UBCs perform complex temporal transformations of in-vivo MF firing patterns.

a. Scheme showing experimental paradigm. We received in vivo recordings of MFs in the flocculus and paraflocculus of macaques (middle) during a smooth pursuit eye movement task (left). We reproduced the in vivo firing patterns in MFs in acute slices of lobule X the mouse cerebellum using a theta stimulation electrode, while making cell-attached recordings of the UBC response (right).

b. MF stimulation with an artificial burst (20 stimuli at 100 spk/s; green trace, top) and instantaneous firing rates of the responses in 4 UBCs (fast, mid-range, slow, and OFF; individual trials in grey, mean in black). Dashed gray lines indicate 0 spk/s.

c. As in b, but for a MF firing pattern recorded in vivo during a smooth pursuit task in which the MF primarily fired in brief high frequency bursts. The numbers of spikes in each burst larger than 2 spikes are indicated in the trace.

d. As in b, but for a MF firing pattern recorded in vivo during a smooth pursuit task with characteristic long-lasting increases and decreases in firing.

Diverse UBC responses to MF bursts of increasing duration.

a. Instantaneous firing rates of four representative UBCs in response to 100 spk/s bursts comprised of 1-20 stimuli (input pattern indicated above in green; dashed gray lines indicate 0 spk/s; cell numbers refer to the index in the summary plot b).

b. Heat maps showing the normalized instantaneous firing rates for all UBCs in response to bursts comprised of 1-20 stimuli. Responses were normalized per cell to the peak firing rate in response to 20 stimuli at 100 spk/s bursts, and sorted by the half-width for cells with clear increases in firing (cell #1-61), or sorted by pause duration for the rest (cell #62-70). Time indicates seconds since start of the MF stimulation (indicated by dotted red line). Red arrows indicate representative UBCs shown in a.

c. Summary plot showing peak increase in firing rate on a log scale, for all different bursts by the number of input spikes also on a log scale. UBCs color coded to correspond to the cell index in b. Cells without significant increases in firing excluded from this plot (#62-70).

d. Separate plots of the peak increase in firing rate in response to 2 and 20 stimuli bursts sorted by cell index as in b.

e. As in c but for the number of spikes evoked by the different MF burst stimulations.

f. As in c but for the half-width of the increase in firing for the different MF burst stimulations.

Differential glutamate receptor contributions to responses evoked by MF bursts of increasing duration.

a. Instantaneous firing rates of five representative UBCs in response to 100 spk/s bursts comprised of 1-20 stimuli (stimulus indicated by green bars). Responses shown for baseline conditions (black), and after addition of antagonists of mGluR2/3 (yellow), AMPAR (red), and mGluR1 (blue). Glutamate receptor antagonists were applied successively on top of the previous antagonist(s) as depicted in the scheme at the top. Cell numbers refer to the index in the summary plot d.

b. Summaries of the peak change in firing rate for the same five cells, with successive different markers for baseline and the different glutamate antagonists, and separate plots for the different MF burst stimulations.

c. As in b but for the number of spikes evoked by the MF stimulation.

d. Heat maps showing the normalized instantaneous firing rates for all UBCs in response to 100 spk/s burst comprised of 1-20 stimuli (columns), for baseline and after addition of glutamate receptor antagonists (rows). Responses were normalized per cell to the peak firing rate in response to the 20x 100 spk/s burst with mGluR2/3 blocked. Cells sorted by their response to the baseline 20 stimuli at 100 spk/s input, either by the half-width of the increase in firing (cell #1-27) or by pause duration (cell #28-31). Time indicates seconds since start of MF stimulation (indicated by dotted red line). Red arrows indicate representative UBCs shown in a-c.

e. Summary plots of the number of spikes evoked by the MF stimulation on a log scale for all UBCs color coded to correspond to the cell index in d. Successive different markers indicate baseline and the different glutamate antagonists, and separate plots for the different MF burst stimulations.

f. Violin plots of the number of spikes after each burst under baseline conditions (-) and after blocking mGluR2/3 (+), normalized to the number of spikes after 20 stimuli at 100 spk/s under baseline conditions. Markers indicate individual UBCs color coded by the cell index in d. (*p<0.01, Wilcoxon signed rank test).

g. Violin plots of the percentage of the number of spikes evoked by MF stimulation that was mediated by AMPARs, estimated from the effect of blocking AMPARs on the response. Markers indicate individual UBCs color coded by the cell index in d. Responses smaller than 5 spikes not shown.

h. As in g but for the component mediated by mGluR1

The UBC population displays a continuum of long-lasting responses to smooth pursuit-like input.

a. Instantaneous firing rates of seven representative UBCs in response to 20 stimuli at 100 spk/s burst (left), and smooth pursuit-like MF input (right) with prolonged 5 spk/s input interposed by 1 s step to 10-60 spk/s. Input pattern indicated above (green traces). Dashed gray lines indicate 0 spk/s; cell numbers refer to the index in the summary plot c.

b. The same as in a but on an expanded timescale, displaying only the 60 spk/s step. Dotted red lines indicate onset and offset of the 60 spk/s step.

c. Heat maps showing the normalized instantaneous firing rates for all UBCs in response to 20 stimuli at 100 spk/s burst (left) and smooth pursuit-like MF input (right). Responses normalized to the peak firing rate separately for burst and smooth pursuit-like MF input. Cell sorted by their response to 20 stimuli at 100 spk/s burst input, either by the half-width of the increase in firing (cell #1-25) or by pause duration (cell #26-31). Dotted red lines indicate the start of the step changes in input rate, red arrows indicate representative UBCs shown in a,b.

d. The same as in c but on an expanded timescale, displaying only the 60 spk/s step.

e. Summary plot of the number of evoked spikes during the 1 s steps compared to the 1 s period preceding the step. Individual UBCs color coded to correspond to the cell index in c.

f. As in e but for the number of evoked spikes in the 3 s period after the 1 s steps.

g. Summary plot of the time to peak for log-gaussian fits of the response to the step to 60 spk/s. Cells sorted and color coded to correspond to the cell index in c. Cells without significant increase in firing after step changes excluded (cell #28-31).

h. Summary plot of the time for the increase in firing to decay by half after a step change. Cells without significant increase in firing after step changes excluded (cell #28-31).

Contributions of mGluR2/3, AMPAR, and mGluR1 to responses evoked by smooth pursuit-like input.

a. Instantaneous firing rates of two representative UBCs in response to 20 stimuli at 100 spk/s bursts (left), and smooth pursuit-like MF input (right) as indicated by the traces at the top (green). Responses shown under baseline conditions and after successive addition of antagonists of mGluR2/3, AMPAR, and mGluR1. Dashed gray lines indicate 0 spk/s; cell numbers refer to the index in the summary plot c.

b. The same as in a but on an expanded timescale, displaying only the 60 spk/s step. Dotted red lines indicate onset and offset of the 60 spk/s step.

c. Heat maps showing the normalized instantaneous firing rates for all UBCs in response 20 stimuli at 100 spk/s bursts (left) and smooth pursuit-like MF input (right), for baseline and after addition of glutamate receptor antagonists (rows). Responses normalized separately for burst and smooth pursuit-like MF input to the respective peak firing rates with mGluR2/3 blocked. Cells sorted by their response to the baseline 20 stimuli at 100 spk/s input, either by the half- width of the increase in firing (cell #1-9) or by the pause duration (cell #10-11). Dotted red lines indicate the start of the step changes in input rate, red arrows indicate representative UBCs shown in a,b.

d. The same as in c but on an expanded timescale, displaying only the 60 spk/s step.

e. Summary plots of the number of evoked spikes in the 1 s period during the step and the 3 s period follow it for all UBCs color coded to correspond to the cell index in c. Successive different markers indicate baseline and the different glutamate antagonists, and separate plots for the different step changes in input.

f. Violin plots of the number of spikes in the 1 s period during the step and the 3 s period after under baseline conditions (-) and after blocking mGluR2/3 (+), normalized to the number of spikes associated with the step to 60 spk/s under baseline conditions. Markers indicate individual UBCs color coded by the cell index in c. (*p<0.01, Wilcoxon signed rank test).

g. Violin plots of the percentage of the number of spikes evoked by MF stimulation that was mediated by AMPARs, estimated from the effect of blocking AMPARs on the response. Markers indicate individual UBCs color coded by the cell index in d. Responses smaller than 5 spikes not shown.

h. As in g but for the component mediated by mGluR1.

NMDA receptors do not significantly contribute to burst responses

a. Instantaneous firing rates of two representative UBCs in response to 100 spk/s bursts comprised of 1-20 stimuli (stimulus indicated above in green). Responses shown for baseline conditions (black), and after addition of an antagonist of NMDA receptors (pink). Cell numbers refer to the index in the summary plot b.

b. Heat maps showing the normalized instantaneous firing rates for all UBCs in response to 100 spk/s burst comprised of 1-20 stimuli (columns), for baseline and after addition of an NMDA receptor antagonist (rows). Responses were normalized per cell to the peak firing rate in the baseline response to the 20 stimuli at 100 spk/s burst. Cells sorted by their response to the baseline 20 stimuli at 100 spk/s input, either by the half-width of the increase in firing (cell #1-8) or by pause duration (cell #9-10). Time indicates seconds since start of MF stimulation (indicated by dotted red line). Red arrows indicate representative UBCs shown in a.

c. Violin plots of the number of spikes after each burst under baseline conditions (-) and after blocking NMDAR (+), normalized to the number of spikes after 20 stimuli at 100 spk/s under baseline conditions. Markers indicate individual UBCs color coded by the cell index in b.

AMPAR auxiliary subunits are expressed differentially in the UBC population

a. UMAP embedding of normalized gene expression in the UBC population for mGluR1.

b. Same as in a but showing AMPAR subunits GluA1-4.

c. Same as in a but showing auxiliary subunits TARP γ-2, γ-7, and γ-8.

d. Same as in a but showing auxiliary subunit GSG1L.

UBC responses to sustained 1 to 5 spk/s MF input.

a. Instantaneous firing rates of five representative UBCs in response to sustained MF input at three different rates (1, 2.5, and 5 spk/s). Dashed gray lines indicate 0 spk/s; cell numbers refer to the index in the summary plot c.

b. As in a but for the average response of all individual inputs excluding the first 5.

c. Heat maps showing the normalized instantaneous firing rates for all UBCs in response to sustained input at 1, 2.5, and 5 spk/s. Responses normalized per cell by their peak firing rate. Cells sorted by their response to 20 stimuli at 100 spk/s bursts as in Fig. 2b. Time indicates seconds since start of sustained MF input. Red arrows indicate representative UBCs shown in a,b.

d. Summary plot showing the peak rate of the average response (as in b) for all UBCs color coded to correspond to the cell index in c.

e. As in d but for the average number of spikes fired.

f. As in d but for the ratio between the average steady state firing rate (200 ms after stimuli) and the peak firing rate shown in d.

NMDA receptors do not significantly contribute to responses to smooth pursuit-like input

a. Instantaneous firing rates of two representative UBCs in response to 20 stimuli at 100 spk/s burst (left), and smooth pursuit-like MF input (right) as indicated by the traces at the top (green). Responses shown under baseline conditions and after addition of an antagonist of NMDA receptors. Dashed gray lines indicate 0 spk/s; cell numbers refer to the index in the summary plot c.

b. The same as in a but on an expanded timescale, displaying only the 60 spk/s step. Dotted red lines indicate onset and offset of the 60 spk/s step.

c. Heat maps showing the normalized instantaneous firing rates for all UBCs in response 20 stimuli at 100 spk/s bursts (left) and smooth pursuit-like MF input (right), for baseline and after addition of NMDA receptor antagonist (rows). Responses normalized to the peak firing rate during baseline conditions separately for burst and smooth pursuit-like MF input. Cells sorted by their response to the baseline 20 stimuli at 100 spk/s input, either by the half-width of the increase in firing (cell #1-8) or by the pause duration (cell #9-10). Dotted red lines indicate the start of the step changes in input rate, red arrows indicate representative UBCs shown in a,b.

d. The same as in c but on an expanded timescale, displaying only the 60 spk/s step.

e. Violin plots of the number of spikes in the 1 s period during the step and the 3 s period after under baseline conditions (-) and after blocking NMDAR (+), normalized to the number of spikes associated with the step to 60 spk/s under baseline conditions. Markers indicate individual UBCs color coded by the cell index in c.

Contribution of different glutamate receptors to UBC responses evoked by sustained 1 to 5 Hz MF stimulation.

a. Instantaneous firing rates of two representative UBCs in response to sustained MF input at three different rates (1, 2.5, and 5 spk/s). Responses shown under baseline conditions and after successive addition of antagonists of mGluR2/3, AMPAR, and mGluR1. Dashed gray lines indicate 0 spk/s; cell numbers refer to the index in the summary plot c.

b. As in a but for the average response of all individual inputs excluding the first 5.

c. Heat maps showing the normalized instantaneous firing rates for all UBCs in response to sustained input at 1, 2.5, and 5 spk/s (columns), for baseline and after addition of glutamate receptor antagonists (rows). Responses normalized per cell to the peak firing rate after application of the mGluR2/3 antagonist. Cells sorted by their response to 20 stimuli at 100 spk/s bursts under baseline conditions as in Fig. 3d (with exception of Fig. 3 cell #20 and #24).

d. Summary plot showing the number of spikes fired in the average response to 1, 2.5, and 5 spk/s sustained input (as in b) for all UBCs color coded to correspond to the cell index in c. Successive different markers indicate baseline and the different glutamate antagonists.