Intrinsic Bursters Increase the Robustness of Rythm Generation in an Excitatory Network
Geoffrey
Nunns
Bioengineering Institute, University of Auckland
Model Status
This model is known to run in both PCEnv and COR. The published results cannot be replicated at this time, and further curation is needed. In addition to this, the paper describes a multi-cell network and uses this as a basis for its figures, this model reproduces a single cell of the pacemaker type, and FieldML will be needed to replicate the model data.
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 depicting the relationships
of the active contraction framework proposed by Hunter
et al. (11). The model is driven by SL and sarcomere
velocity, and intracellular [Ca21]i. Inputs are in bold,
algebraic length dependencies are in italics, processes
described by differential equations are standard font.
The complete 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
$\frac{d V}{d \mathrm{time}}=\frac{-(\mathrm{i\_Na}+\mathrm{i\_NaP}+\mathrm{i\_K}+\mathrm{i\_leak})+\mathrm{i\_tonic\_e}+\mathrm{i\_app}}{C}$
$\mathrm{i\_Na}=\mathrm{g\_Na}\mathrm{m\_infinity}^{3}(1-n)\frac{1}{1000}(V-\mathrm{E\_Na})$
$\mathrm{m\_infinity}=\frac{1}{1+e^{\frac{V-\mathrm{theta\_m}}{\mathrm{omega\_m}}}}$
$\mathrm{i\_K}=\mathrm{g\_K}n^{4}\frac{1}{1000}(V-\mathrm{E\_K})$
$\frac{d n}{d \mathrm{time}}=\frac{\mathrm{n\_infinity}-n}{\mathrm{tau\_n}}\mathrm{n\_infinity}=\frac{1}{1+e^{\frac{V-\mathrm{theta\_n}}{\mathrm{omega\_n}}}}\mathrm{tau\_n}=\frac{\mathrm{tau\_n\_max}}{\cosh \left(\frac{V-\mathrm{theta\_n}}{2\mathrm{omega\_n}}\right)}$
$\mathrm{i\_NaP}=\mathrm{g\_NaP}\mathrm{m\_infinity}h\frac{1}{1000}(V-\mathrm{E\_Na})$
$\mathrm{m\_infinity}=\frac{1}{1+e^{\frac{V-\mathrm{theta\_m}}{\mathrm{omega\_m}}}}$
$\frac{d h}{d \mathrm{time}}=\frac{\mathrm{h\_infinity}-h}{\mathrm{tau\_h}}\mathrm{h\_infinity}=\frac{1}{1+e^{\frac{V-\mathrm{theta\_h}}{\mathrm{omega\_h}}}}\mathrm{tau\_h}=\frac{\mathrm{tau\_h\_max}}{\cosh \left(\frac{V-\mathrm{theta\_h}}{2\mathrm{omega\_h}}\right)}$
$\mathrm{i\_leak}=\mathrm{g\_leak}\frac{1}{1000}(V-\mathrm{E\_leak})$
$\mathrm{i\_tonic\_e}=\mathrm{g\_tonic\_e}\frac{1}{1000}(V-\mathrm{E\_syn\_e})$
Journal of Neurophysiology
gnunns1@jhem.jhu.edu
Fixed "not exactly equivalent but dimensionally equivalent" errors.
This CellML model is known to run in both PCEnv and COR, the units have been checked and are consistent. The CellML model can recreate the published results for the single cell. However, in addition to the single cell model, this publication also describes a multicellular network, and it uses the simulation results from this model as a basis for its figures. Alone, CellML can not describe this kind of model. Instead we will need to embed the current CellML model within a FieldML or openCMISS framework (or other such modelling frameworks) in order to fully implement the multicellular network description.
H
Koizumi
2008-07-17T00:00:00+00:00
2008-07-17T14:19:05+12:00
Geoff Nunns
Geoffrey
Nunns
Rogan
Liston
Purvis
K
Intrinsic Bursters Increase the Robustness of Rythm Generation in an Excitatory Network
97
1515
1526
Jeffrey
Smith
C
Auckland Bioengineering Institute
CellML Team
keyword
electrophysiology
neuron
pacemaker
2007-00-00 00:00
This CellML model is known to run in both PCEnv and COR, the units have been checked and are consistent. The CellML model can recreate the published results for the single cell. However, in addition to the single cell model, this publication also describes a multicellular network, and it uses the simulation results from this model as a basis for its figures. Alone, CellML can not describe this kind of model. Instead we will need to embed the current CellML model within a FieldML or openCMISS framework (or other such modelling frameworks) in order to fully implement the multicellular network description.
Geoffrey
Nunns
Rogan
Robert
Butera
J
17167061
Geoff Nunns