Paradoxical phase response of gamma rhythms facilitates their entrainment in heterogeneous networks

The synchronization of different γ-rhythms arising in different brain areas has been implicated in various cognitive functions. Here, we focus on the effect of the ubiquitous neuronal heterogeneity on the synchronization of ING (interneuronal network gamma) and PING (pyramidal-interneuronal network gamma) rhythms. The synchronization properties of rhythms depends on the response of their collective phase to external input. We therefore determine the macroscopic phase-response curve for finite-amplitude perturbations (fmPRC) of ING- and PING-rhythms in all-to-all coupled networks comprised of linear (IF) or quadratic (QIF) integrate-and-fire neurons. For the QIF networks we complement the direct simulations with the adjoint method to determine the infinitesimal macroscopic PRC (imPRC) within the exact mean-field theory. We show that the intrinsic neuronal heterogeneity can qualitatively modify the fmPRC and the imPRC. Both PRCs can be biphasic and change sign (type II), even though the phase-response curve for the individual neurons is strictly non-negative (type I). Thus, for ING rhythms, say, external inhibition to the inhibitory cells can, in fact, advance the collective oscillation of the network, even though the same inhibition would lead to a delay when applied to uncoupled neurons. This paradoxical advance arises when the external inhibition modifies the internal dynamics of the network by reducing the number of spikes of inhibitory neurons; the advance resulting from this disinhibition outweighs the immediate delay caused by the external inhibition. These results explain how intrinsic heterogeneity allows ING- and PING-rhythms to become synchronized with a periodic forcing or another rhythm for a wider range in the mismatch of their frequencies. Our results identify a potential function of neuronal heterogeneity in the synchronization of coupled γ-rhythms, which may play a role in neural information transfer via communication through coherence.

Paradoxical phase response of gamma rhythms facilitates their entrainment in heterogeneous networks

The synchronization of different gamma rhythms arising in different brain areas has been implicated in various cognitive functions. Here, we focus on the effect of the ubiquitous neuronal heterogeneity on the synchronization of PING (pyramidal-interneuronal network gamma) and ING (interneuronal network gamma) rhythms. The synchronization properties of rhythms depends on the response of their collective phase to external input. We therefore determined the macroscopic phase-response curve for finite-amplitude perturbations (fmPRC), using numerical simulation of all-to-all coupled networks of integrate-and-fire (IF) neurons exhibiting either PING or ING rhythms. We show that the intrinsic neuronal heterogeneity can qualitatively modify the fmPRC. While the phase-response curve for the individual IF-neurons is strictly positive (type I), the fmPRC can be biphasic and exhibit both signs (type II). Thus, for PING rhythms, an external excitation to the excitatory cells can, in fact, delay the collective oscillation of the network, even though the same excitation would lead to an advance when applied to uncoupled neurons. This paradoxical delay arises when the external excitation modifies the internal dynamics of the network by causing additional spikes of inhibitory neurons, whose delaying within-network inhibition outweighs the immediate advance caused by the external excitation. These results explain how intrinsic heterogeneity allows the PING rhythm to become synchronized with a periodic forcing or another PING rhythm for a wider range in the mismatch of their frequencies. We demonstrate a similar mechanism for the synchronization of ING rhythms. Our results identify a potential function of neuronal heterogeneity in the synchronization of coupled gamma rhythms, which may play a role in neural information transfer via communication through coherence.

Theta-nested gamma oscillations in next generation neural mass models

ABSTRACTTheta-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 set-ups able to support collective gamma oscillations: namely, the pyramidal interneuronal network gamma (PING) and the interneuronal network gamma (ING). In both set-ups 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 display always 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 behaviour; 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 set-up. 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 one 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 or model, only by incrementing, at the same time, also the noise or the forcing amplitude. On the basis of our analysis both the PING and ING mechanisms give rise to theta-nested gamma oscillations with almost identical features.

Reconfiguration of the Spinal Interneuronal Network During Locomotion in Vertebrates

Within the spinal cord, the vast network of excitatory and inhibitory interneurons must be functionally reconfigured on an ongoing basis during locomotion to adapt to the environment and meet particular demands of the task. It is clear that different rhythmic motor behaviors are generated by shared and specialized circuitry and that reconfiguration is governed by multiple inputs that dynamically interact at the spinal level.