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

Abstract

The external pallidum (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 the intra-pallidal connectivity on the GPe dynamics. We find that under healthy conditions, the inhibitory coupling determines whether the GPe is close to either a bi-stable or an oscillatory regime. Furthermore, we show that oscillatory input to the GPe, arriving from subthalamic nucleus or 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 gamma rhythm. Finally, we show that these findings generalize to realistic spiking neural networks of sparsely coupled type-I excitable GPe neurons. Significant StatementOur work provides (a) insight into the theoretical implications of a dichotomous GPe organization for its macroscopic dynamic regimes, and (b) 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. Due to 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. 2.

Effects of Neural Heterogeneity on Spiking Neural Network Dynamics

“…To do so, we leverage mean-field theory to examine the dynamics of spiking neural networks by making use of a recently developed mean-field theory for networks of coupled spiking neurons with distributed parameters [19,20]. This theory has been used to examine how neural population dynamics change based on cell-intrinsic properties [21,22], coupling between populations [23][24][25], and mechanisms such as gap junction coupling and synaptic plasticity [26][27][28]. Here, we characterize the distinct contributions of within-type and between-type heterogeneity by adapting the mean-field theory to the case of coupled networks containing distinct functional cell types.…”

“…We next investigated the effect of "within-type" heterogeneity on the dynamics of a population of inhibitory neurons, using a model of fast-spiking inhibitory interneurons [29]. Recurrent inhibitory populations are known to exhibit synchronized oscillations given sufficient excitatory drive [15,21]; here we examined how the transition from asynchronous dynamics to synchronous oscillations is affected by spike-threshold heterogeneity (∆ v ).…”

“…( 22) and eqs. (21), respectively; the synaptic coupling parameters are reported in Tab.IV. As shown in Fig.…”

Dynamical Mechanism of Parkinsonian Beta Oscillation in a Heterogenous Subthalamopallidal Network

“…There are significant differences in mutual inhibition in heterogeneous GPe [44,52], whose changes act to produce a series of alterations in the network. Previous studies have found that altered mutual inhibition within GPe generates and regulates its 𝛽 oscillations [38,39] (Fig. 3E).…”

PyRates -- A Code-Generation Tool for Dynamical Systems Modeling

“…This type of gamma-kernel convolution is a popular model for delay-coupled systems with distributed delays [44]. For example, it has been used in [16] to couple populations of neurons via distributed delays that arise from differences in the structure of the neurons and their connections. The following set of code implements a network of N = 5 coupled leaky integrators in RectiPy, with random coupling weights and gamma kernel parameters as given by eqs.…”