Synaptic and cellular properties of the feedforward inhibitory circuit within the input layer of the cerebellar cortex

Simple spike patterns and synaptic mechanisms encoding sensory and motor signals in Purkinje cells and the cerebellar nuclei

Whisker stimulation in awake mice evokes transient suppression of simple spike probability in crus I/II Purkinje cells. Here, we investigated how simple spike suppression arises synaptically, what it encodes, and how it affects cerebellar output. In vitro, monosynaptic parallel fiber (PF)-excitatory postsynaptic currents (EPSCs) facilitated strongly, whereas disynaptic inhibitory postsynaptic currents (IPSCs) remained stable, maximizing relative inhibitory strength at the onset of PF activity. Short-term plasticity thus favors the inhibition of Purkinje spikes before PFs facilitate. In vivo, whisker stimulation evoked a 2-6 ms synchronous spike suppression, just 6-8 ms (∼4 synaptic delays) after sensory onset, whereas active whisker movements elicited broadly timed spike rate increases that did not modulate sensory-evoked suppression. Firing in the cerebellar nuclei (CbN) inversely correlated with disinhibition from sensory-evoked simple spike suppressions but was decoupled from slow, non-synchronous movement-associated elevations of Purkinje firing rates. Synchrony thus allows the CbN to high-pass filter Purkinje inputs, facilitating sensory-evoked cerebellar outputs that can drive movements.

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.

A system of feed-forward cerebellar circuits that extend and diversify sensory signaling

Sensory signals are processed by the cerebellum to coordinate movements. Numerous cerebellar functions are thought to require the maintenance of a sensory representation that extends beyond the input signal. Granule cells receive sensory input, but they do not prolong the signal and are thus unlikely to maintain a sensory representation for much longer than the inputs themselves. Unipolar brush cells (UBCs) are excitatory interneurons that project to granule cells and transform sensory input into prolonged increases or decreases in firing, depending on their ON or OFF UBC subtype. Further extension and diversification of the input signal could be produced by UBCs that project to one another, but whether this circuitry exists is unclear. Here we test whether UBCs innervate one another and explore how these small networks of UBCs could transform spiking patterns. We characterized two transgenic mouse lines electrophysiologically and immunohistochemically to confirm that they label ON and OFF UBC subtypes and crossed them together, revealing that ON and OFF UBCs innervate one another. A Brainbow reporter was used to label UBCs of the same ON or OFF subtype with different fluorescent proteins, which showed that UBCs innervate their own subtypes as well. Computational models predict that these feed-forward networks of UBCs extend the length of bursts or pauses and introduce delays-transformations that may be necessary for cerebellar functions from modulation of eye movements to adaptive learning across time scales.

Excitation and Inhibition Delays within a Feedforward Inhibitory Pathway Modulate Cerebellar Purkinje Cell Output in Mice

The cerebellar cortex computes sensorimotor information from many brain areas through a feedforward inhibitory (FFI) microcircuit between the input stage, the granule cell (GC) layer, and the output stage, the Purkinje cells (PCs). Although in other brain areas FFI underlies a precise excitation versus inhibition temporal correlation, recent findings in the cerebellum highlighted more complex behaviors at GC-molecular layer interneuron (MLI)-PC pathway. To dissect the temporal organization of this cerebellar FFI pathway, we combined ex vivo patch-clamp recordings of PCs in male mice with a viral-based strategy to express Channelrhodopsin2 in a subset of mossy fibers (MFs), the major excitatory inputs to GCs. We show that although light-mediated MF activation elicited pairs of excitatory and inhibitory postsynaptic currents in PCs, excitation (E) from GCs and inhibition (I) from MLIs reached PCs with a wide range of different temporal delays. However, when GCs were directly stimulated, a low variability in E/I delays was observed. Our results demonstrate that in many recordings MF stimulation recruited different groups of GCs that trigger E and/or I, and expanded PC temporal synaptic integration. Finally, using a computational model of the FFI pathway, we showed that this temporal expansion could strongly influence how PCs integrate GC inputs. Our findings show that specific E/I delays may help PCs encoding specific MF inputs.SIGNIFICANCE STATEMENT Sensorimotor information is conveyed to the cerebellar cortex by mossy fibers. Mossy fiber inputs activate granule cells that excite molecular interneurons and Purkinje cells, the sole output of the cerebellar cortex, leading to a sequence of synaptic excitation and inhibition in Purkinje cells, thus defining a feedforward inhibitory pathway. Using electrophysiological recordings, optogenetic stimulation, and mathematical modeling, we demonstrated that different groups of granule cells can elicit synaptic excitation and inhibition with various latencies onto Purkinje cells. This temporal variability controls how granule cells influence Purkinje cell discharge and may support temporal coding in the cerebellar cortex.

Neurotransmitter content heterogeneity within an interneuron class shapes inhibitory transmission at a central synapse

Neurotransmitter content is deemed the most basic defining criterion for neuronal classes, contrasting with the intercellular heterogeneity of many other molecular and functional features. Here we show, in the adult mouse brain, that neurotransmitter content variegation within a neuronal class is a component of its functional heterogeneity. Golgi cells (GoCs), the well-defined class of cerebellar interneurons inhibiting granule cells (GrCs), contain cytosolic glycine, accumulated by the neuronal transporter GlyT2, and GABA in various proportions. By performing acute manipulations of cytosolic GABA and glycine supply, we find that competition of glycine with GABA reduces the charge of IPSC evoked in GrCs and, more specifically, the amplitude of a slow component of the IPSC decay. We then pair GrCs recordings with optogenetic stimulations of single GoCs, which preserve the intracellular transmitter mixed content. We show that the strength and decay kinetics of GrCs IPSCs, which are entirely mediated by GABAA receptors, are negatively correlated to the presynaptic expression of GlyT2 by GoCs. We isolate a slow spillover component of GrCs inhibition that is also affected by the expression of GlyT2, leading to a 56% decrease in relative charge. Our results support the hypothesis that presynaptic loading of glycine negatively impacts the GABAergic transmission in mixed interneurons, most likely through a competition for vesicular filling. We discuss how the heterogeneity of neurotransmitter supply within mixed interneurons like the GoC class may provide a presynaptic mechanism to tune the gain of microcircuits such as the granular layer, thereby expanding the realm of their possible dynamic behaviors.

An emergent temporal basis set robustly supports cerebellar time-series learning

The cerebellum is considered a "learning machine" essential for time interval estimation underlying motor coordination and other behaviors. Theoretical work has proposed that the cerebellum's input recipient structure, the granule cell layer (GCL), performs pattern separation of inputs that facilitates learning in Purkinje cells (P-cells). However, the relationship between input reformatting and learning has remained debated, with roles emphasized for pattern separation features from sparsification to decorrelation. We took a novel approach by training a minimalist model of the cerebellar cortex to learn complex time-series data from time-varying inputs, typical during movements. The model robustly produced temporal basis sets from these inputs, and the resultant GCL output supported better learning of temporally complex target functions than mossy fibers alone. Learning was optimized at intermediate threshold levels, supporting relatively dense granule cell activity, yet the key statistical features in GCL population activity that drove learning differed from those seen previously for classification tasks. These findings advance testable hypotheses for mechanisms of temporal basis set formation and predict that moderately dense population activity optimizes learning.NEW & NOTEWORTHY During movement, mossy fiber inputs to the cerebellum relay time-varying information with strong intrinsic relationships to ongoing movement. Are such mossy fibers signals sufficient to support Purkinje signals and learning? In a model, we show how the GCL greatly improves Purkinje learning of complex, temporally dynamic signals relative to mossy fibers alone. Learning-optimized GCL population activity was moderately dense, which retained intrinsic input variance while also performing pattern separation.

Long-Term Synaptic Plasticity Tunes the Gain of Information Channels through the Cerebellum Granular Layer

A central hypothesis on brain functioning is that long-term potentiation (LTP) and depression (LTD) regulate the signals transfer function by modifying the efficacy of synaptic transmission. In the cerebellum, granule cells have been shown to control the gain of signals transmitted through the mossy fiber pathway by exploiting synaptic inhibition in the glomeruli. However, the way LTP and LTD control signal transformation at the single-cell level in the space, time and frequency domains remains unclear. Here, the impact of LTP and LTD on incoming activity patterns was analyzed by combining patch-clamp recordings in acute cerebellar slices and mathematical modeling. LTP reduced the delay, increased the gain and broadened the frequency bandwidth of mossy fiber burst transmission, while LTD caused opposite changes. These properties, by exploiting NMDA subthreshold integration, emerged from microscopic changes in spike generation in individual granule cells such that LTP anticipated the emission of spikes and increased their number and precision, while LTD sorted the opposite effects. Thus, akin with the expansion recoding process theoretically attributed to the cerebellum granular layer, LTP and LTD could implement selective filtering lines channeling information toward the molecular and Purkinje cell layers for further processing.

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.

Towards the Simulation of a Realistic Large-Scale Spiking Network on a Desktop Multi-GPU System

The reproduction of the brain ’sactivity and its functionality is the main goal of modern neuroscience. To this aim, several models have been proposed to describe the activity of single neurons at different levels of detail. Then, single neurons are linked together to build a network, in order to reproduce complex behaviors. In the literature, different network-building rules and models have been described, targeting realistic distributions and connections of the neurons. In particular, the Granular layEr Simulator (GES) performs the granular layer network reconstruction considering biologically realistic rules to connect the neurons. Moreover, it simulates the network considering the Hodgkin–Huxley model. The work proposed in this paper adopts the network reconstruction model of GES and proposes a simulation module based on Leaky Integrate and Fire (LIF) model. This simulator targets the reproduction of the activity of large scale networks, exploiting the GPU technology to reduce the processing times. Experimental results show that a multi-GPU system reduces the simulation of a network with more than 1.8 million neurons from approximately 54 to 13 h.

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.

Candelabrum cells are ubiquitous cerebellar cortex interneurons with specialized circuit properties

To understand how the cerebellar cortex transforms mossy fiber (MF) inputs into Purkinje cell (PC) outputs, it is vital to delineate the elements of this circuit. Candelabrum cells (CCs) are enigmatic interneurons of the cerebellar cortex that have been identified based on their morphology, but their electrophysiological properties, synaptic connections and function remain unknown. Here, we clarify these properties using electrophysiology, single-nucleus RNA sequencing, in situ hybridization and serial electron microscopy in mice. We find that CCs are the most abundant PC layer interneuron. They are GABAergic, molecularly distinct and present in all cerebellar lobules. Their high resistance renders CC firing highly sensitive to synaptic inputs. CCs are excited by MFs and granule cells and are strongly inhibited by PCs. CCs in turn primarily inhibit molecular layer interneurons, which leads to PC disinhibition. Thus, inputs, outputs and local signals converge onto CCs to allow them to assume a unique role in controlling cerebellar output.

The anterior paired lateral neuron normalizes odour-evoked activity in the Drosophila mushroom body calyx

To identify and memorize discrete but similar environmental inputs, the brain needs to distinguish between subtle differences of activity patterns in defined neuronal populations. The Kenyon cells (KCs) of the Drosophila adult mushroom body (MB) respond sparsely to complex olfactory input, a property that is thought to support stimuli discrimination in the MB. To understand how this property emerges, we investigated the role of the inhibitory anterior paired lateral (APL) neuron in the input circuit of the MB, the calyx. Within the calyx, presynaptic boutons of projection neurons (PNs) form large synaptic microglomeruli (MGs) with dendrites of postsynaptic KCs. Combining electron microscopy (EM) data analysis and in vivo calcium imaging, we show that APL, via inhibitory and reciprocal synapses targeting both PN boutons and KC dendrites, normalizes odour-evoked representations in MGs of the calyx. APL response scales with the PN input strength and is regionalized around PN input distribution. Our data indicate that the formation of a sparse code by the KCs requires APL-driven normalization of their MG postsynaptic responses. This work provides experimental insights on how inhibition shapes sensory information representation in a higher brain centre, thereby supporting stimuli discrimination and allowing for efficient associative memory formation.

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.

Connecting Biological Detail With Neural Computation: Application to the Cerebellar Granule-Golgi Microcircuit

Neurophysiology and neuroanatomy constrain the set of possible computations that can be performed in a brain circuit. While detailed data on brain microcircuits is sometimes available, cognitive modelers are seldom in a position to take these constraints into account. One reason for this is the intrinsic complexity of accounting for biological mechanisms when describing cognitive function. In this paper, we present multiple extensions to the neural engineering framework (NEF), which simplify the integration of low-level constraints such as Dale's principle and spatially constrained connectivity into high-level, functional models. We focus on a model of eyeblink conditioning in the cerebellum, and, in particular, on systematically constructing temporal representations in the recurrent granule-Golgi microcircuit. We analyze how biological constraints impact these representations and demonstrate that our overall model is capable of reproducing key properties of eyeblink conditioning. Furthermore, since our techniques facilitate variation of neurophysiological parameters, we gain insights into why certain neurophysiological parameters may be as observed in nature. While eyeblink conditioning is a somewhat primitive form of learning, we argue that the same methods apply for more cognitive models as well. We implemented our extensions to the NEF in an open-source software library named "NengoBio" and hope that this work inspires similar attempts to bridge low-level biological detail and high-level function.

Regulating synchronous oscillations of cerebellar granule cells by different types of inhibition

Synchronous oscillations in neural populations are considered being controlled by inhibitory neurons. In the granular layer of the cerebellum, two major types of cells are excitatory granular cells (GCs) and inhibitory Golgi cells (GoCs). GC spatiotemporal dynamics, as the output of the granular layer, is highly regulated by GoCs. However, there are various types of inhibition implemented by GoCs. With inputs from mossy fibers, GCs and GoCs are reciprocally connected to exhibit different network motifs of synaptic connections. From the view of GCs, feedforward inhibition is expressed as the direct input from GoCs excited by mossy fibers, whereas feedback inhibition is from GoCs via GCs themselves. In addition, there are abundant gap junctions between GoCs showing another form of inhibition. It remains unclear how these diverse copies of inhibition regulate neural population oscillation changes. Leveraging a computational model of the granular layer network, we addressed this question to examine the emergence and modulation of network oscillation using different types of inhibition. We show that at the network level, feedback inhibition is crucial to generate neural oscillation. When short-term plasticity was equipped on GoC-GC synapses, oscillations were largely diminished. Robust oscillations can only appear with additional gap junctions. Moreover, there was a substantial level of cross-frequency coupling in oscillation dynamics. Such a coupling was adjusted and strengthened by GoCs through feedback inhibition. Taken together, our results suggest that the cooperation of distinct types of GoC inhibition plays an essential role in regulating synchronous oscillations of the GC population. With GCs as the sole output of the granular network, their oscillation dynamics could potentially enhance the computational capability of downstream neurons.

Multidimensional population activity in an electrically coupled inhibitory circuit in the cerebellar cortex

Inhibitory neurons orchestrate the activity of excitatory neurons and play key roles in circuit function. Although individual interneurons have been studied extensively, little is known about their properties at the population level. Using random-access 3D two-photon microscopy, we imaged local populations of cerebellar Golgi cells (GoCs), which deliver inhibition to granule cells. We show that population activity is organized into multiple modes during spontaneous behaviors. A slow, network-wide common modulation of GoC activity correlates with the level of whisking and locomotion, while faster (<1 s) differential population activity, arising from spatially mixed heterogeneous GoC responses, encodes more precise information. A biologically detailed GoC circuit model reproduced the common population mode and the dimensionality observed experimentally, but these properties disappeared when electrical coupling was removed. Our results establish that local GoC circuits exhibit multidimensional activity patterns that could be used for inhibition-mediated adaptive gain control and spatiotemporal patterning of downstream granule cells.

Astroglial Cx30 differentially impacts synaptic activity from hippocampal principal cells and interneurons

Astrocytes play important roles in brain function via dynamic structural and functional interactions with neurons. Yet the underlying mechanisms remain poorly defined. A typical feature of astrocytes is the high expression of connexins, which mediate their extensive intercellular communication and regulate their structural properties. In particular, connexin 30 (Cx30), one of the two connexins abundantly expressed by astrocytes, was recently shown to be a critical regulator of excitatory synaptic transmission by controlling the astroglial coverage of synapses. However, the role of Cx30 in the regulation of inhibitory synaptic transmission and excitatory/inhibitory balance remains elusive. Here, we investigated the role of astroglial Cx30 on the electrophysiological and morphological properties of five classes of hippocampal CA1 stratum oriens and pyramidale neurons, defined by the unsupervised Ward's clustering. Using Cx30 knockout mice, we found that Cx30 alters specific properties of some subsets of CA1 interneurons, such as resting membrane potential and sag ratio, while other parameters, such as action potential threshold and saturation frequency, were more frequently altered among the different classes of neurons. The excitation-inhibition balance was also differentially and selectively modulated among the different neuron subtypes. Only slight morphological differences were observed on reconstructed neurons. Altogether, these data indicate that Cx30 differentially alters the electrophysiological and morphological properties of hippocampal cell populations, and modulates both their excitatory and inhibitory inputs. Astrocytes, via Cx30, are thus active modulators of both excitatory and inhibitory synapses in the hippocampus.

Calcium Channel-Dependent Induction of Long-Term Synaptic Plasticity at Excitatory Golgi Cell Synapses of Cerebellum

Golgi cells, together with granule cells and mossy fibers, form a neuronal microcircuit regulating information transfer at the cerebellum input stage. Despite theoretical predictions, little was known about long-term synaptic plasticity at Golgi cell synapses. Here, we have used whole-cell patch-clamp recordings and calcium imaging to investigate long-term synaptic plasticity at excitatory synapses impinging on Golgi cells. In acute mouse cerebellar slices, mossy fiber theta-burst stimulation (TBS) could induce either long-term potentiation (LTP) or long-term depression (LTD) at mossy fiber-Golgi cell and granule cell-Golgi cell synapses. This synaptic plasticity showed a peculiar voltage dependence, with LTD or LTP being favored when TBS induction occurred at depolarized or hyperpolarized potentials, respectively. LTP required, in addition to NMDA channels, activation of T-type Ca²⁺ channels, while LTD required uniquely activation of L-type Ca²⁺ channels. Notably, the voltage dependence of plasticity at the mossy fiber-Golgi cell synapses was inverted with respect to pure NMDA receptor-dependent plasticity at the neighboring mossy fiber-granule cell synapse, implying that the mossy fiber presynaptic terminal can activate different induction mechanisms depending on the target cell. In aggregate, this result shows that Golgi cells show cell-specific forms of long-term plasticity at their excitatory synapses, that could play a crucial role in sculpting the response patterns of the cerebellar granular layer.SIGNIFICANCE STATEMENT This article shows for the first time a novel form of Ca²⁺ channel-dependent synaptic plasticity at the excitatory synapses impinging on cerebellar Golgi cells. This plasticity is bidirectional and inverted with respect to NMDA receptor-dependent paradigms, with long-term depression (LTD) and long-term potentiation (LTP) being favored at depolarized and hyperpolarized potentials, respectively. Furthermore, LTP and LTD induction requires differential involvement of T-type and L-type voltage-gated Ca²⁺ channels rather than the NMDA receptors alone. These results, along with recent computational predictions, support the idea that Golgi cell plasticity could play a crucial role in controlling information flow through the granular layer along with cerebellar learning and memory.

Accounting for uncertainty: inhibition for neural inference in the cerebellum

Sensorimotor coordination is thought to rely on cerebellar-based internal models for state estimation, but the underlying neural mechanisms and specific contribution of the cerebellar components is unknown. A central aspect of any inferential process is the representation of uncertainty or conversely precision characterizing the ensuing estimates. Here, we discuss the possible contribution of inhibition to the encoding of precision of neural representations in the granular layer of the cerebellar cortex. Within this layer, Golgi cells influence excitatory granule cells, and their action is critical in shaping information transmission downstream to Purkinje cells. In this review, we equate the ensuing excitation-inhibition balance in the granular layer with the outcome of a precision-weighted inferential process, and highlight the physiological characteristics of Golgi cell inhibition that are consistent with such computations.

Granular layEr Simulator: Design and Multi-GPU Simulation of the Cerebellar Granular Layer

In modern computational modeling, neuroscientists need to reproduce long-lasting activity of large-scale networks, where neurons are described by highly complex mathematical models. These aspects strongly increase the computational load of the simulations, which can be efficiently performed by exploiting parallel systems to reduce the processing times. Graphics Processing Unit (GPU) devices meet this need providing on desktop High Performance Computing. In this work, authors describe a novel Granular layEr Simulator development implemented on a multi-GPU system capable of reconstructing the cerebellar granular layer in a 3D space and reproducing its neuronal activity. The reconstruction is characterized by a high level of novelty and realism considering axonal/dendritic field geometries, oriented in the 3D space, and following convergence/divergence rates provided in literature. Neurons are modeled using Hodgkin and Huxley representations. The network is validated by reproducing typical behaviors which are well-documented in the literature, such as the center-surround organization. The reconstruction of a network, whose volume is 600 × 150 × 1,200 μm³ with 432,000 granules, 972 Golgi cells, 32,399 glomeruli, and 4,051 mossy fibers, takes 235 s on an Intel i9 processor. The 10 s activity reproduction takes only 4.34 and 3.37 h exploiting a single and multi-GPU desktop system (with one or two NVIDIA RTX 2080 GPU, respectively). Moreover, the code takes only 3.52 and 2.44 h if run on one or two NVIDIA V100 GPU, respectively. The relevant speedups reached (up to ~38× in the single-GPU version, and ~55× in the multi-GPU) clearly demonstrate that the GPU technology is highly suitable for realistic large network simulations.

How and Why the Cerebellum Recodes Input Signals: An Alternative to Machine Learning

Mossy fiber input to the cerebellum is received by granule cells where it is thought to be recoded into internal signals received by Purkinje cells, which alone carry the output of the cerebellar cortex. In any neural network, variables are contained in groups of signals as well as signals themselves—which cells are active and how many, for example, and statistical variables coded in rates, such as the mean and range, and which rates are strongly represented, in a defined population. We argue that the primary function of recoding is to confine translation to an effect of some variables and not others—both where input is recoded into internal signals and the translation downstream of internal signals into an effect on Purkinje cells. The cull of variables is harsh. Internal signaling is group coded. This allows coding to exploit statistics for a reliable and precise effect despite needing to work with high-dimensional input which is a highly unpredictably variable. An important effect is to normalize eclectic input signals, so that the basic, repeating cerebellar circuit, preserved across taxa, does not need to specialize (within regional variations). With this model, there is no need to slavishly conserve or compute data coded in single signals. If we are correct, a learning algorithm—for years, a mainstay of cerebellar modeling—would be redundant.

Cerebellar Golgi cell models predict dendritic processing and mechanisms of synaptic plasticity

The Golgi cells are the main inhibitory interneurons of the cerebellar granular layer. Although recent works have highlighted the complexity of their dendritic organization and synaptic inputs, the mechanisms through which these neurons integrate complex input patterns remained unknown. Here we have used 8 detailed morphological reconstructions to develop multicompartmental models of Golgi cells, in which Na, Ca, and K channels were distributed along dendrites, soma, axonal initial segment and axon. The models faithfully reproduced a rich pattern of electrophysiological and pharmacological properties and predicted the operating mechanisms of these neurons. Basal dendrites turned out to be more tightly electrically coupled to the axon initial segment than apical dendrites. During synaptic transmission, parallel fibers caused slow Ca-dependent depolarizations in apical dendrites that boosted the axon initial segment encoder and Na-spike backpropagation into basal dendrites, while inhibitory synapses effectively shunted backpropagating currents. This oriented dendritic processing set up a coincidence detector controlling voltage-dependent NMDA receptor unblock in basal dendrites, which, by regulating local calcium influx, may provide the basis for spike-timing dependent plasticity anticipated by theory.

Compartmentalized Input-Output Organization of Lugaro Cells in the Cerebellar Cortex

Purkinje cells (PCs) are principal cerebellar neurons, and several classes of interneurons modulate their activity. Lugaro cells (LCs) are one such inhibitory interneuron with distinctive cytology and location, but still most enigmatic among cerebellar neurons. Here we serendipitously produced a novel transgenic mouse line, where a half of Yellow Cameleon (YC)(+) cells in the cerebellar cortex were judged to be LCs, and YC(+) LCs were estimated to constitute one-third of the total LC populations. Neurochemically, two-thirds of YC(+) LCs were dually GABAergic/glycinergic, with the rest being GABAergic. Beneath the PC layer, they extended a sheet of somatodendritic meshwork interconnected with neighboring LCs by adherens junctions, and received various inputs from climbing fibers, mossy fibers, granule cell axons, recurrent PC axons, Golgi cell axons, LC axons, and serotonergic fibers. Intriguingly, somatodendritic elements of individual LCs preferentially extended within a given cerebellar compartment defined by aldolase C expression. In turn, YC(+) LCs projected a dense lattice of ascending and transverse axons to the molecular layer, and innervated molecular layer interneurons (basket and stellate cells) and Golgi cells, but not PCs. Of note, ascending axons profusely innervated individual targets within a cerebellar compartment, while transverse axons ran across several compartments and innervated targets sparsely. This unique circuit configuration highlights that LCs integrate various excitatory, inhibitory, and modulatory inputs coming to the belonging cerebellar compartment and that, as an interneuron-selective interneuron, LCs can effectively disinhibit cerebellar cortical activities in a compartment-dependent manner through inhibition of inhibitory interneurons selectively targeting PCs and granule cells.

Frequency-dependent gating of feedforward inhibition in thalamofrontal synapses

Thalamic recruitment of feedforward inhibition is known to enhance the fidelity of the receptive field by limiting the temporal window during which cortical neurons integrate excitatory inputs. Feedforward inhibition driven by the mediodorsal nucleus of the thalamus (MD) has been previously observed, but its physiological function and regulation remain unknown. Accumulating evidence suggests that elevated neuronal activity in the prefrontal cortex is required for the short-term storage of information. Furthermore, the elevated neuronal activity is supported by the reciprocal connectivity between the MD and the medial prefrontal cortex (mPFC). Therefore, detailed knowledge about the synaptic connections during high-frequency activity is critical for understanding the mechanism of short-term memory. In this study, we examined how feedforward inhibition of thalamofrontal connectivity is modulated by activity frequency. We observed greater short-term synaptic depression during disynaptic inhibition than in thalamic excitatory synapses during high-frequency activities. The strength of feedforward inhibition became weaker as the stimulation continued, which, in turn, enhanced the range of firing jitter in a frequency-dependent manner. We postulated that this phenomenon was primarily due to the increased failure rate of evoking action potentials in parvalbumin-expressing inhibitory neurons. These findings suggest that the MD-mPFC pathway is dynamically regulated by an excitatory-inhibitory balance in an activity-dependent manner. During low-frequency activities, excessive excitations are inhibited, and firing is restricted to a limited temporal range by the strong feedforward inhibition. However, during high-frequency activities, such as during short-term memory, the activity can be transferred in a broader temporal range due to the decreased feedforward inhibition.

Synaptic Specificity and Application of Anterograde Transsynaptic AAV for Probing Neural Circuitry

Revealing the organization and function of neural circuits is greatly facilitated by viral tools that spread transsynaptically. Adeno-associated virus (AAV) exhibits anterograde transneuronal transport, however, the synaptic specificity of this spread and its broad application within a diverse set of circuits remains to be explored. Here, using anatomic, functional, and molecular approaches, we provide evidence for the preferential transport of AAV1 to postsynaptically connected neurons and reveal its spread is strongly dependent on synaptic transmitter release. In addition to glutamatergic pathways, AAV1 also spreads through GABAergic synapses to both excitatory and inhibitory cell types. We observed little or no transport, however, through neuromodulatory projections (e.g., serotonergic, cholinergic, and noradrenergic). In addition, we found that AAV1 can be transported through long-distance descending projections from various brain regions to effectively transduce spinal cord neurons. Combined with newly designed intersectional and sparse labeling strategies, AAV1 can be applied within a wide variety of pathways to categorize neurons according to their input sources, morphology, and molecular identities. These properties make AAV1 a promising anterograde transsynaptic tool for establishing a comprehensive cell-atlas of the brain, although its capacity for retrograde transport currently limits its use to unidirectional circuits.SIGNIFICANCE STATEMENT The discovery of anterograde transneuronal spread of AAV1 generates great promise for its application as a unique tool for manipulating input-defined cell populations and mapping their outputs. However, several outstanding questions remain for anterograde transsynaptic approaches in the field: (1) whether AAV1 spreads exclusively or specifically to synaptically connected neurons, and (2) how broad its application could be in various types of neural circuits in the brain. This study provides several lines of evidence in terms of anatomy, functional innervation, and underlying mechanisms, to strongly support that AAV1 anterograde transneuronal spread is highly synapse specific. In addition, several potentially important applications of transsynaptic AAV1 in probing neural circuits are described.

Cerebellar Development and Circuit Maturation: A Common Framework for Spinocerebellar Ataxias

Spinocerebellar ataxias (SCAs) affect the cerebellum and its afferent and efferent systems that degenerate during disease progression. In the cerebellum, Purkinje cells (PCs) are the most vulnerable and their prominent loss in the late phase of the pathology is the main characteristic of these neurodegenerative diseases. Despite the constant advancement in the discovery of affected molecules and cellular pathways, a comprehensive description of the events leading to the development of motor impairment and degeneration is still lacking. However, in the last years the possible causal role for altered cerebellar development and neuronal circuit wiring in SCAs has been emerging. Not only wiring and synaptic transmission deficits are a common trait of SCAs, but also preventing the expression of the mutant protein during cerebellar development seems to exert a protective role. By discussing this tight relationship between cerebellar development and SCAs, in this review, we aim to highlight the importance of cerebellar circuitry for the investigation of SCAs.

Acetylcholine Modulates Cerebellar Granule Cell Spiking by Regulating the Balance of Synaptic Excitation and Inhibition

Sensorimotor integration in the cerebellum is essential for refining motor output, and the first stage of this processing occurs in the granule cell layer. Recent evidence suggests that granule cell layer synaptic integration can be contextually modified, although the circuit mechanisms that could mediate such modulation remain largely unknown. Here we investigate the role of ACh in regulating granule cell layer synaptic integration in male rats and mice of both sexes. We find that Golgi cells, interneurons that provide the sole source of inhibition to the granule cell layer, express both nicotinic and muscarinic cholinergic receptors. While acute ACh application can modestly depolarize some Golgi cells, the net effect of longer, optogenetically induced ACh release is to strongly hyperpolarize Golgi cells. Golgi cell hyperpolarization by ACh leads to a significant reduction in both tonic and evoked granule cell synaptic inhibition. ACh also reduces glutamate release from mossy fibers by acting on presynaptic muscarinic receptors. Surprisingly, despite these consistent effects on Golgi cells and mossy fibers, ACh can either increase or decrease the spike probability of granule cells as measured by noninvasive cell-attached recordings. By constructing an integrate-and-fire model of granule cell layer population activity, we find that the direction of spike rate modulation can be accounted for predominately by the initial balance of excitation and inhibition onto individual granule cells. Together, these experiments demonstrate that ACh can modulate population-level granule cell responses by altering the ratios of excitation and inhibition at the first stage of cerebellar processing.SIGNIFICANCE STATEMENT The cerebellum plays a key role in motor control and motor learning. While it is known that behavioral context can modify motor learning, the circuit basis of such modulation has remained unclear. Here we find that a key neuromodulator, ACh, can alter the balance of excitation and inhibition at the first stage of cerebellar processing. These results suggest that ACh could play a key role in altering cerebellar learning by modifying how sensorimotor input is represented at the input layer of the cerebellum.

Implementation of an Advanced Frequency-Based Hebbian Spike Timing Dependent Plasticity

The brain is provided with an enormous computing capability and exploits neural plasticity to store and elaborate complex information. One of the multiple mechanisms that neural circuits express is the Spike-timing-dependent plasticity (STDP), a form of long-term synaptic plasticity exploiting the time relationship between pre- and post-synaptic action potentials (i.e., neuron spikes). It has been found that in certain cases, for instance at the input stage of the cerebellum, between mossy fibers and granular neurons, the plasticity is not only driven by the timing of the spikes, but also by the oscillation frequency of the inputs. This complex behaviour has been implemented in this work, where we developed a novel form of advanced synaptic plasticity model to be used in a well-established neural network simulator (NEST). The subsequent tests proved the proper functioning of the plasticity and its range of applicability, demonstrating the possibility to adopt it in noisy and variable conditions, similar to the biological settings.

Diverse Neuron Properties and Complex Network Dynamics in the Cerebellar Cortical Inhibitory Circuit

Neuronal inhibition can be defined as a spatiotemporal restriction or suppression of local microcircuit activity. The importance of inhibition relies in its fundamental role in shaping signal processing in single neurons and neuronal circuits. In this context, the activity of inhibitory interneurons proved the key to endow networks with complex computational and dynamic properties. In the last 50 years, the prevailing view on the functional role of cerebellar cortical inhibitory circuits was that excitatory and inhibitory inputs sum spatially and temporally in order to determine the motor output through Purkinje cells (PCs). Consequently, cerebellar inhibition has traditionally been conceived in terms of restricting or blocking excitation. This assumption has been challenged, in particular in the cerebellar cortex where all neurons except granule cells (and unipolar brush cells in specific lobules) are inhibitory and fire spontaneously at high rates. Recently, a combination of electrophysiological recordings in vitro and in vivo, imaging, optogenetics and computational modeling, has revealed that inhibitory interneurons play a much more complex role in regulating cerebellar microcircuit functions: inhibition shapes neuronal response dynamics in the whole circuit and eventually regulate the PC output. This review elaborates current knowledge on cerebellar inhibitory interneurons [Golgi cells, Lugaro cells (LCs), basket cells (BCs) and stellate cells (SCs)], starting from their ontogenesis and moving up to their morphological, physiological and plastic properties, and integrates this knowledge with that on the more renown granule cells and PCs. We will focus on the circuit loops in which these interneurons are involved and on the way they generate feed-forward, feedback and lateral inhibition along with complex spatio-temporal response dynamics. In this perspective, inhibitory interneurons emerge as the real controllers of cerebellar functioning.

Response Dynamics in an Olivocerebellar Spiking Neural Network With Non-linear Neuron Properties

Sensorimotor signals are integrated and processed by the cerebellar circuit to predict accurate control of actions. In order to investigate how single neuron dynamics and geometrical modular connectivity affect cerebellar processing, we have built an olivocerebellar Spiking Neural Network (SNN) based on a novel simplification algorithm for single point models (Extended Generalized Leaky Integrate and Fire, EGLIF) capturing essential non-linear neuronal dynamics (e.g., pacemaking, bursting, adaptation, oscillation and resonance). EGLIF models specifically tuned for each neuron type were embedded into an olivocerebellar scaffold reproducing realistic spatial organization and physiological convergence and divergence ratios of connections. In order to emulate the circuit involved in an eye blink response to two associated stimuli, we modeled two adjacent olivocerebellar microcomplexes with a common mossy fiber input but different climbing fiber inputs (either on or off). EGLIF-SNN model simulations revealed the emergence of fundamental response properties in Purkinje cells (burst-pause) and deep nuclei cells (pause-burst) similar to those reported in vivo. The expression of these properties depended on the specific activation of climbing fibers in the microcomplexes and did not emerge with scaffold models using simplified point neurons. This result supports the importance of embedding SNNs with realistic neuronal dynamics and appropriate connectivity and anticipates the scale-up of EGLIF-SNN and the embedding of plasticity rules required to investigate cerebellar functioning at multiple scales.

Reconstruction and Simulation of a Scaffold Model of the Cerebellar Network

Reconstructing neuronal microcircuits through computational models is fundamental to simulate local neuronal dynamics. Here a scaffold model of the cerebellum has been developed in order to flexibly place neurons in space, connect them synaptically, and endow neurons and synapses with biologically-grounded mechanisms. The scaffold model can keep neuronal morphology separated from network connectivity, which can in turn be obtained from convergence/divergence ratios and axonal/dendritic field 3D geometries. We first tested the scaffold on the cerebellar microcircuit, which presents a challenging 3D organization, at the same time providing appropriate datasets to validate emerging network behaviors. The scaffold was designed to integrate the cerebellar cortex with deep cerebellar nuclei (DCN), including different neuronal types: Golgi cells, granule cells, Purkinje cells, stellate cells, basket cells, and DCN principal cells. Mossy fiber inputs were conveyed through the glomeruli. An anisotropic volume (0.077 mm³) of mouse cerebellum was reconstructed, in which point-neuron models were tuned toward the specific discharge properties of neurons and were connected by exponentially decaying excitatory and inhibitory synapses. Simulations using both pyNEST and pyNEURON showed the emergence of organized spatio-temporal patterns of neuronal activity similar to those revealed experimentally in response to background noise and burst stimulation of mossy fiber bundles. Different configurations of granular and molecular layer connectivity consistently modified neuronal activation patterns, revealing the importance of structural constraints for cerebellar network functioning. The scaffold provided thus an effective workflow accounting for the complex architecture of the cerebellar network. In principle, the scaffold can incorporate cellular mechanisms at multiple levels of detail and be tuned to test different structural and functional hypotheses. A future implementation using detailed 3D multi-compartment neuron models and dynamic synapses will be needed to investigate the impact of single neuron properties on network computation.

Re-evaluating Circuit Mechanisms Underlying Pattern Separation

When animals interact with complex environments, their neural circuits must separate overlapping patterns of activity that represent sensory and motor information. Pattern separation is thought to be a key function of several brain regions, including the cerebellar cortex, insect mushroom body, and dentate gyrus. However, recent findings have questioned long-held ideas on how these circuits perform this fundamental computation. Here, we re-evaluate the functional and structural mechanisms underlying pattern separation. We argue that the dimensionality of the space available for population codes representing sensory and motor information provides a common framework for understanding pattern separation. We then discuss how these three circuits use different strategies to separate activity patterns and facilitate associative learning in the presence of trial-to-trial variability.

Pathway-Specific Drive of Cerebellar Golgi Cells Reveals Integrative Rules of Cortical Inhibition

Cerebellar granule cells (GrCs) constitute over half of all neurons in the vertebrate brain and are proposed to decorrelate convergent mossy fiber (MF) inputs in service of learning. Interneurons within the GrC layer, Golgi cells (GoCs), are the primary inhibitors of this vast population and therefore play a major role in influencing the computations performed within the layer. Despite this central function for GoCs, few studies have directly examined how GoCs integrate inputs from specific afferents, which vary in density to regulate GrC population activity. We used a variety of methods in mice of either sex to study feedforward inhibition recruited by identified MFs, focusing on features that would influence integration by GrCs. Comprehensive 3D reconstruction and quantification of GoC axonal boutons revealed tightly clustered boutons that focus feedforward inhibition in the neighborhood of GoC somata. Acute whole-cell patch-clamp recordings from GrCs in brain slices showed that, despite high GoC bouton density, fast phasic inhibition was very sparse relative to slow spillover mediated inhibition. Dynamic-clamp simulating inhibition combined with optogenetic MF activation at moderate rates supported a predominant role of slow spillover mediated inhibition in reducing GrC activity. Whole-cell recordings from GoCs revealed a role for the density of active MFs in preferentially driving them. Thus, our data provide empirical confirmation of predicted rules by which MFs activate GoCs to regulate GrC activity levels.SIGNIFICANCE STATEMENT A unifying framework in neural circuit analysis is identifying circuit motifs that subserve common computations. Wide-field inhibitory interneurons globally inhibit neighbors and have been studied extensively in the insect olfactory system and proposed to serve pattern separation functions. Cerebellar Golgi cells (GoCs), a type of mammalian wide-field inhibitory interneuron observed in the granule cell layer, are well suited to perform normalization or pattern separation functions, but the relationship between spatial characteristics of input patterns to GoC-mediated inhibition has received limited attention. This study provides unprecedented quantitative structural details of GoCs and identifies a role for population input activity levels in recruiting inhibition using in vitro electrophysiology and optogenetics.

Serotonin regulates dynamics of cerebellar granule cell activity by modulating tonic inhibition

Understanding how afferent information is integrated by cortical structures requires identifying the factors shaping excitation and inhibition within their input layers. The input layer of the cerebellar cortex integrates diverse sensorimotor information to enable learned associations that refine the dynamics of movement. Specifically, mossy fiber afferents relay sensorimotor input into the cerebellum to excite granule cells, whose activity is regulated by inhibitory Golgi cells. To test how this integration can be modulated, we have used an acute brain slice preparation from young adult rats and found that encoding of mossy fiber input in the cerebellar granule cell layer can be regulated by serotonin (5-hydroxytryptamine, 5-HT) via a specific action on Golgi cells. We find that 5-HT depolarizes Golgi cells, likely by activating 5-HT2A receptors, but does not directly act on either granule cells or mossy fibers. As a result of Golgi cell depolarization, 5-HT significantly increases tonic inhibition onto both granule cells and Golgi cells. 5-HT-mediated Golgi cell depolarization is not sufficient, however, to alter the probability or timing of mossy fiber-evoked feed-forward inhibition onto granule cells. Together, increased granule cell tonic inhibition paired with normal feed-forward inhibition acts to reduce granule cell spike probability without altering spike timing. Hence, these data provide a circuit mechanism by which 5-HT can reduce granule cell activity without altering temporal representations of mossy fiber input. Such changes in network integration could enable flexible, state-specific suppression of cerebellar sensorimotor input that should not be learned or enable reversal learning for unwanted associations. NEW & NOTEWORTHY Serotonin (5-hydroxytryptamine, 5-HT) regulates synaptic integration at the input stage of cerebellar processing by increasing tonic inhibition of granule cells. This circuit mechanism reduces the probability of granule cell spiking without altering spike timing, thus suppressing cerebellar input without altering its temporal representation in the granule cell layer.

Optogenetic stimulation of complex spatio-temporal activity patterns by acousto-optic light steering probes cerebellar granular layer integrative properties

Optogenetics provides tools to control afferent activity in brain microcircuits. However, this requires optical methods that can evoke asynchronous and coordinated activity within neuronal ensembles in a spatio-temporally precise way. Here we describe a light patterning method, which combines MHz acousto-optic beam steering and adjustable low numerical aperture Gaussian beams, to achieve fast 2D targeting in scattering tissue. Using mossy fiber afferents to the cerebellar cortex as a testbed, we demonstrate single fiber optogenetic stimulation with micron-scale lateral resolution, >100 µm depth-penetration and 0.1 ms spiking precision. Protracted spatio-temporal patterns of light delivered by our illumination system evoked sustained asynchronous mossy fiber activity with excellent repeatability. Combining optical and electrical stimulations, we show that the cerebellar granular layer performs nonlinear integration, whereby sustained mossy fiber activity provides a permissive context for the transmission of salient inputs, enriching combinatorial views on mossy fiber pattern separation.

NeuroMatic: An Integrated Open-Source Software Toolkit for Acquisition, Analysis and Simulation of Electrophysiological Data

Acquisition, analysis and simulation of electrophysiological properties of the nervous system require multiple software packages. This makes it difficult to conserve experimental metadata and track the analysis performed. It also complicates certain experimental approaches such as online analysis. To address this, we developed NeuroMatic, an open-source software toolkit that performs data acquisition (episodic, continuous and triggered recordings), data analysis (spike rasters, spontaneous event detection, curve fitting, stationarity) and simulations (stochastic synaptic transmission, synaptic short-term plasticity, integrate-and-fire and Hodgkin-Huxley-like single-compartment models). The merging of a wide range of tools into a single package facilitates a more integrated style of research, from the development of online analysis functions during data acquisition, to the simulation of synaptic conductance trains during dynamic-clamp experiments. Moreover, NeuroMatic has the advantage of working within Igor Pro, a platform-independent environment that includes an extensive library of built-in functions, a history window for reviewing the user's workflow and the ability to produce publication-quality graphics. Since its original release, NeuroMatic has been used in a wide range of scientific studies and its user base has grown considerably. NeuroMatic version 3.0 can be found at http://www.neuromatic.thinkrandom.com and https://github.com/SilverLabUCL/NeuroMatic.

Gap Junction Modulation of Low-Frequency Oscillations in the Cerebellar Granule Cell Layer

Local field potential (LFP) oscillations in the granule cell layer (GCL) of the cerebellar cortex have been identified previously in the awake rat and monkey during immobility. These low-frequency oscillations are thought to be generated through local circuit interactions between Golgi cells and granule cells within the GCL. Golgi cells display rhythmic firing and pacemaking properties, and also are electrically coupled through gap junctions within the GCL. Here, we tested if gap junctions in the rat cerebellar cortex contribute to the generation of LFP oscillations in the GCL. We recorded LFP oscillations under urethane anesthesia, and examined the effects of local infusion of gap junction blockers on 5-15 Hz oscillations. Local infusion of the gap junction blockers carbenoxolone and mefloquine resulted in significant decreases in the power of oscillations over a 30-min period, but the power of oscillations was unchanged in control experiments following vehicle injections. In addition, infusion of gap junction blockers had no significant effect on multi-unit activity, suggesting that the attenuation of low-frequency oscillations was likely due to reductions in electrical coupling rather than a decreased excitability within the granule cell layer. Our results indicate that electrical coupling among the Golgi cell networks in the cerebellar cortex contributes to the local circuit mechanisms that promote the occurrence of GCL LFP slow oscillations in the anesthetized rat.

Physiology of the cerebellum

The cerebellum is a central brain structure deeply integrated into major loops with the cerebral cortex, brainstem, and spinal cord. The cerebellum shows a complex regional organization consisting of modules with sagittal orientation. The cerebellum takes part in motor control and its lesions cause a movement incoordination syndrome called ataxia. Recent observations also imply involvement of the cerebellum in cognition and executive control, with an impact on pathologies like dyslexia and autism. The cerebellum operates as a forward controller learning to predict the precise timing of correlated events. The physiologic mechanisms of cerebellar functioning are still the object of intense research. The signals entering the cerebellum through the mossy fibers are processed in the granular layer and transmitted to Purkinje cells, while a collateral pathway activates the deep cerebellar nuclei (DCN). Purkinje cells in turn inhibit DCN, so that the cerebellar cortex operates as a side loop controlling the DCN. Learning is now known to occur through synaptic plasticity at multiple synapses in the granular layer, molecular layer, and DCN, extending the original concept of the Motor Learning Theory that predicted a single form of plasticity at the synapse between parallel fibers and Purkinje cells under the supervision of climbing fibers deriving from the inferior olive. Coordination derives from the precise regulation of timing and gain in the different cerebellar modules. The investigation of cerebellar dynamics using advanced physiologic recordings and computational models is now providing new clues on how the cerebellar network performs its internal computations.

Morphological Constraints on Cerebellar Granule Cell Combinatorial Diversity

Combinatorial expansion by the cerebellar granule cell layer (GCL) is fundamental to theories of cerebellar contributions to motor control and learning. Granule cells (GrCs) sample approximately four mossy fiber inputs and are thought to form a combinatorial code useful for pattern separation and learning. We constructed a spatially realistic model of the cerebellar GCL and examined how GCL architecture contributes to GrC combinatorial diversity. We found that GrC combinatorial diversity saturates quickly as mossy fiber input diversity increases, and that this saturation is in part a consequence of short dendrites, which limit access to diverse inputs and favor dense sampling of local inputs. This local sampling also produced GrCs that were combinatorially redundant, even when input diversity was extremely high. In addition, we found that mossy fiber clustering, which is a common anatomical pattern, also led to increased redundancy of GrC input combinations. We related this redundancy to hypothesized roles of temporal expansion of GrC information encoding in service of learned timing, and we show that GCL architecture produces GrC populations that support both temporal and combinatorial expansion. Finally, we used novel anatomical measurements from mice of either sex to inform modeling of sparse and filopodia-bearing mossy fibers, finding that these circuit features uniquely contribute to enhancing GrC diversification and redundancy. Our results complement information theoretic studies of granule layer structure and provide insight into the contributions of granule layer anatomical features to afferent mixing.SIGNIFICANCE STATEMENT Cerebellar granule cells are among the simplest neurons, with tiny somata and, on average, just four dendrites. These characteristics, along with their dense organization, inspired influential theoretical work on the granule cell layer as a combinatorial expander, where each granule cell represents a unique combination of inputs. Despite the centrality of these theories to cerebellar physiology, the degree of expansion supported by anatomically realistic patterns of inputs is unknown. Using modeling and anatomy, we show that realistic input patterns constrain combinatorial diversity by producing redundant combinations, which nevertheless could support temporal diversification of like combinations, suitable for learned timing. Our study suggests a neural substrate for producing high levels of both combinatorial and temporal diversity in the granule cell layer.

Sparse synaptic connectivity is required for decorrelation and pattern separation in feedforward networks

Pattern separation is a fundamental function of the brain. The divergent feedforward networks thought to underlie this computation are widespread, yet exhibit remarkably similar sparse synaptic connectivity. Marr-Albus theory postulates that such networks separate overlapping activity patterns by mapping them onto larger numbers of sparsely active neurons. But spatial correlations in synaptic input and those introduced by network connectivity are likely to compromise performance. To investigate the structural and functional determinants of pattern separation we built models of the cerebellar input layer with spatially correlated input patterns, and systematically varied their synaptic connectivity. Performance was quantified by the learning speed of a classifier trained on either the input or output patterns. Our results show that sparse synaptic connectivity is essential for separating spatially correlated input patterns over a wide range of network activity, and that expansion and correlations, rather than sparse activity, are the major determinants of pattern separation.

Input decorrelation, expansion recoding and sparse activity have been proposed to separate overlapping activity patterns in feedforward networks. Here the authors use reduced and detailed spiking models to elucidate how synaptic connectivity affects the contribution of these mechanisms to pattern separation in cerebellar cortex.

Non-synaptic signaling from cerebellar climbing fibers modulates Golgi cell activity

Golgi cells are the principal inhibitory neurons at the input stage of the cerebellum, providing feedforward and feedback inhibition through mossy fiber and parallel fiber synapses. In vivo studies have shown that Golgi cell activity is regulated by climbing fiber stimulation, yet there is little functional or anatomical evidence for synapses between climbing fibers and Golgi cells. Here, we show that glutamate released from climbing fibers activates ionotropic and metabotropic receptors on Golgi cells through spillover-mediated transmission. The interplay of excitatory and inhibitory conductances provides flexible control over Golgi cell spiking, allowing either excitation or a biphasic sequence of excitation and inhibition following single climbing fiber stimulation. Together with prior studies of spillover transmission to molecular layer interneurons, these results reveal that climbing fibers exert control over inhibition at both the input and output layers of the cerebellar cortex.

Spatiotemporal network coding of physiological mossy fiber inputs by the cerebellar granular layer

The granular layer, which mainly consists of granule and Golgi cells, is the first stage of the cerebellar cortex and processes spatiotemporal information transmitted by mossy fiber inputs with a wide variety of firing patterns. To study its dynamics at multiple time scales in response to inputs approximating real spatiotemporal patterns, we constructed a large-scale 3D network model of the granular layer. Patterned mossy fiber activity induces rhythmic Golgi cell activity that is synchronized by shared parallel fiber input and by gap junctions. This leads to long distance synchrony of Golgi cells along the transverse axis, powerfully regulating granule cell firing by imposing inhibition during a specific time window. The essential network mechanisms, including tunable Golgi cell oscillations, on-beam inhibition and NMDA receptors causing first winner keeps winning of granule cells, illustrate how fundamental properties of the granule layer operate in tandem to produce (1) well timed and spatially bound output, (2) a wide dynamic range of granule cell firing and (3) transient and coherent gating oscillations. These results substantially enrich our understanding of granule cell layer processing, which seems to promote spatial group selection of granule cell activity as a function of timing of mossy fiber input.

The cerebellum is an organ of peculiar geometrical properties, and has been attributed the function of applying spatiotemporal transforms to sensorimotor data since Eccles. In this work we have analyzed the spatiotemporal response properties of the first part of the cerebellar circuit, the granule layer. On the basis of a biophysically plausible and large-scale model of the cerebellum, constrained by a wealth of anatomical data, we study the network dynamics and firing properties of individual cell populations in response to 'realistic' input patterns. We make specific predictions about the spatiotemporal features of granule layer processing regarding the effects of the gap junction coupled network of Golgi cells on a spatially restricted input, in an effect we denominate first-takes-all. Furthermore, we calculate that the granule cell layer has a wide dynamic range, indicating that this is a system that can transmit large variations of input intensities.

Serial processing of kinematic signals by cerebellar circuitry during voluntary whisking

Purkinje cells (PCs) in Crus 1 represent whisker movement via linear changes in firing rate, but the circuit mechanisms underlying this coding scheme are unknown. Here we examine the role of upstream inputs to PCs-excitatory granule cells (GCs) and inhibitory molecular layer interneurons-in processing of whisking signals. Patch clamp recordings in GCs reveal that movement is accompanied by changes in mossy fibre input rate that drive membrane potential depolarisation and high-frequency bursting activity at preferred whisker angles. Although individual GCs are narrowly tuned, GC populations provide linear excitatory drive across a wide range of movement. Molecular layer interneurons exhibit bidirectional firing rate changes during whisking, similar to PCs. Together, GC populations provide downstream PCs with linear representations of volitional movement, while inhibitory networks invert these signals. The exquisite sensitivity of neurons at each processing stage enables faithful propagation of kinematic representations through the cerebellum.Cerebellar Purkinje cells (PCs) linearly encode whisker position but the precise circuit mechanisms that generate these signals are not well understood. Here the authors use patch clamp recordings to show that selective tuning of granule cell inputs and bidirectional tuning of interneuron inputs are required to generate the kinematic representations in PCs.

Hebbian Spike-Timing Dependent Plasticity at the Cerebellar Input Stage

Spike-timing-dependent plasticity (STDP) is a form of long-term synaptic plasticity exploiting the time relationship between postsynaptic action potentials (APs) and EPSPs. Surprisingly enough, very little was known about STDP in the cerebellum, although it is thought to play a critical role for learning appropriate timing of actions. We speculated that low-frequency oscillations observed in the granular layer may provide a reference for repetitive EPSP/AP phase coupling. Here we show that EPSP-spike pairing at 6 Hz can optimally induce STDP at the mossy fiber-granule cell synapse in rats. Spike timing-dependent long-term potentiation and depression (st-LTP and st-LTD) were confined to a ±25 ms time-window. Because EPSPs led APs in st-LTP while APs led EPSPs in st-LTD, STDP was Hebbian in nature. STDP occurred at 6-10 Hz but vanished >50 Hz or <1 Hz (where only LTP or LTD occurred). STDP disappeared with randomized EPSP/AP pairing or high intracellular Ca²⁺ buffering, and its sign was inverted by GABA-A receptor activation. Both st-LTP and st-LTD required NMDA receptors, but st-LTP also required reinforcing signals mediated by mGluRs and intracellular calcium stores. Importantly, st-LTP and st-LTD were significantly larger than LTP and LTD obtained by modulating the frequency and duration of mossy fiber bursts, probably because STDP expression involved postsynaptic in addition to presynaptic mechanisms. These results thus show that a Hebbian form of STDP occurs at the cerebellum input stage, providing the substrate for phase-dependent binding of mossy fiber spikes to repetitive theta-frequency cycles of granule cell activity.SIGNIFICANCE STATEMENT Long-term synaptic plasticity is a fundamental property of the brain, causing persistent modifications of neuronal communication thought to provide the cellular basis of learning and memory. The cerebellum is critical for learning the appropriate timing of sensorimotor behaviors, but whether and how appropriate spike patterns could drive long-term synaptic plasticity remained unknown. Here, we show that this can actually occur through a form of spike-timing-dependent plasticity (STDP) at the cerebellar inputs stage. Pairing presynaptic and postsynaptic spikes at 6-10 Hz reliably induced STDP at the mossy fiber-granule cell synapse, with potentiation and depression symmetrically distributed within a ±25 ms time window. Thus, STDP can bind plasticity to the mossy fiber burst phase with high temporal precision.

Modeling the Cerebellar Microcircuit: New Strategies for a Long-Standing Issue

The cerebellar microcircuit has been the work bench for theoretical and computational modeling since the beginning of neuroscientific research. The regular neural architecture of the cerebellum inspired different solutions to the long-standing issue of how its circuitry could control motor learning and coordination. Originally, the cerebellar network was modeled using a statistical-topological approach that was later extended by considering the geometrical organization of local microcircuits. However, with the advancement in anatomical and physiological investigations, new discoveries have revealed an unexpected richness of connections, neuronal dynamics and plasticity, calling for a change in modeling strategies, so as to include the multitude of elementary aspects of the network into an integrated and easily updatable computational framework. Recently, biophysically accurate “realistic” models using a bottom-up strategy accounted for both detailed connectivity and neuronal non-linear membrane dynamics. In this perspective review, we will consider the state of the art and discuss how these initial efforts could be further improved. Moreover, we will consider how embodied neurorobotic models including spiking cerebellar networks could help explaining the role and interplay of distributed forms of plasticity. We envisage that realistic modeling, combined with closed-loop simulations, will help to capture the essence of cerebellar computations and could eventually be applied to neurological diseases and neurorobotic control systems.

Only a Minority of the Inhibitory Inputs to Cerebellar Golgi Cells Originates from Local GABAergic Cells

Cerebellar Golgi cells (GoCs) efficiently control the spiking activity of granule cells through GABAA receptor-mediated tonic and phasic inhibition. Recent experiments provided compelling evidence for the extensive interconnection of GoCs through electrical synapses, but their chemical inhibitory synaptic inputs are debated. Here, we investigated the GABAergic synaptic inputs of GoCs using in vitro electrophysiology and quantitative light microscopy (LM) and electron microscopy (EM). We characterized GABAA receptor-mediated IPSCs in GoCs and Lugaro cells (LuCs), and found that IPSCs in GoCs have lower frequencies, smaller amplitudes, and much slower decay kinetics. Pharmacological and LM immunolocalization experiments revealed that GoCs express α3, whereas LuCs express α1 subunit-containing GABAA receptors. The selective expression and clustered distribution of the α3 subunit in GoCs allowed the quantitative analysis of GABAergic synapses on their dendrites in the molecular layer (ML). EM and LM experiments in rats, and wild-type and GlyT2-GFP transgenic mice revealed that only one third of axon terminals establishing GABAergic synapses on GoC dendrites contain GlyT2, ruling out LuCs, globular cells, and any noncortical glycinergic inputs as major inhibitory sources. We also show that axon terminals of stellate/basket cells very rarely innervate GlyT2-GFP-expressing GoCs, indicating that only a minority of the inhibitory inputs to GoCs in the ML originates from local interneurons, and the majority of their inhibitory inputs exclusively releases GABA.

Conditional Spike Transmission Mediated by Electrical Coupling Ensures Millisecond Precision-Correlated Activity among Interneurons In Vivo

Many GABAergic interneurons are electrically coupled and in vitro can display correlated activity with millisecond precision. However, the mechanisms underlying correlated activity between interneurons in vivo are unknown. Using dual patch-clamp recordings in vivo, we reveal that in the presence of spontaneous background synaptic activity, electrically coupled cerebellar Golgi cells exhibit robust millisecond precision-correlated activity which is enhanced by sensory stimulation. This precisely correlated activity results from the cooperative action of two mechanisms. First, electrical coupling ensures slow subthreshold membrane potential correlations by equalizing membrane potential fluctuations, such that coupled neurons tend to approach action potential threshold together. Second, fast spike-triggered spikelets transmitted through gap junctions conditionally trigger postjunctional spikes, depending on both neurons being close to threshold. Electrical coupling therefore controls the temporal precision and degree of both spontaneous and sensory-evoked correlated activity between interneurons, by the cooperative effects of shared synaptic depolarization and spikelet transmission.

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Double patch-clamp recordings from Golgi cells reveal millisecond synchrony in vivo

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Millisecond synchrony requires gap junctions and is enhanced by sensory stimuli

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Gap junctions drive synchrony via slow V_m equalization and fast spikelet transmission

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Modeling shows these findings can be generalized to any electrically coupled neurons

Active Dendrites and Differential Distribution of Calcium Channels Enable Functional Compartmentalization of Golgi Cells

Interneurons are essential to controlling excitability, timing, and synaptic integration in neuronal networks. Golgi cells (GoCs) serve these roles at the input layer of the cerebellar cortex by releasing GABA to inhibit granule cells (grcs). GoCs are excited by mossy fibers (MFs) and grcs and provide feedforward and feedback inhibition to grcs. Here we investigate two important aspects of GoC physiology: the properties of GoC dendrites and the role of calcium signaling in regulating GoC spontaneous activity. Although GoC dendrites are extensive, previous studies concluded they are devoid of voltage-gated ion channels. Hence, the current view holds that somatic voltage signals decay passively within GoC dendrites, and grc synapses onto distal dendrites are not amplified and are therefore ineffective at firing GoCs because of strong passive attenuation. Using whole-cell recording and calcium imaging in rat slices, we find that dendritic voltage-gated sodium channels allow somatic action potentials to activate voltage-gated calcium channels (VGCCs) along the entire dendritic length, with R-type and T-type VGCCs preferentially located distally. We show that R- and T-type VGCCs located in the dendrites can boost distal synaptic inputs and promote burst firing. Active dendrites are thus critical to the regulation of GoC activity, and consequently, to the processing of input to the cerebellar cortex. In contrast, we find that N-type channels are preferentially located near the soma, and control the frequency and pattern of spontaneous firing through their close association with calcium-activated potassium (KCa) channels. Thus, VGCC types are differentially distributed and serve specialized functions within GoCs.

SIGNIFICANCE STATEMENT

Interneurons are essential to neural processing because they modulate excitability, timing, and synaptic integration within circuits. At the input layer of the cerebellar cortex, a single type of interneuron, the Golgi cell (GoC), carries these functions. The extent of inhibition depends on both spontaneous activity of GoCs and the excitatory synaptic input they receive. In this study, we find that different types of calcium channels are differentially distributed, with dendritic calcium channels being activated by somatic activity, boosting synaptic inputs and enabling bursting, and somatic calcium cannels promoting regular firing. We therefore challenge the current view that GoC dendrites are passive and identify the mechanisms that contribute to GoCs regulating the flow of sensory information in the cerebellar cortex.