Detection of sequences in the cerebellar cortex: numerical estimate of the possible number of tidal-wave inducing sequences represented

Gap Junctions May Have A Computational Function In The Cerebellum: A Hypothesis

In the cerebellum, granule cells make parallel fibre contact on (and excite) Golgi cells and Golgi cells inhibit granule cells, forming an open feedback loop. Parallel fibres excite Golgi cells synaptically, each making a single contact. Golgi cells inhibit granule cells in a structure called a glomerulus almost exclusively by GABA spillover acting through extrasynaptic GABAA receptors. Golgi cells are connected dendritically by gap junctions. It has long been suspected that feedback contributes to homeostatic regulation of parallel fibre signals activity, causing the fraction of the population that are active to be maintained at a low level. We present a detailed neurophysiological and computationally-rendered model of functionally grouped Golgi cells which can infer the density of parallel fibre signals activity and convert it into proportional modulation of inhibition of granule cells. The conversion is unlearned and not actively computed; rather, output is simply the computational effect of cell morphology and network architecture. Unexpectedly, the conversion becomes more precise at low density, suggesting that self-regulation is attracted to sparse code, because it is stable. A computational function of gap junctions may not be confined to the cerebellum.

The Shape of Data: a Theory of the Representation of Information in the Cerebellar Cortex

This paper presents a model of rate coding in the cerebellar cortex. The pathway of input to output of the cerebellum forms an anatomically repeating, functionally modular network, whose basic wiring is preserved across vertebrate taxa. Each network is bisected centrally by a functionally defined cell group, a microzone, which forms part of the cerebellar circuit. Input to a network may be from tens of thousands of concurrently active mossy fibres. The model claims to quantify the conversion of input rates into the code received by a microzone. Recoding on entry converts input rates into an internal code which is homogenised in the functional equivalent of an imaginary plane, occupied by the centrally positioned microzone. Homogenised means the code exists in any random sample of parallel fibre signals over a minimum number. The nature of the code and the regimented architecture of the cerebellar cortex mean that the threshold can be represented by space so that the threshold can be met by the physical dimensions of the Purkinje cell dendritic arbour and planar interneuron networks. As a result, the whole population of a microzone receives the same code. This is part of a mechanism which orchestrates functionally indivisible behaviour of the cerebellar circuit and is necessary for coordinated control of the output cells of the circuit. In this model, fine control of Purkinje cells is by input rates to the system and not by learning so that it is in conflict with the for-years-dominant supervised learning model.

Gating by Memory: a Theory of Learning in the Cerebellum

This paper presents a model of learning by the cerebellar circuit. In the traditional and dominant learning model, training teaches finely graded parallel fibre synaptic weights which modify transmission to Purkinje cells and to interneurons that inhibit Purkinje cells. Following training, input in a learned pattern drives a training-modified response. The function is that the naive response to input rates is displaced by a learned one, trained under external supervision. In the proposed model, there is no weight-controlled graduated balance of excitation and inhibition of Purkinje cells. Instead, the balance has two functional states-a switch-at synaptic, whole cell and microzone level. The paper is in two parts. The first is a detailed physiological argument for the synaptic learning function. The second uses the function in a computational simulation of pattern memory. Against expectation, this generates a predictable outcome from input chaos (real-world variables). Training always forces synaptic weights away from the middle and towards the limits of the range, causing them to polarise, so that transmission is either robust or blocked. All conditions teach the same outcome, such that all learned patterns receive the same, rather than a bespoke, effect on transmission. In this model, the function of learning is gating-that is, to select patterns that trigger output merely, and not to modify output. The outcome is memory-operated gate activation which operates a two-state balance of weight-controlled transmission. Group activity of parallel fibres also simultaneously contains a second code contained in collective rates, which varies independently of the pattern code. A two-state response to the pattern code allows faithful, and graduated, control of Purkinje cell firing by the rate code, at gated times.

Visuomotor control in mice and primates

We conduct a comparative evaluation of the visual systems from the retina to the muscles of the mouse and the macaque monkey noting the differences and similarities between these two species. The topics covered include (1) visual-field overlap, (2) visual spatial resolution, (3) V1 cortical point-image [i.e., V1 tissue dedicated to analyzing a unit receptive field], (4) object versus motion encoding, (5) oculomotor range, (6) eye, head, and body movement coordination, and (7) neocortical and cerebellar function. We also discuss blindsight in rodents and primates which provides insights on how the neocortex mediates conscious vision in these species. This review is timely because the field of visuomotor neurophysiology is expanding beyond the macaque monkey to include the mouse; there is therefore a need for a comparative analysis between these two species on how the brain generates visuomotor responses.

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.

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.

Quantitative Comparison Of Vesicular Glutamate Transporters in rat Deep Cerebellar Nuclei

The excitatory synapses of the rat deep cerebellar nuclei (DCN) were quantitatively analyzed by vesicular glutamate transporter 1 and 2 (vGluT1 and vGluT2) immunolabeling. We calculated the number and sizes of the labeled boutons and compared them between lateral/dentate nucleus (LN/DN), posterior interposed nucleus (PIN), anterior interposed nucleus (AIN), and medial nucleus (MN). The density of vGluT1+ boutons differs significantly within these nuclei. In contrast, the vGluT2+ bouton density is more similar between different nuclei. The phylogenetically newer DCN (LN/DN and PIN) have a 39% higher density of vGluT1+ boutons than the phylogenetically older DCN (AIN and MN). The volume of vGluT1+ boutons does not differ between the DCN, however the average volume of vGluT2+ boutons is larger in MN. In summary, our current results confirm and extend our previous findings showing that the increase in dendritic and axonal wiring in phylogenetically newer DCN is associated with an increase in vGluT1+ bouton density.

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.

Exploring the significance of morphological diversity for cerebellar granule cell excitability

The relatively simple and compact morphology of cerebellar granule cells (CGCs) has led to the view that heterogeneity in CGC shape has negligible impact upon the integration of mossy fibre (MF) information. Following electrophysiological recording, 3D models were constructed from high-resolution imaging data to identify morphological features that could influence the coding of MF input patterns by adult CGCs. Quantification of MF and CGC morphology provided evidence that CGCs could be connected to the multiple rosettes that arise from a single MF input. Predictions from our computational models propose that MF inputs could be more densely encoded within the CGC layer than previous models suggest. Moreover, those MF signals arriving onto the dendrite closest to the axon will generate greater CGC excitation. However, the impact of this morphological variability on MF input selectivity will be attenuated by high levels of CGC inhibition providing further flexibility to the MF → CGC pathway. These features could be particularly important when considering the integration of multimodal MF sensory input by individual CGCs.

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.

A Hybrid Model for the Computationally-Efficient Simulation of the Cerebellar Granular Layer

The aim of the present paper is to efficiently describe the membrane potential dynamics of neural populations formed by species having a high density difference in specific brain areas. We propose a hybrid model whose main ingredients are a conductance-based model (ODE system) and its continuous counterpart (PDE system) obtained through a limit process in which the number of neurons confined in a bounded region of the brain tissue is sent to infinity. Specifically, in the discrete model, each cell is described by a set of time-dependent variables, whereas in the continuum model, cells are grouped into populations that are described by a set of continuous variables. Communications between populations, which translate into interactions among the discrete and the continuous models, are the essence of the hybrid model we present here. The cerebellum and cerebellum-like structures show in their granular layer a large difference in the relative density of neuronal species making them a natural testing ground for our hybrid model. By reconstructing the ensemble activity of the cerebellar granular layer network and by comparing our results to a more realistic computational network, we demonstrate that our description of the network activity, even though it is not biophysically detailed, is still capable of reproducing salient features of neural network dynamics. Our modeling approach yields a significant computational cost reduction by increasing the simulation speed at least 270 times. The hybrid model reproduces interesting dynamics such as local microcircuit synchronization, traveling waves, center-surround, and time-windowing.

From cerebellar texture to movement optimization

The cerebellum is a major site for supervised procedural learning and appears to be crucial for optimizing sensorimotor performance. However, the site and origin of the supervising signal are still elusive. Furthermore, its relationship with the prominent neuronal circuitry remains puzzling. In this paper, I will review the relevant information and seek to synthesize a working hypothesis that explains the unique cerebellar structure. The aim of this review was to link the distinctive functions of the cerebellum, as derived from cerebellar lesion studies, with potential elementary computations, as observed by a bottom-up approach from the cerebellar microcircuitry. The parallel fiber geometry is ideal for performing millisecond computations that extract instructive signals. In this scenario, the higher time derivatives of kinematics such as acceleration and/or jerk that occur during motor performance are detected via a tidal wave mechanism and are used (with appropriate gating) as the instructive signal to guide motor smoothing. The advantage of such a mechanism is that movements are optimized by reducing "jerkiness" which, in turn, lowers their energy requirements.

The cerebellar Golgi cell and spatiotemporal organization of granular layer activity

The cerebellar granular layer has been suggested to perform a complex spatiotemporal reconfiguration of incoming mossy fiber signals. Central to this role is the inhibitory action exerted by Golgi cells over granule cells: Golgi cells inhibit granule cells through both feedforward and feedback inhibitory loops and generate a broad lateral inhibition that extends beyond the afferent synaptic field. This characteristic connectivity has recently been investigated in great detail and been correlated with specific functional properties of these neurons. These include theta-frequency pacemaking, network entrainment into coherent oscillations and phase resetting. Important advances have also been made in terms of determining the membrane and synaptic properties of the neuron, and clarifying the mechanisms of activation by input bursts. Moreover, voltage sensitive dye imaging and multi-electrode array (MEA) recordings, combined with mathematical simulations based on realistic computational models, have improved our understanding of the impact of Golgi cell activity on granular layer circuit computations. These investigations have highlighted the critical role of Golgi cells in: generating dense clusters of granule cell activity organized in center-surround structures, implementing combinatorial operations on multiple mossy fiber inputs, regulating transmission gain, and cut-off frequency, controlling spike timing and burst transmission, and determining the sign, intensity and duration of long-term synaptic plasticity at the mossy fiber-granule cell relay. This review considers recent advances in the field, highlighting the functional implications of Golgi cells for granular layer network computation and indicating new challenges for cerebellar research.

Local field potential modeling predicts dense activation in cerebellar granule cells clusters under LTP and LTD control

Local field-potentials (LFPs) are generated by neuronal ensembles and contain information about the activity of single neurons. Here, the LFPs of the cerebellar granular layer and their changes during long-term synaptic plasticity (LTP and LTD) were recorded in response to punctate facial stimulation in the rat in vivo. The LFP comprised a trigeminal (T) and a cortical (C) wave. T and C, which derived from independent granule cell clusters, co-varied during LTP and LTD. To extract information about the underlying cellular activities, the LFP was reconstructed using a repetitive convolution (ReConv) of the extracellular potential generated by a detailed multicompartmental model of the granule cell. The mossy fiber input patterns were determined using a Blind Source Separation (BSS) algorithm. The major component of the LFP was generated by the granule cell spike Na⁺ current, which caused a powerful sink in the axon initial segment with the source located in the soma and dendrites. Reproducing the LFP changes observed during LTP and LTD required modifications in both release probability and intrinsic excitability at the mossy fiber-granule cells relay. Synaptic plasticity and Golgi cell feed-forward inhibition proved critical for controlling the percentage of active granule cells, which was 11% in standard conditions but ranged from 3% during LTD to 21% during LTP and raised over 50% when inhibition was reduced. The emerging picture is that of independent (but neighboring) trigeminal and cortical channels, in which synaptic plasticity and feed-forward inhibition effectively regulate the number of discharging granule cells and emitted spikes generating “dense” activity clusters in the cerebellar granular layer.

A realistic large-scale model of the cerebellum granular layer predicts circuit spatio-temporal filtering properties

The way the cerebellar granular layer transforms incoming mossy fiber signals into new spike patterns to be related to Purkinje cells is not yet clear. Here, a realistic computational model of the granular layer was developed and used to address four main functional hypotheses: center-surround organization, time-windowing, high-pass filtering in responses to spike bursts and coherent oscillations in response to diffuse random activity. The model network was activated using patterns inspired by those recorded in vivo. Burst stimulation of a small mossy fiber bundle resulted in granule cell bursts delimited in time (time windowing) and space (center-surround) by network inhibition. This burst–burst transmission showed marked frequency-dependence configuring a high-pass filter with cut-off frequency around 100 Hz. The contrast between center and surround properties was regulated by the excitatory–inhibitory balance. The stronger excitation made the center more responsive to 10–50 Hz input frequencies and enhanced the granule cell output (with spikes occurring earlier and with higher frequency and number) compared to the surround. Finally, over a certain level of mossy fiber background activity, the circuit generated coherent oscillations in the theta-frequency band. All these processes were fine-tuned by NMDA and GABA-A receptor activation and neurotransmitter vesicle cycling in the cerebellar glomeruli. This model shows that available knowledge on cellular mechanisms is sufficient to unify the main functional hypotheses on the cerebellum granular layer and suggests that this network can behave as an adaptable spatio-temporal filter coordinated by theta-frequency oscillations.

Combinatorial responses controlled by synaptic inhibition in the cerebellum granular layer

The granular layer of cerebellum has been long hypothesized to perform combinatorial operations on incoming signals. Although this assumption is at the basis of main computational theories of cerebellum, it has never been assessed experimentally. Here, by applying high-resolution voltage-sensitive dye imaging techniques, we show that simultaneous activation of two partially overlapping mossy fiber bundles (either with single pulses or high-frequency bursts) can cause combined excitation and combined inhibition, which are compatible with the concepts of coincidence detection and spatial pattern separation predicted by theory. Combined excitation appeared as an area in which the combination of two inputs is greater than the arithmetic sum of the individual inputs and was enhanced by gamma-aminobutyric acid type A (GABA(A)) receptor blockers. Combined inhibition was manifest as an area where two inputs combined resulted in a reduction to less than half of the activity evoked from either one of the two inputs alone and was prevented by GABA(A) receptor blockers. The combinatorial responses occupied small granular layer regions (approximately 30 microm diameter), with combined inhibition being interspersed among extended areas of combined excitation. Moreover, the combinatorial effects lasted for tens of milliseconds and combined inhibition occurred only after termination of the stimuli. These combinatorial operations, if engaged by natural input patterns in vivo, may be important to influence incoming impulses organizing spatiotemporal spike sequences to be relayed to Purkinje cells.