Influences of membrane properties on phase response curve and synchronization stability in a model globus pallidus neuron

A structurally precise mechanism links an epilepsy-associated KCNC2 potassium channel mutation to interneuron dysfunction

De novo heterozygous variants in KCNC2 encoding the voltage-gated potassium (K+) channel subunit Kv3.2 are a recently described cause of developmental and epileptic encephalopathy (DEE). A de novo variant in KCNC2 c.374G > A (p.Cys125Tyr) was identified via exome sequencing in a patient with DEE. Relative to wild-type Kv3.2, Kv3.2-p.Cys125Tyr induces K+ currents exhibiting a large hyperpolarizing shift in the voltage dependence of activation, accelerated activation, and delayed deactivation consistent with a relative stabilization of the open conformation, along with increased current density. Leveraging the cryogenic electron microscopy (cryo-EM) structure of Kv3.1, molecular dynamic simulations suggest that a strong π-π stacking interaction between the variant Tyr125 and Tyr156 in the α-6 helix of the T1 domain promotes a relative stabilization of the open conformation of the channel, which underlies the observed gain of function. A multicompartment computational model of a Kv3-expressing parvalbumin-positive cerebral cortex fast-spiking γ-aminobutyric acidergic (GABAergic) interneuron (PV-IN) demonstrates how the Kv3.2-Cys125Tyr variant impairs neuronal excitability and dysregulates inhibition in cerebral cortex circuits to explain the resulting epilepsy.

Basal ganglia network dynamics and function: Role of direct, indirect and hyper-direct pathways in action selection

Basal ganglia (BG) are a widely recognized neural basis for action selection, but its decision-making mechanism is still a difficult problem for researchers. Therefore, we constructed a spiking neural network inspired by the BG anatomical data. Simulation experiments were based on the principle of dis-inhibition and our functional hypothesis within the BG: the direct pathway, the indirect pathway, and the hyper-direct pathway of the BG jointly implement the initiation execution and termination of motor programs. Firstly, we studied the dynamic process of action selection with the network, which contained intra-group competition and inter-group competition. Secondly, we focused on the effects of the stimulus intensity and the proportion of excitation and inhibition on the GPi/SNr. The results suggested that inhibition and excitation shape action selection. They also explained why the firing rate of GPi/SNr did not continue to increase in the action-selection experiment. Finally, we discussed the experimental results with the functional hypothesis. Uniquely, this paper summarized the decision-making neural mechanism of action selection based on the direct pathway, the indirect pathway, and the hyper-direct pathway within BG.

On the Role of Arkypallidal and Prototypical Neurons for Phase Transitions in the External Pallidum

The external pallidum (globus pallidus pars externa [GPe]) plays a central role for basal ganglia functions and dynamics and, consequently, has been included in most computational studies of the basal ganglia. These studies considered the GPe as a homogeneous neural population. However, experimental studies have shown that the GPe contains at least two distinct cell types (prototypical and arkypallidal cells). In this work, we provide in silico insight into how pallidal heterogeneity modulates dynamic regimes inside the GPe and how they affect the GPe response to oscillatory input. We derive a mean-field model of the GPe system from a microscopic spiking neural network of recurrently coupled prototypical and arkypallidal neurons. Using bifurcation analysis, we examine the influence of dopamine-dependent changes of intrapallidal connectivity on the GPe dynamics. We find that increased self-inhibition of prototypical cells can induce oscillations, whereas increased inhibition of prototypical cells by arkypallidal cells leads to the emergence of a bistable regime. Furthermore, we show that oscillatory input to the GPe, arriving from striatum, leads to characteristic patterns of cross-frequency coupling observed at the GPe. Based on these findings, we propose two different hypotheses of how dopamine depletion at the GPe may lead to phase-amplitude coupling between the parkinsonian beta rhythm and a GPe-intrinsic γ rhythm. Finally, we show that these findings generalize to realistic spiking neural networks of sparsely coupled Type I excitable GPe neurons.SIGNIFICANCE STATEMENT Our work provides (1) insight into the theoretical implications of a dichotomous globus pallidus pars externa (GPe) organization, and (2) an exact mean-field model that allows for future investigations of the relationship between GPe spiking activity and local field potential fluctuations. We identify the major phase transitions that the GPe can undergo when subject to static or periodic input and link these phase transitions to the emergence of synchronized oscillations and cross-frequency coupling in the basal ganglia. Because of the close links between our model and experimental findings on the structure and dynamics of prototypical and arkypallidal cells, our results can be used to guide both experimental and computational studies on the role of the GPe for basal ganglia dynamics in health and disease.

Multistable properties of human subthalamic nucleus neurons in Parkinson's disease

Behaviors are realized through concerted activity in neural circuits. This activity results from a combination of neural connectivity and the properties of the involved neurons. By studying the activity of neurons in the human subthalamic nucleus during surgery for Parkinson’s disease, we report that these neurons have multiple stable states, and that brief electrical stimuli can lead to transitions between states. We thus suggest that these neurons function as finite state machines. The different states could influence the function of key motor circuits of the basal ganglia, and thus knowledge of these states in disease or in response to treatment could help to define new treatment strategies for people with movement disorders.

To understand the function and dysfunction of neural circuits, it is necessary to understand the properties of the neurons participating in the behavior, the connectivity between these neurons, and the neuromodulatory status of the circuits at the time they are producing the behavior. Such knowledge of human neural circuits is difficult, at best, to obtain. Here, we study firing properties of human subthalamic neurons, using microelectrode recordings and microstimulation during awake surgery for Parkinson’s disease. We demonstrate that low-amplitude, brief trains of microstimulation can lead to persistent changes in neuronal firing behavior including switching between firing rates, entering silent periods, or firing several bursts then entering a silent period. We suggest that these multistable states reflect properties of finite state machines and could have implications for the function of circuits involving the subthalamic nucleus. Furthermore, understanding these states could lead to therapeutic strategies aimed at regulating the transitions between states.

Estimating neuronal conductance model parameters using dynamic action potential clamp

BACKGROUND

Parameterization of neuronal membrane conductance models relies on data acquired from current clamp (CC) or voltage clamp (VC) recordings. Although the CC approach provides key information on a neuron's firing properties, it is often difficult to disentangle the influence of multiple conductances that contribute to the excitation properties of a real neuron. Isolation of a single conductance using pharmacological agents or heterologous expression simplifies analysis but requires extensive VC evaluation to explore the complete state behavior of the channel of interest.

NEW METHOD

We present an improved parameterization approach that uses data derived from dynamic action potential clamp (DAPC) recordings to extract conductance equation parameters. We demonstrate the utility of the approach by applying it to the standard Hodgkin-Huxley conductance model although other conductance models could be easily incorporated as well.

RESULTS

Using a fully simulated setup we show that, with as few as five action potentials previously recorded in DAPC mode, sodium conductance equation parameters can be determined with average parameter errors of less than 4% while action potential firing accuracy approaches 100%. In real DAPC experiments, we show that by "training" our model with five or fewer action potentials, subsequent firing lasting for several seconds could be predicted with ˜96% mean firing rate accuracy and 94% temporal overlap accuracy.

COMPARISON WITH EXISTING METHODS

Our DAPC-based approach surpasses the accuracy of VC-based approaches for extracting conductance equation parameters with a significantly reduced temporal overhead.

CONCLUSION

DAPC-based approach will facilitate the rapid and systematic characterization of neuronal channelopathies.

Bayesian Estimation of Phase Dynamics Based on Partially Sampled Spikes Generated by Realistic Model Neurons

A dynamic system showing stable rhythmic activity can be represented by the dynamics of phase oscillators. This would provide a useful mathematical framework through which one can understand the system's dynamic properties. A recent study proposed a Bayesian approach capable of extracting the underlying phase dynamics directly from time-series data of a system showing rhythmic activity. Here we extended this method to spike data that otherwise provide only limited phase information. To determine how this method performs with spike data, we applied it to simulated spike data generated by a realistic neuronal network model. We then compared the estimated dynamics obtained based on the spike data with the dynamics theoretically derived from the model. The method successfully extracted the modeled phase dynamics, particularly the interaction function, when the amount of available data was sufficiently large. Furthermore, the method was able to infer synaptic connections based on the estimated interaction function. Thus, the method was found to be applicable to spike data and practical for understanding the dynamic properties of rhythmic neural systems.

Pallidostriatal Projections Promote β Oscillations in a Dopamine-Depleted Biophysical Network Model

In the basal ganglia, focused rhythmicity is an important feature of network activity at certain stages of motor processing. In disease, however, the basal ganglia develop amplified rhythmicity. Here, we demonstrate how the cellular architecture and network dynamics of an inhibitory loop in the basal ganglia yield exaggerated synchrony and locking to β oscillations, specifically in the dopamine-depleted state. A key component of this loop is the pallidostriatal pathway, a well-characterized anatomical projection whose function has long remained obscure. We present a synaptic characterization of this pathway in mice and incorporate these data into a computational model that we use to investigate its influence over striatal activity under simulated healthy and dopamine-depleted conditions. Our model predicts that the pallidostriatal pathway influences striatal output preferentially during periods of synchronized activity within GPe. We show that, under dopamine-depleted conditions, this effect becomes a key component of a positive feedback loop between the GPe and striatum that promotes synchronization and rhythmicity. Our results generate novel predictions about the role of the pallidostriatal pathway in shaping basal ganglia activity in health and disease.

SIGNIFICANCE STATEMENT

This work demonstrates that functional connections from the globus pallidus externa (GPe) to striatum are substantially stronger onto fast-spiking interneurons (FSIs) than onto medium spiny neurons. Our circuit model suggests that when GPe spikes are synchronous, this pallidostriatal pathway causes synchronous FSI activity pauses, which allow a transient window of disinhibition for medium spiny neurons. In simulated dopamine-depletion, this GPe-FSI activity is necessary for the emergence of strong synchronization and the amplification and propagation of β oscillations, which are a hallmark of parkinsonian circuit dysfunction. These results suggest that GPe may play a central role in propagating abnormal circuit activity to striatum, which in turn projects to downstream basal ganglia structures. These findings warrant further exploration of GPe as a target for interventions for Parkinson's disease.

Sparse pallidal connections shape synchrony in a network model of the basal ganglia

Neural synchrony in the basal ganglia, especially in the beta frequency band (13-30 Hz), is a hallmark of Parkinson's disease and considered as antikinetic. In contrast, the healthy basal ganglia show low levels of synchrony. It is currently unknown where synchrony and oscillations arise in the parkinsonian brain and how they are transmitted through the basal ganglia, as well as what makes them dependent on dopamine. The external part of the globus pallidus has recently been identified as a hub nucleus in the basal ganglia, possessing intrinsic inhibitory connections and possibly also gap junctions. In this study, we show that in a conductance-based network model of the basal ganglia, the combination of sparse, high-conductance inhibitory synapses and sparse, low-conductance gap junctions in the external part of the globus pallidus could effectively desynchronize the whole network. However, when gap junction coupling became strong enough, the effect was impeded and activity synchronized. In particular, sustained periods of beta coherence occurred between some neuron pairs. As gap junctions can change their conductance with the dopamine level, we suggest pallidal gap junction coupling as a mechanism contributing to the development of beta synchrony in the parkinsonian basal ganglia.

On the firing rate dependency of the phase response curve of rat Purkinje neurons in vitro

Synchronous spiking during cerebellar tasks has been observed across Purkinje cells: however, little is known about the intrinsic cellular mechanisms responsible for its initiation, cessation and stability. The Phase Response Curve (PRC), a simple input-output characterization of single cells, can provide insights into individual and collective properties of neurons and networks, by quantifying the impact of an infinitesimal depolarizing current pulse on the time of occurrence of subsequent action potentials, while a neuron is firing tonically. Recently, the PRC theory applied to cerebellar Purkinje cells revealed that these behave as phase-independent integrators at low firing rates, and switch to a phase-dependent mode at high rates. Given the implications for computation and information processing in the cerebellum and the possible role of synchrony in the communication with its post-synaptic targets, we further explored the firing rate dependency of the PRC in Purkinje cells. We isolated key factors for the experimental estimation of the PRC and developed a closed-loop approach to reliably compute the PRC across diverse firing rates in the same cell. Our results show unambiguously that the PRC of individual Purkinje cells is firing rate dependent and that it smoothly transitions from phase independent integrator to a phase dependent mode. Using computational models we show that neither channel noise nor a realistic cell morphology are responsible for the rate dependent shift in the phase response curve.

Interaction function of oscillating coupled neurons

Large scale simulations of electrically coupled neuronal oscillators often employ the phase coupled oscillator paradigm to understand and predict network behavior. We study the nature of the interaction between such coupled oscillators using weakly coupled oscillator theory. By employing piecewise linear approximations for phase response curves and voltage time courses and parametrizing their shapes, we compute the interaction function for all such possible shapes and express it in terms of discrete Fourier modes. We find that reasonably good approximation is achieved with four Fourier modes that comprise of both sine and cosine terms.

Spike width and frequency alter stability of phase-locking in electrically coupled neurons

The stability of phase-locked states of electrically coupled type-1 phase response curve neurons is studied using piecewise linear formulations for their voltage profile and phase response curves. We find that at low frequency and/or small spike width, synchrony is stable, and antisynchrony unstable. At high frequency and/or large spike width, these phase-locked states switch their stability. Increasing the ratio of spike width to spike height causes the antisynchronous state to transition into a stable synchronous state. We compute the interaction function and the boundaries of stability of both these phase-locked states, and present analytical expressions for them. We also study the effect of phase response curve skewness on the boundaries of synchrony and antisynchrony.

Robustness, variability, phase dependence, and longevity of individual synaptic input effects on spike timing during fluctuating synaptic backgrounds: a modeling study of globus pallidus neuron phase response properties

A neuron's phase response curve (PRC) shows how inputs arriving at different times during the spike cycle differentially affect the timing of subsequent spikes. Using a full morphological model of a globus pallidus (GP) neuron, we previously demonstrated that dendritic conductances shape the PRC in a spike frequency-dependent manner, suggesting different functional roles of perisomatic and distal dendritic synapses in the control of patterned network activity. In the present study we extend this analysis to examine the impact of physiologically realistic high conductance states on somatic and dendritic PRCs and the time course of spike train perturbations. First, we found that average somatic and dendritic PRCs preserved their shapes and spike frequency dependence when the model was driven by spatially-distributed, stochastic conductance inputs rather than tonic somatic current. However, responses to inputs during specific synaptic backgrounds often deviated substantially from the average PRC. Therefore, we analyzed the interactions of PRC stimuli with transient fluctuations in the synaptic background on a trial-by-trial basis. We found that the variability in responses to PRC stimuli and the incidence of stimulus-evoked added or skipped spikes were stimulus-phase-dependent and reflected the profile of the average PRC, suggesting commonality in the underlying mechanisms. Clear differences in the relation between the phase of input and variability of spike response between dendritic and somatic inputs indicate that these regions generally represent distinct dynamical subsystems of synaptic integration with respect to influencing the stability of spike time attractors generated by the overall synaptic conductance.