P038 Mimicking Ripple- and Spindle-Like Dynamics in an Amplitude and Velocity-Feedback Oscillator
Pedro Carvalho*1, Wolf Singer1, Felix Effenberger1
1Ernst Strüngmann Institute, Singer Lab, Frankfurt am Main/Hessen, Germany
*Email: prfdecarvalho@gmail.com
Introduction :Ripples and spindles play a fundamental role in learning, memory, and sleep [1]. Yet, the principles of their generation and their functional relevance remain to be fully understood. Here, we show how damped harmonic oscillators (DHOs) subject to feedback can reproduce such characteristic dynamics on the population level (Fig. 1B,C). In our model, one DHO represents the aggregate activity of a recurrently coupled E-I population of spiking neurons [3] and can capture different characteristics of the underlying E-I circuit (e.g. recurrent excitation and inhibition) by feedback connections [2]. Recurrent networks of such nodes were previously shown to reproduce many physiological phenomena [2].
Methods:Using an analytically derived bifurcation diagram (see [2]), we investigate the dynamics of a DHO with feedback along different points in the 2d parameter space (W, b) of the velocity feedback parameter w and the amplitude of a harmonic input b (Fig. 1A). We determine dynamics for different parameter paths (colored lines in Fig. 1A) by performing numerical simulations of the DHO dynamics subject to a harmonic drive. We observe nodal dynamics similar to ripples and spindles (Fig.1B,C) [1].
Results:We show that for a DHO with velocity feedback, the interplay between input frequency (data not shown), the oscillator’s natural frequency, and the trajectory of input parameters in the (b, W) parameter subspace (Fig. 1A) gives rise to dynamics resembling spindles and ripples (Fig. 1B,C). Notably, for each class of these characteristic dynamics, we can identify a specific parameter path in the (b, W) parameter subspace resulting in their generation (Fig. 1A, colored lines). These dynamics are due to a dynamic bifurcation, in which the system transitions between subcritical and supercritical regimes separated by a Hopf bifurcation. In this configuration, ripple- and spindle-like dynamics emerge as a transient phenomenon.
Discussion:By studying the dynamics of DHOs subject to velocity feedback, we show that these oscillators can reproduce ripple- and spindle-like dynamics [1] in an intriguingly simple phenomenological model of the aggregate activity of E-I populations [2,3]. These complex dynamics are shown to result from input-driven dynamic bifurcations of the underlying DHO system. This provides a reductionistic model of ripple and spindle initiation in which simple mechanisms result in complex dynamics (see also [3]). We hope that this model will allow for a better understanding the mechanisms of spindle and ripple initiation, as well as to allow for assessing their role in information processing and consolidation (compare [2]), a topic left for a future study
Figure 1. Ripples and spindles produced by a velocity feedback DHO. A) Bifurcation diagram in the input amplitude (b) and velocity feedback (W) parameter subspace. Blue: stable focus, orange: limit cycles, green and red line parameter paths producing spindles and ripples. B) Reproduction of data from [2]. C) Simulation of ripple and spindle-like dynamics. Colors match parameters paths in (A).
Acknowledgements
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References
[1] Staresina, B.P. et al. How coupled slow oscillations, spindles and ripples coordinate
neuronal processing and communication during human sleep. Nat. Neurosci. (2023).
[2]Spyropoulos, G.et al.Spontaneous variability in gamma dynamics described by a damped harmonic oscillator driven by noise.Nat Commun13, 2019 (2022)
[3] F. Effenberger, P. Carvalho, I. Dubinin, & W. Singer, The functional role of oscillatory
dynamics in neocortical circuits: A computational perspective, Proc. Natl. Acad. Sci.(2025).
