The Cellular Electrophysiological Properties Underlying Multiplexed Coding in Purkinje Cells

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.

A Learning Dendritic Neuron-Based Motion Direction Detective System and Its Application to Grayscale Images

In recent research, dendritic neuron-based models have shown promise in effectively learning and recognizing object motion direction within binary images. Leveraging the dendritic neuron structure and On-Off Response mechanism within the primary cortex, this approach has notably reduced learning time and costs compared to traditional neural networks. This paper advances the existing model by integrating bio-inspired components into a learnable dendritic neuron-based artificial visual system (AVS), specifically incorporating mechanisms from horizontal and bipolar cells. This enhancement enables the model to proficiently identify object motion directions in grayscale images, aligning its threshold with human-like perception. The enhanced model demonstrates superior efficiency in motion direction recognition, requiring less data (90% less than other deep models) and less time for training. Experimental findings highlight the model's remarkable robustness, indicating significant potential for real-world applications. The integration of bio-inspired features not only enhances performance but also opens avenues for further exploration in neural network research. Notably, the application of this model to realistic object recognition yields convincing accuracy at nearly 100%, underscoring its practical utility.

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.

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.

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.

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.

Motor cortex analogue neurons in songbirds utilize Kv3 channels to generate ultranarrow spikes

Complex motor skills in vertebrates require specialized upper motor neurons with precise action potential (AP) firing. To examine how diverse populations of upper motor neurons subserve distinct functions and the specific repertoire of ion channels involved, we conducted a thorough study of the excitability of upper motor neurons controlling somatic motor function in the zebra finch. We found that robustus arcopallialis projection neurons (RAPNs), key command neurons for song production, exhibit ultranarrow spikes and higher firing rates compared to neurons controlling non-vocal somatic motor functions (dorsal intermediate arcopallium [AId] neurons). Pharmacological and molecular data indicate that this striking difference is associated with the higher expression in RAPNs of high threshold, fast-activating voltage-gated Kv3 channels, that likely contain Kv3.1 (KCNC1) subunits. The spike waveform and Kv3.1 expression in RAPNs mirror properties of Betz cells, specialized upper motor neurons involved in fine digit control in humans and other primates but absent in rodents. Our study thus provides evidence that songbirds and primates have convergently evolved the use of Kv3.1 to ensure precise, rapid AP firing in upper motor neurons controlling fast and complex motor skills.

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.

Neuronal morphology enhances robustness to perturbations of channel densities

Biological neurons show significant cell-to-cell variability but have the striking ability to maintain their key firing properties in the face of unpredictable perturbations and stochastic noise. Using a population of multi-compartment models consisting of soma, neurites, and axon for the lateral pyloric neuron in the crab stomatogastric ganglion, we explore how rebound bursting is preserved when the 14 channel conductances in each model are all randomly varied. The coupling between the axon and other compartments is critical for the ability of the axon to spike during bursts and consequently determines the set of successful solutions. When the coupling deviates from a biologically realistic range, the neuronal tolerance of conductance variations is lessened. Thus, the gross morphological features of these neurons enhance their robustness to perturbations of channel densities and expand the space of individual variability that can maintain a desired output pattern.

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.

Discrimination and learning of temporal input sequences in a cerebellar Purkinje cell model

Introduction

Temporal information processing is essential for sequential contraction of various muscles with the appropriate timing and amplitude for fast and smooth motor control. These functions depend on dynamics of neural circuits, which consist of simple neurons that accumulate incoming spikes and emit other spikes. However, recent studies indicate that individual neurons can perform complex information processing through the nonlinear dynamics of dendrites with complex shapes and ion channels. Although we have extensive evidence that cerebellar circuits play a vital role in motor control, studies investigating the computational ability of single Purkinje cells are few.

Methods

We found, through computer simulations, that a Purkinje cell can discriminate a series of pulses in two directions (from dendrite tip to soma, and from soma to dendrite), as cortical pyramidal cells do. Such direction sensitivity was observed in whatever compartment types of dendrites (spiny, smooth, and main), although they have dierent sets of ion channels.

Results

We found that the shortest and longest discriminable sequences lasted for 60 ms (6 pulses with 10 ms interval) and 4,000 ms (20 pulses with 200 ms interval), respectively. and that the ratio of discriminable sequences within the region of the interesting parameter space was, on average, 3.3% (spiny), 3.2% (smooth), and 1.0% (main). For the direction sensitivity, a T-type Ca²⁺ channel was necessary, in contrast with cortical pyramidal cells that have N-methyl-D-aspartate receptors (NMDARs). Furthermore, we tested whether the stimulus direction can be reversed by learning, specifically by simulated long-term depression, and obtained positive results.

Discussion

Our results show that individual Purkinje cells can perform more complex information processing than is conventionally assumed for a single neuron, and suggest that Purkinje cells act as sequence discriminators, a useful role in motor control and learning.

Biologically-Based Computation: How Neural Details and Dynamics Are Suited for Implementing a Variety of Algorithms

The Neural Engineering Framework (Eliasmith & Anderson, 2003) is a long-standing method for implementing high-level algorithms constrained by low-level neurobiological details. In recent years, this method has been expanded to incorporate more biological details and applied to new tasks. This paper brings together these ongoing research strands, presenting them in a common framework. We expand on the NEF's core principles of (a) specifying the desired tuning curves of neurons in different parts of the model, (b) defining the computational relationships between the values represented by the neurons in different parts of the model, and (c) finding the synaptic connection weights that will cause those computations and tuning curves. In particular, we show how to extend this to include complex spatiotemporal tuning curves, and then apply this approach to produce functional computational models of grid cells, time cells, path integration, sparse representations, probabilistic representations, and symbolic representations in the brain.

The Cerebellar Cortex

The cerebellar cortex is an important system for relating neural circuits and learning. Its promise reflects the longstanding idea that it contains simple, repeated circuit modules with only a few cell types and a single plasticity mechanism that mediates learning according to classical Marr-Albus models. However, emerging data have revealed surprising diversity in neuron types, synaptic connections, and plasticity mechanisms, both locally and regionally within the cerebellar cortex. In light of these findings, it is not surprising that attempts to generate a holistic model of cerebellar learning across different behaviors have not been successful. While the cerebellum remains an ideal system for linking neuronal function with behavior, it is necessary to update the cerebellar circuit framework to achieve its great promise. In this review, we highlight recent advances in our understanding of cerebellar-cortical cell types, synaptic connections, signaling mechanisms, and forms of plasticity that enrich cerebellar processing.

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.

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.