Dynamics of ramping bursts in a respiratory neuron model

Abstract

Intensive computational and theoretical work has led to the development of mutliple mathematical models for bursting in respiratory neurons in the pre-Bötzinger Complex (pre-BötC) of the mammalian brainstem. Nonetheless, these previous models have not captured the preinspiratory 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-BötC 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, dura-

Predictions and experimental tests of a new biophysical model of the mammalian respiratory oscillator

“…Our recent biophysical characterization of INaP for these neurons has confirmed that this current is slowly inactivating (Yamanishi et al, 2018), which is a basic assumption of the present and previous models , although the details of the voltage-dependent kinetic properties are more complex than represented by the first-order kinetics in the present and previous models. Moreover, some additional currents or dynamical processes (e.g., inhibitory currents from local circuit connections, synaptic depression) (Thoby- Hayes et al, 2008;Andrew and Del Negro, 2015;Phillips et al, 2018;Baertsch et al, 2018;Juárez-Vidales, et al, 2021;Abdulla et al, 2021;Revill et al, 2021), which are not considered in the model, may play a role in augmenting/shaping inspiratory bursting.…”