Gradients in the mammalian cerebellar cortex enable Fourier-like transformation and improve storing capacity

Neural circuit mechanisms to transform cerebellar population dynamics for motor control in monkeys

We exploit identification of neuron types during extracellular recording to demonstrate how the cerebellar cortex's well-established architecture transforms inputs into outputs. During smooth pursuit eye movements, the floccular complex performs distinct input-output transformations of temporal dynamics and directional response properties. The responses of different interneuron types localize the circuit mechanisms of each transformation. Mossy fibers and unipolar brush cells emphasize eye position dynamics uniformly across the cardinal axes; Purkinje cells and molecular layer interneurons code eye velocity along directionally biased axes; Golgi cells show unmodulated firing. Differential directional response properties of different neuron types localize the directional input-output transformation to the last-order inputs to Purkinje cells. Differential temporal dynamics pinpoint the site of the temporal input-output transformation to granule cells. Specific granule cell population dynamics allow the temporal transformations required in the area we study and generalize to many temporal transformations, providing a complete framework to understand cerebellar circuit computation.

Impact statement

We dissect the circuit computations performed by the floccular complex of the cerebellum during an exemplar sensory-motor behavior, taking advantage of knowledge of the circuit architecture, existence of discrete neuron types, and a newfound ability to identify neuron types from extracellular recordings. Our results describe the contributions of the major neuron types to the cerebellar input-output computations, identify the population dynamics needed in granule cells to support those computations, and to create a basis set to enable temporally-specific motor behavior and motor learning.

Mapping the topography of spatial gene expression with interpretable deep learning

Spatially resolved transcriptomics technologies provide high-throughput measurements of gene expression in a tissue slice, but the sparsity of these data complicates analysis of spatial gene expression patterns. We address this issue by deriving a topographic map of a tissue slice-analogous to a map of elevation in a landscape-using a quantity called the isodepth. Contours of constant isodepths enclose domains with distinct cell type composition, while gradients of the isodepth indicate spatial directions of maximum change in expression. We develop GASTON (gradient analysis of spatial transcriptomics organization with neural networks), an unsupervised and interpretable deep learning algorithm that simultaneously learns the isodepth, spatial gradients and piecewise linear expression functions that model both continuous gradients and discontinuous variation in gene expression. We show that GASTON accurately identifies spatial domains and marker genes across several tissues, gradients of neuronal differentiation and firing in the brain, and gradients of metabolism and immune activity in the tumor microenvironment.

Bias-accounting meta-analyses overcome cerebellar neglect to refine the cerebellar behavioral topography

The cerebellum plays important roles in motor, cognitive, and emotional behaviors. Previous cerebellar coordinate-based meta-analyses and mappings have attributed different behaviors to cerebellar subareas, but an accurate behavioral topography is lacking. Here, we show overrepresentation of superior activation foci, which may be exacerbated by historical cerebellar neglect. Unequal foci distributions render the null hypothesis of standard activation likelihood estimation unsuitable. Our new method, cerebellum-specific activation-likelihood estimation (C-SALE), finds behavioral convergence beyond baseline activation rates. It does this by testing experimental foci versus null models sampled from a data-driven, biased probability distribution of finding foci at any cerebellar location. Cerebellar mappings were made across five BrainMap task domains and thirty-five subdomains, illustrating improved specificity of the new method. Twelve of forty (sub)domains reached convergence in specific cerebellar subregions, supporting dual motor representations and placing cognition in posterior-lateral regions. Repeated subsampling revealed that whereas action, language and working memory were relatively stable, other behaviors produced unstable meta-analytic maps. Lastly, meta-analytic connectivity modeling in the same debiased framework was used to reveal coactivation networks of cerebellar behavioral clusters. In sum, we created a new method for cerebellar meta-analysis that accounts for data biases and can be flexibly adapted to any part of the brain. Our findings provide a refined understanding of cerebellar involvement in human behaviors, highlighting regions for future investigation in both basic and clinical applications.

Increased understanding of complex neuronal circuits in the cerebellar cortex

The prevailing belief has been that the fundamental structures of cerebellar neuronal circuits, consisting of a few major neuron types, are simple and well understood. Given that the cerebellum has long been known to be crucial for motor behaviors, these simple yet organized circuit structures seemed beneficial for theoretical studies proposing neural mechanisms underlying cerebellar motor functions and learning. On the other hand, experimental studies using advanced techniques have revealed numerous structural properties that were not traditionally defined. These include subdivided neuronal types and their circuit structures, feedback pathways from output Purkinje cells, and the multidimensional organization of neuronal interactions. With the recent recognition of the cerebellar involvement in non-motor functions, it is possible that these newly identified structural properties, which are potentially capable of generating greater complexity than previously recognized, are associated with increased information capacity. This, in turn, could contribute to the wide range of cerebellar functions. However, it remains largely unknown how such structural properties contribute to cerebellar neural computations through the regulation of neuronal activity or synaptic transmissions. To promote further research into cerebellar circuit structures and their functional significance, we aim to summarize the newly identified structural properties of the cerebellar cortex and discuss future research directions concerning cerebellar circuit structures and their potential functions.

Local synaptic inhibition mediates cerebellar granule cell pattern separation and enables learned sensorimotor associations

The cerebellar cortex has a key role in generating predictive sensorimotor associations. To do so, the granule cell layer is thought to establish unique sensorimotor representations for learning. However, how this is achieved and how granule cell population responses contribute to behavior have remained unclear. To address these questions, we have used in vivo calcium imaging and granule cell-specific pharmacological manipulation of synaptic inhibition in awake, behaving mice. These experiments indicate that inhibition sparsens and thresholds sensory responses, limiting overlap between sensory ensembles and preventing spiking in many granule cells that receive excitatory input. Moreover, inhibition can be recruited in a stimulus-specific manner to powerfully decorrelate multisensory ensembles. Consistent with these results, granule cell inhibition is required for accurate cerebellum-dependent sensorimotor behavior. These data thus reveal key mechanisms for granule cell layer pattern separation beyond those envisioned by classical models.

Cerebellar state estimation enables resilient coupling across behavioural domains

Cerebellar computations are necessary for fine behavioural control and may rely on internal models for estimation of behaviourally relevant states. Here, we propose that the central cerebellar function is to estimate how states interact with each other, and to use these estimates to coordinates extra-cerebellar neuronal dynamics underpinning a range of interconnected behaviours. To support this claim, we describe a cerebellar model for state estimation that includes state interactions, and link this model with the neuronal architecture and dynamics observed empirically. This is formalised using the free energy principle, which provides a dual perspective on a system in terms of both the dynamics of its physical-in this case neuronal-states, and the inferential process they entail. As a demonstration of this proposal, we simulate cerebellar-dependent synchronisation of whisking and respiration, which are known to be tightly coupled in rodents, as well as limb and tail coordination during locomotion. In summary, we propose that the ubiquitous involvement of the cerebellum in behaviour arises from its central role in precisely coupling behavioural domains.

Mapping the topography of spatial gene expression with interpretable deep learning

Spatially resolved transcriptomics technologies provide high-throughput measurements of gene expression in a tissue slice, but the sparsity of this data complicates the analysis of spatial gene expression patterns such as gene expression gradients. We address these issues by deriving a topographic map of a tissue slice-analogous to a map of elevation in a landscape-using a novel quantity called the isodepth. Contours of constant isodepth enclose spatial domains with distinct cell type composition, while gradients of the isodepth indicate spatial directions of maximum change in gene expression. We develop GASTON, an unsupervised and interpretable deep learning algorithm that simultaneously learns the isodepth, spatial gene expression gradients, and piecewise linear functions of the isodepth that model both continuous gradients and discontinuous spatial variation in the expression of individual genes. We validate GASTON by showing that it accurately identifies spatial domains and marker genes across several biological systems. In SRT data from the brain, GASTON reveals gradients of neuronal differentiation and firing, and in SRT data from a tumor sample, GASTON infers gradients of metabolic activity and epithelial-mesenchymal transition (EMT)-related gene expression in the tumor microenvironment.

Developmental timing-dependent organization of synaptic connections between mossy fibers and granule cells in the cerebellum

The long-standing hypothesis that synapses between mossy fibers (MFs) and cerebellar granule cells (GCs) are organized according to the origins of MFs and locations of GC axons, parallel fibers (PFs), is supported by recent findings. However, the mechanisms of such organized synaptic connections remain unknown. Here, using our technique that enabled PF location-dependent labeling of GCs in mice, we confirmed that synaptic connections of GCs with specific MFs originating from the pontine nucleus (PN-MFs) and dorsal column nuclei (DCoN-MFs) were gently but differentially organized according to their PF locations. We then found that overall MF-GC synaptic connectivity was biased in a way that dendrites of GCs having nearby PFs tended to connect with the same MF terminals, implying that the MF origin- and PF location-dependent organization is associated with the overall biased MF-GC synaptic connectivity. Furthermore, the development of PN-MFs preceded that of DCoN-MFs, which matches the developmental sequence of GCs that preferentially connect with each type of these MFs. Thus, our results revealed that overall MF-GC synaptic connectivity is biased in terms of PF locations, and suggested that such connectivity is likely the result of synaptic formation between developmental timing-matched partners.

Synaptic basis of a sub-second representation of time in a neural circuit model

Temporal sequences of neural activity are essential for driving well-timed behaviors, but the underlying cellular and circuit mechanisms remain elusive. We leveraged the well-defined architecture of the cerebellum, a brain region known to support temporally precise actions, to explore theoretically whether the experimentally observed diversity of short-term synaptic plasticity (STP) at the input layer could generate neural dynamics sufficient for sub-second temporal learning. A cerebellar circuit model equipped with dynamic synapses produced a diverse set of transient granule cell firing patterns that provided a temporal basis set for learning precisely timed pauses in Purkinje cell activity during simulated delay eyelid conditioning and Bayesian interval estimation. The learning performance across time intervals was influenced by the temporal bandwidth of the temporal basis, which was determined by the input layer synaptic properties. The ubiquity of STP throughout the brain positions it as a general, tunable cellular mechanism for sculpting neural dynamics and fine-tuning behavior.

Computational models of neurotransmission at cerebellar synapses unveil the impact on network computation

The neuroscientific field benefits from the conjoint evolution of experimental and computational techniques, allowing for the reconstruction and simulation of complex models of neurons and synapses. Chemical synapses are characterized by presynaptic vesicle cycling, neurotransmitter diffusion, and postsynaptic receptor activation, which eventually lead to postsynaptic currents and subsequent membrane potential changes. These mechanisms have been accurately modeled for different synapses and receptor types (AMPA, NMDA, and GABA) of the cerebellar cortical network, allowing simulation of their impact on computation. Of special relevance is short-term synaptic plasticity, which generates spatiotemporal filtering in local microcircuits and controls burst transmission and information flow through the network. Here, we present how data-driven computational models recapitulate the properties of neurotransmission at cerebellar synapses. The simulation of microcircuit models is starting to reveal how diverse synaptic mechanisms shape the spatiotemporal profiles of circuit activity and computation.

Mesodiencephalic junction GABAergic inputs are processed separately from motor cortical inputs in the basilar pons

The basilar pontine nuclei (bPN) are known to receive excitatory input from the entire neocortex and constitute the main source of mossy fibers to the cerebellum. Various potential inhibitory afferents have been described, but their origin, synaptic plasticity, and network function have remained elusive. Here we identify the mesodiencephalic junction (MDJ) as a prominent source of monosynaptic GABAergic inputs to the bPN. We found no evidence that these inputs converge with motor cortex (M1) inputs at the single neuron or at the local network level. Tracing the inputs to GABAergic MDJ neurons revealed inputs to these neurons from neocortical areas. Additionally, we observed little short-term synaptic facilitation or depression in afferents from the MDJ, enabling MDJ inputs to carry sign-inversed neocortical inputs. Thus, our results show a prominent source of GABAergic inhibition to the bPN that could enrich input to the cerebellar granule cell layer.

The Cerebellar Cortex

The cerebellar cortex is an important system for relating neural circuits and learning. Its promise reflects the longstanding idea that it contains simple, repeated circuit modules with only a few cell types and a single plasticity mechanism that mediates learning according to classical Marr-Albus models. However, emerging data have revealed surprising diversity in neuron types, synaptic connections, and plasticity mechanisms, both locally and regionally within the cerebellar cortex. In light of these findings, it is not surprising that attempts to generate a holistic model of cerebellar learning across different behaviors have not been successful. While the cerebellum remains an ideal system for linking neuronal function with behavior, it is necessary to update the cerebellar circuit framework to achieve its great promise. In this review, we highlight recent advances in our understanding of cerebellar-cortical cell types, synaptic connections, signaling mechanisms, and forms of plasticity that enrich cerebellar processing.

Cerebellar Coordination of Neuronal Communication in Cerebral Cortex

Cognitive processes involve precisely coordinated neuronal communications between multiple cerebral cortical structures in a task specific manner. Rich new evidence now implicates the cerebellum in cognitive functions. There is general agreement that cerebellar cognitive function involves interactions between the cerebellum and cerebral cortical association areas. Traditional views assume reciprocal interactions between one cerebellar and one cerebral cortical site, via closed-loop connections. We offer evidence supporting a new perspective that assigns the cerebellum the role of a coordinator of communication. We propose that the cerebellum participates in cognitive function by modulating the coherence of neuronal oscillations to optimize communications between multiple cortical structures in a task specific manner.

Transcranial direct current stimulation of cerebellum alters spiking precision in cerebellar cortex: A modeling study of cellular responses

Transcranial direct current stimulation (tDCS) of the cerebellum has rapidly raised interest but the effects of tDCS on cerebellar neurons remain unclear. Assessing the cellular response to tDCS is challenging because of the uneven, highly stratified cytoarchitecture of the cerebellum, within which cellular morphologies, physiological properties, and function vary largely across several types of neurons. In this study, we combine MRI-based segmentation of the cerebellum and a finite element model of the tDCS-induced electric field (EF) inside the cerebellum to determine the field imposed on the cerebellar neurons throughout the region. We then pair the EF with multicompartment models of the Purkinje cell (PC), deep cerebellar neuron (DCN), and granule cell (GrC) and quantify the acute response of these neurons under various orientations, physiological conditions, and sequences of presynaptic stimuli. We show that cerebellar tDCS significantly modulates the postsynaptic spiking precision of the PC, which is expressed as a change in the spike count and timing in response to presynaptic stimuli. tDCS has modest effects, instead, on the PC tonic firing at rest and on the postsynaptic activity of DCN and GrC. In Purkinje cells, anodal tDCS shortens the repolarization phase following complex spikes (-14.7 ± 6.5% of baseline value, mean ± S.D.; max: -22.7%) and promotes burstiness with longer bursts compared to resting conditions. Cathodal tDCS, instead, promotes irregular spiking by enhancing somatic excitability and significantly prolongs the repolarization after complex spikes compared to baseline (+37.0 ± 28.9%, mean ± S.D.; max: +84.3%). tDCS-induced changes to the repolarization phase and firing pattern exceed 10% of the baseline values in Purkinje cells covering up to 20% of the cerebellar cortex, with the effects being distributed along the EF direction and concentrated in the area under the electrode over the cerebellum. Altogether, the acute effects of tDCS on cerebellum mainly focus on Purkinje cells and modulate the precision of the response to synaptic stimuli, thus having the largest impact when the cerebellar cortex is active. Since the spatiotemporal precision of the PC spiking is critical to learning and coordination, our results suggest cerebellar tDCS as a viable therapeutic option for disorders involving cerebellar hyperactivity such as ataxia.

Transcranial direct current stimulation (tDCS) of the cerebellum is gaining momentum as a neuromodulation tool for the treatment of neurological diseases like movement disorders. Nonetheless, the response of cells in the cerebellum to tDCS is unclear and hardly generalizes from our understanding of tDCS of the cerebral cortex. We use computational models to investigate the response of several types of cerebellar neurons to the electric field induced by tDCS and show that, differently from the cerebral cortex, tDCS has significant acute effects on the cerebellar cortex. These effects (i) primarily alter the way Purkinje cells encode synaptic stimuli from the molecular layer and (ii) can help hyperactive cells regain postsynaptic spiking precision. Since the spatiotemporal precision of the Purkinje cell spiking is critical to learning and coordination, the study shows how tDCS can operate at the cellular level to treat movement disorders like tremor and ataxia.

Calcium dependence of neurotransmitter release at a high fidelity synapse

The Ca²⁺-dependence of the priming, fusion, and replenishment of synaptic vesicles are fundamental parameters controlling neurotransmitter release and synaptic plasticity. Despite intense efforts, these important steps in the synaptic vesicles’ cycle remain poorly understood due to the technical challenge in disentangling vesicle priming, fusion, and replenishment. Here, we investigated the Ca²⁺-sensitivity of these steps at mossy fiber synapses in the rodent cerebellum, which are characterized by fast vesicle replenishment mediating high-frequency signaling. We found that the basal free Ca²⁺ concentration (<200 nM) critically controls action potential-evoked release, indicating a high-affinity Ca²⁺ sensor for vesicle priming. Ca²⁺ uncaging experiments revealed a surprisingly shallow and non-saturating relationship between release rate and intracellular Ca²⁺ concentration up to 50 μM. The rate of vesicle replenishment during sustained elevated intracellular Ca²⁺ concentration exhibited little Ca²⁺-dependence. Finally, quantitative mechanistic release schemes with five Ca²⁺ binding steps incorporating rapid vesicle replenishment via parallel or sequential vesicle pools could explain our data. We thus show that co-existing high- and low-affinity Ca²⁺ sensors mediate priming, fusion, and replenishment of synaptic vesicles at a high-fidelity synapse.

GluA4 facilitates cerebellar expansion coding and enables associative memory formation

AMPA receptors (AMPARs) mediate excitatory neurotransmission in the central nervous system (CNS) and their subunit composition determines synaptic efficacy. Whereas AMPAR subunits GluA1–GluA3 have been linked to particular forms of synaptic plasticity and learning, the functional role of GluA4 remains elusive. Here, we demonstrate a crucial function of GluA4 for synaptic excitation and associative memory formation in the cerebellum. Notably, GluA4-knockout mice had ~80% reduced mossy fiber to granule cell synaptic transmission. The fidelity of granule cell spike output was markedly decreased despite attenuated tonic inhibition and increased NMDA receptor-mediated transmission. Computational network modeling incorporating these changes revealed that deletion of GluA4 impairs granule cell expansion coding, which is important for pattern separation and associative learning. On a behavioral level, while locomotor coordination was generally spared, GluA4-knockout mice failed to form associative memories during delay eyeblink conditioning. These results demonstrate an essential role for GluA4-containing AMPARs in cerebellar information processing and associative learning.

Projection-dependent heterogeneity of cerebellar granule cell calcium responses

Cerebellar granule cells (GCs) relay mossy fiber (MF) inputs to Purkinje cell dendrites via their axons, the parallel fibers (PFs), which are individually located at a given sublayer of the molecular layer (ML). Although a certain degree of heterogeneity among GCs has been recently reported, variability of GC responses to MF inputs has never been associated with their most notable structural variability, location of their projecting PFs in the ML. Here, we utilize an adeno-associated virus (AAV)-mediated labeling technique that enables us to categorize GCs according to the location of their PFs, and compare the Ca²⁺ responses to MF stimulations between three groups of GCs, consisting of either GCs having PFs at the deep (D-GCs), middle (M-GCs), or superficial (S-GCs) sublayer. Our structural analysis revealed that there was no correlation between position of GC soma in the GC layer and location of its PF in the ML, confirming that our AAV-mediated labeling was important to test the projection-dependent variability of the Ca²⁺ responses in GCs. We then found that the Ca²⁺ responses of D-GCs differed from those of M-GCs. Pharmacological experiments implied that the different Ca²⁺ responses were mainly attributable to varied distributions of GABA_A receptors (GABA_ARs) at the synaptic and extrasynaptic regions of GC dendrites. In addition to GABA_AR distributions, amounts of extrasynaptic NMDA receptors appear to be also varied, because Ca²⁺ responses were different between D-GCs and M-GCs when glutamate spillover was enhanced. Whereas the Ca²⁺ responses of S-GCs were mostly equivalent to those of D-GCs and M-GCs, the blockade of GABA uptake resulted in larger Ca²⁺ responses in S-GCs compared with D-GCs and M-GCs, implying existence of mechanisms leading to more excitability in S-GCs with increased GABA release. Thus, this study reveals MF stimulation-mediated non-uniform Ca²⁺ responses in the cerebellar GCs associated with the location of their PFs in the ML, and raises a possibility that combination of inherent functional variability of GCs and their specific axonal projection contributes to the information processing through the GCs.

Topographic gradients of intrinsic dynamics across neocortex

The intrinsic dynamics of neuronal populations are shaped by both microscale attributes and macroscale connectome architecture. Here we comprehensively characterize the rich temporal patterns of neural activity throughout the human brain. Applying massive temporal feature extraction to regional haemodynamic activity, we systematically estimate over 6000 statistical properties of individual brain regions' time-series across the neocortex. We identify two robust spatial gradients of intrinsic dynamics, one spanning a ventromedial-dorsolateral axis and dominated by measures of signal autocorrelation, and the other spanning a unimodal-transmodal axis and dominated by measures of dynamic range. These gradients reflect spatial patterns of gene expression, intracortical myelin and cortical thickness, as well as structural and functional network embedding. Importantly, these gradients are correlated with patterns of meta-analytic functional activation, differentiating cognitive versus affective processing and sensory versus higher-order cognitive processing. Altogether, these findings demonstrate a link between microscale and macroscale architecture, intrinsic dynamics, and cognition.

Cellular-resolution mapping uncovers spatial adaptive filtering at the rat cerebellum input stage

Long-term synaptic plasticity is thought to provide the substrate for adaptive computation in brain circuits but very little is known about its spatiotemporal organization. Here, we combined multi-spot two-photon laser microscopy in rat cerebellar slices with realistic modeling to map the distribution of plasticity in multi-neuronal units of the cerebellar granular layer. The units, composed by ~300 neurons activated by ~50 mossy fiber glomeruli, showed long-term potentiation concentrated in the core and long-term depression in the periphery. This plasticity was effectively accounted for by an NMDA receptor and calcium-dependent induction rule and was regulated by the inhibitory Golgi cell loops. Long-term synaptic plasticity created effective spatial filters tuning the time-delay and gain of spike retransmission at the cerebellum input stage and provided a plausible basis for the spatiotemporal recoding of input spike patterns anticipated by the motor learning theory.

Casali, Tognolina et al. use two-photon laser microscopy to spatially map long-term synaptic plasticity in rat cerebellar granular cells following stimulation of mossy fibers. Their data allow them to apply realistic modeling to test hypotheses about the synaptic spiking dynamics and reveal the importance of synaptic inhibition to defining these microcircuits.