Spatial and functional architecture of the mammalian brain stem respiratory network: a hierarchy of three oscillatory mechanisms
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model represents a postinspiratory (post-I) neuron. It forms part of the brain stem respiratory network computational model described by Smith et al. 2007, and modified by Dr Carlo Laing.
Model Structure
Abstract: Mammalian central pattern generators (CPGs) producing rhythmic movements exhibit extremely robust and flexible behavior. Network architectures that enable these features are not well understood. Here we studied organization of the brain stem respiratory CPG. By sequential rostral to caudal transections through the pontine-medullary respiratory network within an in situ perfused rat brain stem-spinal cord preparation, we showed that network dynamics reorganized and new rhythmogenic mechanisms emerged. The normal three-phase respiratory rhythm transformed to a two-phase and then to a one-phase rhythm as the network was reduced. Expression of the three-phase rhythm required the presence of the pons, generation of the two-phase rhythm depended on the integrity of Botzinger and pre-Botzinger complexes and interactions between them, and the one-phase rhythm was generated within the pre-Botzinger complex. Transformation from the three-phase to a two-phase pattern also occurred in intact preparations when chloride-mediated synaptic inhibition was reduced. In contrast to the three-phase and two-phase rhythms, the one-phase rhythm was abolished by blockade of persistent sodium current (I(NaP)). A model of the respiratory network was developed to reproduce and explain these observations. The model incorporated interacting populations of respiratory neurons within spatially organized brain stem compartments. Our simulations reproduced the respiratory patterns recorded from intact and sequentially reduced preparations. Our results suggest that the three-phase and two-phase rhythms involve inhibitory network interactions, whereas the one-phase rhythm depends on I(NaP). We conclude that the respiratory network has rhythmogenic capabilities at multiple levels of network organization, allowing expression of motor patterns specific for various physiological and pathophysiological respiratory behaviors.
model diagram
Schematic of the computational model of the brain stem respiratory network. Model includes interacting neuronal populations within major brain stem respiratory compartments (Pons, BotC, pre-BotC, and rVRG). Spheres represent neuronal populations (excitatory, red; inhibitory, blue; motoneuronal, brown); green triangles represent sources of tonic excitatory drives (in pons, RTN/BotC, and pre-BotC compartments) to different neural populations. Excitatory and inhibitory synaptic connections are indicated by arrows and small circles, respectively. Simulated
'transections' (dashed lines) mimic those performed in situ.
The original paper reference is cited below:
Spatial and functional architecture of the mammalian brain stem respiratory network: a hierarchy of three oscillatory mechanisms, Smith JC, Abdala AP, Koizumi H, Rybak IA, Paton JF, 2007, Journal of Neurophysiology, 98, 3370-3387. PubMed ID: 17913982.
In order to facilitate the import of this cell model by the synaptic coupling model the current model is encapsulated in a top component called "post_I".
Catherine Lloyd
post_I
top component which encapsulates the entire post-I neuron model
$\frac{d V}{d \mathrm{time}}=\frac{-(\mathrm{i\_Na}+\mathrm{i\_K}+\mathrm{i\_Ca}+\mathrm{i\_KCa}+\mathrm{i\_L}+\mathrm{i\_synE}+\mathrm{i\_synI})}{C}$
$\mathrm{i\_Na}=\mathrm{g\_Na}m^{3}h\frac{1}{1000}(V-\mathrm{E\_Na})$
$\frac{d m}{d \mathrm{time}}=\frac{(1+e^{\frac{-(V+43.8)}{6}})^{-1}-m}{\frac{0.252}{\cosh \left(\frac{V+43.8}{14}\right)}}$
$\frac{d h}{d \mathrm{time}}=\frac{(1+e^{\frac{V+67.5}{10.8}})^{-1}-h}{\frac{8.456}{\cosh \left(\frac{V+67.5}{12.8}\right)}}$
$\mathrm{i\_K}=\mathrm{g\_K}m^{4}\frac{1}{1000}(V-\mathrm{E\_K})$
$\frac{d m}{d \mathrm{time}}=a-(a+b)ma=\frac{0.001(V+44.0)}{1-e^{\frac{-(V+44.0)}{5.0}}}b=0.17e^{\frac{-(V+49.0)}{40.0}}$
$\mathrm{i\_Ca}=\mathrm{g\_Ca}mh\frac{1}{1000}(V-\mathrm{E\_Ca})$
$\frac{d m}{d \mathrm{time}}=\frac{(1+e^{\frac{-(V+27.4)}{5.7}})^{-1}-m}{0.5}$
$\frac{d h}{d \mathrm{time}}=\frac{(1+e^{\frac{V+52.4}{5.2}})^{-1}-h}{18.0}$
$\mathrm{i\_KCa}=\mathrm{g\_KCa}m^{2}\frac{1}{1000}(V-\mathrm{E\_K})$
$\frac{d m}{d \mathrm{time}}=\frac{1.25E8\mathrm{Ca}^{2}-(1.25E8\mathrm{Ca}^{2}+2.5)m}{1000.0\mathrm{kappa}}$
$\mathrm{i\_L}=\mathrm{g\_L}\frac{1}{1000}(V-\mathrm{E\_L})$
$\mathrm{i\_synE}=\mathrm{g\_synE}\frac{1}{1000}(V-\mathrm{E\_synE})$
$\mathrm{i\_synI}=\mathrm{g\_synI}\frac{1}{1000}(V-\mathrm{E\_synI})$
$\frac{d \mathrm{Ca}}{d \mathrm{time}}=-2.072E-5\frac{\mathrm{Ca}+0.001}{\mathrm{Ca}+0.031}\mathrm{i\_Ca}+\frac{5E-5-\mathrm{Ca}}{500.00}$
$\frac{d \mathrm{s\_i}}{d \mathrm{time}}=\frac{-\mathrm{s\_i}}{\mathrm{tau\_I}}$
$\mathrm{E\_Ca}=13.27\lg \left(\frac{4.0}{\mathrm{Ca}}\right)\mathrm{g\_synI}=0.04\mathrm{S2}+0.01\mathrm{S3}$
Postinspiratory neuron
Lloyd
Catherine
May
c.lloyd@auckland.ac.nz
The University of Auckland
Auckland Bioengineering Institute
keyword
neuron
neurobiology
network
17913982
Smith
J
C
Abdala
A
P
Koizumi
H
Rybak
I
A
Paton
J
F
Spatial and functional architecture of the mammalian brain stem respiratory network: a hierarchy of three oscillatory mechanisms
2007-12
Journal of Neurophysiology
98
3370
3387