title: Multiple timescale mixed bursting dynamics in a respiratory neuron model.
abstract: Experimental results in rodent medullary slices containing the pre-Bötzinger complex (pre-BötC) have identified multiple bursting mechanisms based on persistent sodium current (INaP) and intracellular Ca2+. The classic two-timescale approach to the analysis of pre-BötC bursting treats the inactivation of INaP, the calcium concentration, as well as the Ca2+-dependent inactivation of IP3as slow variables and considers other evolving quantities as fast variables. Based on its time course, however, it appears that a novel mixed bursting (MB) solution, observed both in recordings and in model pre-BötC neurons, involves at least three timescales. In this work, we consider a single-compartment model of a pre-BötC inspiratory neuron that can exhibit both INaPand Ca2+oscillations and has the ability to produce MB solutions. We use methods of dynamical systems theory, such as phase plane analysis, fast-slow decomposition, and bifurcation analysis, to better understand the mechanisms underlying the MB solution pattern. Rather surprisingly, we discover that a third timescale is not actually required to generate mixed bursting solutions. Through our analysis of timescales, we also elucidate how the pre-BötC neuron model can be tuned to improve the robustness of the MB solution.
authors: Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA, 15260, USA.
authors: Yangyang
authors: Y
authors: Wang
authors: Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA, 15260, USA. rubin@math.pitt.edu.
authors: Jonathan E
authors: http://orcid.org/0000-0002-1513-1551
authors: JE
authors: Rubin
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D003198:Computer Simulation; D066298:In Vitro Techniques; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D012125:Respiratory Center / Q000166:cytology*; D012377:Rodentia; D013997:Time Factors
keywords: Bursting; Calcium; Multiple timescales; Persistent sodium current; Respiratory neuron