Intrinsic Bursters Increase the Robustness of Rythm Generation in an Excitatory Network
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model runs in OpenCell and COR to reproduce the published results (Figure 2A where g_tonic = 0.2 nS and g_NaP = 1.5 nS, note that E_L = -57.5 mv in accordance with the original Butera 1999 model). The CellML model should be run for a duration of 20000 ms with a step size of 0.1 ms and a high point density of 100000 points/graph. This model represents a single non-pacemaker cell.
Model Structure
Abstract: The pre-Botzinger complex (pBC) is a vital subcircuit of the respiratory central pattern generator. Although the existence of neurons with pacemaker-like bursting properties in this network is not questioned, their role in network rhythmogenesis is unresolved. Modeling is ideally suited to address this debate because of the ease with which biophysical parameters of individual cells and network architecture can be manipulated. We modeled the parameter variability of experimental data from pBC bursting pacemaker and nonpacemaker neurons using a modified version of our previously developed pBC neuron and network models. To investigate the role of pacemakers in networkwide rhythmogenesis, we simulated networks of these neurons and varied the fraction of the population made up of pacemakers. For each number of pacemaker neurons, we varied the amount of tonic drive to the network and measured the frequency of synchronous networkwide bursting produced. Both excitatory networks with all-to-all coupling and sparsely connected networks were explored for several levels of synaptic coupling strength. Networks containing only nonpacemakers were able to produce networkwide bursting, but with a low probability of bursting and low input and output ranges. The results indicate that inclusion of pacemakers in an excitatory network increases robustness of the network by more than tripling the input and output ranges compared with networks containing no pacemakers. The largest increase in dynamic range occurs when the number of pacemakers in the network is greater than 20% of the population. Experimental tests of the model predictions are proposed.
model diagram
Schematic diagram of the cell model.
The original paper reference is cited below:
Intrinsic Bursters Increase the Robustness of Rythm Generation in an Excitatory Network, L.K. Purvis, J.C. Smith, H. Koizumi, R.J. Butera 2007, Journal of Neurophysiology, 97, 1515-1526. PubMed ID: 17167061
$\frac{d V}{d \mathrm{time}}=\frac{-(\mathrm{i\_Na}+\mathrm{i\_NaP}+\mathrm{i\_K}+\mathrm{i\_leak})+\mathrm{i\_tonic\_e}+\mathrm{i\_app}}{C}$
$\mathrm{i\_Na}=\mathrm{g\_Na}\mathrm{m\_infinity}^{3}(1-n)\frac{1}{1000}(V-\mathrm{E\_Na})$
$\mathrm{m\_infinity}=\frac{1}{1+e^{\frac{V-\mathrm{theta\_m}}{\mathrm{omega\_m}}}}$
$\mathrm{i\_K}=\mathrm{g\_K}n^{4}\frac{1}{1000}(V-\mathrm{E\_K})$
$\frac{d n}{d \mathrm{time}}=\frac{\mathrm{n\_infinity}-n}{\mathrm{tau\_n}}\mathrm{n\_infinity}=\frac{1}{1+e^{\frac{V-\mathrm{theta\_n}}{\mathrm{omega\_n}}}}\mathrm{tau\_n}=\frac{\mathrm{tau\_n\_max}}{\cosh \left(\frac{V-\mathrm{theta\_n}}{2\mathrm{omega\_n}}\right)}$
$\mathrm{i\_NaP}=\mathrm{g\_NaP}\mathrm{m\_infinity}h\frac{1}{1000}(V-\mathrm{E\_Na})$
$\mathrm{m\_infinity}=\frac{1}{1+e^{\frac{V-\mathrm{theta\_m}}{\mathrm{omega\_m}}}}$
$\frac{d h}{d \mathrm{time}}=\frac{\mathrm{h\_infinity}-h}{\mathrm{tau\_h}}\mathrm{h\_infinity}=\frac{1}{1+e^{\frac{V-\mathrm{theta\_h}}{\mathrm{omega\_h}}}}\mathrm{tau\_h}=\frac{\mathrm{tau\_h\_max}}{\cosh \left(\frac{V-\mathrm{theta\_h}}{2\mathrm{omega\_h}}\right)}$
$\mathrm{i\_leak}=\mathrm{g\_leak}\frac{1}{1000}(V-\mathrm{E\_leak})$
$\mathrm{i\_tonic\_e}=\mathrm{g\_tonic\_e}\frac{1}{1000}(V-\mathrm{E\_syn\_e})$
Intrinsic Bursters Increase the Robustness of Rythm Generation in an Excitatory Network: Single Non-Pacemaker Cell
Lloyd
Catherine
May
c.lloyd@auckland.ac.nz
The University of Auckland
Auckland Bioengineering Institute
keyword
electrophysiology
neuron
neurobiology
pacemaker
17167061
Purvis
L
K
Smith
J
C
Koizumi
H
Butera
R
J
Intrinsic Bursters Increase the Robustness of Rythm Generation in an Excitatory Network
2007-02
Journal of Neurophysiology
97
1515
1526