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

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 a feedback-based inhibition-first model, which relies 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 excitatory drive and strong inhibitory coupling. For IFA, the speed at which the excitatory drive changes is critical. 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 feedback-based inhibition-first ripple model.