Firing rate equations require a spike synchrony mechanism to correctly describe fast oscillations in inhibitory networks

Devalle, Federico; Roxin, Alex; Montbrió, Ernest

doi:10.1371/journal.pcbi.1005881

Cited by 98 publications

(191 citation statements)

References 94 publications

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“…Despite the fact that at a macroscopic level the network dynamics of a single population with exponential synapses is exactly described in the limit N → ∞ by three degrees of freedom (5) our and previous analysis 20 have not reported evidences of chaotic motions for a sin- gle inhibitory population. The situation is different for an excitatory population, as briefly discussed in 7 , or in presence of an external forcing as shown in the previous sub-section.…”

Section: Two Populations In a Master-slave Configurationcontrasting

confidence: 69%

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Cross frequency coupling in next generation inhibitory neural mass models

Ceni

Olmi

Torcini

et al. 2019

Preprint

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Coupling among neural rhythms is one of the most important mechanisms at the basis of cognitive processes in the brain. In this study we consider a neural mass model, rigorously obtained from the microscopic dynamics of an inhibitory spiking network with exponential synapses, able to autonomously generate collective oscillations (COs). These oscillations emerge via a super-critical Hopf bifurcation, and their frequencies are controlled by the synaptic time scale, the synaptic coupling and the excitability of the neural population. Furthermore, we show that two inhibitory populations in a master-slave configuration with different synaptic time scales can display various collective dynamical regimes: namely, damped oscillations towards a stable focus, periodic and quasi-periodic oscillations, and chaos. Finally, when bidirectionally coupled the two inhibitory populations can exhibit different types of θ-γ cross-frequency couplings (CFCs): namely, phase-phase and phase-amplitude CFC. The coupling between θ and γ COs is enhanced in presence of a external θ forcing, reminiscent of the type of modulation induced in Hippocampal and Cortex circuits via optogenetic drive.In healthy conditions, the brain’s activity reveals a series of intermingled oscillations, generated by large ensembles of neurons, which provide a functional substrate for information processing. How single neuron properties influence neuronal population dynamics is an unsolved question, whose solution could help in the understanding of the emergent collective behaviors arising during cognitive processes. Here we consider a neural mass model, which reproduces exactly the macroscopic activity of a network of spiking neurons. This mean-field model is employed to shade some light on an important and ubiquitous neural mechanism underlying information processing in the brain: the θ-γ cross-frequency coupling. In particular, we will explore in detail the conditions under which two coupled inhibitory neural populations can generate these functionally relevant coupled rhythms.

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Section: Two Populations In a Master-slave Configurationcontrasting

confidence: 69%

“…By equating (20) and (21) we can find the values of J (H) where the Hopf bifurcation occurs, namely that bounds the oscillating region and that is reported in Eq. (11).…”

Section: Discussionmentioning

confidence: 99%

Cross frequency coupling in next generation inhibitory neural mass models

Ceni

Olmi

Torcini

et al. 2019

Preprint

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“…As verified in [21] for instantaneous PSPs this formulation represents a quite good guidance for the understanding of the emergence of sustained COs in the network, despite the fact that the MF asymptotic solutions are always stable foci. Instead in the present case, analogously to what found for structurally homogeneous networks of heterogeneous neurons in [57], we observe that for IPSPs of finite duration oscillations can emerge in the network as well as in the mean-field, as shown in Fig. 1.…”

Section: Effective Mean-field Model For a Sparse Qif Networksupporting

confidence: 88%

“…A fundamental parameter controlling the emergence of COs in the MF model is the synaptic time τ d , indeed in absence of this time scale no oscillations are present at the MF level [21]. On the other hand too large values of τ d also lead to COs suppression, since the present model reduces to a Wilson-Cowan model for a single inhibitory population, that it is know to be unable to display oscillations [57]. As shown in Figs.…”

Section: B Phase Diagrams Of the Mean-field Modelmentioning

confidence: 75%

“…More specifically we have studied balanced sparse inhibitory networks of quadratic integrate-and-fire (QIF) neurons pulse coupled via inhibitory post-synaptic potentials (IPSPs), characterized by a finite synaptic time scale. For this sparse network we derived an effective mean-field (MF) by employing recently developed reduction techniques for QIF networks [9,21,57,58]. In the MF model, in proximity of the sub-critical Hopf bifurcations, we report regions of bistability involving one stable focus and one stable limit cycle.…”

Section: Introductionmentioning

confidence: 99%

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Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons

Segneri

Volo

et al. 2019

Preprint

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Oscillations are a hallmark of neural population activity in various brain regions with a spectrum covering a wide range of frequencies. Within this spectrum gamma oscillations have received particular attention due to their ubiquitous nature and to their correlation with higher brain functions. Recently, it has been reported that gamma oscillations in the hippocampus of behaving rodents are segregated in two distinct frequency bands: slow and fast. These two gamma rhythms correspond to dfferent states of the network, but their origin has been not yet clarified. Here, we show theoretically and numerically that a single inhibitory population can give rise to coexisting slow and fast gamma rhythms corresponding to collective oscillations of a balanced spiking network. The slow and fast gamma rhythms are generated via two different mechanisms: the fast one being driven by the coordinated tonic neural firing and the slow one by endogenous fluctuations due to irregular neural activity. We show that almost instantaneous stimulations can switch the collective gamma oscillations from slow to fast and vice versa. Furthermore, to make a closer contact with the experimental observations, we consider the modulation of the gamma rhythms induced by a slower (theta) rhythm driving the network dynamics. In this context, depending on the strength of the forcing, we observe phase-amplitude and phase-phase coupling between the fast and slow gamma oscillations and the theta forcing. Phase-phase coupling reveals different theta-phases preferences for the two coexisting gamma rhythms.

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Comparison between an exact and a heuristic neural mass model with second-order synapses

et al. 2022

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Neural mass models (NMMs) are designed to reproduce the collective dynamics of neuronal populations. A common framework for NMMs assumes heuristically that the output firing rate of a neural population can be described by a static nonlinear transfer function (NMM1). However, a recent exact mean-field theory for quadratic integrate-and-fire (QIF) neurons challenges this view by showing that the mean firing rate is not a static function of the neuronal state but follows two coupled nonlinear differential equations (NMM2). Here we analyze and compare these two descriptions in the presence of second-order synaptic dynamics. First, we derive the mathematical equivalence between the two models in the infinitely slow synapse limit, i.e., we show that NMM1 is an approximation of NMM2 in this regime. Next, we evaluate the applicability of this limit in the context of realistic physiological parameter values by analyzing the dynamics of models with inhibitory or excitatory synapses. We show that NMM1 fails to reproduce important dynamical features of the exact model, such as the self-sustained oscillations of an inhibitory interneuron QIF network. Furthermore, in the exact model but not in the limit one, stimulation of a pyramidal cell population induces resonant oscillatory activity whose peak frequency and amplitude increase with the self-coupling gain and the external excitatory input. This may play a role in the enhanced response of densely connected networks to weak uniform inputs, such as the electric fields produced by noninvasive brain stimulation.

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Firing rate equations require a spike synchrony mechanism to correctly describe fast oscillations in inhibitory networks

Cited by 98 publications

References 94 publications

Cross frequency coupling in next generation inhibitory neural mass models

Cross frequency coupling in next generation inhibitory neural mass models

Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons

Comparison between an exact and a heuristic neural mass model with second-order synapses

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