ePoster

Neuronal spike generation via a homoclinic orbit bifurcation increases irregularity and chaos in balanced networks

Moritz Drangmeister, Rainer Engelken, Jan-Hendrik Schleimer, Susanne Schreiber
Bernstein Conference 2024(2024)
Goethe University, Frankfurt, Germany

Conference

Bernstein Conference 2024

Goethe University, Frankfurt, Germany

Resources

Authors & Affiliations

Moritz Drangmeister, Rainer Engelken, Jan-Hendrik Schleimer, Susanne Schreiber

Abstract

Recent theoretical models and experimental data have revealed that many neurons can exhibit homoclinic (HOM) spike-onset bifurcations by tuning variables like temperature, extracellular ion concentrations, or channel expression levels within the physiologically plausible range. In this HOM regime, spike trains have burst-like irregular firing induced by stochastic switches between attractors. While single-neuron bifurcations leading to HOM dynamics are well-studied (Hesse et al., 2022; Contreras et al., 2021; Hürkey et al., 2023; Schleimer et al., 2021; Niemeyer et al., 2021), their impact on recurrent neural network behavior remains poorly understood. Recurrent spiking networks in a balanced state often (Monteforte et al., (2010), though not always (Monteforte et al., 2012), exhibit chaotic activity and it remains unclear how stochastic burstiness on the single neuron level affects chaos and fundamental network dynamics such as attractor dimension and dynamical entropy rate. In this study, we focus on the transition in neuronal spiking dynamics at the saddle-node loop (SNL) point. This transition switches the spike-onset from a saddle-node on an invariant circle (SNIC) bifurcation to a homoclinic (HOM) bifurcation in quadratic integrate-and-fire (QIF) neurons as the reset voltage is elevated beyond the SNL point (Hesse et al., 2017). We observe that an increase in the reset voltage leads to stochastic burst-like spiking activity in the recurrent network. In this network state, we identify slow-frequency components within the power spectrum and a mean coefficient of variation (CV) for interspike intervals greater than one, both of which are accurately described by a self-consistent renewal approximation. We show that the relative information rate in the network shifts from low-pass to a intermediate frequency band. Concurrently, we find that the maximum Lyapunov exponent and Kolmogorov-Sinai entropy rate are enhanced in the network, while the Kaplan Yorke attractor dimension is reduced. Our findings open avenues for studying the computational implications of enhanced chaos, particularly in the context of task optimization within recurrent networks. This study links individual neuron biophysics with collective dynamics in large recurrent circuits, thereby highlighting the computational relevance of single-cell dynamics.

Unique ID: bernstein-24/neuronal-spike-generation-homoclinic-0969a1fe