Exact firing rate model reveals the differential effects of chemical versus electrical synapses in spiking networks

Pietras, Bastian; Devalle, Federico; Roxin, Alex; Daffertshofer, Andreas; Montbrió, Ernest

doi:10.1103/physreve.100.042412

Cited by 55 publications

(59 citation statements)

References 77 publications

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“…Thus, our model lends itself to multi-scale approaches. It can easily be extended by additional biological details, such as plasticity mechanisms (Gast et al, 2020) or gap junctions (Pietras et al, 2019).…”

Section: Discussionmentioning

confidence: 99%

On the role of arkypallidal and prototypical neurons for phase transitions in the external pallidum

Gast

Gong

Schmidt

et al. 2021

Preprint

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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.

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Section: Discussionmentioning

confidence: 99%

On the role of arkypallidal and prototypical neurons for phase transitions in the external pallidum

Gast

Gong

Schmidt

et al. 2021

Preprint

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“…Note that in recent work [212] the authors showed that one can take the limit → 0 in the above derivation, thus simplifying the analysis and allowing one to treat synaptic and gap junctional coupling (in an infinite network of QIF neurons) on equal footing.…”

Section: Populations Of Theta Neuronsmentioning

confidence: 99%

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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“…In particu-lar, this formulation has allowed to derive a closed lowdimensional set of macroscopic equations describing exactly the evolution of the population firing rate and of the mean membrane potential [21]. In the very last years the Montbrió-Pazó-Roxin (MPR) model [21] is emerging as a representative of a new generation of neural mass models able to successfuly capture relevant aspects of neural dynamics [22][23][24][25][26][27][28][29][30][31][32][33].…”

Section: L(y)mentioning

confidence: 99%

“…. ) in (28), have the form of higher-order derivatives of w 0 with respect to V and a; therefore they yield a zero contribution to the estimation of V . Thus, Eq.…”

Section: Firing Rate and Mean Membrane Potential For Perturbed Lorentmentioning

confidence: 99%

A reduction methodology for fluctuation driven population dynamics

Goldobin

Volo

Torcini

2021

Preprint

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Lorentzian distributions have been largely employed in statistical mechanics to obtain exact results for heterogeneous systems. Analytic continuation of these results is impossible even for slightly deformed Lorentzian distributions, due to the divergence of all the moments (cumulants). We have solved this problem by introducing a pseudo-cumulants’ expansion. This allows us to develop a reduction methodology for heterogeneous spiking neural networks subject to extrinsinc and endogenous noise sources, thus generalizing the mean-field formulation introduced in [E. Montbrió et al., Phys. Rev. X 5, 021028 (2015)].

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Exact firing rate model reveals the differential effects of chemical versus electrical synapses in spiking networks

Cited by 55 publications

References 77 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

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

A reduction methodology for fluctuation driven population dynamics

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