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

Mathematical models of C-type and N-type inactivating heteromeric voltage gated potassium channels

Voltage gated potassium channels can be composed of either four identical, or different, pore-forming protein subunits. While the voltage gated channels with identical subunits have been extensively studied both physiologically and mathematically, those with multiple subunit types, termed heteromeric channels, have not been. Here we construct, and explore the predictive outputs of, mechanistic models for heteromeric voltage gated potassium channels that possess either N-type or C-type inactivation kinetics. For both types of inactivation, we first build Markov models of four identical pore-forming inactivating subunits. Combining this with previous results regarding non-inactivating heteromeric channels, we are able to define models for heteromeric channels containing both non-inactivating and inactivating subunits of any ratio. We simulate each model through three unique voltage clamp protocols to identify steady state properties. In doing so, we generate predictions about the impact of adding additional inactivating subunits on a total channel's kinetics. We show that while N-type inactivating subunits appear to have a non-linear impact on the level of inactivation the channel experiences, the effect of C-type inactivating subunits is almost linear. Finally, to combat the computational issues of working with a large number of state variables we define model reductions for both types of heteromeric channels. For the N-type heteromers we derive a quasi-steady-state approximation and indicate where the approximation is appropriate. With the C-type heteromers we are able to write an explicit model reduction bringing models of greater than 10 dimensions down to 2.

Purkinje cell hyperexcitability and depressive-like behavior in mice lacking erg3 (ether-à-go-go-related gene) K+ channel subunits

Potassium channels stabilize the resting potential and neuronal excitability. Among them, erg (ether-à-go-go-related gene) K+ channels represent a subfamily of voltage-gated channels, consisting of erg1, erg2, and erg3 subunits; however, their subunit-specific neuronal functions in vivo are barely understood. To find erg3- and erg1-mediated functions, we generated global Kcnh7 (erg3) and conditional Kcnh2 (erg1) knockout mice. We found that erg3 channels stabilize the resting potential and dampen spontaneous activity in cerebellar Purkinje cells (PCs) and hippocampal CA1 neurons, whereas erg1 channels have suprathreshold functions. Lack of erg3 subunits induced hyperexcitability with increased action potential firing in PCs, but not in CA1 neurons. Notably, erg3 depletion caused depressive-like behavior with reduced locomotor activity, strongly decreased digging behavior, and shorter latencies to fall off a rotating wheel, while learning and memory remained unchanged. Our data show that erg K+ channels containing erg3 subunits mediate a neuronal subthreshold K+ current that plays important roles in the regulation of locomotor behavior in vivo.

Branch-specific clustered parallel fiber input controls dendritic computation in Purkinje cells

Most central neurons have intricately branched dendritic trees that integrate massive numbers of synaptic inputs. Intrinsic active mechanisms in dendrites can be heterogeneous and be modulated in a branch-specific way. However, it remains poorly understood how heterogeneous intrinsic properties contribute to processing of synaptic input. We propose the first computational model of the cerebellar Purkinje cell with dendritic heterogeneity, in which each branch is an individual unit and is characterized by its own set of ion channel conductance densities. When simultaneously activating a cluster of parallel fiber synapses, we measure the peak amplitude of a response and observe how changes in P-type calcium channel conductance density shift the dendritic responses from a linear one to a bimodal one including dendritic calcium spikes and vice-versa. These changes relate to the morphology of each branch. We show how dendritic calcium spikes propagate and how Kv4.3 channels block spreading depolarization to nearby branches.

Fgf17: A regulator of the mid/hind brain boundary in mammals

The Fibroblast growth factor (FGFs) family consists of at least 22 members that exert their function by binding and activating fibroblast growth factor receptors (FGFRs). The Fgf8/FgfD subfamily member, Fgf17, is located on human chromosome 8p21.3 and mouse chromosome 14 D2. In humans, FGF17 can be alternatively spliced to produce two isoforms (FGF17a and b) whereas three isoforms are present in mice (Fgf17a, b, and c), however, only Fgf17a and Fgf17b produce functional proteins. Fgf17 is a secreted protein with a cleavable N-terminal signal peptide and contains two binding domains, namely a conserved core region and a heparin binding site. Fgf17 mRNA is expressed in a wide range of different tissues during development, including the rostral patterning centre, midbrain-hindbrain boundary, tailbud mesoderm, olfactory placode, mammary glands, and smooth muscle precursors of major arteries. Given its broad expression pattern during development, it is surprising that adult Fgf17-/- mice displayed a rather mild phenotype; such that mutants only exhibited morphological changes in the frontal cortex and mid/hind brain boundary and changes in certain social behaviours. In humans, FGF17 mutations are implicated in several diseases, including Congenital Hypogonadotropic Hypogonadism and Kallmann Syndrome. FGF17 mutations contribute to CHH/KS in 1.1% of affected individuals, often presenting in conjunction with mutations in other FGF pathway genes like FGFR1 and FLRT3. FGF17 mutations were also identified in patients diagnosed with Dandy-Walker malformation and Pituitary Stalk Interruption Syndrome, however, it remains unclear how FGF17 is implicated in these diseases. Altered FGF17 expression has been observed in several cancers, including prostate cancer, hematopoietic cancers (acute myeloid leukemia and acute lymphoblastic leukemia), glioblastomas, perineural invasion in cervical cancer, and renal cell carcinomas. Furthermore, FGF17 has demonstrated neuroprotective effects, particularly during ischemic stroke, and has been shown to improve cognitive function in ageing mice.

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.

A biophysically comprehensive model of urothelial afferent neurons: implications for sensory signalling in urinary bladder

The urothelium is the innermost layer of the bladder wall; it plays a pivotal role in bladder sensory transduction by responding to chemical and mechanical stimuli. The urothelium also acts as a physical barrier between urine and the outer layers of the bladder wall. There is intricate sensory communication between the layers of the bladder wall and the neurons that supply the bladder, which eventually translates into the regulation of mechanical activity. In response to natural stimuli, urothelial cells release substances such as ATP, nitric oxide (NO), substance P, acetylcholine (ACh), and adenosine. These act on adjacent urothelial cells, myofibroblasts, and urothelial afferent neurons (UAN), controlling the contractile activity of the bladder. There is rising evidence on the importance of urothelial sensory signalling, yet a comprehensive understanding of the functioning of the urothelium-afferent neurons and the factors that govern it remains elusive to date. Until now, the biophysical studies done on UAN have been unable to provide adequate information on the ion channel composition of the neuron, which is paramount to understanding the electrical functioning of the UAN and, by extension, afferent signalling. To this end, we have attempted to model UAN to decipher the ionic mechanisms underlying the excitability of the UAN. In contrast to previous models, our model was built and validated using morphological and biophysical properties consistent with experimental findings for the UAN. The model included all the channels thus far known to be expressed in UAN, including; voltage-gated sodium and potassium channels, N, L, T, P/Q, R-type calcium channels, large-conductance calcium-dependent potassium (BK) channels, small conductance calcium-dependent (SK) channels, Hyperpolarisation activated cation (HCN) channels, transient receptor potential melastatin (TRPM8), transient receptor potential vanilloid (TRPV1) channel, calcium-activated chloride(CaCC) channels, and internal calcium dynamics. Our UAN model a) was constrained as far as possible by experimental data from the literature for the channels and the spiking activity, b) was validated by reproducing the experimental responses to current-clamp and voltage-clamp protocols c) was used as a base for modelling the non-urothelial afferent neurons (NUAN). Using our models, we also gained insights into the variations in ion channels between UAN and NUAN neurons.

Human Purkinje cells outperform mouse Purkinje cells in dendritic complexity and computational capacity

Purkinje cells in the cerebellum are among the largest neurons in the brain and have been extensively investigated in rodents. However, their morphological and physiological properties remain poorly understood in humans. In this study, we utilized high-resolution morphological reconstructions and unique electrophysiological recordings of human Purkinje cells ex vivo to generate computational models and estimate computational capacity. An inter-species comparison showed that human Purkinje cell had similar fractal structures but were larger than those of mouse Purkinje cells. Consequently, given a similar spine density (2/μm), human Purkinje cell hosted approximately 7.5 times more dendritic spines than those of mice. Moreover, human Purkinje cells had a higher dendritic complexity than mouse Purkinje cells and usually emitted 2-3 main dendritic trunks instead of one. Intrinsic electro-responsiveness was similar between the two species, but model simulations revealed that the dendrites could process ~6.5 times (n = 51 vs. n = 8) more input patterns in human Purkinje cells than in mouse Purkinje cells. Thus, while human Purkinje cells maintained spike discharge properties similar to those of rodents during evolution, they developed more complex dendrites, enhancing computational capacity.

Poly(N-acryloylglycine-acrylamide) Hydrogel Mimics the Cellular Microenvironment and Promotes Neurite Growth with Protection from Oxidative Stress

In this work, the glycine-based acryloyl monomer is polymerized to obtain a neurogenic polymeric hydrogel for regenerative applications. The synthesized poly(N-acryloylglycine-acrylamide) [poly(NAG-b-A)] nanohydrogel exhibits high swelling (∼1500%) and is mechanically very stable, biocompatible, and proliferative in nature. The poly(NAG-b-A) nanohydrogel provides a stable 3D extracellular mimetic environment and promotes healthy neurite growth for primary cortical neurons by facilitating cellular adhesion, proliferation, actin filament stabilization, and neuronal differentiation. Furthermore, the protective role of the poly(NAG-b-A) hydrogel for the neurons in oxidative stress conditions is revealed and it is found that it is a clinically relevant material for neuronal regenerative applications, such as for promoting nerve regeneration via GSK3β inhibition. This hydrogel additionally plays an important role in modulating the biological microenvironment, either as an agonist and antagonist or as an antioxidant. Furthermore, it favors the physiological responses and eases the neurite growth efficiency. Additionally, we found out that the conversion of glycine-based acryloyl monomers into their corresponding polymer modulates the mechanical performance, mimics the cellular microenvironment, and accelerates the self-healing capability due to the responsive behavior towards reactive oxygen species (ROS). Thus, the p(NAG-b-A) hydrogel could be a potential candidate to induce neuronal regeneration since it provides a physical cue and significantly boosts neurite outgrowth and also maintains the microtubule integrity in neuronal cells.

A GPU-based computational framework that bridges neuron simulation and artificial intelligence

Biophysically detailed multi-compartment models are powerful tools to explore computational principles of the brain and also serve as a theoretical framework to generate algorithms for artificial intelligence (AI) systems. However, the expensive computational cost severely limits the applications in both the neuroscience and AI fields. The major bottleneck during simulating detailed compartment models is the ability of a simulator to solve large systems of linear equations. Here, we present a novel Dendritic Hierarchical Scheduling (DHS) method to markedly accelerate such a process. We theoretically prove that the DHS implementation is computationally optimal and accurate. This GPU-based method performs with 2-3 orders of magnitude higher speed than that of the classic serial Hines method in the conventional CPU platform. We build a DeepDendrite framework, which integrates the DHS method and the GPU computing engine of the NEURON simulator and demonstrate applications of DeepDendrite in neuroscience tasks. We investigate how spatial patterns of spine inputs affect neuronal excitability in a detailed human pyramidal neuron model with 25,000 spines. Furthermore, we provide a brief discussion on the potential of DeepDendrite for AI, specifically highlighting its ability to enable the efficient training of biophysically detailed models in typical image classification tasks.

A multi-layer mean-field model of the cerebellum embedding microstructure and population-specific dynamics

Mean-field (MF) models are computational formalism used to summarize in a few statistical parameters the salient biophysical properties of an inter-wired neuronal network. Their formalism normally incorporates different types of neurons and synapses along with their topological organization. MFs are crucial to efficiently implement the computational modules of large-scale models of brain function, maintaining the specificity of local cortical microcircuits. While MFs have been generated for the isocortex, they are still missing for other parts of the brain. Here we have designed and simulated a multi-layer MF of the cerebellar microcircuit (including Granule Cells, Golgi Cells, Molecular Layer Interneurons, and Purkinje Cells) and validated it against experimental data and the corresponding spiking neural network (SNN) microcircuit model. The cerebellar MF was built using a system of equations, where properties of neuronal populations and topological parameters are embedded in inter-dependent transfer functions. The model time constant was optimised using local field potentials recorded experimentally from acute mouse cerebellar slices as a template. The MF reproduced the average dynamics of different neuronal populations in response to various input patterns and predicted the modulation of the Purkinje Cells firing depending on cortical plasticity, which drives learning in associative tasks, and the level of feedforward inhibition. The cerebellar MF provides a computationally efficient tool for future investigations of the causal relationship between microscopic neuronal properties and ensemble brain activity in virtual brain models addressing both physiological and pathological conditions.

Heuristic Tree-Partition-Based Parallel Method for Biophysically Detailed Neuron Simulation

Biophysically detailed neuron simulation is a powerful tool to explore the mechanisms behind biological experiments and bridge the gap between various scales in neuroscience research. However, the extremely high computational complexity of detailed neuron simulation restricts the modeling and exploration of detailed network models. The bottleneck is solving the system of linear equations. To accelerate detailed simulation, we propose a heuristic tree-partition-based parallel method (HTP) to parallelize the computation of the Hines algorithm, the kernel for solving linear equations, and leverage the strong parallel capability of the graphic processing unit (GPU) to achieve further speedup. We formulate the problem of how to get a fine parallel process as a tree-partition problem. Next, we present a heuristic partition algorithm to obtain an effective partition to efficiently parallelize the equation-solving process in detailed simulation. With further optimization on GPU, our HTP method achieves 2.2 to 8.5 folds speedup compared to the state-of-the-art GPU method and 36 to 660 folds speedup compared to the typical Hines algorithm.

A cerebellum inspired spiking neural network as a multi-model for pattern classification and robotic trajectory prediction

Spiking neural networks were introduced to understand spatiotemporal information processing in neurons and have found their application in pattern encoding, data discrimination, and classification. Bioinspired network architectures are considered for event-driven tasks, and scientists have looked at different theories based on the architecture and functioning. Motor tasks, for example, have networks inspired by cerebellar architecture where the granular layer recodes sparse representations of the mossy fiber (MF) inputs and has more roles in motor learning. Using abstractions from cerebellar connections and learning rules of deep learning network (DLN), patterns were discriminated within datasets, and the same algorithm was used for trajectory optimization. In the current work, a cerebellum-inspired spiking neural network with dynamics of cerebellar neurons and learning mechanisms attributed to the granular layer, Purkinje cell (PC) layer, and cerebellar nuclei interconnected by excitatory and inhibitory synapses was implemented. The model’s pattern discrimination capability was tested for two tasks on standard machine learning (ML) datasets and on following a trajectory of a low-cost sensor-free robotic articulator. Tuned for supervised learning, the pattern classification capability of the cerebellum-inspired network algorithm has produced more generalized models than data-specific precision models on smaller training datasets. The model showed an accuracy of 72%, which was comparable to standard ML algorithms, such as MLP (78%), Dl4jMlpClassifier (64%), RBFNetwork (71.4%), and libSVM-linear (85.7%). The cerebellar model increased the network’s capability and decreased storage, augmenting faster computations. Additionally, the network model could also implicitly reconstruct the trajectory of a 6-degree of freedom (DOF) robotic arm with a low error rate by reconstructing the kinematic parameters. The variability between the actual and predicted trajectory points was noted to be ± 3 cm (while moving to a position in a cuboid space of 25 × 30 × 40 cm). Although a few known learning rules were implemented among known types of plasticity in the cerebellum, the network model showed a generalized processing capability for a range of signals, modulating the data through the interconnected neural populations. In addition to potential use on sensor-free or feed-forward based controllers for robotic arms and as a generalized pattern classification algorithm, this model adds implications to motor learning theory.

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.

Alterations of the axon initial segment in multiple sclerosis grey matter

Grey matter damage has been established as a key contributor to disability progression in multiple sclerosis. Aside from neuronal loss and axonal transections, which predominate in cortical demyelinated lesions, synaptic alterations have been detected in both demyelinated plaques and normal-appearing grey matter, resulting in functional neuronal damage. The axon initial segment is a key element of neuronal function, responsible for action potential initiation and maintenance of neuronal polarity. Despite several reports of profound axon initial segment alterations in different pathological models, among which experimental auto-immune encephalomyelitis, whether the axon initial segment is affected in multiple sclerosis is still unknown. Using immunohistochemistry, we analysed axon initial segments from control and multiple sclerosis tissue, focusing on layer 5/6 pyramidal neurons in the neocortex and Purkinje cells in the cerebellum and performed analysis on the parameters known to control neuronal excitability, i.e. axon initial segment length and position. We found that the axon initial segment length was increased only in pyramidal neurons of inactive demyelinated lesions, compared with normal appearing grey matter tissue. In contrast, in both cell types, the axon initial segment position was altered, with an increased soma-axon initial segment gap, in both active and inactive demyelinated lesions. In addition, using a computational model, we show that this increased gap between soma and axon initial segment might increase neuronal excitability. Taken together, these results show, for the first time, changes of axon initial segments in multiple sclerosis, in active as well as inactive grey matter lesions in both neocortex and cerebellum, which might alter neuronal function.

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.

Cerebellum Involvement in Dystonia During Associative Motor Learning: Insights From a Data-Driven Spiking Network Model

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.

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.

GIRK1-Mediated Inwardly Rectifying Potassium Current Is a Candidate Mechanism Behind Purkinje Cell Excitability, Plasticity, and Neuromodulation

G-protein-coupled inwardly rectifying potassium (GIRK) channels contribute to the resting membrane potential of many neurons and play an important role in controlling neuronal excitability. Although previous studies have revealed a high expression of GIRK subunits in the cerebellum, their functional role has never been clearly described. Using patch-clamp recordings in mice cerebellar slices, we examined the properties of the GIRK currents in Purkinje cells (PCs) and investigated the effects of a selective agonist of GIRK1-containing channels, ML297 (ML), on PC firing and synaptic plasticity. We demonstrated that GIRK channel activation decreases the PC excitability by inhibiting both sodium and calcium spikes and, in addition, modulates the complex spike response evoked by climbing fiber stimulation. Our results indicate that GIRK channels have also a marked effect on synaptic plasticity of the parallel fiber-PC synapse, as the application of ML297 increased the expression of LTP while preventing LTD. We, therefore, propose that the recruitment of GIRK channels represents a crucial mechanism by which neuromodulators can control synaptic strength and membrane conductance for proper refinement of the neural network involved in memory storage and higher cognitive functions.

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.

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.

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.

High-Resolution Structures of K+ Channels

Potassium channels are present in every living cell and essential to setting up a stable, non-zero transmembrane electrostatic potential which manifests the off-equilibrium livelihood of the cell. They are involved in other cellular activities and regulation, such as the controlled release of hormones, the activation of T-cells for immune response, the firing of action potential in muscle cells and neurons, etc. Pharmacological reagents targeting potassium channels are important for treating various human diseases linked to dysfunction of the channels. High-resolution structures of these channels are very useful tools for delineating the detailed chemical basis underlying channel functions and for structure-based design and optimization of their pharmacological and pharmaceutical agents. Structural studies of potassium channels have revolutionized biophysical understandings of key concepts in the field - ion selectivity, conduction, channel gating, and modulation, making them multi-modality targets of pharmacological regulation. In this chapter, I will select a few high-resolution structures to illustrate key structural insights, proposed allostery behind channel functions, disagreements still open to debate, and channel-lipid interactions and co-evolution. The known structural consensus allows the inference of conserved molecular mechanisms shared among subfamilies of K⁺ channels and makes it possible to develop channel-specific pharmaceutical agents.

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.

Fundamental Mechanisms of Autoantibody-Induced Impairments on Ion Channels and Synapses in Immune-Mediated Cerebellar Ataxias

In the last years, different kinds of limbic encephalitis associated with autoantibodies against ion channels and synaptic receptors have been described. Many studies have demonstrated that such autoantibodies induce channel or receptor dysfunction. The same mechanism is discussed in immune-mediated cerebellar ataxias (IMCAs), but the pathogenesis has been less investigated. The aim of the present review is to evaluate what kind of cerebellar ion channels, their related proteins, and the synaptic machinery proteins that are preferably impaired by autoantibodies so as to develop cerebellar ataxias (CAs). The cerebellum predictively coordinates motor and cognitive functions through a continuous update of an internal model. These controls are relayed by cerebellum-specific functions such as precise neuronal discharges with potassium channels, synaptic plasticity through calcium signaling pathways coupled with voltage-gated calcium channels (VGCC) and metabotropic glutamate receptors 1 (mGluR1), a synaptic organization with glutamate receptor delta (GluRδ), and output signal formation through chained GABAergic neurons. Consistently, the association of CAs with anti-potassium channel-related proteins, anti-VGCC, anti-mGluR1, and GluRδ, and anti-glutamate decarboxylase 65 antibodies is observed in IMCAs. Despite ample distributions of AMPA and GABA receptors, however, CAs are rare in conditions with autoantibodies against these receptors. Notably, when the autoantibodies impair synaptic transmission, the autoimmune targets are commonly classified into three categories: release machinery proteins, synaptic adhesion molecules, and receptors. This physiopathological categorization impacts on both our understanding of the pathophysiology and clinical prognosis.

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

Cerebellar granule cells (GCs) make up the majority of all neurons in the vertebrate brain, but heterogeneities among GCs and potential functional consequences are poorly understood. Here, we identified unexpected gradients in the biophysical properties of GCs in mice. GCs closer to the white matter (inner-zone GCs) had higher firing thresholds and could sustain firing with larger current inputs than GCs closer to the Purkinje cell layer (outer-zone GCs). Dynamic Clamp experiments showed that inner- and outer-zone GCs preferentially respond to high- and low-frequency mossy fiber inputs, respectively, enabling dispersion of the mossy fiber input into its frequency components as performed by a Fourier transformation. Furthermore, inner-zone GCs have faster axonal conduction velocity and elicit faster synaptic potentials in Purkinje cells. Neuronal network modeling revealed that these gradients improve spike-timing precision of Purkinje cells and decrease the number of GCs required to learn spike-sequences. Thus, our study uncovers biophysical gradients in the cerebellar cortex enabling a Fourier-like transformation of mossy fiber inputs.

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

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

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

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

Biophysical Psychiatry-How Computational Neuroscience Can Help to Understand the Complex Mechanisms of Mental Disorders

The brain is the most complex of human organs, and the pathophysiology underlying abnormal brain function in psychiatric disorders is largely unknown. Despite the rapid development of diagnostic tools and treatments in most areas of medicine, our understanding of mental disorders and their treatment has made limited progress during the last decades. While recent advances in genetics and neuroscience have a large potential, the complexity and multidimensionality of the brain processes hinder the discovery of disease mechanisms that would link genetic findings to clinical symptoms and behavior. This applies also to schizophrenia, for which genome-wide association studies have identified a large number of genetic risk loci, spanning hundreds of genes with diverse functionalities. Importantly, the multitude of the associated variants and their prevalence in the healthy population limit the potential of a reductionist functional genetics approach as a stand-alone solution to discover the disease pathology. In this review, we outline the key concepts of a "biophysical psychiatry," an approach that employs large-scale mechanistic, biophysics-founded computational modelling to increase transdisciplinary understanding of the pathophysiology and strive toward robust predictions. We discuss recent scientific advances that allow a synthesis of previously disparate fields of psychiatry, neurophysiology, functional genomics, and computational modelling to tackle open questions regarding the pathophysiology of heritable mental disorders. We argue that the complexity of the increasing amount of genetic data exceeds the capabilities of classical experimental assays and requires computational approaches. Biophysical psychiatry, based on modelling diseased brain networks using existing and future knowledge of basic genetic, biochemical, and functional properties on a single neuron to a microcircuit level, may allow a leap forward in deriving interpretable biomarkers and move the field toward novel treatment options.

Complex Electroresponsive Dynamics in Olivocerebellar Neurons Represented With Extended-Generalized Leaky Integrate and Fire Models

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.

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.

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.

Complex Dynamics in Simplified Neuronal Models: Reproducing Golgi Cell Electroresponsiveness

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.

Challenges and Perspectives of Quantitative Functional Sodium Imaging (fNaI)

Brain function has been investigated via the blood oxygenation level dependent (BOLD) effect using magnetic resonance imaging (MRI) for the past decades. Advances in sodium imaging offer the unique chance to access signal changes directly linked to sodium ions (23Na) flux across the cell membrane, which generates action potentials, hence signal transmission in the brain. During this process 23Na transiently accumulates in the intracellular space. Here we show that quantitative functional sodium imaging (fNaI) at 3T is potentially sensitive to 23Na concentration changes during finger tapping, which can be quantified in gray and white matter regions key to motor function. For the first time, we measured a 23Na concentration change of 0.54 mmol/l in the ipsilateral cerebellum, 0.46 mmol/l in the contralateral primary motor cortex (M1), 0.27 mmol/l in the corpus callosum and -11 mmol/l in the ipsilateral M1, suggesting that fNaI is sensitive to distributed functional alterations. Open issues persist on the role of the glymphatic system in maintaining 23Na homeostasis, the role of excitation and inhibition as well as volume distributions during neuronal activity. Haemodynamic and physiological signal recordings coupled to realistic models of tissue function will be critical to understand the mechanisms of such changes and contribute to meeting the overarching challenge of measuring neuronal activity in vivo.

Beta-gamma burst stimulations of the inferior olive induce high-frequency oscillations in the deep cerebellar nuclei

The cerebellum displays various sorts of rhythmic activities covering both low- and high-frequency oscillations. These cerebellar high-frequency oscillations were observed in the cerebellar cortex. Here, we hypothesised that not only is the cerebellar cortex a generator of high-frequency oscillations but also that the deep cerebellar nuclei may also play a similar role. Thus, we analysed local field potentials and single-unit activities in the deep cerebellar nuclei before, during and after electric stimulation in the inferior olive of awake mice. A high-frequency oscillation of 350 Hz triggered by the stimulation of the inferior olive, within the beta-gamma range, was observed in the deep cerebellar nuclei. The amplitude and frequency of the oscillation were independent of the frequency of stimulation. This oscillation emerged during the period of stimulation and persisted after the end of the stimulation. The oscillation coincided with the inhibition of deep cerebellar neurons. As the inhibition of the deep cerebellar nuclei is related to inhibitory inputs from Purkinje cells, we speculate that the oscillation represents the unmasking of the synchronous activation of another subtype of deep cerebellar neuronal subtype, devoid of GABA receptors and under the direct control of the climbing fibres from the inferior olive. Still, the mechanism sustaining this oscillation remains to be deciphered. Our study sheds new light on the role of the olivo-cerebellar loop as the final output control of the intercerebellar circuitry.

Physiology of the cerebellum

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

Kv3 Channels: Enablers of Rapid Firing, Neurotransmitter Release, and Neuronal Endurance

The intrinsic electrical characteristics of different types of neurons are shaped by the K+ channels they express. From among the more than 70 different K+ channel genes expressed in neurons, Kv3 family voltage-dependent K+ channels are uniquely associated with the ability of certain neurons to fire action potentials and to release neurotransmitter at high rates of up to 1,000 Hz. In general, the four Kv3 channels Kv3.1-Kv3.4 share the property of activating and deactivating rapidly at potentials more positive than other channels. Each Kv3 channel gene can generate multiple protein isoforms, which contribute to the high-frequency firing of neurons such as auditory brain stem neurons, fast-spiking GABAergic interneurons, and Purkinje cells of the cerebellum, and to regulation of neurotransmitter release at the terminals of many neurons. The different Kv3 channels have unique expression patterns and biophysical properties and are regulated in different ways by protein kinases. In this review, we cover the function, localization, and modulation of Kv3 channels and describe how levels and properties of the channels are altered by changes in ongoing neuronal activity. We also cover how the protein-protein interaction of these channels with other proteins affects neuronal functions, and how mutations or abnormal regulation of Kv3 channels are associated with neurological disorders such as ataxias, epilepsies, schizophrenia, and Alzheimer's disease.

The Slow Dynamics of Intracellular Sodium Concentration Increase the Time Window of Neuronal Integration: A Simulation Study

Changes in intracellular Na⁺ concentration ([Na⁺]_i) are rarely taken into account when neuronal activity is examined. As opposed to Ca²⁺, [Na⁺]_i dynamics are strongly affected by longitudinal diffusion, and therefore they are governed by the morphological structure of the neurons, in addition to the localization of influx and efflux mechanisms. Here, we examined [Na⁺]_i dynamics and their effects on neuronal computation in three multi-compartmental neuronal models, representing three distinct cell types: accessory olfactory bulb (AOB) mitral cells, cortical layer V pyramidal cells, and cerebellar Purkinje cells. We added [Na⁺]_i as a state variable to these models, and allowed it to modulate the Na⁺ Nernst potential, the Na⁺-K⁺ pump current, and the Na⁺-Ca²⁺ exchanger rate. Our results indicate that in most cases [Na⁺]_i dynamics are significantly slower than [Ca²⁺]_i dynamics, and thus may exert a prolonged influence on neuronal computation in a neuronal type specific manner. We show that [Na⁺]_i dynamics affect neuronal activity via three main processes: reduction of EPSP amplitude in repeatedly active synapses due to reduction of the Na⁺ Nernst potential; activity-dependent hyperpolarization due to increased activity of the Na⁺-K⁺ pump; specific tagging of active synapses by extended Ca²⁺ elevation, intensified by concurrent back-propagating action potentials or complex spikes. Thus, we conclude that [Na⁺]_i dynamics should be considered whenever synaptic plasticity, extensive synaptic input, or bursting activity are examined.

Synaptic Activation of a Detailed Purkinje Cell Model Predicts Voltage-Dependent Control of Burst-Pause Responses in Active Dendrites

The dendritic processing in cerebellar Purkinje cells (PCs), which integrate synaptic inputs coming from hundreds of thousands granule cells and molecular layer interneurons, is still unclear. Here we have tested a leading hypothesis maintaining that the significant PC output code is represented by burst-pause responses (BPRs), by simulating PC responses in a biophysically detailed model that allowed to systematically explore a broad range of input patterns. BPRs were generated by input bursts and were more prominent in Zebrin positive than Zebrin negative (Z+ and Z-) PCs. Different combinations of parallel fiber and molecular layer interneuron synapses explained type I, II and III responses observed in vivo. BPRs were generated intrinsically by Ca-dependent K channel activation in the somato-dendritic compartment and the pause was reinforced by molecular layer interneuron inhibition. BPRs faithfully reported the duration and intensity of synaptic inputs, such that synaptic conductance tuned the number of spikes and release probability tuned their regularity in the millisecond range. Interestingly, the burst and pause of BPRs depended on the stimulated dendritic zone reflecting the different input conductance and local engagement of voltage-dependent channels. Multiple local inputs combined their actions generating complex spatio-temporal patterns of dendritic activity and BPRs. Thus, local control of intrinsic dendritic mechanisms by synaptic inputs emerges as a fundamental PC property in activity regimens characterized by bursting inputs from granular and molecular layer neurons.

STIM1 Regulates Somatic Ca2+ Signals and Intrinsic Firing Properties of Cerebellar Purkinje Neurons

Control of Ca²⁺ flux between the cytosol and intracellular Ca²⁺ stores is essential for maintaining normal cellular function. It has been well established in both neuronal and non-neuronal cells that stromal interaction molecule 1 (STIM1) initiates and regulates refilling Ca²⁺ into the ER. Here, we describe a novel, additional role for STIM1, the regulation of free cytosolic Ca²⁺, and the consequent control of spike firing in neurons. Among central neurons, cerebellar Purkinje neurons express the highest level of STIM1, and they fire continuously in the absence of stimulation, making somatic Ca²⁺ homeostasis of particular importance. By using Purkinje neuron-specific STIM1 knock-out (STIM1^PKO) male mice, we found that the deletion of STIM1 delayed clearance of cytosolic Ca²⁺ in the soma during ongoing neuronal firing. Deletion of STIM1 also reduced the Purkinje neuronal excitability and impaired intrinsic plasticity without affecting long-term synaptic plasticity. In vestibulo-ocular reflex learning, STIM1^PKO male mice showed severe deficits in memory consolidation, whereas they were normal in memory acquisition. Our results suggest that STIM1 is critically involved in the regulation of the neuronal excitability and the intrinsic plasticity of the Purkinje neurons as well as cerebellar memory consolidation.SIGNIFICANCE STATEMENT Stromal interaction molecule 1 (STIM1), which regulates the refilling of ER Ca²⁺, has been investigated in several systems including the CNS. In addition to a previous study showing that STIM1 regulates dendritic ER Ca²⁺ refilling and mGluR1-mediated synaptic transmission, we provide compelling evidence describing a novel role of STIM1 in spike firing Purkinje neurons. We found that STIM1 regulates cytosolic Ca²⁺ clearance of the soma during spike firing, and the interruption of this cytosolic Ca²⁺ clearing disrupts neuronal excitability and cerebellar memory consolidation. Our results provide new insights into neuronal functions of STIM1 from single neuronal Ca²⁺ dynamics to behavior level.

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.

Mathematical model of the atrioventricular nodal double response tachycardia and double-fire pathology

A proposed model consisting of two coupled models (Hodgkin-Huxley and Yanagihara-Noma-Irisawa model) is considered as a description of the heart's action potential. System of ordinary differential equations is used to recreate pathological behaviour in the conducting heart's system such as double fire and the most common tachycardia: atrioventricular nodal reentrant tachycardia (AVNRT). Part of the population has an abnormal accessory pathways: fast and slow (Fujiki, 2008). These pathways in the atrioventricular node (AV node) are anatomical and functional contributions of supraventricular tachycardia. However, the appearance of two pathways in the AV node may be a contribution of arrhythmia, which is caused by coexistent conduction by two pathways (called double fire). The difference in the conduction time between these pathways is the most important factor. This is the reason to introduce three types of couplings and delay to our system in order to reproduce various types of the AVNRT. In our research, introducing the feedback loops and couplings entails the creation of waves which can correspond to the re-entry waves occurring in the AVNRT. Our main aim is to study solutions of the given equations and take into consideration the influence of feedback and delays which occur in these pathological modes. We also present stability analysis for both components, that is Hodgkin-Huxley and Yanagihara-Noma-Irisawa models, as well as for the final double-fire model.

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.

[Influence of cefuroxime sodium on synaptic plasticity of parallel fiber-Purkinje cells in young rats]

OBJECTIVE

To investigate the influence of cefuroxime sodium (CS) on the electrophysiological function of cerebellar Purkinje cells (PCs) in Sprague-Dawley rats.

METHODS

Postnatal day 7 (P7) Sprague-Dawley rats were divided into early administration I and II groups (administered from P7 to P14) and late administration group (administered from P14 to P21), and all the groups received intraperitoneally injected CS. The control groups for early and late administration groups were also established and treated with intraperitoneally injected normal saline of the same volume. There were 10 rats in each group. The rats in the early administration I group and early administration control group were sacrificed on P15, and those in the early administration II group, late administration group, and late administration control group were sacrificed on P22. The whole-cell patch-clamp technique was used to record inward current and action potential of PCs on cerebellar slices, as well as the long-term depression (LTD) of excitatory postsynaptic current (EPSC) in PCs induced by low-frequency stimulation of parallel fiber (PF).

RESULTS

Compared with the control groups, the early and late administration groups had a slightly higher magnitude of inward current and a slightly higher amplitude of action potential of PCs (P>0.05). All administration groups had a significantly higher degree of EPSC inhibition than the control groups (P<0.01), and the early administration II group had a significantly greater degree of EPSC inhibition than the late administration group (P<0.01).

CONCLUSIONS

Early CS exposure after birth affects the synaptic plasticity of PF-PCs in the cerebellum of young rats, which persists after drug withdrawal.

At the Edge of Chaos: How Cerebellar Granular Layer Network Dynamics Can Provide the Basis for Temporal Filters

Models of the cerebellar microcircuit often assume that input signals from the mossy-fibers are expanded and recoded to provide a foundation from which the Purkinje cells can synthesize output filters to implement specific input-signal transformations. Details of this process are however unclear. While previous work has shown that recurrent granule cell inhibition could in principle generate a wide variety of random outputs suitable for coding signal onsets, the more general application for temporally varying signals has yet to be demonstrated. Here we show for the first time that using a mechanism very similar to reservoir computing enables random neuronal networks in the granule cell layer to provide the necessary signal separation and extension from which Purkinje cells could construct basis filters of various time-constants. The main requirement for this is that the network operates in a state of criticality close to the edge of random chaotic behavior. We further show that the lack of recurrent excitation in the granular layer as commonly required in traditional reservoir networks can be circumvented by considering other inherent granular layer features such as inverted input signals or mGluR2 inhibition of Golgi cells. Other properties that facilitate filter construction are direct mossy fiber excitation of Golgi cells, variability of synaptic weights or input signals and output-feedback via the nucleocortical pathway. Our findings are well supported by previous experimental and theoretical work and will help to bridge the gap between system-level models and detailed models of the granular layer network.

The 40-year history of modeling active dendrites in cerebellar Purkinje cells: emergence of the first single cell "community model"

The subject of the effects of the active properties of the Purkinje cell dendrite on neuronal function has been an active subject of study for more than 40 years. Somewhat unusually, some of these investigations, from the outset have involved an interacting combination of experimental and model-based techniques. This article recounts that 40-year history, and the view of the functional significance of the active properties of the Purkinje cell dendrite that has emerged. It specifically considers the emergence from these efforts of what is arguably the first single cell "community" model in neuroscience. The article also considers the implications of the development of this model for future studies of the complex properties of neuronal dendrites.