In classical theories of cerebellar cortex, high-dimensional sensorimotor representations are used to separate neuronal activity patterns, improving associative learning and motor performance. Recent experimental studies suggest that cerebellar granule cell (GrC) population activity is low-dimensional. To examine sensorimotor representations from the point of view of downstream Purkinje cell ‘decoders’, we used three-dimensional acousto-optic lens two-photon microscopy to record from hundreds of GrC axons. Here we show that GrC axon population activity is high dimensional and distributed with little fine-scale spatial structure during spontaneous behaviors. Moreover, distinct behavioral states are represented along orthogonal dimensions in neuronal activity space. These results suggest that the cerebellar cortex supports high-dimensional representations and segregates behavioral state-dependent computations into orthogonal subspaces, as reported in the neocortex. Our findings match the predictions of cerebellar pattern separation theories and suggest that the cerebellum and neocortex use population codes with common features, despite their vastly different circuit structures.
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The SilverLab LabVIEW Imaging Software is available on GitHub at https://github.com/SilverLabUCL/SilverLab-Microscope-Software. Analysis scripts are available at https://github.com/SilverLabUCL/ParallelFibres.
Wolpert, D. M., Miall, R. C. & Kawato, M. Internal models in the cerebellum. Trends Cogn. Sci. 2, 338–347 (1998).
Brooks, J. X., Carriot, J. & Cullen, K. E. Learning to expect the unexpected: rapid updating in primate cerebellum during voluntary self-motion. Nat. Neurosci. 18, 1310–1317 (2015).
Raymond, J. L. & Medina, J. F. Computational principles of supervised learning in the cerebellum. Annu. Rev. Neurosci. 41, 233–253 (2018).
Kelly, R. M. & Strick, P. L. Cerebellar loops with motor cortex and prefrontal cortex of a nonhuman primate. J. Neurosci. 23, 8432–8444 (2003).
van Kan, P. L., Gibson, A. R. & Houk, J. C. Movement-related inputs to intermediate cerebellum of the monkey. J. Neurophysiol. 69, 74–94 (1993).
Arenz, A., Silver, R. A., Schaefer, A. T. & Margrie, T. W. The contribution of single synapses to sensory representation in vivo. Science 321, 977–980 (2008).
Proville, R. D. et al. Cerebellum involvement in cortical sensorimotor circuits for the control of voluntary movements. Nat. Neurosci. 17, 1233–1239 (2014).
Rancz, E. A. et al. High-fidelity transmission of sensory information by single cerebellar mossy fibre boutons. Nature 450, 1245–1248 (2007).
Chabrol, F. P., Arenz, A., Wiechert, M. T., Margrie, T. W. & DiGregorio, D. A. Synaptic diversity enables temporal coding of coincident multisensory inputs in single neurons. Nat. Neurosci. 18, 718–727 (2015).
Marr, D. A theory of cerebellar cortex. J. Physiol. 202, 437–470 (1969).
Albus, J. S. A theory of cerebellar function. Math. Biosci. 10, 25–61 (1971).
Cayco-Gajic, N. A. & Silver, R. A. Re-evaluating circuit mechanisms underlying pattern separation. Neuron 101, 584–602 (2019).
Cayco-Gajic, N. A., Clopath, C. & Silver, R. A. Sparse synaptic connectivity is required for decorrelation and pattern separation in feedforward networks. Nat. Commun. 8, 1116 (2017).
Litwin-Kumar, A., Harris, K. D., Axel, R., Sompolinsky, H. & Abbott, L. F. Optimal degrees of synaptic connectivity. Neuron 93, 1153–1164 (2017).
Fusi, S., Miller, E. K. & Rigotti, M. Why neurons mix: high dimensionality for higher cognition. Curr. Opin. Neurobiol. 37, 66–74 (2016).
Stringer, C., Pachitariu, M., Steinmetz, N., Carandini, M. & Harris, K. D. High-dimensional geometry of population responses in visual cortex. Nature 571, 361–365 (2019).
Rigotti, M. et al. The importance of mixed selectivity in complex cognitive tasks. Nature 497, 585–590 (2013).
Stringer, C. et al. Spontaneous behaviors drive multidimensional, brainwide activity. Science 364, 255 (2019).
Knogler, L. D., Markov, D. A., Dragomir, E. I., Štih, V. & Portugues, R. Sensorimotor representations in cerebellar granule cells in larval zebrafish are dense, spatially organized, and non-temporally patterned. Curr. Biol. 27, 1288–1302 (2017).
Wagner, M. J. et al. Shared cortex-cerebellum dynamics in the execution and learning of a motor task. Cell 177, 669–682 (2019).
Gao, P. & Ganguli, S. On simplicity and complexity in the brave new world of large-scale neuroscience. Curr. Opin. Neurobiol. 32, 148–155 (2015).
Chen, S., Augustine, G. J. & Chadderton, P. Serial processing of kinematic signals by cerebellar circuitry during voluntary whisking. Nat. Commun. 8, 232 (2017).
Shambes, G. M., Gibson, J. M. & Welker, W. Fractured somatotopy in granule cell tactile areas of rat cerebellar hemispheres revealed by micromapping. Brain Behav. Evol. 15, 94–140 (1978).
Giovannucci, A. et al. Cerebellar granule cells acquire a widespread predictive feedback signal during motor learning. Nat. Neurosci. 20, 727–734 (2017).
Ozden, I., Dombeck, D. A., Hoogland, T. M., Tank, D. W. & Wang, S. S.-H. Widespread state-dependent shifts in cerebellar activity in locomoting mice. PLoS ONE 7, e42650 (2012).
Rebola, N. et al. Distinct nanoscale calcium channel and synaptic vesicle topographies contribute to the diversity of synaptic function. Neuron 104, 693–710 (2019).
Nadella, K. M. N. S. et al. Random-access scanning microscopy for 3D imaging in awake behaving animals. Nat. Methods 13, 1001–1004 (2016).
Pichitpornchai, C., Rawson, J. A. & Rees, S. Morphology of parallel fibres in the cerebellar cortex of the rat: an experimental light and electron microscopic study with biocytin. J. Comp. Neurol. 342, 206–220 (1994).
Wilms, C. D. & Häusser, M. Reading out a spatiotemporal population code by imaging neighbouring parallel fibre axons in vivo. Nat. Commun. 6, 6464 (2015).
Gallego, J. A., Perich, M. G., Miller, L. E. & Solla, S. A. Neural manifolds for the control of movement. Neuron 94, 978–984 (2017).
Li, N., Daie, K., Svoboda, K. & Druckmann, S. Robust neuronal dynamics in premotor cortex during motor planning. Nature 532, 459–464 (2016).
Elsayed, G. F., Lara, A. H., Kaufman, M. T., Churchland, M. M. & Cunningham, J. P. Reorganization between preparatory and movement population responses in motor cortex. Nat. Commun. 7, 13239 (2016).
Lange, W. Cell number and cell density in the cerebellar cortex of man and some other mammals. Cell Tissue Res. 157, 115–124 (1975).
Chen, S., Augustine, G. J. & Chadderton, P. The cerebellum linearly encodes whisker position during voluntary movement. eLife 5, e10509 (2016).
Zhou, H. et al. Cerebellar modules operate at different frequencies. eLife 3, e02536 (2014).
De Zeeuw, C. I. Bidirectional learning in upbound and downbound microzones of the cerebellum. Nat. Rev. Neurosci. 22, 92–110 (2021).
Krakauer, J. W., Ghazanfar, A. A., Gomez-Marin, A., MacIver, M. A. & Poeppel, D. Neuroscience needs behavior: correcting a reductionist bias. Neuron 93, 480–490 (2017).
Musall, S., Urai, A. E., Sussillo, D. & Churchland, A. K. Harnessing behavioral diversity to understand neural computations for cognition. Curr. Opin. Neurobiol. 58, 229–238 (2019).
Silver, R. A. Neuronal arithmetic. Nat. Rev. Neurosci. 11, 474–489 (2010).
Walter, J. T. & Khodakhah, K. The linear computational algorithm of cerebellar Purkinje cells. J. Neurosci. 26, 12861–12872 (2006).
Brunel, N., Hakim, V., Isope, P., Nadal, J.-P. & Barbour, B. Optimal information storage and the distribution of synaptic weights: perceptron versus Purkinje cell. Neuron 43, 745–757 (2004).
Valera, A. M. et al. Stereotyped spatial patterns of functional synaptic connectivity in the cerebellar cortex. eLife 5, e09862 (2016).
Suvrathan, A., Payne, H. L. & Raymond, J. L. Timing rules for synaptic plasticity matched to behavioral function. Neuron 92, 959–967 (2016).
Ito, M. Control of mental activities by internal models in the cerebellum. Nat. Rev. Neurosci. 9, 304–313 (2008).
Vyas, S. et al. Neural population dynamics underlying motor learning transfer. Neuron 97, 1177–1186 (2018).
Gao, Z. et al. A cortico-cerebellar loop for motor planning. Nature 563, 113–116 (2018).
Chabrol, F. P., Blot, A. & Mrsic-Flogel, T. D. Cerebellar contribution to preparatory activity in motor neocortex. Neuron 103, 506–519 (2019).
Peters, A. J., Lee, J., Hedrick, N. G., O’Neil, K. & Komiyama, T. Reorganization of corticospinal output during motor learning. Nat. Neurosci. 20, 1133–1141 (2017).
Person, A. L. Corollary discharge signals in the cerebellum. Biol. Psychiatry Cogn. Neurosci. Neuroimaging 4, 813–819 (2019).
Semedo, J. D., Zandvakili, A., Machens, C. K., Yu, B. M. & Kohn, A. Cortical areas interact through a communication subspace. Neuron 102, 249–259 (2019).
Chen, T.-W. et al. Ultrasensitive fluorescent proteins for imaging neuronal activity. Nature 499, 295–300 (2013).
Huang, C.-C. et al. Convergence of pontine and proprioceptive streams onto multimodal cerebellar granule cells. eLife 2, e00400 (2013).
Nunzi, M. G., Russo, M. & Mugnaini, E. Vesicular glutamate transporters VGLUT1 and VGLUT2 define two subsets of unipolar brush cells in organotypic cultures of mouse vestibulocerebellum. Neuroscience 122, 359–371 (2003).
Hioki, H. et al. Differential distribution of vesicular glutamate transporters in the rat cerebellar cortex. Neuroscience 117, 1–6 (2003).
Kirkby, P. A., Srinivas Nadella, K. M. N. & Silver, R. A. A compact acousto-optic lens for 2D and 3D femtosecond based 2-photon microscopy. Opt. Express 18, 13721–13745 (2010).
Fernández-Alfonso, T. et al. Monitoring synaptic and neuronal activity in 3D with synthetic and genetic indicators using a compact acousto-optic lens two-photon microscope. J. Neurosci. Methods 222, 69–81 (2014).
Griffiths, V. A. et al. Real-time 3D movement correction for two-photon imaging in behaving animals. Nat. Methods 17, 741–748 (2020).
Guizar-Sicairos, M., Thurman, S. T. & Fienup, J. R. Efficient subpixel image registration algorithms. Opt. Lett. 33, 156–158 (2008).
Mathis, A. et al. DeepLabCut: markerless pose estimation of user-defined body parts with deep learning. Nat. Neurosci. 21, 1281–1289 (2018).
Sofroniew, N. J., Cohen, J. D., Lee, A. K. & Svoboda, K. Natural whisker-guided behavior by head-fixed mice in tactile virtual reality. J. Neurosci. 34, 9537–9550 (2014).
Hill, D. N., Curtis, J. C., Moore, J. D. & Kleinfeld, D. Primary motor cortex reports efferent control of vibrissa motion on multiple timescales. Neuron 72, 344–356 (2011).
Jelitai, M., Puggioni, P., Ishikawa, T., Rinaldi, A. & Duguid, I. Dendritic excitation–inhibition balance shapes cerebellar output during motor behaviour. Nat. Commun. 7, 13722 (2016).
Pnevmatikakis, E. A. et al. Simultaneous denoising, deconvolution, and demixing of calcium imaging data. Neuron 89, 285–299 (2016).
Zhou, P. et al. Efficient and accurate extraction of in vivo calcium signals from microendoscopic video data. eLife 7, e28728 (2018).
Pachitariu, M. et al. Suite2p: beyond 10,000 neurons with standard two-photon microscopy. Preprint at bioRxiv https://doi.org/10.1101/061507 (2017).
Björck, Ȧke & Golub, G. H. Numerical methods for computing angles between linear subspaces. Math. Comput. 27, 579–594 (1973).
Owen, A. B. & Perry, P. O. Bi-cross-validation of the SVD and the nonnegative matrix factorization. Ann. Appl. Stat. 3, 564–594 (2009).
This project was supported by the Wellcome Trust (095667 and 203048) and the Agence Nationale de la Recherche (ANR-17-EURE-0017). R.A.S. is supported by a Wellcome Trust Principal Research Fellowship. F.L. was supported by a postdoctoral Fondation Fyssen fellowship, a Marie Curie fellowship (Project No 331710, FP7 program) and the Wellcome Trust (203048). F.L. is now funded by the Centre National de la Recherche Scientifique. H.G. was funded by the Wellcome Trust PhD program (203734). We acknowledge the GENIE Program and the Janelia Research Campus of Howard Hughes Medical Institute for making the GCaMP6 material available. We thank A. Hantmann (Janelia Research Campus) for providing the Slc17a7-Cre transgenic mice and A. Litwin-Kumar, T. Otis, K. D. Harris, D. Attwell, L. Justus, T. J. Younts, A. Valera, J. S. Rothman and T. Fernandez Alfonso for their comments on the manuscript.
R.A.S. is a named inventor on patents owned by UCL Business relating to linear and non-linear acousto-optic lens 3D laser scanning technology. The remaining authors declare no competing financial interests.
Peer review information Nature Neuroscience thanks the anonymous reviewers for their contribution to the peer review of this work.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
a, Schematic representing a dorsal view of the cerebellum. The black circle represents the 5 mm cranial window above Crus I. Coloured blobs show the approximate location of the virus injection and GCaMP6f expression for the animals in this study. b, Top view of a cranial window above Crus I. The green channel (left) shows expression of GCaMP6f in lobule Crus I. Green fluorescence is widespread due to the spatial extent of parallel fiber projections. The red channel (right), shows a clump of retrobeads at the injection site (arrow). c, Confocal tile scanning of a coronal section of Crus I where granule cells (GrCs) were transfected with GCaMP6f. Note the absence of labelled cell bodies in the molecular and Purkinje cell layers. d, Confocal image with a smaller field of view to show GCaMP6f expression in GrC somata and axons. Labels: Cr. 1: Crus1 lobule; Cr. 2: Crus2; lob. VI: cerebellar lobule VI in the vermis, Simp.: simplex lobule, PM: paramedian lobule, ML: molecular layer, PC: Purkinje cell, GrCL: GrC layer.
a, Strings of bright varicosities from active axons were traced by hand to obtain orientations of parallel fiber segments. Inset shows the histogram of the angle of individual parallel fiber segments from the average parallel fiber orientation (n = 13, N = 5). White arrow indicates average parallel fiber orientation for this experiment, and purple the acceptance angle for parallel fiber identification (two standard deviations of the distribution in the inset). b, Examples of candidate varicosity groupings that pass (left, green box, each side 13.7 μm) and fail (right, red box) the first grouping criterion. Varicosities indicated by yellow contours. Title indicates angle between candidate parallel fiber given by linear fit (dotted white line) and the average parallel fiber direction for that experiment (white arrow). c, Example histogram of correlation coefficient for pairs of varicosities in different patches, used for the second grouping criterion. Dotted line indicates the threshold correlation (95th percentile) for this experiment. d-f, Example of correlated varicosities that pass the third grouping criterion. d, Example activity of the two varicosities (r = 0.74). e, Activity of varicosity 1 plotted against activity of varicosity 2 (grey). Blue line indicates fit from linear regression. Black circle indicates baseline activity distribution (95% confidence interval). Red line indicates vector v onto which activity is projected to calculate the linear deviation ratio for the third criterion. f, Histogram of activity from (e) projected onto v (grey histogram), and analytically calculated distribution of the baseline distribution projected onto v (orange curve). The ratio of the variances of these distributions is used for the third criterion (linear deviation ratio = 1.03). g-i, Same as d-f for a pair of varicosities that fail the third grouping criterion (r = 0.69, linear deviation ratio = 3.12). Red arrows in (g) indicate transients that are missed in one varicosity. Red arrow in (i) shows the large tail of the distribution.
a, Left: Example traces of different behavioural variables: whisker set point (WSP), whisking amplitude (WA), wheel motion index (WMI), and locomotion speed (LS). Right: Histograms of correlations of parallel fiber Ca2+ activity (ΔF/F) with WSP, WA, WMI and LS (n = 13, N = 5). Red and blue indicate parallel fibers that are positively or negatively correlated with each behavioural variable respectively (p < 0.05, two-sided shuffle test). Grey indicates parallel fibers that are not significantly correlated with that behaviour. Pie charts reveal a similar fraction of positively modulated (PM, 58–67%), negatively modulated (NM, 16–22%) and non-modulated GrCs (13–20%) regardless of behavioural variable. b, Correlation between all pairs of behavioural variables for each experiment (grey circles). Black bars indicate mean across experiments (p = 2.4 × 10−4 for all pairs of behavioural variables, two-sided Wilcoxon signed rank test, n = 13, N = 5). Error bars indicate s.e.m.
Extended Data Fig. 4 Pairwise correlation and spatial dependence of parallel fiber correlations at the onset of locomotion.
a, ΔF/F traces of positively modulated (PM) and negatively modulated (NM) parallel fibers in grey (top) together with locomotion speed and bead fluorescence, from a single experiment aligned at locomotion onset. Bottom: Grey indicates individual traces and the black indicates the mean. b, Example experiment showing temporal dispersion of parallel fiber activation during locomotion onsets. Top and middle panels show average ΔF/F (zscored) of PM and NM parallel fibers calculated over locomotion onsets. Locomotion onsets were randomly split into training (50%) and test (50%) data, and parallel fibers were sorted according to the time lag of their peak correlation (PM) or anticorrelation (NM) with locomotion speed during the training data. Bottom panels show average locomotion speed during training and test onsets. c, Distribution of pairwise correlations for pairs of positively (black, top) and negatively (black, bottom) modulated parallel fibers during 1 s interval surrounding locomotion onsets (n = 12, N = 5). Red and blue curves indicate distributions of correlations during random periods in the active state (for positively modulated and negatively modulated parallel fiber pairs, respectively). Arrowheads represent the means. d, Relationship between correlations between putative axons at locomotion onsets as a function of inter-fiber distance, for positively modulated pairs (red), negatively modulated pairs (blue), and all pairs (grey; n = 12, N = 5). Shaded regions indicate s.e.m. Thick lines indicate double exponential fit to the data.
a, Example of three non-modulated parallel fibers (top) compared to positively modulated and negatively modulated parallel fibers (same example shown in Fig. 1e for full experiment). Magenta/cyan indicates AS/QW. b, Distribution of signal-to-noise ratios (SNRs; Methods) for all non-modulated parallel fibers (top), as well as positively modulated (centre) and negatively modulated parallel fibers (bottom) (n = 13, N = 5).
Extended Data Fig. 6 Fraction of positively, negatively and non-modulated parallel fibers across experiments.
Histograms of changes in ΔF/F response during the AS relative to QW across all parallel fibers for all 13 experiments across 5 mice. Positively modulated (red) and negatively modulated (blue) parallel fibers, as well as parallel fibers which were not significantly modulated by behavioural state (grey). Pie charts indicate the proportion of each class across experiments.
a, Schematic illustrating how distances between parallel fibers were calculated. Left: example of two patches with three parallel fibers, each with different numbers of varicosities. Black unidirectional arrow indicates average parallel fiber direction. To calculate the distance between parallel fibers, the position of the centre of its varicosities is projected onto the dimension orthogonal to the average fiber vector (red line). The XY distance (dXY) is the distance in the projected dimension. Right: Same schematic, rotated to show Z-dimension. The XYZ distance (dXYZ) is the distance in the projection plane (red). b and c, Correlations between varicosities or putative axons as a function of inter-fiber distance, for positively modulated pairs (red), negatively modulated pairs (blue), and all pairs (grey; n = 13, N = 5). Shaded regions indicate s.e.m. Thick lines indicate double exponential fit to the data. b, Correlations and XY distances (dXY) for ungrouped varicosities (within the same patch). Note similar trend to grouped data, except for stronger peak at small distances (< 2 μm) (c.f. Figure 1c). c, Correlations and XYZ distances (dXYZ) for putative axons across all patches.
Parallel fiber population activity visualized by plotting first three principal components. Each panel indicates a different mouse (N = 5 in combination with Fig. 3b). Colour indicates projection along the quiet wakefulness (QW; cyan) to active state (AS; magenta) state dimension.
a, Average cross-validated unexplained variance for locomotion speed based on the first principal component (PC), the first 10 PCs, and the optimal number of PCs. Each circle indicates a different experiment (n = 11, N = 5; two-sided Wilcoxon signed rank test). b, Average cross-validated unexplained variance for locomotion speed based on the best parallel fiber (PF) for each recording and for lasso regression on the population activity (n = 11, N = 5; two-sided Wilcoxon signed rank test). c, Range of optimal number of parallel fibers to minimize the cross-validated unexplained variance. Each marker represents a different experiment. d, Correlation between the lasso regression coefficients of the optimal decoders for locomotion speed and for whisker set point, plotted against average decoder error (unexplained variance averaged for speed and whisker set point; two-sided Spearman correlation: r = −0.73, p = 0.02; n = 11, N = 5). For each decoder, regression coefficients were averaged over 10 random samples of training/test data. Error bars in a and b denote s.e.m.
Extended Data Fig. 10 Lower bound of dimensionality increases linearly with maximum variance explained in simulated data.
We tested our procedure for estimating dimensionality in a simple model of random 60-dimensional representations in populations of 300 neurons corrupted with increasing levels of noise. Each black line represents the mean variance explained for a fixed standard deviation of the noise distribution. Shading represents s.e.m. across different random representations. Inset: linear relationship between lower bound of the dimensionality and the maximum variance explained.
Supplementary Figs. 1–4 and Supplementary Table 1.
AOL 3D two-photon ‘patch’ imaging of GrC axon activity in the molecular layer of an awake behaving mouse. Movie of 13 simultaneously imaged patches (14 × 68 μm) of GrC axons (parallel fibers) expressing GCaMP6f located at different depths in the molecular layer of Crus I regions of the cerebellar cortex in a behaving mouse. Locomotion and whisker set point shown below. Data were acquired with real-time movement correction, and images were post hoc corrected, as for all data used in this study. The acquisition rate was 15 Hz (30-s recording, speed 2× real time).
Transitions between spontaneous behaviors captured in population activity. Left, example movie of a mouse spontaneously switching between periods of active locomotion and whisking (AS, magenta; QW, cyan). Right, 2D projection of population activity. Color indicates projection onto the state dimension (Methods). The projection plane was chosen manually to show the separate transients for QW→AS and AS→QW transitions.
Orthogonal representations of AS and QW. Movie showing rotation of AS (magenta) and QW (cyan) manifolds for an example experiment. Axes represent the first three principal components (PC1–3) of the full population activity.
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Lanore, F., Cayco-Gajic, N.A., Gurnani, H. et al. Cerebellar granule cell axons support high-dimensional representations. Nat Neurosci 24, 1142–1150 (2021). https://doi.org/10.1038/s41593-021-00873-x