We consider multi-dimensional, Hodgkin-Huxley type models for single neurons in respiratory and motor components of the brainstem. Such models allow for the analysis of how specific ion currents contribute to the generation and control of a variety of complicated temporal voltage patterns that are observed experimentally. For this analysis to proceed, we nondimensionalize the original models...
Fast mechanisms responsible for action potential generation are modulated by slower processes that can lead to complex sequences of firing regimes. We use a dataset that provides an unusual window into a progression of transitions in neural activity, from baseline excitability to depolarization block and back. The dataset consists of whole-cell patch-clamp recordings of neurons during...
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...
We provide a short introduction to the SNARE-SM model proposed in \cite{rodrigues2016time} to describe the release of neurotransmitters in synapses. We highlight the use of slow-fast dynamics to recreate experimental data exhibiting delay between an input stimulus and the corresponding (asynchronous) neurotransmitter release. In particular, we analyse the possible scenarios in a 2D singularly...
The activity of insulin-secreting beta-cells within pancreatic islets of Langerhans is oscillatory, with a period of approximately 5 min. There are hundreds of islets in the mouse pancreas and hundreds of thousands in the human pancreas, and they are physically isolated from one another. Yet somehow that exhibit a great deal of synchrony. In addition, there is often an ultradian rhythm in...
Early afterdepolarizations (EADs) are abnormal behaviors that can lead to heart failure and even cardiac death. In this presentation, we review
recent results and we mathematically investigate the occurrence and development of these phenomena in two realistic ventricular myocyte models: the rabbit model of Sato (2009) and the human model of OโHara (2011). These models are of high dimension,...
Two identical oscillators with mutual inhibition provide a conceptual framework for modeling a latching mechanism in cell cycle regulation. In this talk, we study two such coupled oscillator models and investigate mechanisms of symmetry-breaking. In both models, inhibitory coupling induces stable alternating large-amplitude oscillations corresponding to the normal cell cycle. However, the...
Bursting is a common firing pattern in neurons, characterized by alternating active (spiking) and silent phases. While the transition from tonic spiking to bursting has been widely studied, the mechanisms underlying spike-adding within a burst remain less understood. We investigate spike-adding in a three-dimensional neuronal model with three distinct timescales. Using the FitzHughโNagumo...
Biological systems often feature aspects that evolve on highly disparate timescales. While substantial theoretical work has led to the development of extensive mathematical theory about dynamics of multi-timescale systems, open frontiers remain. This minisymposium will explore recent advances on several of these fronts in the context of problems arising in electrically excitable systems,...
