Modulation of the dynamics of cerebellar Purkinje cells through the interaction of excitatory and inhibitory feedforward pathways

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.

The neuronal and synaptic dynamics underlying post-inhibitory rebound burst related to major depressive disorder in the lateral habenula neuron model

A burst behavior observed in the lateral habenula (LHb) neuron related to major depressive disorder has attracted much attention. The burst is induced from silence by the excitatory N-methyl-D-aspartate (NMDA) synapse or by the inhibitory stimulation, i.e., a post-inhibitory rebound (PIR) burst, which has not been explained clearly. In the present paper, the neuronal and synaptic dynamics for the PIR burst are acquired in a theoretical neuron model. At first, dynamic cooperations between the fast rise of inhibitory γ-aminobutyric acid (GABA) synapse, slow rise of NMDA synapse, and T-type calcium current to evoke the PIR burst are obtained. Similar to the inhibitory pulse stimulation, fast rising GABA current can reduce the membrane potential to a level low enough to de-inactivate the low threshold T-type calcium current to evoke a PIR spike, which can enhance the slow rising NMDA current activated at a time before or after the PIR spike. The NMDA current following the PIR spike exhibits slow decay to induce multiple spikes to form the PIR burst. Such results present a theoretical explanation and a candidate for the PIR burst in real LHb neurons. Then, the dynamical mechanism for the PIR spike mediated by the T-type calcium channel is obtained. At large conductance of T-type calcium channel, the resting state corresponds to a stable focus near Hopf bifurcation and exhibits an "uncommon" threshold curve with membrane potential much lower than the resting membrane potential. Inhibitory modulation induces membrane potential decreased to run across the threshold curve to evoke the PIR spike. At small conductance of the T-type calcium channel, a stable node appears and manifests a common threshold curve with higher membrane potential, resulting in non-PIR phenomenon. The results present the dynamic cooperations between neuronal dynamics and fast/slow dynamics of different synapses for the PIR burst observed in the LHb neuron, which is helpful for the modulations to major depressive disorder.

Anisotropy and Frequency Dependence of Signal Propagation in the Cerebellar Circuit Revealed by High-Density Multielectrode Array Recordings

The cerebellum is one of the most connected structures of the central nervous system and receives inputs over an extended frequency range. Nevertheless, the frequency dependence of cerebellar cortical processing remains elusive. In this work, we characterized cerebellar cortex responsiveness to mossy fibers activation at different frequencies and reconstructed the spread of activity in the sagittal and coronal planes of acute mouse cerebellar slices using a high-throughput high-density multielectrode array (HD-MEA). The enhanced spatiotemporal resolution of HD-MEA revealed the frequency dependence and spatial anisotropy of cerebellar activation. Mossy fiber inputs reached the Purkinje cell layer even at the lowest frequencies, but the efficiency of transmission increased at higher frequencies. These properties, which are likely to descend from the topographic organization of local inhibition, intrinsic electroresponsiveness, and short-term synaptic plasticity, are critical elements that have to be taken into consideration to define the computational properties of the cerebellar cortex and its pathological alterations.

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.

Toward a cerebello-thalamo-cortical computational model of spinocerebellar ataxia

Computational neural network modelling is an emerging approach for optimization of drug treatment of neurological disorders and fine-tuning of rehabilitation strategies. In the current study, we constructed a cerebello-thalamo-cortical computational neural network model to simulate a mouse model of cerebellar ataxia (pcd^5J mice) by manipulating cerebellar bursts through reduction of GABAergic inhibitory input. Cerebellar output neurons were projected to the thalamus and bidirectionally connected with the cortical network. Our results showed that reduction of inhibitory input in the cerebellum orchestrated the cortical local field potential (LFP) dynamics to generate specific motor outputs of oscillations of the theta, alpha, and beta bands in the computational model as well as in mouse motor cortical neurons. The therapeutic potential of deep brain stimulation (DBS) was tested in the computational model by increasing the sensory input to restore cortical output. Ataxia mice showed normalization of the motor cortex LFP after cerebellum DBS. We provide a novel approach to computational modelling to investigate the effect of DBS by mimicking cerebellar ataxia involving degeneration of Purkinje cells. Simulated neural activity coincides with findings from neural recordings of ataxia mice. Our computational model could thus represent cerebellar pathologies and provide insight into how to improve disease symptoms by restoring neuronal electrophysiological properties using DBS.

Dissecting cascade computational components in spiking neural networks

Finding out the physical structure of neuronal circuits that governs neuronal responses is an important goal for brain research. With fast advances for large-scale recording techniques, identification of a neuronal circuit with multiple neurons and stages or layers becomes possible and highly demanding. Although methods for mapping the connection structure of circuits have been greatly developed in recent years, they are mostly limited to simple scenarios of a few neurons in a pairwise fashion; and dissecting dynamical circuits, particularly mapping out a complete functional circuit that converges to a single neuron, is still a challenging question. Here, we show that a recent method, termed spike-triggered non-negative matrix factorization (STNMF), can address these issues. By simulating different scenarios of spiking neural networks with various connections between neurons and stages, we demonstrate that STNMF is a persuasive method to dissect functional connections within a circuit. Using spiking activities recorded at neurons of the output layer, STNMF can obtain a complete circuit consisting of all cascade computational components of presynaptic neurons, as well as their spiking activities. For simulated simple and complex cells of the primary visual cortex, STNMF allows us to dissect the pathway of visual computation. Taken together, these results suggest that STNMF could provide a useful approach for investigating neuronal systems leveraging recorded functional neuronal activity.

It is well known that the computation of neuronal circuits is carried out through the staged and cascade structure of different types of neurons. Nevertheless, the information, particularly sensory information, is processed in a network primarily with feedforward connections through different pathways. A peculiar example is the early visual system, where light is transcoded by the retinal cells, routed by the lateral geniculate nucleus, and reached the primary visual cortex. One meticulous interest in recent years is to map out these physical structures of neuronal pathways. However, most methods so far are limited to taking snapshots of a static view of connections between neurons. It remains unclear how to obtain a functional and dynamical neuronal circuit beyond the simple scenarios of a few randomly sampled neurons. Using simulated spiking neural networks of visual pathways with different scenarios of multiple stages, mixed cell types, and natural image stimuli, we demonstrate that a recent computational tool, named spike-triggered non-negative matrix factorization, can resolve these issues. It enables us to recover the entire structural components of neural networks underlying the computation, together with the functional components of each individual neuron. Utilizing it for complex cells of the primary visual cortex allows us to reveal every underpinning of the nonlinear computation. Our results, together with other recent experimental and computational efforts, show that it is possible to systematically dissect neural circuitry with detailed structural and functional components.

Unraveling neural coding of dynamic natural visual scenes via convolutional recurrent neural networks

Traditional models of retinal system identification analyze the neural response to artificial stimuli using models consisting of predefined components. The model design is limited to prior knowledge, and the artificial stimuli are too simple to be compared with stimuli processed by the retina. To fill in this gap with an explainable model that reveals how a population of neurons work together to encode the larger field of natural scenes, here we used a deep-learning model for identifying the computational elements of the retinal circuit that contribute to learning the dynamics of natural scenes. Experimental results verify that the recurrent connection plays a key role in encoding complex dynamic visual scenes while learning biological computational underpinnings of the retinal circuit. In addition, the proposed models reveal both the shapes and the locations of the spatiotemporal receptive fields of ganglion cells.

Regulating synchronous oscillations of cerebellar granule cells by different types of inhibition

Synchronous oscillations in neural populations are considered being controlled by inhibitory neurons. In the granular layer of the cerebellum, two major types of cells are excitatory granular cells (GCs) and inhibitory Golgi cells (GoCs). GC spatiotemporal dynamics, as the output of the granular layer, is highly regulated by GoCs. However, there are various types of inhibition implemented by GoCs. With inputs from mossy fibers, GCs and GoCs are reciprocally connected to exhibit different network motifs of synaptic connections. From the view of GCs, feedforward inhibition is expressed as the direct input from GoCs excited by mossy fibers, whereas feedback inhibition is from GoCs via GCs themselves. In addition, there are abundant gap junctions between GoCs showing another form of inhibition. It remains unclear how these diverse copies of inhibition regulate neural population oscillation changes. Leveraging a computational model of the granular layer network, we addressed this question to examine the emergence and modulation of network oscillation using different types of inhibition. We show that at the network level, feedback inhibition is crucial to generate neural oscillation. When short-term plasticity was equipped on GoC-GC synapses, oscillations were largely diminished. Robust oscillations can only appear with additional gap junctions. Moreover, there was a substantial level of cross-frequency coupling in oscillation dynamics. Such a coupling was adjusted and strengthened by GoCs through feedback inhibition. Taken together, our results suggest that the cooperation of distinct types of GoC inhibition plays an essential role in regulating synchronous oscillations of the GC population. With GCs as the sole output of the granular network, their oscillation dynamics could potentially enhance the computational capability of downstream neurons.