Dynamics of ramping bursts in a respiratory neuron model

• Main Authors: Abdulla, Muhammad U, Phillips, Ryan S, Rubin, Jonathan E
• Format: Journal Article
• Language: English
• Published: 07-05-2021
• Subjects: Mathematics - Dynamical Systems; Quantitative Biology - Neurons and Cognition
• DOI: 10.48550/arxiv.2105.03548

Intensive computational and theoretical work has led to the development of
mutliple mathematical models for bursting in respiratory neurons in the
pre-B\"otzinger Complex (pre-B\"otC) of the mammalian brainstem. Nonetheless,
these previous models have not captured the pre-inspiratory ramping aspects of
these neurons' activity patterns, in which relatively slow tonic spiking
gradually progresses to faster spiking and a full blown burst, with a
corresponding gradual development of an underlying plateau potential. In this
work, we show that the incorporation of the dynamics of the extracellular
potassium ion concentration into an existing model for pre-B\"otC neuron
bursting, along with some parameter updates, suffices to induce this ramping
behavior. Using fast-slow decomposition, we show that this activity can be
considered as a form of parabolic bursting, but with burst termination at a
homoclinic bifurcation rather than as a SNIC bifurcation. We also investigate
the parameter-dependence of these solutions and show that the proposed model
yields a greater dynamic range of burst frequencies, durations, and duty cycles
than those produced by other models in the literature.