Supplementary Methods

Determining quantal parameters with MPFA and CV analysis

EPSCswere recorded in three solutions containing different Ca2+ and Mg2+, which imposed different PRs. The spillover-corrected variance and mean were determined17for each condition and the relationship between variance (2) and mean current (I) was fit with a multinomial model of release that assumes a uniform PR across sites (a reasonable assumption at the MF17):

(1)

where QP is the quantal size at the time of the peak of the quantal EPSC component and CVQI=0.38 and CVQII=0.31 are the coefficients of variation of intrasite and intersite quantal variability7,17. Fits were accepted when the 2 value gave a P0.05 and when PR at 8 mM Ca2+ was >0.60, which ensures accurate estimation of N (ref. 7). We have previously shown17 that at MF-GC synapses quanta summate linearly even at high PR and the EPSC variance decreases at high Ca2+. N therefore represents the number of vesicular release sites per connection, which does not change with PR. N is not necessarily equal to the number of anatomical synaptic contacts, although they are comparable on average17. PR was calculated at each Ca2+ as I/(NQP) and the relative error inPR was estimated to be 10-21% at 2 mM. PR and QP were estimated for subsequent pulses in the train from the spillover-corrected CV of the EPSC amplitudes by assuming N was constant:

(2).

Short-term plasticity model for extracting the time course of recovery from presynaptic depression

R was estimated by fitting the changes in PR during a 5-pulse train at 100 Hz with a simple model of release2,21. PR was expressed as the product of the probability that a RRV is available at the release site (R) and that a RRV is released (U). Following an action potential, the fraction of vesicles available is reduced and recovers with a time constant R. Moreover, the release probability of available vesicles increases through a simple facilitation mechanism21: U1 is the initial probability and the running value, U, increases at each pulse by U1(1-U) and decays to U1 with a single exponential F. Thus, at the (n+1)th stimulus:

(3)

(4)

(5)

where t is the time interval between the nth and (n+1)th EPSC.

We estimated R for each connection by fixing F to the measured mean value (Fig. 3c), U1 to the cell-specific initial PR and R1 to 1, since at 8 mM PR=1.010.03, which suggests full occupancy of the release sites. The best fit was determined with a random search algorithm: values for R were iteratively chosen (50,000) from a Gaussian distribution with CV=0.5 centred on the running ‘best’ value determined using the least-squares criterion. Across all the connections, the residuals were ≤ 12% of PR, which fall within the estimated relative errors. Robustness of our estimate of R was tested by examining different facilitation mechanisms: 1) F was increased by up to 3 standard deviations above its estimate, 2) F was let free to vary within a distribution centred on the estimated value (12 ms, CV=0.67 from the fit), 3) a scaling factor  was added, so that the pulse increase in U was U1(1-U). An initial guess for  (0.52) and the width of its distribution (CV=0.35) were obtained by matching the amplitude of facilitation recorded in low Ca2+ (PR=0.11 from failure rate and N=5)7. The fit to this model converged to =1 confirming the validity of our approach.

Serial and parallel models of vesicle reloading at the MF

A stochastic model of the kinetic scheme shown in Figure 4e was developed to test our conclusions. This included the synaptic plasticity model describedabove and a releasable pool which was refilled at a constant rate of 8 vesicles per second (kP). We included desensitization assuming the same onset time course as shown in Figure 2g and the steady-state level measured from spontaneous events. We estimated the initial PR (0.69) for that set of cells in which the 6,000-pulse train was carried out using the significant correlation between the PPR and the initial PR obtained from fluctuation analysis (r=-0.87, P<0.01; n=9). Whether or not a vesicle was refilled was determined at each time point from the rate of recovery of the RRV (kRR). kRR was the product of the limiting rate (1/12 vesicles ms-1) and the fraction of vesicles in the releasable pool. This is a predictive model as all parameters were fixed to experimentally determined values.

A parallel model was also developed to determine an upper limit for the TDP time. This assumed that the RRV is refilled with a limiting rate of 1/12 vesicles ms-1 from a pool of 4 docked vesicles that are replenished in parallel from the releasable pool. Both steps were concentration dependent. The rate of replenishment of docked vesicles from the releasable pool was estimated for the parallel model by fitting the model to the reduction in the mean EPSC during the 6,000-pulse train.

Supplementary Figure 1

Short-term plasticity during pharmacological block of AMPAR desensitization. a, Mean EPSCs during a five-pulse 100-Hz train, in control and in the presence of 25 M cyclothiazide (CTZ) and 1.5-2 mM kynurenic acid (kyn). b, Mean EPSCs amplitude in control and in drugs (n=6). c, EPSC amplitude during the train, normalized by the first EPSC, in control and drugs together with the mean normalizedPR obtained from CV analysis.

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