Abstract
High-frequency oscillations (above 30 Hz) have been observed in sensory and higher-order brain areas, and are believed to constitute a general hallmark of functional neuronal activation. Fast inhibition in interneuronal networks has been suggested as a general mechanism for the generation of high-frequency oscillations. Certain classes of interneurons exhibit subthreshold oscillations, but the effect of this intrinsic neuronal property on the population rhythm is not completely understood. We study the influence of intrinsic damped subthreshold oscillations in the emergence of collective high-frequency oscillations, and elucidate the dynamical mechanisms that underlie this phenomenon. We simulate neuronal networks composed of either Integrate-and-Fire (IF) or Generalized Integrate-and-Fire (GIF) neurons. The IF model displays purely passive subthreshold dynamics, while the GIF model exhibits subthreshold damped oscillations. Individual neurons receive inhibitory synaptic currents mediated by spiking activity in their neighbors as well as noisy synaptic bombardment, and fire irregularly at a lower rate than population frequency. We identify three factors that affect the influence of single-neuron properties on synchronization mediated by inhibition: i) the firing rate response to the noisy background input, ii) the membrane potential distribution, and iii) the shape of Inhibitory Post-Synaptic Potentials (IPSPs). For hyperpolarizing inhibition, the GIF IPSP profile (factor iii)) exhibits post-inhibitory rebound, which induces a coherent spike-mediated depolarization across cells that greatly facilitates synchronous oscillations. This effect dominates the network dynamics, hence GIF networks display stronger oscillations than IF networks. However, the restorative current in the GIF neuron lowers firing rates and narrows the membrane potential distribution (factors i) and ii), respectively), which tend to decrease synchrony. If inhibition is shunting instead of hyperpolarizing, post-inhibitory rebound is not elicited and factors i) and ii) dominate, yielding lower synchrony in GIF networks than in IF networks.
Highlights
Fast oscillations (30–100 Hz and higher) have been observed in several brain areas, and have been proposed as a general substrate of neural computation [1,2,3,4]
The theory of weakly coupled oscillators showed how the phase response of individual neurons can predict the patterns of phase relationships that are observed at the network level
Single Neuron Dynamics Before we consider the dynamics of networks of neurons coupled by inhibitory conductances, it is instructive to characterize how individual neurons respond to the background noisy input alone, which represents input from other brain areas and is the main source of depolarization and variability in the model
Summary
Fast oscillations (30–100 Hz and higher) have been observed in several brain areas, and have been proposed as a general substrate of neural computation [1,2,3,4]. Most theoretical studies have focused on the mechanisms of collective synchronization in the regime where individual neurons fire regularly and can be considered as quasi-periodic oscillators [14,15,16,17]. As we show in this study, the intrinsic neuronal properties that are more important for the generation of collective oscillations depend critically on the dynamical regime where individual neurons operate. Noise Every neuron receives a spatially independent background term Ibg, which is composed of an excitatory and an inhibitory component with associated reversal potentials Eexc and Einh: Ibg(t)~ginh(t)(Einh{v(t))zgexc(t)(Eexc{v(t)): ð6Þ. We maintain a fixed ratio between the background inhibitory and excitatory conductance, both in terms of mean values and variability (unless stated otherwise).
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