European Conference on Mathematical and Theoretical Biology (ECMTB 2026)

Multiscale Organization in a novel Cartwheel Interneuron Model: From averaging to folded node dynamics

MS101-03

15 Jul 2026, 11:50

20m

15.12 - HS (University of Graz)

Minisymposium Talk Neuroscience and Neural Systems Advances in multiple timescale dynamics in neurons and related excitable systems

Speakers

Jonathan Rubin (University of Pittsburgh) Matteo Martin (University of Padova) Morten Gram Pedersen (University of Padova)

Description

A recent eleven-dimensional cartwheel cell (CWC) model \cite{[1]} has provided insight into the evolution of the electrical activity of this interneuron. Specifically, CWCs transit from bursting, via continuous spiking, to complex spiking, as the applied current (IApp) increases \cite{[2]}. Reductions in the maximal conductance of BK (gBK) or L-type Ca2+ (gCaL) channels lead to the loss of continuous spiking, and loss of bursting and complex spiking, respectively. Here, we provide a mathematical explanation of these transitions by analyzing a six-dimensional reduction of the model. The reduced system has three timescales with one fast, three slow, and two super-slow variables. We find that studying the super-slow dynamics, specifically the existence and the stability of the super slow equilibrium point through averaging theory, is informative for understanding the mechanism underlying the transitions between activity patterns as IApp, gBK, and gCaL change. Complementary results are obtained by considering the system as a two-time scale problem where the slow and the super-slow variables are all treated as slow. This approach reveals that the small-amplitude oscillations seen in bursting and complex spiking originate from a folded node structure. The associated geometric features provide an alternative perspective on the regulation of the electrical activity. Overall, by integrating two- and three-timescale analyses, this work provides a coherent framework for understanding CWC dynamics.

Bibliography

@misc{[1],
author = {Matteo Martin and Jonathan E. Rubin and Morten Gram Pedersen},
doi = {10.1101/2025.08.01.668076},
month = {8},
title = {On the role of L-type Ca ²⁺ and BK channels in a biophysical model of cartwheel interneurons},
year = {2025}
}
@article{[2],
author = {Yuil Kim and Laurence O. Trussell},
doi = {10.1152/jn.00536.2006},
issn = {0022-3077},
issue = {2},
journal = {Journal of Neurophysiology},
month = {2},
pages = {1705-1725},
title = {Ion Channels Generating Complex Spikes in Cartwheel Cells of the Dorsal Cochlear Nucleus},
volume = {97},
year = {2007}
}