Abstract
Experimental results in rodent medullary slices containing the pre-Botzinger complex (pre-BotC) have identified multiple bursting mechanisms based on persistent sodium current (I (NaP)) and intracellular Ca2+. The classic two-timescale approach to the analysis of pre-BotC bursting treats the inactivation of I (NaP), the calcium concentration, as well as the Ca2+-dependent inactivation of IP (3) as 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-BotC neurons, involves at least three timescales. In this work, we consider a single-compartment model of a pre-BotC inspiratory neuron that can exhibit both I (NaP) and 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-BotC neuron model can be tuned to improve the robustness of the MB solution.
