Brain neurons exhibit complex electroresponsive properties – including intrinsic subthreshold oscillations and pacemaking, resonance and phase-reset – which are thought to play a critical role in controlling neural network dynamics. Although these properties emerge from detailed representations of molecular-level mechanisms in “realistic” models, they cannot usually be generated by simplified neuronal models (although these may show spike-frequency adaptation and bursting). We report here that this whole set of properties can be generated by the extended generalized leaky integrate-and-fire (E-GLIF) neuron model. E-GLIF derives from the GLIF model family and is therefore mono-compartmental, keeps the limited computational load typical of a linear low-dimensional system, admits analytical solutions and can be tuned through gradient-descent algorithms. Importantly, E-GLIF is designed to maintain a correspondence between model parameters and neuronal membrane mechanisms through a minimum set of equations. In order to test its potential, E-GLIF was used to model a specific neuron showing rich and complex electroresponsiveness, the cerebellar Golgi cell, and was validated against experimental electrophysiological data recorded from Golgi cells in acute cerebellar slices. During simulations, E-GLIF was activated by stimulus patterns, including current steps and synaptic inputs, identical to those used for the experiments. The results demonstrate that E-GLIF can reproduce the whole set of complex neuronal dynamics typical of these neurons – including intensity-frequency curves, spike-frequency adaptation, post-inhibitory rebound bursting, spontaneous subthreshold oscillations, resonance, and phase-reset – providing a new effective tool to investigate brain dynamics in large-scale simulations.

The neurons of the olivocerebellar circuit exhibit complex electroresponsive dynamics, which are thought to play a fundamental role for network entraining, plasticity induction, signal processing, and noise filtering. In order to reproduce these properties in single-point neuron models, we have optimized the Extended-Generalized Leaky Integrate and Fire (E-GLIF) neuron through a multi-objective gradient-based algorithm targeting the desired input–output relationships. In this way, E-GLIF was tuned toward the unique input–output properties of Golgi cells, granule cells, Purkinje cells, molecular layer interneurons, deep cerebellar nuclei cells, and inferior olivary cells. E-GLIF proved able to simulate the complex cell-specific electroresponsive dynamics of the main olivocerebellar neurons including pacemaking, adaptation, bursting, post-inhibitory rebound excitation, subthreshold oscillations, resonance, and phase reset. The integration of these E-GLIF point-neuron models into olivocerebellar Spiking Neural Networks will allow to evaluate the impact of complex electroresponsive dynamics at the higher scales, up to motor behavior, in closed-loop simulations of sensorimotor tasks.

The cerebellum plays a crucial role in sensorimotor control and cerebellar disorders compromise adaptation and learning of motor responses. However, the link between alterations at network level and cerebellar dysfunction is still unclear. In principle, this understanding would benefit of the development of an artificial system embedding the salient neuronal and plastic properties of the cerebellum and operating in closed-loop. To this aim, we have exploited a realistic spiking computational model of the cerebellum to analyse the network correlates of cerebellar impairment. The model was modified to reproduce three different damages of the cerebellar cortex: (i) a loss of the main output neurons (Purkinje Cells), (ii) a lesion to the main cerebellar afferents (Mossy Fibers), and (iii) a damage to a major mechanism of synaptic plasticity (Long Term Depression). The modified network models were challenged with an Eye-Blink Classical Conditioning test, a standard learning paradigm used to evaluate cerebellar impairment, in which the outcome was compared to reference results obtained in human or animal experiments. In all cases, the model reproduced the partial and delayed conditioning typical of the pathologies, indicating that an intact cerebellar cortex functionality is required to accelerate learning by transferring acquired information to the cerebellar nuclei. Interestingly, depending on the type of lesion, the redistribution of synaptic plasticity and response timing varied greatly generating specific adaptation patterns. Thus, not only the present work extends the generalization capabilities of the cerebellar spiking model to pathological cases, but also predicts how changes at the neuronal level are distributed across the network, making it usable to infer cerebellar circuit alterations occurring in cerebellar pathologies.

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

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The modeling of extended microcircuits is emerging as an effective tool to simulate the neurophysiological correlates of brain activity and to investigate brain dysfunctions. However, for specific networks, a realistic modeling approach based on the combination of available physiological, morphological and anatomical data is still an open issue. One of the main problems in the generation of realistic networks lies in the strategy adopted to build network connectivity. Here we propose a method to implement a neuronal network at single cell resolution by using the geometrical probability volumes associated with pre- and postsynaptic neurites. This allows us to build a network with plausible connectivity properties without the explicit use of computationally intensive touch detection algorithms using full 3D neuron reconstructions. The method has been benchmarked for the mouse hippocampus CA1 area, and the results show that this approach is able to generate full-scale brain networks at single cell resolution that are in good agreement with experimental findings. This geometric reconstruction of axonal and dendritic occupancy, by effectively reflecting morphological and anatomical constraints, could be integrated into structured simulators generating entire circuits of different brain areas facilitating the simulation of different brain regions with realistic models.

11Brain neurons exhibit complex electroresponsive properties -including intrinsic subthreshold 12 oscillations and pacemaking, resonance and phase-reset -which are thought to play a critical role 13 in controlling neural network dynamics. Although these properties emerge from detailed 14representations of molecular-level mechanisms in "realistic" models, they cannot usually be 15 generated by simplified neuronal models (although these may show spike-frequency adaptation 16 and bursting). We report here that this whole set of properties can be generated by the extended 17 generalized leaky integrate-and-fire (E-GLIF) neuron model. E-GLIF derives from the GLIF 18 model family and is therefore mono-compartmental, keeps the limited computational load typical 19 of a linear low-dimensional system, admits analytical solutions and can be tuned through gradient-20 descent algorithms. Importantly, E-GLIF is designed to maintain a correspondence between model 21 parameters and neuronal membrane mechanisms through a minimum set of equations. In order to 22 test its potential, E-GLIF was used to model a specific neuron showing rich and complex 23 electroresponsiveness, the cerebellar Golgi cell, and was validated against experimental 24 electrophysiological data recorded from Golgi cells in acute cerebellar slices. During simulations, 25 E-GLIF was activated by stimulus patterns, including current steps and synaptic inputs, identical 26 to those used for the experiments. The results demonstrate that E-GLIF can reproduce the whole 27 set of complex neuronal dynamics typical of these neurons -including intensity-frequency curves, 28 spike-frequency adaptation, depolarization-induced and post-inhibitory rebound bursting, 29 spontaneous subthreshold oscillations, resonance and phase-reset, -providing a new effective tool 30to investigate brain dynamics in large-scale simulations. 31Word count (body of the text): 8047. Figures: 9. Tables: 5 . 32 33 65 Gerstner, 2005). However, the nonlinearity entailed more difficulties in optimizing model 66 parameters and in computational efficiency. Therefore, recently, new linear adaptive point models 67have been developed (Generalized LIF, GLIF), with spike-triggered currents and moving threshold 68 as the source of adaptation (Mihalaş and Niebur, 2009) and with stochastic processes in firing 69 emission (Pozzorini et al., 2015; Rössert et al., 2016). The possibility to use a linear and 70 analytically solvable neuron model is fundamental when simulating large-scale SNNs, since 71 computational efficiency can be enhanced without severe loss in spike time accuracy and realism 72 (Hanuschkin et al., 2010). However, GLIF can hardly generate phenomena like subthreshold 73 oscillations, resonance and phase-reset, which are critical for large-scale network entrainment and 74 communication (Buzsáki, 2004; Buzsáki and Draghun, 2004). 75We propose here an extended GLIF (E-GLIF) model, which achieves a sound compromise 76 between model complexity, biological plausibility and computational efficienc...

Dystonia is a movement disorder characterized by sustained or intermittent muscle contractions causing abnormal, often repetitive movements, postures, or both. Although dystonia is traditionally associated with basal ganglia dysfunction, recent evidence has been pointing to a role of the cerebellum, a brain area involved in motor control and learning. Cerebellar abnormalities have been correlated with dystonia but their potential causative role remains elusive. Here, we simulated the cerebellar input-output relationship with high-resolution computational modeling. We used a data-driven cerebellar Spiking Neural Network and simulated a cerebellum-driven associative learning task, Eye-Blink Classical Conditioning (EBCC), which is characteristically altered in relation to cerebellar lesions in several pathologies. In control simulations, input stimuli entrained characteristic network dynamics and induced synaptic plasticity along task repetitions, causing a progressive spike suppression in Purkinje cells with consequent facilitation of deep cerebellar nuclei cells. These neuronal processes caused a progressive acquisition of eyelid Conditioned Responses (CRs). Then, we modified structural or functional local neural features in the network reproducing alterations reported in dystonic mice. Either reduced olivocerebellar input or aberrant Purkinje cell burst-firing resulted in abnormal learning curves imitating the dysfunctional EBCC motor responses (in terms of CR amount and timing) of dystonic mice. These behavioral deficits might be due to altered temporal processing of sensorimotor information and uncoordinated control of muscle contractions. Conversely, an imbalance of excitatory and inhibitory synaptic densities on Purkinje cells did not reflect into significant EBCC deficit. The present work suggests that only certain types of alterations, including reduced olivocerebellar input and aberrant PC burst-firing, are compatible with the EBCC changes observed in dystonia, indicating that some cerebellar lesions can have a causative role in the pathogenesis of symptoms.