Voltage- and Branch-Specific Climbing Fiber Responses in Purkinje Cells

Computational Modeling of Extrasynaptic NMDA Receptors: Insights into Dendritic Signal Amplification Mechanisms

Dendritic structures play a pivotal role in the computational processes occurring within neurons. Signal propagation along dendrites relies on both passive conduction and active processes related to voltage-dependent ion channels. Among these channels, extrasynaptic N-methyl-D-aspartate channels (exNMDA) emerge as a significant contributor. Prior studies have mainly concentrated on interactions between synapses and nearby exNMDA (100 nm-10 µm from synapse), activated by presynaptic membrane glutamate. This study concentrates on the correlation between synaptic inputs and distal exNMDA (>100 µm), organized in clusters that function as signal amplifiers. Employing a computational model of a dendrite, we elucidate the mechanism underlying signal amplification in exNMDA clusters. Our findings underscore the pivotal role of the optimal spatial positioning of the NMDA cluster in determining signal amplification efficiency. Additionally, we demonstrate that exNMDA subunits characterized by a large conduction decay constant. Specifically, NR2B subunits exhibit enhanced effectiveness in signal amplification compared to subunits with steeper conduction decay. This investigation extends our understanding of dendritic computational processes by emphasizing the significance of distant exNMDA clusters as potent signal amplifiers. The implications of our computational model shed light on the spatial considerations and subunit characteristics that govern the efficiency of signal amplification in dendritic structures, offering valuable insights for future studies in neurobiology and computational neuroscience.

Mesoscale simulations predict the role of synergistic cerebellar plasticity during classical eyeblink conditioning

According to the motor learning theory by Albus and Ito, synaptic depression at the parallel fibre to Purkinje cells synapse (pf-PC) is the main substrate responsible for learning sensorimotor contingencies under climbing fibre control. However, recent experimental evidence challenges this relatively monopolistic view of cerebellar learning. Bidirectional plasticity appears crucial for learning, in which different microzones can undergo opposite changes of synaptic strength (e.g. downbound microzones-more likely depression, upbound microzones-more likely potentiation), and multiple forms of plasticity have been identified, distributed over different cerebellar circuit synapses. Here, we have simulated classical eyeblink conditioning (CEBC) using an advanced spiking cerebellar model embedding downbound and upbound modules that are subject to multiple plasticity rules. Simulations indicate that synaptic plasticity regulates the cascade of precise spiking patterns spreading throughout the cerebellar cortex and cerebellar nuclei. CEBC was supported by plasticity at the pf-PC synapses as well as at the synapses of the molecular layer interneurons (MLIs), but only the combined switch-off of both sites of plasticity compromised learning significantly. By differentially engaging climbing fibre information and related forms of synaptic plasticity, both microzones contributed to generate a well-timed conditioned response, but it was the downbound module that played the major role in this process. The outcomes of our simulations closely align with the behavioural and electrophysiological phenotypes of mutant mice suffering from cell-specific mutations that affect processing of their PC and/or MLI synapses. Our data highlight that a synergy of bidirectional plasticity rules distributed across the cerebellum can facilitate finetuning of adaptive associative behaviours at a high spatiotemporal resolution.

Aging, Neurodegenerative Disorders, and Cerebellum

An important part of the central nervous system (CNS), the cerebellum is involved in motor control, learning, reflex adaptation, and cognition. Diminished cerebellar function results in the motor and cognitive impairment observed in patients with neurodegenerative disorders such as Alzheimer's disease (AD), vascular dementia (VD), Parkinson's disease (PD), Huntington's disease (HD), spinal muscular atrophy (SMA), amyotrophic lateral sclerosis (ALS), Friedreich's ataxia (FRDA), and multiple sclerosis (MS), and even during the normal aging process. In most neurodegenerative disorders, impairment mainly occurs as a result of morphological changes over time, although during the early stages of some disorders such as AD, the cerebellum also serves a compensatory function. Biological aging is accompanied by changes in cerebellar circuits, which are predominantly involved in motor control. Despite decades of research, the functional contributions of the cerebellum and the underlying molecular mechanisms in aging and neurodegenerative disorders remain largely unknown. Therefore, this review will highlight the molecular and cellular events in the cerebellum that are disrupted during the process of aging and the development of neurodegenerative disorders. We believe that deeper insights into the pathophysiological mechanisms of the cerebellum during aging and the development of neurodegenerative disorders will be essential for the design of new effective strategies for neuroprotection and the alleviation of some neurodegenerative disorders.

Recent data on the cerebellum require new models and theories

The cerebellum has been a popular topic for theoretical studies because its structure was thought to be simple. Since David Marr and James Albus related its function to motor skill learning and proposed the Marr-Albus cerebellar learning model, this theory has guided and inspired cerebellar research. In this review, we summarize the theoretical progress that has been made within this framework of error-based supervised learning. We discuss the experimental progress that demonstrates more complicated molecular and cellular mechanisms in the cerebellum as well as new cell types and recurrent connections. We also cover its involvement in diverse non-motor functions and evidence of other forms of learning. Finally, we highlight the need to explain these new experimental findings into an integrated cerebellar model that can unify its diverse computational functions.

Climbing fiber multi-innervation of mouse Purkinje dendrites with arborization common to human

Canonically, each Purkinje cell (PC) in the adult cerebellum receives only one climbing fiber (CF) from the inferior olive. Underlying current theories of cerebellar function is the notion that this highly conserved one-to-one relationship renders Purkinje dendrites into a single computational compartment. However, we discovered that multiple primary dendrites are a near-universal morphological feature in humans. Using tract tracing, immunolabeling, and in vitro electrophysiology, we found that in mice ~25% of mature multibranched cells receive more than one CF input. Two-photon calcium imaging in vivo revealed that separate dendrites can exhibit distinct response properties to sensory stimulation, indicating that some multibranched cells integrate functionally independent CF-receptive fields. These findings indicate that PCs are morphologically and functionally more diverse than previously thought.

Basket to Purkinje Cell Inhibitory Ephaptic Coupling Is Abolished in Episodic Ataxia Type 1

Dominantly inherited missense mutations of the KCNA1 gene, which encodes the KV1.1 potassium channel subunit, cause Episodic Ataxia type 1 (EA1). Although the cerebellar incoordination is thought to arise from abnormal Purkinje cell output, the underlying functional deficit remains unclear. Here we examine synaptic and non-synaptic inhibition of Purkinje cells by cerebellar basket cells in an adult mouse model of EA1. The synaptic function of basket cell terminals was unaffected, despite their intense enrichment for KV1.1-containing channels. In turn, the phase response curve quantifying the influence of basket cell input on Purkine cell output was maintained. However, ultra-fast non-synaptic ephaptic coupling, which occurs in the cerebellar 'pinceau' formation surrounding the axon initial segment of Purkinje cells, was profoundly reduced in EA1 mice in comparison with their wild type littermates. The altered temporal profile of basket cell inhibition of Purkinje cells underlines the importance of Kv1.1 channels for this form of signalling, and may contribute to the clinical phenotype of EA1.

Diverse role of NMDA receptors for dendritic integration of neural dynamics

Neurons, represented as a tree structure of morphology, have various distinguished branches of dendrites. Different types of synaptic receptors distributed over dendrites are responsible for receiving inputs from other neurons. NMDA receptors (NMDARs) are expressed as excitatory units, and play a key physiological role in synaptic function. Although NMDARs are widely expressed in most types of neurons, they play a different role in the cerebellar Purkinje cells (PCs). Utilizing a computational PC model with detailed dendritic morphology, we explored the role of NMDARs at different parts of dendritic branches and regions. We found somatic responses can switch from silent, to simple spikes and complex spikes, depending on specific dendritic branches. Detailed examination of the dendrites regarding their diameters and distance to soma revealed diverse response patterns, yet explain two firing modes, simple and complex spike. Taken together, these results suggest that NMDARs play an important role in controlling excitability sensitivity while taking into account the factor of dendritic properties. Given the complexity of neural morphology varying in cell types, our work suggests that the functional role of NMDARs is not stereotyped but highly interwoven with local properties of neuronal structure.

Constrain Bias Addition to Train Low-Latency Spiking Neural Networks

In recent years, a third-generation neural network, namely, spiking neural network, has received plethora of attention in the broad areas of Machine learning and Artificial Intelligence. In this paper, a novel differential-based encoding method is proposed and new spike-based learning rules for backpropagation is derived by constraining the addition of bias voltage in spiking neurons. The proposed differential encoding method can effectively exploit the correlation between the data and improve the performance of the proposed model, and the new learning rule can take complete advantage of the modulation properties of bias on the spike firing threshold. We experiment with the proposed model on the environmental sound dataset RWCP and the image dataset MNIST and Fashion-MNIST, respectively, and assign various conditions to test the learning ability and robustness of the proposed model. The experimental results demonstrate that the proposed model achieves near-optimal results with a smaller time step by maintaining the highest accuracy and robustness with less training data. Among them, in MNIST dataset, compared with the original spiking neural network with the same network structure, we achieved a 0.39% accuracy improvement.

Multimodal parameter spaces of a complex multi-channel neuron model

One of the most common types of models that helps us to understand neuron behavior is based on the Hodgkin-Huxley ion channel formulation (HH model). A major challenge with inferring parameters in HH models is non-uniqueness: many different sets of ion channel parameter values produce similar outputs for the same input stimulus. Such phenomena result in an objective function that exhibits multiple modes (i.e., multiple local minima). This non-uniqueness of local optimality poses challenges for parameter estimation with many algorithmic optimization techniques. HH models additionally have severe non-linearities resulting in further challenges for inferring parameters in an algorithmic fashion. To address these challenges with a tractable method in high-dimensional parameter spaces, we propose using a particular Markov chain Monte Carlo (MCMC) algorithm, which has the advantage of inferring parameters in a Bayesian framework. The Bayesian approach is designed to be suitable for multimodal solutions to inverse problems. We introduce and demonstrate the method using a three-channel HH model. We then focus on the inference of nine parameters in an eight-channel HH model, which we analyze in detail. We explore how the MCMC algorithm can uncover complex relationships between inferred parameters using five injected current levels. The MCMC method provides as a result a nine-dimensional posterior distribution, which we analyze visually with solution maps or landscapes of the possible parameter sets. The visualized solution maps show new complex structures of the multimodal posteriors, and they allow for selection of locally and globally optimal value sets, and they visually expose parameter sensitivities and regions of higher model robustness. We envision these solution maps as enabling experimentalists to improve the design of future experiments, increase scientific productivity and improve on model structure and ideation when the MCMC algorithm is applied to experimental data.

Structure, Function, and Genetics of the Cerebellum in Autism

Autism spectrum disorders are common neurodevelopmental disorders that are defined by core behavioral symptoms but have diverse genetic and environmental risk factors. Despite its etiological heterogeneity, several unifying theories of autism have been proposed, including a central role for cerebellar dysfunction. The cerebellum follows a protracted course of development that culminates in an exquisitely crafted brain structure containing over half of the neurons in the entire brain densely packed into a highly organized structure. Through its complex network of connections with cortical and subcortical brain regions, the cerebellum acts as a sensorimotor regulator and affects changes in executive and limbic processing. In this review, we summarize the structural, functional, and genetic contributions of the cerebellum to autism.

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.

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.

Interactions among diameter, myelination, and the Na/K pump affect axonal resilience to high-frequency spiking

The reliability of spike propagation in axons is determined by complex interactions among ionic currents, ion pumps, and morphological properties. We use compartment-based modeling to reveal that interactions of diameter, myelination, and the Na/K pump determine the reliability of high-frequency spike propagation. By acting as a “reservoir” of nodal Na⁺ influx, myelinated compartments efficiently increase propagation reliability. Although spike broadening was thought to oppose fast spiking, its effect on spike propagation is complicated, depending on the balance of Na⁺ channel inactivation gate recovery, Na⁺ influx, and axial charge. Our findings suggest that slow Na⁺ removal influences axonal resilience to high-frequency spike propagation and that different strategies may be required to overcome this constraint in different neurons.

Axons reliably conduct action potentials between neurons and/or other targets. Axons have widely variable diameters and can be myelinated or unmyelinated. Although the effect of these factors on propagation speed is well studied, how they constrain axonal resilience to high-frequency spiking is incompletely understood. Maximal firing frequencies range from ∼1 Hz to >300 Hz across neurons, but the process by which Na/K pumps counteract Na⁺ influx is slow, and the extent to which slow Na⁺ removal is compatible with high-frequency spiking is unclear. Modeling the process of Na⁺ removal shows that large-diameter axons are more resilient to high-frequency spikes than are small-diameter axons, because of their slow Na⁺ accumulation. In myelinated axons, the myelinated compartments between nodes of Ranvier act as a “reservoir” to slow Na⁺ accumulation and increase the reliability of axonal propagation. We now find that slowing the activation of K⁺ current can increase the Na⁺ influx rate, and the effect of minimizing the overlap between Na⁺ and K⁺ currents on spike propagation resilience depends on complex interactions among diameter, myelination, and the Na/K pump density. Our results suggest that, in neurons with different channel gating kinetic parameters, different strategies may be required to improve the reliability of axonal propagation.

Parvalbumin subtypes of cerebellar Purkinje cells contribute to differential intrinsic firing properties

Purkinje cells (PCs) are central to cerebellar information coding and appreciation for the diversity of their firing patterns and molecular profiles is growing. Heterogeneous subpopulations of PCs have been identified that display differences in intrinsic firing properties without clear mechanistic insight into what underlies the divergence in firing parameters. Although long used as a general PC marker, we report that the calcium binding protein parvalbumin labels a subpopulation of PCs, based on high and low expression, with a conserved distribution pattern across the animals examined. We trained a convolutional neural network to recognize the parvalbumin subtypes and create maps of whole cerebellar distribution and find that PCs within these areas have differences in spontaneous firing that can be modified by altering calcium buffer content. These subtypes also show differential responses to potassium and calcium channel blockade, suggesting a mechanistic role for variability in PC intrinsic firing through differences in ion channel composition. It is proposed that ion channels drive the diversity in PC intrinsic firing phenotype and parvalbumin calcium buffering provides capacity for the highest firing rates observed. These findings open new avenues for detailed classification of PC subtypes.

The Cellular Electrophysiological Properties Underlying Multiplexed Coding in Purkinje Cells

Neuronal firing patterns are crucial to underpin circuit level behaviors. In cerebellar Purkinje cells (PCs), both spike rates and pauses are used for behavioral coding, but the cellular mechanisms causing code transitions remain unknown. We use a well-validated PC model to explore the coding strategy that individual PCs use to process parallel fiber (PF) inputs. We find increasing input intensity shifts PCs from linear rate-coders to burst-pause timing-coders by triggering localized dendritic spikes. We validate dendritic spike properties with experimental data, elucidate spiking mechanisms, and predict spiking thresholds with and without inhibition. Both linear and burst-pause computations use individual branches as computational units, which challenges the traditional view of PCs as linear point neurons. Dendritic spike thresholds can be regulated by voltage state, compartmentalized channel modulation, between-branch interaction and synaptic inhibition to expand the dynamic range of linear computation or burst-pause computation. In addition, co-activated PF inputs between branches can modify somatic maximum spike rates and pause durations to make them carry analog signals. Our results provide new insights into the strategies used by individual neurons to expand their capacity of information processing.

SIGNIFICANCE STATEMENT Understanding how neurons process information is a fundamental question in neuroscience. Purkinje cells (PCs) were traditionally regarded as linear point neurons. We used computational modeling to unveil their electrophysiological properties underlying the multiplexed coding strategy that is observed during behaviors. We demonstrate that increasing input intensity triggers localized dendritic spikes, shifting PCs from linear rate-coders to burst-pause timing-coders. Both coding strategies work at the level of individual dendritic branches. Our work suggests that PCs have the ability to implement branch-specific multiplexed coding at the cellular level, thereby increasing the capacity of cerebellar coding and learning.

Dendritic coincidence detection in Purkinje neurons of awake mice

Dendritic coincidence detection is fundamental to neuronal processing yet remains largely unexplored in awake animals. Specifically, the underlying dendritic voltage–calcium relationship has not been directly addressed. Here, using simultaneous voltage and calcium two-photon imaging of Purkinje neuron spiny dendrites, we show how coincident synaptic inputs and resulting dendritic spikes modulate dendritic calcium signaling during sensory stimulation in awake mice. Sensory stimulation increased the rate of postsynaptic potentials and dendritic calcium spikes evoked by climbing fiber and parallel fiber synaptic input. These inputs are integrated in a time-dependent and nonlinear fashion to enhance the sensory-evoked dendritic calcium signal. Intrinsic supralinear dendritic mechanisms, including voltage-gated calcium channels and metabotropic glutamate receptors, are recruited cooperatively to expand the dynamic range of sensory-evoked dendritic calcium signals. This establishes how dendrites can use multiple interplaying mechanisms to perform coincidence detection, as a fundamental and ongoing feature of dendritic integration in behaving animals.

Spatially resolved dendritic integration: towards a functional classification of neurons

The vast tree-like dendritic structure of neurons allows them to receive and integrate input from many neurons. A wide variety of neuronal morphologies exist, however, their role in dendritic integration, and how it shapes the response of the neuron, is not yet fully understood. Here, we study the evolution and interactions of dendritic spikes in excitable neurons with complex real branch structures. We focus on dozens of digitally reconstructed illustrative neurons from the online repository NeuroMorpho.org, which contains over 130,000 neurons. Yet, our methods can be promptly extended to any other neuron. This approach allows us to estimate and map specific and heterogeneous patterns of activity observed across extensive dendritic trees with thousands of compartments. We propose a classification of neurons based on the location of the soma (centrality) and the number of branches connected to the soma. These are key topological factors in determining the neuron's energy consumption, firing rate, and the dynamic range, which quantifies the range in synaptic input rate that can be reliably encoded by the neuron's firing rate. Moreover, we find that bifurcations, the structural building blocks of complex dendrites, play a major role in increasing the dynamic range of neurons. Our results provide a better understanding of the effects of neuronal morphology in the diversity of neuronal dynamics and function.

Firing rate-dependent phase responses of Purkinje cells support transient oscillations

Both spike rate and timing can transmit information in the brain. Phase response curves (PRCs) quantify how a neuron transforms input to output by spike timing. PRCs exhibit strong firing-rate adaptation, but its mechanism and relevance for network output are poorly understood. Using our Purkinje cell (PC) model, we demonstrate that the rate adaptation is caused by rate-dependent subthreshold membrane potentials efficiently regulating the activation of Na+ channels. Then, we use a realistic PC network model to examine how rate-dependent responses synchronize spikes in the scenario of reciprocal inhibition-caused high-frequency oscillations. The changes in PRC cause oscillations and spike correlations only at high firing rates. The causal role of the PRC is confirmed using a simpler coupled oscillator network model. This mechanism enables transient oscillations between fast-spiking neurons that thereby form PC assemblies. Our work demonstrates that rate adaptation of PRCs can spatio-temporally organize the PC input to cerebellar nuclei.

Synergistic excitability plasticity in cerebellar functioning

The cerebellum, a universal processor for sensory acquisition and internal models, and its association with synaptic and nonsynaptic plasticity have been envisioned as the biological correlates of learning, perception, and even thought. Indeed, the cerebellum is no longer considered merely as the locus of motor coordination and its learning. Here, we introduce the mechanisms underlying the induction of multiple types of plasticity in cerebellar circuit and give an overview focusing on the plasticity of nonsynaptic intrinsic excitability. The discovery of long-term potentiation of synaptic responsiveness in hippocampal neurons led investigations into changes of their intrinsic excitability. This activity-dependent potentiation of neuronal excitability is distinct from that of synaptic efficacy. Systematic examination of excitability plasticity has indicated that the modulation of various types of Ca²⁺ - and voltage-dependent K⁺ channels underlies the phenomenon, which is also triggered by immune activity. Intrinsic plasticity is expressed specifically on dendrites and modifies the integrative processing and filtering effect. In Purkinje cells, modulation of the discordance of synaptic current on soma and dendrite suggested a novel type of cellular learning mechanism. This property enables a plausible synergy between synaptic efficacy and intrinsic excitability, by amplifying electrical conductivity and influencing the polarity of bidirectional synaptic plasticity. Furthermore, the induction of intrinsic plasticity in the cerebellum correlates with motor performance and cognitive processes, through functional connections from the cerebellar nuclei to neocortex and associated regions: for example, thalamus and midbrain. Taken together, recent advances in neuroscience have begun to shed light on the complex functioning of nonsynaptic excitability and the synergy.

Using deep neural networks to detect complex spikes of cerebellar Purkinje cells

Purkinje cell “complex spikes,” fired at perplexingly low rates, play a crucial role in cerebellum-based motor learning. Careful interpretations of these spikes require manually detecting them, since conventional online or offline spike sorting algorithms are optimized for classifying much simpler waveform morphologies. We present a novel deep learning approach for identifying complex spikes, which also measures additional relevant neurophysiological features, with an accuracy level matching that of human experts yet with very little time expenditure.

Intrinsic Plasticity of Cerebellar Purkinje Cells Contributes to Motor Memory Consolidation

Intrinsic plasticity of cerebellar Purkinje cells (PCs) has recently been demonstrated in cerebellar local circuits; however, its physiological impact on cerebellar learning and memory remains elusive. Here, we suggest that intrinsic plasticity of PCs is tightly involved in motor memory consolidation based on findings from PC-specific STIM1 knockout male mice, which show severe memory consolidation deficiency in vestibulo-ocular reflex memory. Gain-up training of the vestibulo-ocular reflex produced a decrease in the synaptic weight of PCs in both the WT and KO groups. However, intrinsic plasticity was impaired only in the knockout mice. Furthermore, the observed defects in the intrinsic plasticity of PCs led to the formation of aberrant neural plasticity in the vestibular nucleus neurons. Our results suggest that synergistic modulation of intrinsic and synaptic plasticity in PCs is required for the changes in downstream plasticity in the vestibular nucleus, and thereby contributing to the long-term storage of motor memory.SIGNIFICANCE STATEMENT Synaptic plasticity is a well-known mechanism for learning and memory. Although plasticity of excitability, intrinsic plasticity, of the cerebellar Purkinje cell has been reported in both directions (potentiation and depression), the physiological role of intrinsic plasticity still remains ambiguous. In this study, we suggest that both synaptic and intrinsic plasticity are required for successful memory consolidation in cerebellar eye movement learning. Despite successful induction and maintenance of synaptic plasticity, we found deficits of memory consolidation when there were defects in intrinsic plasticity. Our results suggest that intrinsic plasticity of cerebellar Purkinje cell has a significant role in motor memory consolidation.

Simulation of a Human-Scale Cerebellar Network Model on the K Computer

Computer simulation of the human brain at an individual neuron resolution is an ultimate goal of computational neuroscience. The Japanese flagship supercomputer, K, provides unprecedented computational capability toward this goal. The cerebellum contains 80% of the neurons in the whole brain. Therefore, computer simulation of the human-scale cerebellum will be a challenge for modern supercomputers. In this study, we built a human-scale spiking network model of the cerebellum, composed of 68 billion spiking neurons, on the K computer. As a benchmark, we performed a computer simulation of a cerebellum-dependent eye movement task known as the optokinetic response. We succeeded in reproducing plausible neuronal activity patterns that are observed experimentally in animals. The model was built on dedicated neural network simulation software called MONET (Millefeuille-like Organization NEural neTwork), which calculates layered sheet types of neural networks with parallelization by tile partitioning. To examine the scalability of the MONET simulator, we repeatedly performed simulations while changing the number of compute nodes from 1,024 to 82,944 and measured the computational time. We observed a good weak-scaling property for our cerebellar network model. Using all 82,944 nodes, we succeeded in simulating a human-scale cerebellum for the first time, although the simulation was 578 times slower than the wall clock time. These results suggest that the K computer is already capable of creating a simulation of a human-scale cerebellar model with the aid of the MONET simulator.

Intrinsic Excitability Increase in Cerebellar Purkinje Cells after Delay Eye-Blink Conditioning in Mice

Cerebellar-based learning is thought to rely on synaptic plasticity, particularly at synaptic inputs to Purkinje cells. Recently, however, other complementary mechanisms have been identified. Intrinsic plasticity is one such mechanism, and depends in part on the downregulation of calcium-dependent SK-type K+ channels, which contribute to a medium-slow afterhyperpolarization (AHP) after spike bursts, regulating membrane excitability. In the hippocampus, intrinsic plasticity plays a role in trace eye-blink conditioning; however, corresponding excitability changes in the cerebellum in associative learning, such as in trace or delay eye-blink conditioning, are less well studied. Whole-cell patch-clamp recordings were obtained from Purkinje cells in cerebellar slices prepared from male mice ∼48 h after they learned a delay eye-blink conditioning task. Over a period of repeated training sessions, mice received either paired trials of a tone coterminating with a periorbital shock (conditioning) or trials in which these stimuli were randomly presented in an unpaired manner (pseudoconditioning). Purkinje cells from conditioned mice show a significantly reduced AHP after trains of parallel fiber stimuli and after climbing fiber evoked complex spikes. The number of spikelets in the complex spike waveform is increased after conditioning. Moreover, we find that SK-dependent intrinsic plasticity is occluded in conditioned, but not pseudoconditioned mice. These findings show that excitability is enhanced in Purkinje cells after delay eye-blink conditioning, and point toward a downregulation of SK channels as a potential underlying mechanism. The observation that this learning effect lasts at least up to 2 d after training shows that intrinsic plasticity regulates excitability in the long term.SIGNIFICANCE STATEMENT Plasticity of membrane excitability ("intrinsic plasticity") has been observed in invertebrate and vertebrate neurons, coinduced with synaptic plasticity or in isolation. Although the cellular phenomenon per se is well established, it remains unclear what role intrinsic plasticity plays in learning and if it even persists long enough to serve functions in engram physiology beyond aiding synaptic plasticity. Here, we demonstrate that cerebellar Purkinje cells upregulate excitability in delay eye-blink conditioning, a form of motor learning. This plasticity is observed 48 h after training and alters synaptically evoked spike firing and integrative properties of these neurons. These findings show that intrinsic plasticity enhances the spike firing output of Purkinje cells and persists over the course of days.

Modification of Synaptic-Input Clustering by Intrinsic Excitability Plasticity on Cerebellar Purkinje Cell Dendrites

The role of dendrites in the integration of widespread synaptic activity has been studied in experiments and theories (Johnston et al., 1996; Magee, 2007). However, whether the conduction of synaptic currents from dendrites to the soma depends on excitability of those dendritic branches is unclear. How modulation of the branch excitability affects the conduction of synaptic inputs and their selection on dendrites is also elusive. Here, I performed simultaneous voltage-clamp recordings from the soma and dendrites of single cerebellar Purkinje neurons in male Sprague-Dawley rats and analyzed the relationship between spontaneous EPSCs on both sides. I found that EPSCs on distal dendrites have a salient discordance in amplitude compared with those on the soma. Furthermore, individual ratios of the EPSC concurrently recorded on the soma and dendrites were not unique, but discrete, suggesting the occurrence of various attenuations in different paths of dendritic branches to the soma. The obtained data and simulations indicate several distinct groups (4.5 ± 0.3, n = 22 somatodendritic recordings) of co-occurred synaptic inputs in Purkinje cell dendrites. This clustering of synaptic currents was suggested to emerge at farther distances than the secondary bifurcations. Finally, ratios of the co-EPSCs were uniformly distributed after either intrinsic plasticity induction or SK-channel blockade. Overall, results suggest that in Purkinje cells the excitability along the dendrite processes modulates the conduction of EPSCs and makes active inputs heterogeneous through SK channel activity, intrinsic plasticity, and dendritic branching. These properties of dendrites may confer branch-specific computational power to neurons.SIGNIFICANCE STATEMENT I have previously studied the "non-synaptic" plasticity of the intrinsic excitability in the cerebellar Purkinje cells (Belmeguenai et al., 2010), and branch-specific increase of intrinsic excitability of the dendrites (Ohtsuki et al., 2012b; Ohtsuki and Hansel, 2018) through the downregulation of SK (small conductance Ca2+-activated K+) channels. In this study, I show that a dendritic filtering of synaptic electroconductivity is heterogeneous among the branches on distal dendrites and that the increase in the dendritic excitability accompanied with the intrinsic plasticity alters a state with the heterogeneity to a globally excitable state in Purkinje neurons. My findings propose a new learning model relying on the intrinsic excitability plasticity of the dendritic branch fields.

Climbing Fibers Provide Graded Error Signals in Cerebellar Learning

The cerebellum plays a critical role in coordinating and learning complex movements. Although its importance has been well recognized, the mechanisms of learning remain hotly debated. According to the classical cerebellar learning theory, depression of parallel fiber synapses instructed by error signals from climbing fibers, drives cerebellar learning. The uniqueness of long-term depression (LTD) in cerebellar learning has been challenged by evidence showing multi-site synaptic plasticity. In Purkinje cells, long-term potentiation (LTP) of parallel fiber synapses is now well established and it can be achieved with or without climbing fiber signals, making the role of climbing fiber input more puzzling. The central question is how individual Purkinje cells extract global errors based on climbing fiber input. Previous data seemed to demonstrate that climbing fibers are inefficient instructors, because they were thought to carry “binary” error signals to individual Purkinje cells, which significantly constrains the efficiency of cerebellar learning in several regards. In recent years, new evidence has challenged the traditional view of “binary” climbing fiber responses, suggesting that climbing fibers can provide graded information to efficiently instruct individual Purkinje cells to learn. Here we review recent experimental and theoretical progress regarding modulated climbing fiber responses in Purkinje cells. Analog error signals are generated by the interaction of varying climbing fibers inputs with simultaneous other synaptic input and with firing states of targeted Purkinje cells. Accordingly, the calcium signals which trigger synaptic plasticity can be graded in both amplitude and spatial range to affect the learning rate and even learning direction. We briefly discuss how these new findings complement the learning theory and help to further our understanding of how the cerebellum works.

Spike burst-pause dynamics of Purkinje cells regulate sensorimotor adaptation

Cerebellar Purkinje cells mediate accurate eye movement coordination. However, it remains unclear how oculomotor adaptation depends on the interplay between the characteristic Purkinje cell response patterns, namely tonic, bursting, and spike pauses. Here, a spiking cerebellar model assesses the role of Purkinje cell firing patterns in vestibular ocular reflex (VOR) adaptation. The model captures the cerebellar microcircuit properties and it incorporates spike-based synaptic plasticity at multiple cerebellar sites. A detailed Purkinje cell model reproduces the three spike-firing patterns that are shown to regulate the cerebellar output. Our results suggest that pauses following Purkinje complex spikes (bursts) encode transient disinhibition of target medial vestibular nuclei, critically gating the vestibular signals conveyed by mossy fibres. This gating mechanism accounts for early and coarse VOR acquisition, prior to the late reflex consolidation. In addition, properly timed and sized Purkinje cell bursts allow the ratio between long-term depression and potentiation (LTD/LTP) to be finely shaped at mossy fibre-medial vestibular nuclei synapses, which optimises VOR consolidation. Tonic Purkinje cell firing maintains the consolidated VOR through time. Importantly, pauses are crucial to facilitate VOR phase-reversal learning, by reshaping previously learnt synaptic weight distributions. Altogether, these results predict that Purkinje spike burst-pause dynamics are instrumental to VOR learning and reversal adaptation.

Cerebellar Purkinje cells regulate accurate eye movement coordination. However, it remains unclear how cerebellar-dependent oculomotor adaptation depends on the interplay between Purkinje cell characteristic response patterns: tonic, high frequency bursting, and post-complex spike pauses. We explore the role of Purkinje spike burst-pause dynamics in VOR adaptation. A biophysical model of Purkinje cell is at the core of a spiking network model, which captures the cerebellar microcircuit properties and incorporates spike-based synaptic plasticity mechanisms at different cerebellar sites. We show that Purkinje spike burst-pause dynamics are critical for (1) gating the vestibular-motor response association during VOR acquisition; (2) mediating the LTD/LTP balance for VOR consolidation; (3) reshaping synaptic efficacy distributions for VOR phase-reversal adaptation; (4) explaining the reversal VOR gain discontinuities during sleeping.

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.