and LTD predicted by simulation in theabsence of AA-mediated PKC activation (shown in Figure 9A) is superposed with34

the control relationship (shown in Figure 7C). Relationships obtained by 1 s and
30 s duration of [Ca2+]i elevation are shown. (B-D) KCa value (B), maximum
amount of LTD (C), and Hill coefficient (D) without the positive feedback loop areplotted against duration of [Ca2+]i elevation. These values were obtained from Hillequation used in Figure 9A. For comparison, control data shown in Figures 7D-F
are also plotted as gray squares. (E) Simulated relationships between peak[Ca2+]i and LTD in the absence of activation of PKC by AA. These relationships
were not corrected with the effects of non-uniform distribution of [Ca2+]i andnoise. (F) Relationships between peak [Ca2+]i and LTD measured experimentallyin the presence of PLA2 inhibitor, OBAA (shown in Figure 9F) is superposed withthe control relationship (shown in Figure 5A). (G-I) KCa value (G), maximum
amount of LTD (H), and Hill coefficient (I) are plotted against duration of UV
pulse. These parameters were obtained from Hill equation used in Figure 9F. For
comparison, control data shown in Figures 5B-5D are also plotted as gray circles.

35

Table S1
ID

Reaction name
PKC_bind_Ca

kf = 0.25 s-1µM-2

a2

PKC-Ca_memb-1

kf = 1 s

kb = 0.1 s

a3

PKC_bind_AA

kf = 0.2 s-1µM-1

kb = 10 s-1

a1

a4

PKC-AA_bind_Ca#

Kinetic parameters-1

kf = 0.25 s µM
-1

-2

-1

a5

PKC-Ca_bind_AA

kf = 0.2 s µM

b1

PKC_phos_Raf

Km = 11.5 µM

kb = 1 s-1-1-1

kb = 1 s

kb = 10 s-1

kcat = 0.0335 s-1
-1

Refs

Kd = 2 µM

1

Keq = 101

Kd = 50 µM

2

Kd = 2 µM

1

Kd = 50 µM

2

k-1/kcat = 4

3, 4

b2

PP2A_deph_Raf-P

Km = 15.7 µM

kcat = 6 s

k-1/kcat = 45b3

Raf_act_MEKKm = 0.398 µM

kcat = 0.105 s-1

k-1/kcat = 4

6b4

Raf_act_MEK-P

Km = 0.398 µM

kcat = 0.105 s-1

k-1/kcat = 46

k-1/kcat = 45, 7, 8-1

b5

PP2A_deph_MEK-PP

Km = 15.7 µM

kcat = 6 sb6

PP2A_deph_MEK-P

Km = 15.7 µM

kcat = 6 s-1

b7

MEK_act_MAPKKm = 0.0463 µM

k-1/kcat = 45, 7, 8kcat = 0.15 s-1

k-1/kcat = 4

9, 10

-1

k-1/kcat = 4

9, 10

b8

MEK_act_MAPK-P

Km = 0.0463 µM

kcat = 0.15 s

b9

MKP_deph_MAPK-PP

Km = 0.16667 µM

kcat = 1 s-1

k-1/kcat = 4

11, 12-1

b10

MKP_deph_MEPK-P

Km = 0.16667 µM

kcat = 1 s

k-1/kcat = 4

11, 12c1

MAPK_phos_PLA2

Km = 25.6 µM

kcat = 20 s-1

k-1/kcat = 4

13, 14c2

PLA2-P_deg

kf = 0.17 s-1

kb = 0 s-1-1

c3

PLA2_bind_Ca

kf = 0.01 s

c4

PLA2-PIP2_bind_Ca

kf = 0.01 s-1

c5

PLA2_bind_PIP2

kf = 0.0012 s-1

c6

PLA2-Ca_bind_PIP2

kf = 0.0012 s

c7

PLA2-Ca_prd_AA

Km = 20 µM

Kd = 10 µM

16kb = 0.1 s-1

kb = 0.1 s

-1

15
-1

Kd = 10 µM

16kb = 0.48 s-1

Kd = 400 µM

4kb = 0.48 s-1

Kd = 400 µM

4

k-1/kcat = 417

k-1/kcat = 417kcat = 54 s-1-1

c8

PLA2-PIP2_prd_AA

Km = 20 µM

kcat = 11.04 s

c9

PLA2-PIP2-Ca_prd_AA

Km = 20 µM

kcat = 36 s-1

k-1/kcat = 4

17

c10

PLA2-P_prd_AA

Km = 20 µM

kcat = 120 s-1

k-1/kcat = 4

17

-1

c11

AA_degkf = 0.4 s

d1

PKC_phos_AMPAR

Km = 3.5 µM

d2

PP2A_deph_AMPAR-P-1

kb = 0 s

kcat = 0.05 s-1-1

Km = 15.7 µM

kcat = 6 s

kf and kb are defined by formula S8.
k1, k-1, and kcat are defined by formula S9.
Kd: dissociation constant (Kd = kb/kf)
Keq: equilibrium constant (Keq = kb/kf)
Km: Michaelis constant (Km = (k-1 + kcat)/k1 )#References are shown below Table S2.

36

15
k-1/kcat = 44

k-1/kcat = 45

Table S2
Molecular name

Full name

PKC

Protein kinase C

PP2A

Protein phosphatase 2A

Raf#

Concentration

Refs

1 µM

18

0.045 µM

19Raf

0.5 µM

20

MEK

MAPK or ERK kinase

0.5 µM

9, 21

MAPK

Mitogen-activated protein kinase

1 µM

13, 21MKP

MAPK phoaphatase

PLA2

0.0032 µM

22

Phospholipase A2

0.4 µM

16

PIP2

Phosphatidylinositol bisphosphate

10 µM

4

APC

Aracholonylphosphatidylcholine

30 µM

23

AMPAR

AMPA receptor

0.5 µM

24#

References:(1) Oancea and Meyer, 1998; (2) Schaechter and Benowitz, 1993; (3) Chen et al., 1993; (4)Kuroda et al., 2001; (5) Pato et al., 1993; (6) Force et al., 1994; (7) Kyriakis et al., 1992; (8) Ahn
et al., 1999; (9) Seger et al., 1992; (10) Haystead et al., 1992; (11) Charles et al., 1992; (12)Charles et al., 1993; (13) Sanghera et al., 1990; (14) Nemenoff et al., 1993; (15) Bhalla andIyengar, 1999; (16) Leslie and Channon, 1990; (17) Channon and Leslie, 1990; (18) Marquez etal., 1992; (19) Mumby et al., 1985; (20) Storm et al., 1990; (21) Huang and Ferrell, 1996; (22)Sun et al., 1993; (23) Wijkander and Sundler, 1991; (24) Tanaka et al., 2005

37

Table S3
Sensitivities (standard deviation)
##

ID

a1
a2
a3
a4
a5
b1
b2
b3
b4
b5
b6
b7
b8
b9
b10
c1
c2
c3
c4
c5
c6
c7
c8
c9
c10
c11
d1
d2

maxbasal
11.55
14.66
1.02
12.69
0.02
10.35
10.39
10.38
10.38
12.67
10.38
12.66
12.52
12.63
12.66
12.36
12.53
0.04
0.02
0.02
0.02
0.02
17.08
0.02
11.36
10.82
20.13
23.47

basal

‫ ז‬or kcat
KCa

0
0
0
0
0
18.43
18.54
18.39
18.36
18.44
18.44
18.30
18.13
18.26
18.29
18.31
18.65
0
0
0.02
0
0
18.64
0
24.47
26.39
1.50
10.98

1.93
0.77
0.05
0.55
0.14
1.14
0.06
1.24
0.06
0.70
0.06
1.22
1.24
1.20
0.68
1.21
3.20
0.14
0
0.26
0
0.37
1.63
0
1.17
0.09
0.12
0.09

LTD
max
11.46
14.67
1.01
12.52
0.02
10.99
7.87
10.93
7.87
10.17
7.87
11.04
10.77
10.77
10.18
10.72
11.14
0.03
0.01
0.04
0.01
0.05
10.45
0.01
11.10
7.31
21.56
31.85

Hill
coef.
65.52
33.07
22.00
43.68
34.19
18.94
25.01
19.86
25.01
24.72
25.01
20.74
23.12
23.15
24.71
23.12
18.43
36.51
4.29
34.82
0.30
31.01
24.40
3.26
23.21
25.10
39.66
32.64

maxbasal
17.12
16.55
10.47
0.02
13.46
9.81
10.39
10.39
10.36
12.68
10.39
11.09
12.67
12.67
12.67
12.55

basal

Kd, Keq, or Km
KCa
LTD
max
0
3.76
16.95
0
2.64
16.57
26.35
0.04
7.93
0
0.26
0.02
0
0.94
13.58
18.49
1.02
11.81
18.40
0.06
7.86
18.40
0.06
7.87
18.38
0.99
10.95
18.25
1.28
10.61
18.29
0.06
7.87
0.27
0.69
10.81
18.30
1.19
10.97
18.31
0.71
10.18
18.30
0.70
10.18
18.64
1.38
11.08

Hill
coef.
33.41
58.83
25.08
42.03
46.43
18.93
25.01
25.01
19.85
24.91
25.01
21.06
21.87
24.72
24.72
21.89

0.16
0.02
18.64
0.02
0.08
18.63
0.02
12.13

0
0
18.17
0
0
18.43
0
19.72

0.85
0
0.88
0.03
0.91
1.39
0.04
0.68

0.09
0.01
1.38
0.02
0.04
2.59
0.02
9.38

27.75
1.31
2.13
22.97
31.87
24.20
22.29
24.80

29.06
25.75

18.10
11.89

0.58
0.18

41.07
34.71

34.89
29.84

##

‫ ;ז‬time constant of biochemical reactions.
To multiply ‫ ז‬with x, both kf and kb was divided by x.

Table S4
Molecular name
PKC
PP2A
Raf
MEK
MAPK
MKP
PLA2
PIP2
APC
AMPAR

max-basal
9.60
10.16
9.61
10.38
11.05
10.39
10.82
18.64
10.75
5.33

Sensitivities (standard deviation)
basal
KCa
LTDmax
44.94
43.85
19.20
19.28
0.27
18.32
26.38
18.17
20.15
0.10

38

1.02
0.07
1.16
0.36
0.76
0.06
0.09
1.50
0.09
0.22

44.38
8.51
12.94
11.48
10.76
7.87
7.30
3.82
7.36
5.43

Hill coef.
18.92
25.09
18.83
22.12
19.75
25.01
25.10
24.27
25.10
22.96