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 preBötzinger 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 ($g_{\rm CAN}$) and inositol-triphosphate ($\rm IP_3$), 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 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 of 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.

Figures (15)

• Figure 1: Activity patterns of the dimensionless model \ref{['eq:pBC_ICa_slow']}, derived from model \ref{['eq:pBC_Ica']}, depend on parameter values $g_{\rm NaP}$ and $g_{\rm Ca}$, for $g_{\rm CAN}=0.7$ and $[\rm IP_3]=0.5$. (i) The range of $g_{\rm Ca}$ and $g_{\rm NaP}$ for different solution patterns. White color denotes quiescence and other colors are tonic spiking (light blue) or bursting (dark blue, orange or red). Panels (A) through (F) illustrate sample traces for each activity pattern corresponding to labeled parameter values in panel (i). The red dashed line in panels (E) and (F) marks burst onset, highlighting a key difference between the two (N)C-Bursting regions (orange and red): in the orange region, the burst initiates before $ca$ spikes, whereas in the red region, $ca$ spikes before burst onset.
• Figure 1: Projection of the $I_{\rm NaP}$-dependent N-burst solution of \ref{['eq:pBC_ICa_slow']} along with the bifurcation diagrams for $g_{\rm NaP}=2$, $g_{\rm Ca}=0.00002$, $[\rm IP_3]=0.5$, and varying values of $g_{\rm CAN}$. (A) $g_{\rm CAN}=0.7$. Projection of the solution (black) and the bifurcation diagram for the fast $(v,n)$ subsystem with respect to $h$, along with the $h$-nullcline (green). The S-shaped light blue curve (solid where attracting, dashed otherwise) denotes the equilibria of the $v,n$ equations and represents the projection of the critical manifold $M_s$. The dark purple curves show the maximum and minimum $v$ along two families of periodic orbits born at the subcritical Andronov-Hopf bifurcation (HB). The yellow circle and red diamond respectively denote the lower saddle-node (SN) bifurcation of $M_s$ and the homoclinic (HC) bifurcation in which the outer periodic orbit branch terminates. (B): The effect of $g_{\rm CAN}$ on the solution trajectory and bifurcation diagram. From right to left, $g_{\rm CAN}=0.14, 0.7, 1.6$. (C): Projection of bursting solutions from panel (B) onto the 2-parameter bifurcation diagram in the $(h, g_{\rm CAN_{Tot}})$-space, where $g_{\rm CAN_{Tot}}=g_{\rm CAN}f([\rm Ca])$ is given in \ref{['eq:pBC_ICAN_activation']}.
• Figure 1: Numerical computation of $l$-values at (top panel) burst initiation, (middle panel) burst termination, and (bottom panel) the length of the trajectory traversed in the silent phase by $l$, as a function of increasing $[\rm IP_3]$, for C-bursting with parameters: $g_{\rm Ca} = 0.0005$, $g_{\rm CAN} = 0.7$, and $g_{\rm NaP} = 0$. Also marked by dashed lines in magenta are the $[\rm IP_3]$ reference values used for our qualitative analysis in \ref{['fig:CB_analysis_ip3']}.
• Figure 1: Some example voltage and calcium temporal traces from \ref{['eq:pBC_ICa_slow']} exhibiting mixed bursting, occurring during the transition from tonic spiking to induced (N)C-bursting (see \ref{['fig:ts_to_cb']}), with parameters: $g_{\rm Ca} = 0.0002$, $g_{\rm CAN} = 0.7$, [${\rm IP_3}] = 0.4$, and (A) $g_{\rm NaP} = 2$, (B) $g_{\rm NaP} = 3$, (C) $g_{\rm NaP} = 4$.
• Figure 1: Two-parameter bifurcation diagrams of the full system \ref{['eq:pBC_ICa_slow']} in the $([{\rm IP_3}], g_{\rm Ca})$-space, with $g_{\rm NaP} = 0$. (A) $g_{\rm CAN} = 0.7$; (B) $g_{\rm CAN} = 1.4$. The Hopf bifurcation curve (HB) is shown in blue, and the torus bifurcation curve (TR) is shown in magenta. Activity patterns of the full system \ref{['eq:pBC_ICa_slow']} are superimposed.