Cross frequency coupling in next generation inhibitory neural mass models

Ceni, Andrea; Olmi, Simona; Torcini, Alessandro; Angulo-Garcia, David

doi:10.1101/745828

Cited by 7 publications

(7 citation statements)

References 56 publications

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“…This finding was unique for the oscillatory regime of the GPe. Similarly, complex patterns of cross-frequency coupling have been reported previously in an instantaneously coupled two-population QIF model with sinusoidal forcing in the alpha frequency range (10 Hz) (Ceni et al, 2020). Thus, our results show under which conditions the GPe system can express the characteristic dynamics that have been identified in more abstract models of two populations with mutual inhibition.…”

Section: Discussionsupporting

confidence: 87%

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

et al. 2021

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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.

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Section: Discussionsupporting

confidence: 87%

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

et al. 2021

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“…These neural mass models are extremely relevant to mimick neural dynamics for two reasons. On one side, because they are not derived heuristically, since they reproduce exactly the dynamics of excitatory and inhibitory networks of spiking neurons for any degree of synchronization (Montbrió et al, 2015;Devalle et al, 2017;Ceni et al, 2019). On another side, these neural masses reproduce the macroscopic dynamics of quadratic integrate-and-fire neurons, which are normal forms of class I neurons, therefore they are S as a function of the stimulation frequency ν θ .…”

Section: Discussionmentioning

confidence: 99%

Theta-Nested Gamma Oscillations in Next Generation Neural Mass Models

Segneri

Olmi

et al. 2020

Front. Comput. Neurosci.

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Theta-nested gamma oscillations have been reported in many areas of the brain and are believed to represent a fundamental mechanism to transfer information across spatial and temporal scales. In a series of recent experiments in vitro it has been possible to replicate with an optogenetic theta frequency stimulation several features of cross-frequency coupling (CFC) among theta and gamma rhythms observed in behaving animals. In order to reproduce the main findings of these experiments we have considered a new class of neural mass models able to reproduce exactly the macroscopic dynamics of spiking neural networks. In this framework, we have examined two setups able to support collective gamma oscillations: namely, the pyramidal interneuronal network gamma (PING) and the interneuronal network gamma (ING). In both setups we observe the emergence of theta-nested gamma oscillations by driving the system with a sinusoidal theta-forcing in proximity of a Hopf bifurcation. These mixed rhythms always display phase amplitude coupling. However, two different types of nested oscillations can be identified: one characterized by a perfect phase locking between theta and gamma rhythms, corresponding to an overall periodic behavior; another one where the locking is imperfect and the dynamics is quasi-periodic or even chaotic. From our analysis it emerges that the locked states are more frequent in the ING setup. In agreement with the experiments, we find theta-nested gamma oscillations for forcing frequencies in the range [1:10] Hz, whose amplitudes grow proportionally to the forcing intensity and which are clearly modulated by the theta phase. Furthermore, analogously to the experiments, the gamma power and the frequency of the gamma-power peak increase with the forcing amplitude. At variance with experimental findings, the gamma-power peak does not shift to higher frequencies by increasing the theta frequency. This effect can be obtained, in our model, only by incrementing, at the same time, also the stimulation power. An effect achieved by increasing the amplitude either of the noise or of the forcing term proportionally to the theta frequency. On the basis of our analysis both the PING and the ING mechanism give rise to theta-nested gamma oscillations with almost identical features.

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“…Finally, we note that if in addition the excitability of neurons varies periodically, more complicated dynamics and macroscopic chaos can be observed [205]. While this example covers networks of Theta neurons, the same approach applies to networks with QIF neurons with direct synaptic coupling as given by (38); see, for example, the analyses in [207][208][209].…”

Section: Populations Of Theta Neuronsmentioning

confidence: 97%

Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review

et al. 2020

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Many biological and neural systems can be seen as networks of interacting periodic processes. Importantly, their functionality, i.e., whether these networks can perform their function or not, depends on the emerging collective dynamics of the network. Synchrony of oscillations is one of the most prominent examples of such collective behavior and has been associated both with function and dysfunction. Understanding how network structure and interactions, as well as the microscopic properties of individual units, shape the emerging collective dynamics is critical to find factors that lead to malfunction. However, many biological systems such as the brain consist of a large number of dynamical units. Hence, their analysis has either relied on simplified heuristic models on a coarse scale, or the analysis comes at a huge computational cost. Here we review recently introduced approaches, known as the Ott-Antonsen and Watanabe-Strogatz reductions, allowing one to simplify the analysis by bridging small and large scales. Thus, reduced model equations are obtained that exactly describe the collective dynamics for each subpopulation in the oscillator network via few collective variables only. The resulting equations are next-generation models: Rather than being heuristic, they exactly link microscopic and macroscopic descriptions and therefore accurately capture microscopic properties of the underlying system. At the same time, they are sufficiently simple to analyze without great computational effort. In the last decade, these reduction methods have become instrumental in understanding how network structure and interactions shape the collective dynamics and the emergence of synchrony. We review this progress based on concrete examples and outline possible limitations. Finally, we discuss how linking the reduced models with experimental data can guide the way towards the development of new treatment approaches, for example, for neurological disease.

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Cross frequency coupling in next generation inhibitory neural mass models

Cited by 7 publications

References 56 publications

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

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

Theta-Nested Gamma Oscillations in Next Generation Neural Mass Models

Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review

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