Axonal Na+ channels ensure fast spike activation and back-propagation in cerebellar granule cells

Purkinje cell models: past, present and future

The investigation of the dynamics of Purkinje cell (PC) activity is crucial to unravel the role of the cerebellum in motor control, learning and cognitive processes. Within the cerebellar cortex (CC), these neurons receive all the incoming sensory and motor information, transform it and generate the entire cerebellar output. The relatively homogenous and repetitive structure of the CC, common to all vertebrate species, suggests a single computation mechanism shared across all PCs. While PC models have been developed since the 70's, a comprehensive review of contemporary models is currently lacking. Here, we provide an overview of PC models, ranging from the ones focused on single cell intracellular PC dynamics, through complex models which include synaptic and extrasynaptic inputs. We review how PC models can reproduce physiological activity of the neuron, including firing patterns, current and multistable dynamics, plateau potentials, calcium signaling, intrinsic and synaptic plasticity and input/output computations. We consider models focusing both on somatic and on dendritic computations. Our review provides a critical performance analysis of PC models with respect to known physiological data. We expect our synthesis to be useful in guiding future development of computational models that capture real-life PC dynamics in the context of cerebellar computations.

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.

Model simulations unveil the structure-function-dynamics relationship of the cerebellar cortical microcircuit

The cerebellar network is renowned for its regular architecture that has inspired foundational computational theories. However, the relationship between circuit structure, function and dynamics remains elusive. To tackle the issue, we developed an advanced computational modeling framework that allows us to reconstruct and simulate the structure and function of the mouse cerebellar cortex using morphologically realistic multi-compartmental neuron models. The cerebellar connectome is generated through appropriate connection rules, unifying a collection of scattered experimental data into a coherent construct and providing a new model-based ground-truth about circuit organization. Naturalistic background and sensory-burst stimulation are used for functional validation against recordings in vivo, monitoring the impact of cellular mechanisms on signal propagation, inhibitory control, and long-term synaptic plasticity. Our simulations show how mossy fibers entrain the local neuronal microcircuit, boosting the formation of columns of activity travelling from the granular to the molecular layer providing a new resource for the investigation of local microcircuit computation and of the neural correlates of 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.

Modeling analysis of subthreshold voltage signaling along hippocampal mossy fiber axons

Axons are classically thought of as electrically well isolated from other parts of the neurons due to the shape of a long cable-like structure. In contrast to this classical view on axonal compartmentalization, recent studies revealed that subthreshold depolarization of soma and dendrite passively propagates to the axons for a substantial distance, as demonstrated in some experimentally accessible axons including hippocampal mossy fibers and cortical pyramidal cell axons. Passive propagation of subthreshold dendritic EPSPs to the axons, defined as EPreSPs (excitatory presynaptic potentials), has been demonstrated to affect transmitter release from the axon terminals. To further characterize and explore the functional significance of passive subthreshold voltage signaling along the axons, the model of EPreSPs along hippocampal mossy fibers, proposed by Alle and Geiger, was reconstructed on the NEURON simulator. To test the effect of EPreSPs on action potentials and transmitter release from the axon terminals, additional conductances were incorporated into the previous passive propagation model. These include the axonal sodium, potassium, and leak channels as well as presynaptic calcium channels composed of P/Q-, N-, and R-types, which are reconstructed from the properties of those recorded from mossy fiber boutons experimentally. In this revised model, the preceding subthreshold EPreSPs slightly reduced the action potential-evoked presynaptic calcium currents by a decrease in the amplitude of action potentials due to the slow depolarization. It should be mentioned that EPreSPs by themselves elicited small calcium currents during subthreshold depolarization through these high-voltage activated calcium channels. Since the previous experimental study by simultaneous pre and postsynaptic recordings demonstrated that EPreSPs enhanced action potential-evoked transmitter release from the mossy fiber terminals, it has been suggested that different mechanisms from the enhancement of action potential-evoked presynaptic calcium entry may involve enhanced transmitter release by EPreSP. Small calcium entry by subthreshold EPreSPs may enhance transmitter release from the mossy fiber terminals by acting as high-affinity calcium sensors for enhancing transmitter release. Another form of axonal subthreshold voltage signaling, GABA-EPreSPs elicited by a spillover of GABA from surrounding interneurons, was also explored. Functional consequences of the two modes of axonal subthreshold voltage signaling were discussed with the simulation results.

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.

Electrical match between initial segment and somatodendritic compartment for action potential backpropagation in retinal ganglion cells

The action potential of most vertebrate neurons initiates in the axon initial segment (AIS) and is then transmitted to the soma where it is regenerated by somatodendritic sodium channels. For successful transmission, the AIS must produce a strong axial current, so as to depolarize the soma to the threshold for somatic regeneration. Theoretically, this axial current depends on AIS geometry and Na⁺ conductance density. We measured the axial current of mouse retinal ganglion cells using whole cell recordings with post hoc AIS labeling. We found that this current is large, implying high Na⁺ conductance density, and carries a charge that covaries with capacitance so as to depolarize the soma by ∼30 mV. Additionally, we observed that the axial current attenuates strongly with depolarization, consistent with sodium channel inactivation, but temporally broadens so as to preserve the transmitted charge. Thus, the AIS appears to be organized so as to reliably backpropagate the axonal action potential.NEW & NOTEWORTHY We measured the axial current produced at spike initiation by the axon initial segment of mouse retinal ganglion cells. We found that it is a large current, requiring high sodium channel conductance density, which covaries with cell capacitance so as to ensure a ∼30 mV depolarization. During sustained depolarization the current attenuated, but it broadened to preserve somatic depolarization. Thus, properties of the initial segment are adjusted to ensure backpropagation of the axonal action potential.

Real-Time Simulation of a Cerebellar Scaffold Model on Graphics Processing Units

Large-scale simulation of detailed computational models of neuronal microcircuits plays a prominent role in reproducing and predicting the dynamics of the microcircuits. To reconstruct a microcircuit, one must choose neuron and synapse models, placements, connectivity, and numerical simulation methods according to anatomical and physiological constraints. For reconstruction and refinement, it is useful to be able to replace one module easily while leaving the others as they are. One way to achieve this is via a scaffolding approach, in which a simulation code is built on independent modules for placements, connections, and network simulations. Owing to the modularity of functions, this approach enables researchers to improve the performance of the entire simulation by simply replacing a problematic module with an improved one. Casali et al. (2019) developed a spiking network model of the cerebellar microcircuit using this approach, and while it reproduces electrophysiological properties of cerebellar neurons, it takes too much computational time. Here, we followed this scaffolding approach and replaced the simulation module with an accelerated version on graphics processing units (GPUs). Our cerebellar scaffold model ran roughly 100 times faster than the original version. In fact, our model is able to run faster than real time, with good weak and strong scaling properties. To demonstrate an application of real-time simulation, we implemented synaptic plasticity mechanisms at parallel fiber-Purkinje cell synapses, and carried out simulation of behavioral experiments known as gain adaptation of optokinetic response. We confirmed that the computer simulation reproduced experimental findings while being completed in real time. Actually, a computer simulation for 2 s of the biological time completed within 750 ms. These results suggest that the scaffolding approach is a promising concept for gradual development and refactoring of simulation codes for large-scale elaborate microcircuits. Moreover, a real-time version of the cerebellar scaffold model, which is enabled by parallel computing technology owing to GPUs, may be useful for large-scale simulations and engineering applications that require real-time signal processing and motor control.

Nav1.3 and FGF14 are primary determinants of the TTX-sensitive sodium current in mouse adrenal chromaffin cells

Adrenal chromaffin cells (CCs) in rodents express rapidly inactivating, tetrodotoxin (TTX)-sensitive sodium channels. The resulting current has generally been attributed to Nav1.7, although a possible role for Nav1.3 has also been suggested. Nav channels in rat CCs rapidly inactivate via two independent pathways which differ in their time course of recovery. One subpopulation recovers with time constants similar to traditional fast inactivation and the other ∼10-fold slower, but both pathways can act within a single homogenous population of channels. Here, we use Nav1.3 KO mice to probe the properties and molecular components of Nav current in CCs. We find that the absence of Nav1.3 abolishes all Nav current in about half of CCs examined, while a small, fast inactivating Nav current is still observed in the rest. To probe possible molecular components underlying slow recovery from inactivation, we used mice null for fibroblast growth factor homology factor 14 (FGF14). In these cells, the slow component of recovery from fast inactivation is completely absent in most CCs, with no change in the time constant of fast recovery. The use dependence of Nav current reduction during trains of stimuli in WT cells is completely abolished in FGF14 KO mice, directly demonstrating a role for slow recovery from inactivation in determining Nav current availability. Our results indicate that FGF14-mediated inactivation is the major determinant defining use-dependent changes in Nav availability in CCs. These results establish that Nav1.3, like other Nav isoforms, can also partner with FGF subunits, strongly regulating Nav channel function.

The effects of the general anesthetic sevoflurane on neurotransmission: an experimental and computational study

The brain functions can be reversibly modulated by the action of general anesthetics. Despite a wide number of pharmacological studies, an extensive analysis of the cellular determinants of anesthesia at the microcircuits level is still missing. Here, by combining patch-clamp recordings and mathematical modeling, we examined the impact of sevoflurane, a general anesthetic widely employed in the clinical practice, on neuronal communication. The cerebellar microcircuit was used as a benchmark to analyze the action mechanisms of sevoflurane while a biologically realistic mathematical model was employed to explore at fine grain the molecular targets of anesthetic analyzing its impact on neuronal activity. The sevoflurane altered neurotransmission by strongly increasing GABAergic inhibition while decreasing glutamatergic NMDA activity. These changes caused a notable reduction of spike discharge in cerebellar granule cells (GrCs) following repetitive activation by excitatory mossy fibers (mfs). Unexpectedly, sevoflurane altered GrCs intrinsic excitability promoting action potential generation. Computational modelling revealed that this effect was triggered by an acceleration of persistent sodium current kinetics and by an increase in voltage dependent potassium current conductance. The overall effect was a reduced variability of GrCs responses elicited by mfs supporting the idea that sevoflurane shapes neuronal communication without silencing neural circuits.

Stellate cell computational modeling predicts signal filtering in the molecular layer circuit of cerebellum

The functional properties of cerebellar stellate cells and the way they regulate molecular layer activity are still unclear. We have measured stellate cells electroresponsiveness and their activation by parallel fiber bursts. Stellate cells showed intrinsic pacemaking, along with characteristic responses to depolarization and hyperpolarization, and showed a marked short-term facilitation during repetitive parallel fiber transmission. Spikes were emitted after a lag and only at high frequency, making stellate cells to operate as delay-high-pass filters. A detailed computational model summarizing these physiological properties allowed to explore different functional configurations of the parallel fiber-stellate cell-Purkinje cell circuit. Simulations showed that, following parallel fiber stimulation, Purkinje cells almost linearly increased their response with input frequency, but such an increase was inhibited by stellate cells, which leveled the Purkinje cell gain curve to its 4 Hz value. When reciprocal inhibitory connections between stellate cells were activated, the control of stellate cells over Purkinje cell discharge was maintained only at very high frequencies. These simulations thus predict a new role for stellate cells, which could endow the molecular layer with low-pass and band-pass filtering properties regulating Purkinje cell gain and, along with this, also burst delay and the burst-pause responses pattern.

Human-scale Brain Simulation via Supercomputer: A Case Study on the Cerebellum

Performance of supercomputers has been steadily and exponentially increasing for the past 20 years, and is expected to increase further. This unprecedented computational power enables us to build and simulate large-scale neural network models composed of tens of billions of neurons and tens of trillions of synapses with detailed anatomical connections and realistic physiological parameters. Such "human-scale" brain simulation could be considered a milestone in computational neuroscience and even in general neuroscience. Towards this milestone, it is mandatory to introduce modern high-performance computing technology into neuroscience research. In this article, we provide an introductory landscape about large-scale brain simulation on supercomputers from the viewpoints of computational neuroscience and modern high-performance computing technology for specialists in experimental as well as computational neurosciences. This introduction to modeling and simulation methods is followed by a review of various representative large-scale simulation studies conducted to date. Then, we direct our attention to the cerebellum, with a review of more simulation studies specific to that region. Furthermore, we present recent simulation results of a human-scale cerebellar network model composed of 86 billion neurons on the Japanese flagship supercomputer K (now retired). Finally, we discuss the necessity and importance of human-scale brain simulation, and suggest future directions of such large-scale brain simulation research.

Non-invasive suppression of essential tremor via phase-locked disruption of its temporal coherence

Aberrant neural oscillations hallmark numerous brain disorders. Here, we first report a method to track the phase of neural oscillations in real-time via endpoint-corrected Hilbert transform (ecHT) that mitigates the characteristic Gibbs distortion. We then used ecHT to show that the aberrant neural oscillation that hallmarks essential tremor (ET) syndrome, the most common adult movement disorder, can be transiently suppressed via transcranial electrical stimulation of the cerebellum phase-locked to the tremor. The tremor suppression is sustained shortly after the end of the stimulation and can be phenomenologically predicted. Finally, we use feature-based statistical-learning and neurophysiological-modelling to show that the suppression of ET is mechanistically attributed to a disruption of the temporal coherence of the aberrant oscillations in the olivocerebellar loop, thus establishing its causal role. The suppression of aberrant neural oscillation via phase-locked driven disruption of temporal coherence may in the future represent a powerful neuromodulatory strategy to treat brain disorders.

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.

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.

Multiple signals evoked by unisensory stimulation converge onto cerebellar granule and Purkinje cells in mice

The cerebellum receives signals directly from peripheral sensory systems and indirectly from the neocortex. Even a single tactile stimulus can activate both of these pathways. Here we report how these different types of signals are integrated in the cerebellar cortex. We used in vivo whole-cell recordings from granule cells and unit recordings from Purkinje cells in mice in which primary somatosensory cortex (S1) could be optogenetically inhibited. Tactile stimulation of the upper lip produced two-phase granule cell responses (with latencies of ~8 ms and 29 ms), for which only the late phase was S1 dependent. In Purkinje cells, complex spikes and the late phase of simple spikes were S1 dependent. These results indicate that individual granule cells combine convergent inputs from the periphery and neocortex and send their outputs to Purkinje cells, which then integrate those signals with climbing fiber signals from the neocortex.

Optimization of Efficient Neuron Models With Realistic Firing Dynamics. The Case of the Cerebellar Granule Cell

Biologically relevant large-scale computational models currently represent one of the main methods in neuroscience for studying information processing primitives of brain areas. However, biologically realistic neuron models tend to be computationally heavy and thus prevent these models from being part of brain-area models including thousands or even millions of neurons. The cerebellar input layer represents a canonical example of large scale networks. In particular, the cerebellar granule cells, the most numerous cells in the whole mammalian brain, have been proposed as playing a pivotal role in the creation of somato-sensorial information representations. Enhanced burst frequency (spiking resonance) in the granule cells has been proposed as facilitating the input signal transmission at the theta-frequency band (4–12 Hz), but the functional role of this cell feature in the operation of the granular layer remains largely unclear. This study aims to develop a methodological pipeline for creating neuron models that maintain biological realism and computational efficiency whilst capturing essential aspects of single-neuron processing. Therefore, we selected a light computational neuron model template (the adaptive-exponential integrate-and-fire model), whose parameters were progressively refined using an automatic parameter tuning with evolutionary algorithms (EAs). The resulting point-neuron models are suitable for reproducing the main firing properties of a realistic granule cell from electrophysiological measurements, including the spiking resonance at the theta-frequency band, repetitive firing according to a specified intensity-frequency (I-F) curve and delayed firing under current-pulse stimulation. Interestingly, the proposed model also reproduced some other emergent properties (namely, silent at rest, rheobase and negligible adaptation under depolarizing currents) even though these properties were not set in the EA as a target in the fitness function (FF), proving that these features are compatible even in computationally simple models. The proposed methodology represents a valuable tool for adjusting AdEx models according to a FF defined in the spiking regime and based on biological data. These models are appropriate for future research of the functional implication of bursting resonance at the theta band in large-scale granular layer network models.

Parameter tuning differentiates granule cell subtypes enriching transmission properties at the cerebellum input stage

The cerebellar granule cells (GrCs) are classically described as a homogeneous neuronal population discharging regularly without adaptation. We show that GrCs in fact generate diverse response patterns to current injection and synaptic activation, ranging from adaptation to acceleration of firing. Adaptation was predicted by parameter optimization in detailed computational models based on available knowledge on GrC ionic channels. The models also predicted that acceleration required additional mechanisms. We found that yet unrecognized TRPM4 currents specifically accounted for firing acceleration and that adapting GrCs outperformed accelerating GrCs in transmitting high-frequency mossy fiber (MF) bursts over a background discharge. This implied that GrC subtypes identified by their electroresponsiveness corresponded to specific neurotransmitter release probability values. Simulations showed that fine-tuning of pre- and post-synaptic parameters generated effective MF-GrC transmission channels, which could enrich the processing of input spike patterns and enhance spatio-temporal recoding at the cerebellar input stage.

Mechanisms of GABAB receptor enhancement of extrasynaptic GABAA receptor currents in cerebellar granule cells

Many neurons, including cerebellar granule cells, exhibit a tonic GABA current mediated by extrasynaptic GABA_A receptors. This current is a critical regulator of firing and the target of many clinically relevant compounds. Using a combination of patch clamp electrophysiology and photolytic uncaging of RuBi-GABA we show that GABA_B receptors are tonically active and enhance extrasynaptic GABA_A receptor currents in cerebellar granule cells. This enhancement is not associated with meaningful changes in GABA_A receptor potency, mean channel open-time, open probability, or single-channel current. However, there was a significant (~40%) decrease in the number of channels participating in the GABA uncaging current and an increase in receptor desensitization. Furthermore, we find that adenylate cyclase, PKA, CaMKII, and release of Ca²⁺ from intracellular stores are necessary for modulation of GABA_A receptors. Overall, this work reveals crosstalk between postsynaptic GABA_A and GABA_B receptors and identifies the signaling pathways and mechanisms involved.

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.

Consensus paper: Decoding the Contributions of the Cerebellum as a Time Machine. From Neurons to Clinical Applications

Time perception is an essential element of conscious and subconscious experience, coordinating our perception and interaction with the surrounding environment. In recent years, major technological advances in the field of neuroscience have helped foster new insights into the processing of temporal information, including extending our knowledge of the role of the cerebellum as one of the key nodes in the brain for this function. This consensus paper provides a state-of-the-art picture from the experts in the field of the cerebellar research on a variety of crucial issues related to temporal processing, drawing on recent anatomical, neurophysiological, behavioral, and clinical research.The cerebellar granular layer appears especially well-suited for timing operations required to confer millisecond precision for cerebellar computations. This may be most evident in the manner the cerebellum controls the duration of the timing of agonist-antagonist EMG bursts associated with fast goal-directed voluntary movements. In concert with adaptive processes, interactions within the cerebellar cortex are sufficient to support sub-second timing. However, supra-second timing seems to require cortical and basal ganglia networks, perhaps operating in concert with cerebellum. Additionally, sensory information such as an unexpected stimulus can be forwarded to the cerebellum via the climbing fiber system, providing a temporally constrained mechanism to adjust ongoing behavior and modify future processing. Patients with cerebellar disorders exhibit impairments on a range of tasks that require precise timing, and recent evidence suggest that timing problems observed in other neurological conditions such as Parkinson's disease, essential tremor, and dystonia may reflect disrupted interactions between the basal ganglia and cerebellum.The complex concepts emerging from this consensus paper should provide a foundation for further discussion, helping identify basic research questions required to understand how the brain represents and utilizes time, as well as delineating ways in which this knowledge can help improve the lives of those with neurological conditions that disrupt this most elemental sense. The panel of experts agrees that timing control in the brain is a complex concept in whom cerebellar circuitry is deeply involved. The concept of a timing machine has now expanded to clinical disorders.

Proprioceptive Recognition with Artificial Neural Networks Based on Organizations of Spinocerebellar Tract and Cerebellum

Muscle kinematics and kinetics are nonlinearly encoded by proprioceptors, and the changes in muscle length and velocity are integrated into Ia afferent. Besides, proprioceptive signals from multiple muscles are probably mixed in afferent pathways, which all lead to difficulties in proprioceptive recognition for the cerebellum. In this study, the artificial neural networks, whose organizations are biologically based on the spinocerebellar tract and cerebellum, are utilized to decode the proprioceptive signals. Consistent with the controversy of the proprioceptive division in the dorsal spinocerebellar tract, the spinocerebellar tract networks incorporated two distinct inferences, (1) the centralized networks, which mixed Ia, II, and Ib and processed them together; (2) the decentralized networks, which processed Ia, II, and Ib afferents separately. The cerebellar networks were based on the Marr-Albus model to recognize the kinematic states. The networks were trained by a specific movement, and the trained networks were subsequently required to predict kinematic states of six movements. The results demonstrated that the centralized networks, which were more consistent with the physiological findings in recent years, had better recognition accuracy than the decentralized networks, and the networks were still effective even when proprioceptive afferents from multiple muscles were integrated.

Balanced Activity between Kv3 and Nav Channels Determines Fast-Spiking in Mammalian Central Neurons

Fast-spiking (FS) neurons can fire action potentials (APs) up to 1,000 Hz and play key roles in vital functions such as sound location, motor coordination, and cognition. Here we report that the concerted actions of Kv3 voltage-gated K⁺ (Kv) and Na⁺ (Nav) channels are sufficient and necessary for inducing and maintaining FS. Voltage-clamp analysis revealed a robust correlation between the Kv3/Nav current ratio and FS. Expressing Kv3 channels alone could convert ∼30%-60% slow-spiking (SS) neurons to FS in culture. In contrast, co-expression of either Nav1.2 or Nav1.6 together with Kv3.1 or Kv3.3, but not alone or with Kv1.2, converted SS to FS with 100% efficiency. Furthermore, RNA-sequencing-based genome-wide analysis revealed that the Kv3/Nav ratio and Kv3 expression levels strongly correlated with the maximal AP frequencies. Therefore, FS is established by the properly balanced activities of Kv3 and Nav channels and could be further fine-tuned by channel biophysical features and localization patterns.

Temporal constrained objects for modelling neuronal dynamics

BACKGROUND

Several new programming languages and technologies have emerged in the past few decades in order to ease the task of modelling complex systems. Modelling the dynamics of complex systems requires various levels of abstractions and reductive measures in representing the underlying behaviour. This also often requires making a trade-off between how realistic a model should be in order to address the scientific questions of interest and the computational tractability of the model.

METHODS

In this paper, we propose a novel programming paradigm, called temporal constrained objects, which facilitates a principled approach to modelling complex dynamical systems. Temporal constrained objects are an extension of constrained objects with a focus on the analysis and prediction of the dynamic behaviour of a system. The structural aspects of a neuronal system are represented using objects, as in object-oriented languages, while the dynamic behaviour of neurons and synapses are modelled using declarative temporal constraints. Computation in this paradigm is a process of constraint satisfaction within a time-based simulation.

RESULTS

We identified the feasibility and practicality in automatically mapping different kinds of neuron and synapse models to the constraints of temporal constrained objects. Simple neuronal networks were modelled by composing circuit components, implicitly satisfying the internal constraints of each component and interface constraints of the composition. Simulations show that temporal constrained objects provide significant conciseness in the formulation of these models. The underlying computational engine employed here automatically finds the solutions to the problems stated, reducing the code for modelling and simulation control. All examples reported in this paper have been programmed and successfully tested using the prototype language called TCOB. The code along with the programming environment are available at http://github.com/compneuro/TCOB_Neuron.

DISCUSSION

Temporal constrained objects provide powerful capabilities for modelling the structural and dynamic aspects of neural systems. Capabilities of the constraint programming paradigm, such as declarative specification, the ability to express partial information and non-directionality, and capabilities of the object-oriented paradigm especially aggregation and inheritance, make this paradigm the right candidate for complex systems and computational modelling studies. With the advent of multi-core parallel computer architectures and techniques or parallel constraint-solving, the paradigm of temporal constrained objects lends itself to highly efficient execution which is necessary for modelling and simulation of large brain circuits.

Typical gray matter axons in mammalian brain fail to conduct action potentials faithfully at fever-like temperatures

We studied the ability of typical unmyelinated cortical axons to conduct action potentials at fever‐like temperatures because fever often gives CNS symptoms. We investigated such axons in cerebellar and hippocampal slices from 10 to 25 days old rats at temperatures between 30 and 43°C. By recording with two electrodes along axonal pathways, we confirmed that the axons were able to initiate action potentials, but at temperatures >39°C, the propagation of the action potentials to a more distal recording site was reduced. This temperature‐sensitive conduction may be specific for the very thin unmyelinated axons because similar recordings from myelinated CNS axons did not show conduction failures. We found that the conduction fidelity improved with 1 mmol/L TEA in the bath, probably due to block of voltage‐sensitive potassium channels responsible for the fast repolarization of action potentials. Furthermore, by recording electrically activated antidromic action potentials from the soma of cerebellar granule cells, we showed that the axons failed less if they were triggered 10–30 msec after another action potential. This was because individual action potentials were followed by a depolarizing after‐potential, of constant amplitude and shape, which facilitated conduction of the following action potentials. The temperature‐sensitive conduction failures above, but not below, normal body temperature, and the failure‐reducing effect of the spike's depolarizing after‐potential, are two intrinsic mechanisms in normal gray matter axons that may help us understand how the hyperthermic brain functions.

Understanding Cerebellum Granular Layer Network Computations through Mathematical Reconstructions of Evoked Local Field Potentials

Background

The cerebellar granular layer input stage of cerebellum receives information from tactile and sensory regions of the body. The somatosensory activity in the cerebellar granular layer corresponds to sensory and tactile input has been observed by recording Local Field Potential (LFP) from the Crus-IIa regions of cerebellum in brain slices and in anesthetized animals.

Purpose

In this paper, a detailed biophysical model of Wistar rat cerebellum granular layer network model and LFP modelling schemas were used to simulate circuit's evoked response.

Methods

Point Source Approximation and Line Source Approximation were used to reconstruct the network LFP. The LFP mechanism in in vitro was validated in network model and generated the in vivo LFP using the same mechanism.

Results

The network simulations distinctly displayed the Trigeminal and Cortical (TC) wave components generated by 2 independent bursts implicating the generation of TC waves by 2 independent granule neuron populations. Induced plasticity was simulated to estimate granule neuron activation related population responses. As a prediction, cerebellar dysfunction (ataxia) was also studied using the model. Dysfunction at individual neurons in the network was affected by the population response.

Conclusion

Our present study utilizes available knowledge on known mechanisms in a single cell and associates network function to population responses.

The basis of sharp spike onset in standard biophysical models

In most vertebrate neurons, spikes initiate in the axonal initial segment (AIS). When recorded in the soma, they have a surprisingly sharp onset, as if sodium (Na) channels opened abruptly. The main view stipulates that spikes initiate in a conventional manner at the distal end of the AIS, then progressively sharpen as they backpropagate to the soma. We examined the biophysical models used to substantiate this view, and we found that spikes do not initiate through a local axonal current loop that propagates along the axon, but through a global current loop encompassing the AIS and soma, which forms an electrical dipole. Therefore, the phenomenon is not adequately modeled as the backpropagation of an electrical wave along the axon, since the wavelength would be as large as the entire system. Instead, in these models, we found that spike initiation rather follows the critical resistive coupling model proposed recently, where the Na current entering the AIS is matched by the axial resistive current flowing to the soma. Besides demonstrating it by examining the balance of currents at spike initiation, we show that the observed increase in spike sharpness along the axon is artifactual and disappears when an appropriate measure of rapidness is used; instead, somatic onset rapidness can be predicted from spike shape at initiation site. Finally, we reproduce the phenomenon in a two-compartment model, showing that it does not rely on propagation. In these models, the sharp onset of somatic spikes is therefore not an artifact of observing spikes at the incorrect location, but rather the signature that spikes are initiated through a global soma-AIS current loop forming an electrical dipole.

Single Neuron Optimization as a Basis for Accurate Biophysical Modeling: The Case of Cerebellar Granule Cells

In realistic neuronal modeling, once the ionic channel complement has been defined, the maximum ionic conductance (G_i-max) values need to be tuned in order to match the firing pattern revealed by electrophysiological recordings. Recently, selection/mutation genetic algorithms have been proposed to efficiently and automatically tune these parameters. Nonetheless, since similar firing patterns can be achieved through different combinations of G_i-max values, it is not clear how well these algorithms approximate the corresponding properties of real cells. Here we have evaluated the issue by exploiting a unique opportunity offered by the cerebellar granule cell (GrC), which is electrotonically compact and has therefore allowed the direct experimental measurement of ionic currents. Previous models were constructed using empirical tuning of G_i-max values to match the original data set. Here, by using repetitive discharge patterns as a template, the optimization procedure yielded models that closely approximated the experimental G_i-max values. These models, in addition to repetitive firing, captured additional features, including inward rectification, near-threshold oscillations, and resonance, which were not used as features. Thus, parameter optimization using genetic algorithms provided an efficient modeling strategy for reconstructing the biophysical properties of neurons and for the subsequent reconstruction of large-scale neuronal network models.

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.

SUMOylation of NaV1.2 channels mediates the early response to acute hypoxia in central neurons

The mechanism for the earliest response of central neurons to hypoxia-an increase in voltage-gated sodium current (INa)-has been unknown. Here, we show that hypoxia activates the Small Ubiquitin-like Modifier (SUMO) pathway in rat cerebellar granule neurons (CGN) and that SUMOylation of NaV1.2 channels increases INa. The time-course for SUMOylation of single NaV1.2 channels at the cell surface and changes in INa coincide, and both are prevented by mutation of NaV1.2-Lys38 or application of a deSUMOylating enzyme. Within 40 s, hypoxia-induced linkage of SUMO1 to the channels is complete, shifting the voltage-dependence of channel activation so that depolarizing steps evoke larger sodium currents. Given the recognized role of INa in hypoxic brain damage, the SUMO pathway and NaV1.2 are identified as potential targets for neuroprotective interventions.

Distributed Circuit Plasticity: New Clues for the Cerebellar Mechanisms of Learning

The cerebellum is involved in learning and memory of sensory motor skills. However, the way this process takes place in local microcircuits is still unclear. The initial proposal, casted into the Motor Learning Theory, suggested that learning had to occur at the parallel fiber-Purkinje cell synapse under supervision of climbing fibers. However, the uniqueness of this mechanism has been questioned, and multiple forms of long-term plasticity have been revealed at various locations in the cerebellar circuit, including synapses and neurons in the granular layer, molecular layer and deep-cerebellar nuclei. At present, more than 15 forms of plasticity have been reported. There has been a long debate on which plasticity is more relevant to specific aspects of learning, but this question turned out to be hard to answer using physiological analysis alone. Recent experiments and models making use of closed-loop robotic simulations are revealing a radically new view: one single form of plasticity is insufficient, while altogether, the different forms of plasticity can explain the multiplicity of properties characterizing cerebellar learning. These include multi-rate acquisition and extinction, reversibility, self-scalability, and generalization. Moreover, when the circuit embeds multiple forms of plasticity, it can easily cope with multiple behaviors endowing therefore the cerebellum with the properties needed to operate as an effective generalized forward controller.

FHF-independent conduction of action potentials along the leak-resistant cerebellar granule cell axon

Neurons in vertebrate central nervous systems initiate and conduct sodium action potentials in distinct subcellular compartments that differ architecturally and electrically. Here, we report several unanticipated passive and active properties of the cerebellar granule cell's unmyelinated axon. Whereas spike initiation at the axon initial segment relies on sodium channel (Na_v)-associated fibroblast growth factor homologous factor (FHF) proteins to delay Na_v inactivation, distal axonal Na_vs show little FHF association or FHF requirement for high-frequency transmission, velocity and waveforms of conducting action potentials. In addition, leak conductance density along the distal axon is estimated as <1% that of somatodendritic membrane. The faster inactivation rate of FHF-free Na_vs together with very low axonal leak conductance serves to minimize ionic fluxes and energetic demand during repetitive spike conduction and at rest. The absence of FHFs from Na_vs at nodes of Ranvier in the central nervous system suggests a similar mechanism of current flux minimization along myelinated axons.

FHFs are known to regulate voltage-gated sodium channels (NaVs). Here, the authors compare the role of FHFs in cerebellar granule cell propagation, and find NaVs in the distal axon function independently of FHFs, allowing for faster inactivation rates and reducing energy demands during repetitive spiking.

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.

Computational Modeling of Single Neuron Extracellular Electric Potentials and Network Local Field Potentials using LFPsim

Local Field Potentials (LFPs) are population signals generated by complex spatiotemporal interaction of current sources and dipoles. Mathematical computations of LFPs allow the study of circuit functions and dysfunctions via simulations. This paper introduces LFPsim, a NEURON-based tool for computing population LFP activity and single neuron extracellular potentials. LFPsim was developed to be used on existing cable compartmental neuron and network models. Point source, line source, and RC based filter approximations can be used to compute extracellular activity. As a demonstration of efficient implementation, we showcase LFPs from mathematical models of electrotonically compact cerebellum granule neurons and morphologically complex neurons of the neocortical column. LFPsim reproduced neocortical LFP at 8, 32, and 56 Hz via current injection, in vitro post-synaptic N_2a, N_2b waves and in vivo T-C waves in cerebellum granular layer. LFPsim also includes a simulation of multi-electrode array of LFPs in network populations to aid computational inference between biophysical activity in neural networks and corresponding multi-unit activity resulting in extracellular and evoked LFP signals.

Improved Methods for Fluorescence Microscopy Detection of Macromolecules at the Axon Initial Segment

The axonal initial segment (AIS) is the subcellular compartment required for initiation of the action potential in neurons. Scaffolding and regulatory proteins at the AIS cluster with ion channels ensuring the integrity of electrical signaling. Interference with the configuration of this protein network can lead to profound effects on neuronal polarity, excitability, cell-to-cell connectivity and brain circuit plasticity. As such, the ability to visualize AIS components with precision provides an invaluable opportunity for parsing out key molecular determinants of neuronal function. Fluorescence-based immunolabeling is a sensitive method for morphological and molecular characterization of fine structures in neurons. Yet, even when combined with confocal microscopy, detection of AIS elements with immunofluorescence has been limited by the loss of antigenicity caused by fixative materials. This technical barrier has posed significant limitations in detecting AIS components alone or in combination with other markers. Here, we designed improved protocols targeted to confocal immunofluorescence detection of the AIS marker fibroblast growth factor 14 (FGF14) in combination with the cytoskeletal-associated protein Ankyrin-G, the scaffolding protein βIV-spectrin, voltage-gated Na⁺ (Nav) channels (especially the Nav1.6 isoform) and critical cell type-specific neuronal markers such as parvalbumin, calbindin, and NeuN in the mouse brain. Notably, we demonstrate that intracardiac perfusion of animals with a commercially available solution containing 1% formaldehyde and 0.5% methanol, followed by brief fixation with cold acetone is an optimal and sensitive protocol for FGF14 and other AIS marker detection that guarantees excellent tissue integrity. With variations in the procedure, we also significantly improved the detection of Nav1.6, a Nav isoform known for its fixative-sensitivity. Overall, this study provides an ensemble of immunohistochemical recipes that permit excellent staining of otherwise invisible molecules within well-preserved tissue architecture. While improving the specific investigation of AIS physiology and cell biology, our thorough study can also serve as a roadmap for optimizing immunodetection of other fixative-sensitive proteins expanding the repertoire of enabling methods for brain studies.

Control of cerebellar granule cell output by sensory-evoked Golgi cell inhibition

Classical feed-forward inhibition involves an excitation-inhibition sequence that enhances the temporal precision of neuronal responses by narrowing the window for synaptic integration. In the input layer of the cerebellum, feed-forward inhibition is thought to preserve the temporal fidelity of granule cell spikes during mossy fiber stimulation. Although this classical feed-forward inhibitory circuit has been demonstrated in vitro, the extent to which inhibition shapes granule cell sensory responses in vivo remains unresolved. Here we combined whole-cell patch-clamp recordings in vivo and dynamic clamp recordings in vitro to directly assess the impact of Golgi cell inhibition on sensory information transmission in the granule cell layer of the cerebellum. We show that the majority of granule cells in Crus II of the cerebrocerebellum receive sensory-evoked phasic and spillover inhibition prior to mossy fiber excitation. This preceding inhibition reduces granule cell excitability and sensory-evoked spike precision, but enhances sensory response reproducibility across the granule cell population. Our findings suggest that neighboring granule cells and Golgi cells can receive segregated and functionally distinct mossy fiber inputs, enabling Golgi cells to regulate the size and reproducibility of sensory responses.

Synaptic representation of locomotion in single cerebellar granule cells

The cerebellum plays a crucial role in the regulation of locomotion, but how movement is represented at the synaptic level is not known. Here, we use in vivo patch-clamp recordings to show that locomotion can be directly read out from mossy fiber synaptic input and spike output in single granule cells. The increase in granule cell spiking during locomotion is enhanced by glutamate spillover currents recruited during movement. Surprisingly, the entire step sequence can be predicted from input EPSCs and output spikes of a single granule cell, suggesting that a robust gait code is present already at the cerebellar input layer and transmitted via the granule cell pathway to downstream Purkinje cells. Thus, synaptic input delivers remarkably rich information to single neurons during locomotion.

The effect of desflurane on neuronal communication at a central synapse

Although general anesthetics are thought to modify critical neuronal functions, their impact on neuronal communication has been poorly examined. We have investigated the effect induced by desflurane, a clinically used general anesthetic, on information transfer at the synapse between mossy fibers and granule cells of cerebellum, where this analysis can be carried out extensively. Mutual information values were assessed by measuring the variability of postsynaptic output in relationship to the variability of a given set of presynaptic inputs. Desflurane synchronized granule cell firing and reduced mutual information in response to physiologically relevant mossy fibers patterns. The decrease in spike variability was due to an increased postsynaptic membrane excitability, which made granule cells more prone to elicit action potentials, and to a strengthened synaptic inhibition, which markedly hampered membrane depolarization. These concomitant actions on granule cells firing indicate that desflurane re-shapes the transfer of information between neurons by providing a less informative neurotransmission rather than completely silencing neuronal activity.

Action potential processing in a detailed Purkinje cell model reveals a critical role for axonal compartmentalization

The Purkinje cell (PC) is among the most complex neurons in the brain and plays a critical role for cerebellar functioning. PCs operate as fast pacemakers modulated by synaptic inputs but can switch from simple spikes to complex bursts and, in some conditions, show bistability. In contrast to original works emphasizing dendritic Ca-dependent mechanisms, recent experiments have supported a primary role for axonal Na-dependent processing, which could effectively regulate spike generation and transmission to deep cerebellar nuclei (DCN). In order to account for the numerous ionic mechanisms involved (at present including Nav1.6, Cav2.1, Cav3.1, Cav3.2, Cav3.3, Kv1.1, Kv1.5, Kv3.3, Kv3.4, Kv4.3, KCa1.1, KCa2.2, KCa3.1, Kir2.x, HCN1), we have elaborated a multicompartmental model incorporating available knowledge on localization and gating of PC ionic channels. The axon, including initial segment (AIS) and Ranvier nodes (RNs), proved critical to obtain appropriate pacemaking and firing frequency modulation. Simple spikes initiated in the AIS and protracted discharges were stabilized in the soma through Na-dependent mechanisms, while somato-dendritic Ca channels contributed to sustain pacemaking and to generate complex bursting at high discharge regimes. Bistability occurred only following Na and Ca channel down-regulation. In addition, specific properties in RNs K currents were required to limit spike transmission frequency along the axon. The model showed how organized electroresponsive functions could emerge from the molecular complexity of PCs and showed that the axon is fundamental to complement ionic channel compartmentalization enabling action potential processing and transmission of specific spike patterns to DCN.

Axon-somatic back-propagation in detailed models of spinal alpha motoneurons

Antidromic action potentials following distal stimulation of motor axons occasionally fail to invade the soma of alpha motoneurons in spinal cord, due to their passing through regions of high non-uniformity. Morphologically detailed conductance-based models of cat spinal alpha motoneurons have been developed, with the aim to reproduce and clarify some aspects of the electrophysiological behavior of the antidromic axon-somatic spike propagation. Fourteen 3D morphologically detailed somata and dendrites of cat spinal alpha motoneurons have been imported from an open-access web-based database of neuronal morphologies, NeuroMorpho.org, and instantiated in neurocomputational models. An axon hillock, an axonal initial segment and a myelinated axon are added to each model. By sweeping the diameter of the axonal initial segment (AIS) and the axon hillock, as well as the maximal conductances of sodium channels at the AIS and at the soma, the developed models are able to show the relationships between different geometric and electrophysiological configurations and the voltage attenuation of the antidromically traveling wave. In particular, a greater than usually admitted sodium conductance at AIS is necessary and sufficient to overcome the dramatic voltage attenuation occurring during antidromic spike propagation both at the myelinated axon-AIS and at the AIS-soma transitions.

Components of action potential repolarization in cerebellar parallel fibres

Repolarization of the presynaptic action potential is essential for transmitter release, excitability and energy expenditure. Little is known about repolarization in thin, unmyelinated axons forming en passant synapses, which represent the most common type of axons in the mammalian brain's grey matter.We used rat cerebellar parallel fibres, an example of typical grey matter axons, to investigate the effects of K(+) channel blockers on repolarization. We show that repolarization is composed of a fast tetraethylammonium (TEA)-sensitive component, determining the width and amplitude of the spike, and a slow margatoxin (MgTX)-sensitive depolarized after-potential (DAP). These two components could be recorded at the granule cell soma as antidromic action potentials and from the axons with a newly developed miniaturized grease-gap method. A considerable proportion of fast repolarization remained in the presence of TEA, MgTX, or both. This residual was abolished by the addition of quinine. The importance of proper control of fast repolarization was demonstrated by somatic recordings of antidromic action potentials. In these experiments, the relatively broad K(+) channel blocker 4-aminopyridine reduced the fast repolarization, resulting in bursts of action potentials forming on top of the DAP. We conclude that repolarization of the action potential in parallel fibres is supported by at least three groups of K(+) channels. Differences in their temporal profiles allow relatively independent control of the spike and the DAP, whereas overlap of their temporal profiles provides robust control of axonal bursting properties.

Regulation of output spike patterns by phasic inhibition in cerebellar granule cells

The complex interplay of multiple molecular mechanisms taking part to synaptic integration is hard to disentangle experimentally. Therefore, we developed a biologically realistic computational model based on the rich set of data characterizing the cerebellar glomerulus microcircuit. A specific issue was to determine the relative role of phasic and tonic inhibition in dynamically regulating granule cell firing, which has not been clarified yet. The model comprised the excitatory mossy fiber—granule cell and the inhibitory Golgi cell—granule cell synapses and accounted for vesicular release processes, neurotransmitter diffusion and activation of different receptor subtypes. Phasic inhibition was based on stochastic GABA release and spillover causing activation of two major classes of postsynaptic receptors, α1 and α6, while tonic inhibition was based on steady regulation of a Cl⁻ leakage. The glomerular microcircuit model was validated against experimental responses to mossy fiber bursts while metabotropic receptors were blocked. Simulations showed that phasic inhibition controlled the number of spikes during burst transmission but predicted that it specifically controlled time-related parameters (firing initiation and conclusion and first spike precision) when the relative phase of excitation and inhibition was changed. In all conditions, the overall impact of α6 was larger than that of α1 subunit-containing receptors. However, α1 receptors controlled granule cell responses in a narrow ±10 ms band while α6 receptors showed broader ±50 ms tuning. Tonic inhibition biased these effects without changing their nature substantially. These simulations imply that phasic inhibitory mechanisms can dynamically regulate output spike patterns, as well as calcium influx and NMDA currents, at the mossy fiber—granule cell relay of cerebellum without the intervention of tonic inhibition.

Computational modeling predicts the ionic mechanism of late-onset responses in unipolar brush cells

Unipolar Brush Cells (UBCs) have been suggested to play a critical role in cerebellar functioning, yet the corresponding cellular mechanisms remain poorly understood. UBCs have recently been reported to generate, in addition to early-onset glutamate receptor-dependent synaptic responses, a late-onset response (LOR) composed of a slow depolarizing ramp followed by a spike burst (Locatelli et al., 2013). The LOR activates as a consequence of synaptic activity and involves an intracellular cascade modulating H- and TRP-current gating. In order to assess the LOR mechanisms, we have developed a UBC multi-compartmental model (including soma, dendrite, initial segment, and axon) incorporating biologically realistic representations of ionic currents and a cytoplasmic coupling mechanism regulating TRP and H channel gating. The model finely reproduced UBC responses to current injection, including a burst triggered by a low-threshold spike (LTS) sustained by CaLVA currents, a persistent discharge sustained by CaHVA currents, and a rebound burst following hyperpolarization sustained by H- and CaLVA-currents. Moreover, the model predicted that H- and TRP-current regulation was necessary and sufficient to generate the LOR and its dependence on the intensity and duration of mossy fiber activity. Therefore, the model showed that, using a basic set of ionic channels, UBCs generate a rich repertoire of bursts, which could effectively implement tunable delay-lines in the local microcircuit.

Realistic modeling of neurons and networks: towards brain simulation

Realistic modeling is a new advanced methodology for investigating brain functions. Realistic modeling is based on a detailed biophysical description of neurons and synapses, which can be integrated into microcircuits. The latter can, in turn, be further integrated to form large-scale brain networks and eventually to reconstruct complex brain systems. Here we provide a review of the realistic simulation strategy and use the cerebellar network as an example. This network has been carefully investigated at molecular and cellular level and has been the object of intense theoretical investigation. The cerebellum is thought to lie at the core of the forward controller operations of the brain and to implement timing and sensory prediction functions. The cerebellum is well described and provides a challenging field in which one of the most advanced realistic microcircuit models has been generated. We illustrate how these models can be elaborated and embedded into robotic control systems to gain insight into how the cellular properties of cerebellar neurons emerge in integrated behaviors. Realistic network modeling opens up new perspectives for the investigation of brain pathologies and for the neurorobotic field.

Complementing Neurophysiology Education for Developing Countries via Cost-Effective Virtual Labs: Case Studies and Classroom Scenarios

Classroom-level neuroscience experiments vary from detailed protocols involving chemical, physiological and imaging techniques to computer-based modeling. The application of Information and Communication Technology (ICT) is revolutionizing the current laboratory scenario in terms of active learning especially for distance education cases. Virtual web-based labs are an asset to educational institutions confronting economic issues in maintaining equipment, facilities and other conditions needed for good laboratory practice. To enhance education, we developed virtual laboratories in neuroscience and explored their first-level use in (Indian) University education in the context of developing countries. Besides using interactive animations and remotely-triggered experimental devices, a detailed mathematical simulator was implemented on a web-based software platform. In this study, we focused on the perceptions of technology adoption for a virtual neurophysiology laboratory as a new pedagogy tool for complementing college laboratory experience. The study analyses the effect of virtual labs on users assessing the relationship between cognitive, social and teaching presence. Combining feedback from learners and teachers, the study suggests enhanced motivation for students and improved teaching experience for instructors.

Melatonin protects rat cerebellar granule cells against electromagnetic field-induced increases in Na(+) currents through intracellular Ca(2+) release

Although melatonin (MT) has been reported to protect cells against oxidative damage induced by electromagnetic radiation, few reports have addressed whether there are other protective mechanisms. Here, we investigated the effects of MT on extremely low-frequency electromagnetic field (ELF-EMF)-induced Nav activity in rat cerebellar granule cells (GCs). Exposing cerebellar GCs to ELF-EMF for 60 min. significantly increased the Nav current (INa ) densities by 62.5%. MT (5 μM) inhibited the ELF-EMF-induced INa increase. This inhibitory effect of MT is mimicked by an MT2 receptor agonist and was eliminated by an MT2 receptor antagonist. The Nav channel steady-state activation curve was significantly shifted towards hyperpolarization by ELF-EMF stimulation but remained unchanged by MT in cerebellar GC that were either exposed or not exposed to ELF-EMF. ELF-EMF exposure significantly increased the intracellular levels of phosphorylated PKA in cerebellar GCs, and both MT and IIK-7 did not reduce the ELF-EMF-induced increase in phosphorylated PKA. The inhibitory effects of MT on ELF-EMF-induced Nav activity was greatly reduced by the calmodulin inhibitor KN93. Calcium imaging showed that MT did not increase the basal intracellular Ca(2+) level, but it significantly elevated the intracellular Ca(2+) level evoked by the high K(+) stimulation in cerebellar GC that were either exposed or not exposed to ELF-EMF. In the presence of ruthenium red, a ryanodine-sensitive receptor blocker, the MT-induced increase in intracellular calcium levels was reduced. Our data show for the first time that MT protects against neuronal INa that result from ELF-EMF exposure through Ca(2+) influx-induced Ca(2+) release.

The organization of plasticity in the cerebellar cortex: from synapses to control

The cerebellum is thought to play a critical role in procedural learning, but the relationship between this function and the underlying cellular and synaptic mechanisms remains largely speculative. At present, at least nine forms of long-term synaptic and nonsynaptic plasticity (some of which are bidirectional) have been reported in the cerebellar cortex and deep cerebellar nuclei. These include long-term potentiation (LTP) and long-term depression at the mossy fiber-granule cell synapse, at the synapses formed by parallel fibers, climbing fibers, and molecular layer interneurons on Purkinje cells, and at the synapses formed by mossy fibers and Purkinje cells on deep cerebellar nuclear cells, as well as LTP of intrinsic excitability in granule cells, Purkinje cells, and deep cerebellar nuclear cells. It is suggested that the complex properties of cerebellar learning would emerge from the distribution of plasticity in the network and from its dynamic remodeling during the different phases of learning. Intrinsic and extrinsic factors may hold the key to explain how the different forms of plasticity cooperate to select specific transmission channels and to regulate the signal-to-noise ratio through the cerebellar cortex. These factors include regulation of neuronal excitation by local inhibitory networks, engagement of specific molecular mechanisms by spike bursts and theta-frequency oscillations, and gating by external neuromodulators. Therefore, a new and more complex view of cerebellar plasticity is emerging with respect to that predicted by the original "Motor Learning Theory," opening issues that will require experimental and computational testing.

Cell layers and neuropil: contrast-enhanced MRI of mouse brain in vivo

Contrast-enhanced T₁- and T₂-weighted MRI at 9.4 T and in-plane resolutions of 25 and 30 µm has been demonstrated to differentiate between neural tissues in mouse brain in vivo, including granule cell layers, principal cell layers, general neuropil, specialized neuropil and white matter. In T₁-weighted MRI of the olfactory bulb, hippocampus and cerebellum, contrast obtained by the intracranial administration of gadopentetate dimeglumine (Gd-DTPA) reflects the extra- and intracellular spaces of gray matter in agreement with histological data. General neuropil areas are highlighted, whereas other tissues present with lower signal intensities. The induced contrast is similar to that in plain T₂-weighted MRI, but offers a 16-30-fold higher contrast-to-noise ratio. Systemic administration of manganese chloride increases the signal-to-noise ratio in T₁-weighted MRI to a significantly greater extent in principal cell layers and specialized neuropil than in granule cell layers, whereas gadolinium-enhanced MRI indicates no larger intracellular spaces in these tissues. Granule cell layers are enhanced no more than general neuropil by manganese, whereas gadolinium-enhanced MRI indicates significantly larger intracellular spaces in the cell layers. These discrepancies suggest that the signal increase after manganese administration reflects cellular activity which is disproportionate to the intracellular space. As a result, principal cell layers and specialized neuropil become highlighted, whereas granule cell layers, general neuropil and white matter present with lower signal intensities.