<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : plant_model_1981.xml
CREATED : 23rd January 2003
LAST MODIFIED : 9th April 2003
AUTHOR : Catherine Lloyd
The Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Plant's 1981 mathematical model of bursting nerve cells.
CHANGES:
09/04/2003 - AAC - Added publication date information.
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="plant_1981" name="plant_1981">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Bifurcation and resonance in a model for bursting nerve cells</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
To our knowledge this CellML model is an accurate translation of the published model however it does not replicate the published results. The model runs in both OpenCell and COR and the units are consistent. The only information missing from the published paper was the initial values for the gates. These have been set to 0.1 for model completeness but it may be these values which are causing the model to break.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: In this paper we consider a model for the phenomenon of bursting in nerve cells. Experimental evidence indicates that this phenomenon is due to the interaction of multiple conductances with very different kinetics, and the model incorporates this evidence. As a parameter is varied the model undergoes a transition between two oscillatory waveforms; a corresponding transition is observed experimentally. After establishing the periodicity of the subcritical oscillatory solution, the nature of the transition is studied. It is found to be a resonance bifurcation, with the solution branching at the critical point to another periodic solution of the same period. Using this result a comparison is made between the model and experimental observations. The model is found to predict and allow an interpretation of these observations.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Bifurcation and resonance in a model for bursting nerve cells, R.E. Plant, 1981, <emphasis>Journal of Mathematical Biology</emphasis>, 11, 15-32. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=7252375&dopt=Abstract">PubMed ID: 7252375</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>diagram of the model</title>
</objectinfo>
<imagedata fileref="plant_1981.png"/>
</imageobject>
</mediaobject>
<caption>A schematic representation of the transmebrane ionic currents described by the Plant 1981 model of a bursting neuron. The model includes a voltage dependent sodium current, I<subscript>I</subscript>; a slowly activating calcium current, I<subscript>Ca</subscript>; a voltage gated potassium current, I<subscript>K</subscript>; a calcium activated potassium current, I<subscript>K,Ca</subscript>; and a leak current, I<subscript>L</subscript>.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
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<rdf:RDF>
<rdf:Bag rdf:about="rdf:#9ac2a308-5989-44a7-af3b-64ce9a902fd9">
<rdf:li>neuron</rdf:li>
<rdf:li>bifurcation</rdf:li>
<rdf:li>calcium dynamics</rdf:li>
<rdf:li>electrophysiology</rdf:li>
<rdf:li>neurobiology</rdf:li>
</rdf:Bag>
<rdf:Description rdf:about="rdf:#09155c89-f797-4141-81fb-a1de9e85262b">
<vCard:N rdf:resource="rdf:#2859d7c3-b308-4a89-b523-d01337c265a8"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#55e44aa9-1736-4efa-946f-b28068974d81">
<dcterms:W3CDTF>2003-04-09</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a6d0ca3a-fb23-4fe5-a274-ba09d110c4d0">
<dc:subject rdf:resource="rdf:#c4c1528a-31e0-4580-bcd6-7ab8828af612"/>
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<rdf:Description rdf:about="rdf:#95c5f101-c265-4a85-a692-85301c3fad6b">
<vCard:Given>R</vCard:Given>
<vCard:Family>Plant</vCard:Family>
<vCard:Other>E</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#83361748-1756-4463-8274-ac189c377aff">
<dc:creator rdf:resource="rdf:#14d6d6e9-0411-4e21-8511-0d36d2d78643"/>
<rdf:value>
This is the CellML description of Plant's 1981 mathematical model of
bursting nerve cells.
</rdf:value>
</rdf:Description>
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<rdf:Description rdf:about="rdf:#14d6d6e9-0411-4e21-8511-0d36d2d78643">
<vCard:FN>Catherine Lloyd</vCard:FN>
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<rdf:Description rdf:about="rdf:#2859d7c3-b308-4a89-b523-d01337c265a8">
<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8b00a725-39ca-4964-9d32-942b8d230dc4">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
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Plant's 1981 mathematical model of bursting nerve cells.
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Bifurcation and resonance in a model for bursting nerve cells
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The University of Auckland, Auckland Bioengineering Institute
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