Dual Mechanisms for Heterogeneous Responses of Inspiratory Neurons to Noradrenergic Modulation

Abstract. Respiration is an essential involuntary function necessary for survival. This poses a challenge for the control of breathing. The pre-Bötzinger complex (preBötC) is a heterogeneous neuronal network responsible for driving the inspiratory rhythm. While neuromodulators such as norepinephrine (NE) allow it to be both robust and flexible for all living beings to interact with their environment, the basis for how neuromodulation impacts neuron-specific properties remains poorly understood. In this work, we examine how NE influences different preBötC neuronal subtypes by modeling its effects through modulating two key parameters: calcium-activated nonspecific cationic current gating conductance ([Formula: see text]) and inositol-triphosphate ([Formula: see text]), guided by experimental studies. Our computational model captures the experimentally observed differential effects of NE on distinct preBötC bursting patterns. We show that this dual-modulation mechanism is critical for inducing conditional bursting and identify specific parameter regimes where silent neurons remain inactive in the presence of NE. Furthermore, using methods from dynamical systems theory, we uncover the mechanisms by which NE differentially modulates burst frequency and duration in NaP-dependent and CAN-dependent bursting neurons. These results align well with previously reported experimental findings and provide a deeper understanding of cell-specific neuromodulatory responses within the respiratory network. Relevance to Life Sciences. Experimental studies have shown that NE can stabilize inspiratory activity in healthy networks, yet destabilize it under pathological conditions. Whether NE exerts stabilizing versus destabilizing effects on inspiratory rhythmogenesis likely depends on its heterogeneous actions on distinct neuronal subpopulations within the preBötC. Our modeling identifies a dual-modulation mechanism, through modulation of [Formula: see text] and [Formula: see text], that governs neuron-specific responses to NE and helps explain its experimentally observed differential effects on preBötC neurons. It also reveals the emergence of mixed bursting oscillations during the induction of conditional bursting activity from spiking neurons, with initial irregular activity occurring before stabilization. This work provides a mechanistic foundation for understanding how NE specifically modulates preBötC neurons and offers a basis for investigating how neuron-type-specific neuromodulatory responses interact to shape respiratory network function in both healthy and diseased states. Mathematical Content. We apply techniques from dynamical systems theory to analyze the preBötC model neuron that involves multiple distinct timescales and exhibits differential responses to NE depending on its intrinsic state. Our approach combines phase-plane analysis, bifurcation analysis, and geometric singular perturbation theory (GSPT). These analyses not only uncover the mechanisms by which NE differentially modulates distinct types of preBötC neurons but also generate testable predictions for future experiments.