MS07 - NEUR-1
Senate Chamber (#2145) in The Ohio Union

Uncovering activity patterns, oscillations and other key dynamics of neuronal (and other) networks

Thursday, July 20 at 04:00pm

SMB2023 SMB2023 Follow Thursday during the "MS07" time block.
Room assignment: Senate Chamber (#2145) in The Ohio Union.
Note: this minisymposia has multiple sessions. The other session is MS06-NEUR-1 (click here).

Share this


Cheng Ly, Janet Best, Pamela Pyzza, Yangyang Wang


The complexities of neural and other cellular networks currently cannot be elucidated by experiments alone. The detailed circuit electrophysiology at the cellular level, and at large-scale networks require contemporary mathematics and computation to uncover deep insights for how they function. This two-part mini-symposium brings together a broad group of researchers who will discuss their modeling approaches to understand neuro-based phenomena both theoretically and applied to various systems (sleep, sensory, reproductive, gut microbiome, etc.) driven by experimental data in healthy and/or pathological conditions. The researchers will focus on topics that range from analyzing circuit mechanisms of neuron spike dynamics and variability, network connectivity, neural oscillations and other spatiotemporal patterns of activity.

Ngoc Anh Phan

University of Iowa (Department of Mathematics)
"Robustness of mixed mode oscillations and mixed mode bursting oscillations in three-timescale neuronal systems."
We are concerned with two types of complex oscillatory dynamics that frequently occur in multiple-timescale dynamical systems, namely mixed mode oscillations (MMOs) and mixed mode bursting oscillations (MMBOs). These phenomena involve the alternation of small-amplitude oscillations (SAOs) and large-amplitude oscillations or bursting oscillations. SAOs during the silent phase can arise from canard dynamics associated with folded singularities or a slow passage through a delayed Andronov-Hopf bifurcation (DHB) of the fast subsystem. In this work, we investigate the dynamic mechanisms underlying MMOs and MMBOs in two three-timescale neuronal systems. We identify the conditions under which the two separate mechanisms in the two-timescale setting, canard and DHB, can interact in the three-timescale context to produce more robust MMOs or MMBOs. This work can shed light on the fundamental principles governing these complex oscillatory behaviors in multiple-timescale systems.
Additional authors: Yangyang Wang, Department of Mathematics, University of Iowa

Sushmita John

University of Pittsburgh (Mathematics)
"Slow negative feedback enhances robustness of square-wave bursting"
Square-wave bursting is an activity pattern common to a variety of neuronal and endocrine cell models that has been linked to central pattern generation for respiration and other physiological functions. Many of the reduced mathematical models that exhibit square-wave bursting yield transitions to an alternative pseudo-plateau bursting pattern with small parameter changes. This susceptibility to activity change could represent a problematic feature in settings where the release events triggered by spike production are necessary for function. In this work, we analyze how model bursting and other activity patterns vary with changes in a timescale associated with the conductance of a fast inward current. Specifically, using numerical simulations and dynamical systems methods, such as fast-slow decomposition and bifurcation and phase-plane analysis, we demonstrate and explain how the presence of a slow negative feedback associated with a gradual reduction of a fast inward current in these models helps to maintain the presence of spikes within the active phases of bursts. Therefore, although such a negative feedback is not necessary for burst production, we find that its presence generates a robustness that may be important for function.
Additional authors: Bernd Krauskopf, University of Auckland; Hinke M. Osinga, University of Auckland; Jonathan E. Rubin, University of Pittsburgh

Victoria Booth

University of Michigan (Mathematics)
"Neural rhythms generated by spatially heterogeneous neuromodulation"
Oscillatory neural firing activity or neural rhythms, have been shown to play critical roles in perception, attention, learning, and memory, especially rhythms in the theta (5-10 Hz) and gamma (30-100Hz) frequency bands. Available data suggest that forebrain acetylcholine (ACh) signaling promotes gamma and theta rhythms, although the mechanism has not been identified. Recent evidence suggests that cholinergic signaling is both temporally and spatially constrained, in contrast to the traditional notion of slow, spatially homogeneous, and diffuse neuromodulation. Using biophysically-based excitatory-inhibitory (E-I) neural network models, we find that spatially constrained cholinergic stimulation can generate theta-modulated gamma rhythms. We simulate the effects of ACh on neural excitability by varying the conductance of a muscarinic receptor-regulated K+ current. In E-I networks with local excitatory connectivity and global inhibitory connectivity, we demonstrate that stable gamma- modulated firing arises within regions with high ACh signaling, while theta or mixed theta- gamma activity occurs at the peripheries of these regions. High gamma activity also alternates between different high ACh regions, at theta frequency. Our results are the first to indicate a causal role for spatially heterogenous ACh signaling in the emergence of theta-gamma rhythmicity.
Additional authors: Yihao Yang, Department of Physics, University of Michigan; Michal Zochowski, Department of Physics and Biophysics Program, University of Michigan

Fernando Antoneli

Universidade Federal de Sao Paulo (Centro de Bioinformatica Medica)
"Network Dynamics: Theory and Examples"
A coupled cell system is a network of interacting dynamical systems. Dynamical network models assume that the output from each node is important and that signals from two or more nodes can be compared so that a notion of pattern of synchrony makes sense. One may ask: How does network architecture (who is talking to whom) affect the kinds of synchronous solutions that are expected in network equations. This talk will discuss necessary and sufficient conditions for synchrony in terms of network architecture, spatio-temporal symmetries of periodic solutions, as well as some curious synchrony-breaking bifurcations.
Additional authors: Martin Golubitsky; Ohio State University; Ian Stewart; Warwick University; Ana Paula Dias; Universidade do Porto; Yunjiao Wang; Texas Southern University;

#SMB2023 Follow
Annual Meeting for the Society for Mathematical Biology, 2023.