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1 Figure S1 Multiplicative scaling of the granule cell input-output relation is not dependent on input rate. Input-output relations with short-term depression (STD) from Fig. 1d after normalizing by the maximum firing rate from the respective fits and subtracting the mossy fibre (MF) input stimulation rate at the half maximal value. The scale factor between the control (solid line) and inhibition (dashed line, +inh) was 1.8. Error bars indicate s.e.m. 1

2 Figure S2 Effects of synaptic plasticity and tonic inhibition on gain modulation in a conductance-based integrate-and-fire model. a, Relative peak amplitude of steady-state synaptic AMPAR conductance versus excitatory input rate. Solid line shows model with parameters (δ = 0.5, τ d = 40 ms) that best fit the MF- GC synaptic data (circles). Inset: model synaptic trains with and without STD (δ = 0.5 and 1.0) at 86 Hz. b, Model input-output relations with and without STD, in the absence (solid lines) and presence (dashed lines) of tonic inhibition (G inh = ps). Bold dashed lines denote G inh = 500 ps, the experimental value. c, Model G exc f relations for various levels of depression (+STD; δ = ), facilitation (+STF; δ = 1.1, 1.2) and no plasticity (-STD; δ = 1.0). d, Change in gain ( Gain) due to tonic inhibition (±inh) computed from fits (equation (5), Methods) to the model input-output relations, plotted versus G inh and δ. Colour scale shown at top. Bottom graph shows Gain for G inh = 500 ps, which increases for increasing levels of STD. 2

3 Figure S3 Gain modulation by phasic inhibition in an integrate-and-fire model. a, Input-output relations of the integrate-and-fire model driven with AMPAR synaptic trains with and without STD (δ = 0.5 and 1.0; Fig S2c) in the absence (solid lines) and presence (dashed lines) of various levels of phasic inhibitory input (inh; 50, 100, 150 Hz; peak conductance = 663 ps, τ d2 = 6.9 ms). b, Change in gain and offset as a function of phasic inhibition rate determined from fits (equation (5), Methods) to the input-output relations in a. 3

4 Figure S4 Voltage dependence of synaptic NMDAR conductance. a, Voltage dependence of the synaptic NMDAR conductance recorded in GCs (circles) computed from peak of average NMDAR synaptic currents (inset). NMDA currents were recorded in the presence of 5 µm NBQX at different voltages (+20 to -80 mv) as indicated by colours (n=6). Stimulation transients were blanked 1 ms from their onset. Solid line (black) shows conductance generated by SM-1 amplifier after tuning its characteristics to best match the data. Dashed lines denote the range of the average GC membrane potential during stimulation, as in b. Error bars indicate s.e.m. b, Average membrane potential recorded during the dynamic clamp experiments in Fig. 3 as a function of MF stimulation rate with and without AMPAR STD (blue and red; n=11). 4

5 Figure S5 Predicted input-output relations for single MF stimulation assuming a purely additive shift in the relationship between GC firing and mean excitatory conductance. Predicted input-output relations (blue lines) calculated from equation (5) in Methods, using the G exc f curve in Fig. 4d and FG exc curves in inset. Inset: solid line shows FG exc curve derived from the curve fit to the control (+STD) data in Fig. 4c data. Dashed line is the same curve shifted 0.2 ns along the G exc axis. The change in the input-output relation predicted from a purely additive shift in the FG exc relation match the data well. Error bars indicate s.e.m. 5

6 Table S1. Fit parameters. Fig. Eq. Data F 0 (Hz) F max (Hz) H 50 n m (ps/hz) λ (Hz) 1d 5 -STD 0* * 1d 5 -STD + inh 0* * 1d 5 +STD 0* * 105.1* 1d 5 +STD + inh 0* * 105.1* 2b 3 -STD b 4 +STD c 5 -STD 0* c 5 -STD + inh 0* d inset 5 -STD * 3b 3 -STD b 4 +STD c 5 -STD 0* * 3c 5 -STD + inh 0* * 3c 5 +STD 0* * 138.0* 3c 5 +STD + inh 0* * 138.0* 4c 5 MF stim 0* 313.8* * 181.3* 4c 5 MF stim+inh 0* 313.8* * 181.3* 4d 4 MF stim b 5 -STD b 5 -STD + inh 50 Hz b 5 -STD + inh b 5 -STD + inh d 5 +STD 0* d 5 +STD + inh 30 0* d 5 +STD + inh 45 0* d 5 +STD + inh 60 0* H 50 denotes G exc 50 (ns), except for the fits in Fig. 5, where it denotes the half-maximal output firing rate (Hz). * Values fixed during the curve fit. Mossy fiber stimulation (MF stim). Inhibition (inh). AMPAR Short-term depression (STD). For the fits in Fig. 4c, F max was not well-constrained, and therefore fixed to the largest F max in our data set; this produced little change in Gain and Offset values reported in Fig. 4e. 6