Reading out a spatiotemporal population code by imaging neighbouring parallel fibre axons in vivo

The spatiotemporal pattern of synaptic inputs to the dendritic tree is crucial for synaptic integration and plasticity. However, it is not known if input patterns driven by sensory stimuli are structured or random. Here we investigate the spatial patterning of synaptic inputs by directly monitoring presynaptic activity in the intact mouse brain on the micron scale. Using in vivo calcium imaging of multiple neighbouring cerebellar parallel fibre axons, we find evidence for clustered patterns of axonal activity during sensory processing. The clustered parallel fibre input we observe is ideally suited for driving dendritic spikes, postsynaptic calcium signalling, and synaptic plasticity in downstream Purkinje cells, and is thus likely to be a major feature of cerebellar function during sensory processing.

a: Nearest neighbour distributions for 1000 PFs at the density of our labelling (green) and at 2.8% of the labelling density (blue, corresponding to the responding fraction we find, but randomly distributed), as well as the nearest neighbour distribution for 1000 PFs at the native density of 6 per µm 2 (red) and at 2.8% of this density (orange). The median nearest neighbour distances for these four densities are plotted in the inset (same colour code). Further details in Supplementary  The Purkinje cells responding to the stimulus with an initial transient increase in spiking (24/31 recordings in 11 mice) showed an average peak response (as determined from 4 ms bin width PSTH constructed over 100 trials) of 96 ± 28 Hz with the strongest responding cell peaking at 155 Hz. While many cells respond to the airpuff stimulation with increases in spike rate, these increases were generally short-lived, with 8 of the 10 strongest-responding cells producing a peak in the PSTH of just one bin (at 4 ms bin width). This is also reflected in the low number of extra spikes introduced by the stimulation (median = 0.4 extra spikes; n = 24 recordings with an excitatory component in the PSTH, determined using baseline firingcorrected cumulative spike times as previously described 3 ). Indeed, over the whole population Purkinje cells showed a stimulus evoked net reduction in spiking (median = -0.12 'extra spikes'). Thus, our sensory stimulus can trigger changes in spiking comparable to those previously observed with brief sensory stimulation 1, 4 . On the other hand, the activity levels evoked by our stimulus are much smaller than those reported in Purkinje cells during sensory-motor behaviour. During such behavioural tasks Purkinje cells can reach much higher firing frequencies (over 300 Hz have been reported 5-7 ) than we found for an isolated stimulus with such behaviourally relevant increases lasting much longer (often > 100 ms [8][9][10] ). This demonstrates that our stimulus is far from saturating Purkinje cell spiking responses.
In some experiments Purkinje cells were hyperpolarized (see Supplementary Figure 1b,f), revealing sensory-evoked EPSPs with a very large variability in amplitude. In most cases the PSP contained two distinct excitatory components, which were also reflected in the spiking responses. The timing of these components matches the timing of the two peaks in the PF event latencies (see Supplementary Figure 3b) and is consistent with the activation of trigeminal and corticopontine mossy fibre inputs projecting to crus II 11 . At less hyperpolarized potentials (~-65 mV), a strong inhibitory component was observed, which often terminated the excitatory component. Supplementary Figure 1f shows a representative recording, with the excitatory component being restricted to a FWHM of 3.3 ms by feedforward inhibition. This inhibitory component is also reflected in the spiking pattern of nonhyperpolarized recordings, where 28 out of 31 cells showed a transient decrease in spiking, commonly following the initial increase (median number of dropped spikes = 0.5, n = 28 recordings; see Supplementary Figure 1g,h).

Supplementary Note 2: Estimating number and timing of APs underlying single PF responses
Linescans were used to estimate the number of action potentials underlying sensory-evoked Ca 2+ transients in single parallel fibre boutons. Previous in vitro studies have shown that single action potentials in granule cells produce highly reliable Ca 2+ transients in single parallel fibre boutons, and that the bouton Ca 2+ transients provide an accurate readout of the number of granule cell action potentials 12,13 . Using high-speed linescans (1 kHz) across single parallel fibre boutons in vivo, inspection of the rising phase of individual events allowed us to identify clear inflections characteristic of multiple action potentials (Supplementary Figure 2a). We found that 83% (n = 164/198 responses) of all sensoryevoked Ca 2+ transients exhibited clear shoulders in the rising phase, implying multiple underlying action potentials. This is consistent with in vivo patch-clamp recording experiments from granule cells showing that sensory stimulation produces bursts consisting of variable numbers of action potentials 14 . To estimate action potential numbers, the rising phases were analysed in more detail: inflections were taken to be indicative of an underlying action potential if a nearly instantaneous rise above noise level was interrupted by at least 3 points with no further such rise (interpreted as the onset of transient decay). On average, we estimated that sensory-evoked responses consisted of 2.6 ± 0.9 (SD; n = 101 responses) action potentials, with an average frequency of 134 ± 73 Hz (SD, n = 191 APs).
Linescans also allowed the estimation of response latencies by comparing stimulus onset and response onset (see Supplementary Figure 2bc). We find that the latencies are bimodally distributed, with peaks at ~10 ms and ~22 ms. We find that 46% of PF responses occur within a 4 ms time window 10 ms after stimulus onset. A further 18% occur within a 4 ms time window with 22 ms latency. These two peaks are expected to correspond to the short latency trigeminal and longer latency corticopontine inputs to crus II 11 . Thus, the majority of inputs are active within two narrow time windows, allowing for efficient postsynaptic integration.

Supplementary Note 3: Effect of different forms of anaesthesia
Besides the difference in the number of spontaneously active PFs (see main text), we found that stimulus response rates were increased under light isoflurane anaesthesia (median response rate = 0.59, n = 58 fibres) when compared with ketamine-xylazine (median response rate 0.3, n = 136 fibres; p = 0.0004, two-sided Mann-Whitney).
In contrast, the clustering we find was not affected by the anaesthesia regime: The nearest neighbour distances between co-active fibres in the maps (e.g. Fig. 3) are not significantly different between KX and IF (two-tailed p = 0.8086, Mann-Whitney test, n = 21 pairs in 3 maps KX vs. 108 pairs in 13 maps IF, median NN distance = 8.0 µm vs. 8.8 µm), the cluster size in the activation maps is also not significantly different (two-tailed p = 0.1362, Mann-Whitney test, n = 19 clusters vs. 51 clusters, median cluster size = 2 for both). This is a strong indication for the robustness of our finding of clustered parallel fibre activation.

Functional relevance
For the interpretation of our results, it is important to consider that only ~0.4% of all PFs in the region are labelled in our preparation, implying that clusters will contain more responding fibres than the 2 -5 that we have imaged and that the distances between co-active fibres will thus be shorter. To estimate how pronounced this latter effect is, we simulated fields of different fibre densities. To simulate the activation density we observed, we used the actual PF density 16 ; our labelling density; or 2.8% of each of these, using 1000 fibres for each the four scenarios (see Supplementary Table 3). For the resulting fields of fibres we determined the nearest neighbour distance distributions and the median nearest neighbour distances (see Supplementary Figure 4a). We find that the median nearest neighbour distance is 16fold smaller when going from our labelling density to the actual PF density, for both the 'all fibres' scenario and the randomly distributed active fibres scenario. We used randomly distributed active fibres in this simulation (to avoid making any assumptions about a mathematical model of clustering). As clustered points by definition have shorter nearest neighbour distances than randomly distributed points, this analysis provides a "worst case" upper limit for the distances between co-activated fibres. Given the strong decrease in nearest neighbour distance when going from our labelled fibre density to the actual fibre density, the distances between all co-activated fibres will therefore be significantly shorter than observed in our experiments.
When considering the postsynaptic consequences of clustered parallel fibre activity, a main determinant will be the spatial configuration of these inputs on the dendrites of the postsynaptic cell: i.e. do the clustered PFs target neighbouring spines, the same spiny branchlet, or different branchlets. To determine if the distances between co-active fibres that we extrapolate above are on a scale that would allow multiple fibres from a given cluster to target the same spiny branchlet, we extracted the spiny branchlet length distribution from a published, reconstructed rat Purkinje cell model 17 . We find that for randomly distributed active PFs (assuming 2.8% activation rate), over 95% of the nearest neighbour distances are shorter than the median spiny branchlet length (7.1 µm; orange trace in Supplementary Figure 4b). As clustered fibres will be even more densely packed, this suggests that the clustering we find is likely to be of relevance to synaptic integration in individual spiny branchlets of post-synaptic Purkinje cells.
Besides distance between fibres, the orientation of a PF pair relative to a spiny branchlet will be important in determining the postsynaptic effect of that fibre pair. To estimate the influence of PF-cluster to branchlet orientation, it is necessary to consider the space covered by spines from a single spiny branchlet in comparison to the distances between co-activate fibres. Based on their anatomical work, Fox & Barnard 18 found that given the dense packing of spines, a spiny branchlet roughly corresponds to a cylinder with a diameter of 3 µm on average. Comparing this to our extrapolated average nearest-neighbour distance of 2.2 µm (for random distribution, due to clustering this is expected to be significantly shorter), it is clear that while orientation will surely play a role, its effect on the readout of clustered PF input is expected to be small. This is all the more true for metabotropic signalling.
Importantly, each PF is predicted to synapse onto 135 PCs/mm (in rats 19 ). As a consequence, there are a large number of target cells, each receiving inputs from a given PF cluster in a different post-synaptic spatial configuration. Together with the above density analysis, this clearly shows that the clustering we report here is sufficiently tight to allow coactive PFs to make contact with the same PC dendritic branchlet in multiple PCs along a beam, influencing the integration of PF input by PCs.