Intra-ripple frequency accommodation in an inhibitory network model for hippocampal ripple oscillations

Abstract

Hippocampal ripple oscillations have been implicated in important cognitive functions such as memory consolidation and planning. Multiple computational models have been proposed to explain the emergence of ripple oscillations, relying either on excitation or inhibition as the main pacemaker. Nevertheless, the generating mechanism of ripples remains unclear. An interesting dynamical feature of experimentally measured ripples, which may advance model selection, is intra-ripple frequency accommodation (IFA): a decay of the instantaneous ripple frequency over the course of a ripple event. So far, only the "bifurcation-based" inhibition-first model, which is based on delayed inhibitory synaptic coupling, has been shown to reproduce IFA. Here we use an analytical mean-field approach and numerical simulations of a leaky integrate-and-fire spiking network to explain the mechanism of IFA. We develop a drift-based approximation for the oscillation dynamics of the population rate and the mean membrane potential of interneurons under strong drive and strong inhibitory coupling. We demonstrate that IFA arises due to a speed-dependent hysteresis effect in the dynamics of the mean membrane potential, when the interneurons receive transient, sharp wave-associated excitation. We thus predict that the IFA asymmetry vanishes in the limit of slowly changing drive, but is otherwise a robust feature of the bifurcation-based inhibition-first ripple model.

Intra-ripple frequency accommodation in an inhibitory network model for hippocampal ripple oscillations

“…To accurately capture the resulting oscillation dynamics, it would thus be necessary to capture not only the first, but also the second moment of the moving membrane potential distribution. We developed such an extension of the Gaussian-drift approximation for a toy model of pulse-coupled oscillators with linear phase-response curve, which mimicks the effect of an inhibitory reversal potential [60]. We find again that IFA is caused by a hysteresis effect, but now with respect to two variables: the mean and the variance of the membrane potential distribution.…”

“…Absolute refractoriness. If an absolute refractory period is added to the reduced model in its default parameter setting (Table 2), the membrane potential distribution becomes bimodal and the network activity oscillates with alternating clusters of active neurons [60]-a state that is beyond the scope of our theory. Unimodality of the membrane potential distribution can easily be recovered by increasing the noise intensity.…”

“…Unimodality of the membrane potential distribution can easily be recovered by increasing the noise intensity. In the regime of sparse synchrony the network frequency is then virtually independent of the refractory period [60]. The refractory period only leads to a slight delay of the point of full synchrony, which also occurs at a lower network frequency due to the decrease in mean unit firing rate.…”

An E-I Firing Rate Model for Gamma Oscillations

“…Such weakly synchronized oscillations we believe are captured by our rate models in which oscillations arise by supercritical Hopf bifurcations (here and in [33]). The weakly modulated I-I oscillation and emergence by Hopf bifurcation was also analyzed using a Fokker-Planck approximation for an LIF network with delay and pulse-coupled inhibition [63]. While these approaches have provided valuable insights, the underlying assumptions and form of solutions carry limitations and both include delays.…”