MIMICKING RIPPLE- AND SPINDLE-LIKE DYNAMICS IN AN AMPLITUDE AND VELOCITY-FEEDBACK OSCILLATOR

Ripples and spindles play a fundamental role in learning, memory, and sleep. Yet, their underlying principles remain to be fully understood. Here, using a damped harmonic oscillator (DHO) as a minimal model for a recurrently coupled E-I population of spiking neurons, we show how amplitude and velocity feedback mechanisms can reproduce characteristic ripple and spindle dynamics on the population level (Fig. 1B,C).
We systematically investigate how changing the velocity feedback, parametrized by “W”, and the amplitude “b” of a harmonic input leads to qualitatively distinct oscillatory behavior, which can be summarized in an analytically derived, two-parameter phase diagram (Fig. 1A).
We show that the interplay between input frequency, the DHO’s natural frequency, and specific parameter paths in the (W,b) subspace (Fig. 1A, colored lines) gives rise to spindle- and ripple-like dynamics (Fig. 1B,C). Notably, these characteristic dynamics are the result of input-driven dynamic bifurcations, providing a reductionistic model of ripple and spindle initiation.
We believe that this model improves the understanding of the mechanisms of spindle and ripple events and allows for assessing their role in information processing and consolidation, a topic left for future study.

Fig.1: Ripples and spindles produced by a velocity feedback DHO. A) Bifurcation diagram in the (W,b) parameter subspace. Blue: stable focus, orange: limit cycles, green and red line parameter paths producing spindles and ripples. B) Reproduction of data from another study. C) Simulation of ripple and spindle-like dynamics. Colors match the parameter paths in (A).