- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-06-17 15:36:39+12:00
- Desc:
- committing version01 of plant_1981
- Permanent Source URI:
- http://models.cellml.org/workspace/plant_1981/rawfile/2523327e4098a8139b32950c0d5c579217ed79b3/plant_1981.cellml
<?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_version01" name="plant_1981_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Parabolic Bursting in Neurons</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
When exposed to a threshold concentration of glucose, pancreatic beta-cells from a wide range of species exhibit a complicated pattern of electrical activity. Bursts of action potential spikes (the "active" phase) are observed, separated by a "silent" phase of membrane repolarisation. At even higher glucose concentrations, continuous action potentials are seen. This electrical activity has two important physiological correlates: increased cytosolic Ca<superscript>2+</superscript> concentration ([Ca<superscript>2+</superscript>]<subscript>i</subscript>) and increased rate of insulin secretion during the active phase. It is generally accepted that the rise in [Ca<superscript>2+</superscript>]<subscript>i</subscript> plays a major role in insulin secretion and that the action potential spikes during a burst are responsible for the rise in [Ca<superscript>2+</superscript>]<subscript>i</subscript>.
</para>
<para>
Bursting in pancreatic beta-cells is a well studied phenomenon, and many mathematical models describing the process have been developed, including:
<itemizedlist>
<listitem>
<para>
<ulink url="${HTML_EXMPL_MITOCHONDRIAL_CA_HANDLING}">Magnus and Keizer, 1997</ulink>
</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_CHAY_MODEL97}">Chay, 1997</ulink>
</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_MAGNUS_MODEL}">Magnus and Keizer, 1999</ulink>
</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_GALL_MODEL}">Gall and Susa, 1999</ulink>
</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_BERTRAM_MODEL}">Bertram <emphasis>et al.</emphasis>, 2000</ulink>
</para>
</listitem>
</itemizedlist>
</para>
<para>
Another well studied example of busting is found in neurons (for example see the model by <ulink url="${HTML_EXMPL_FRIEL_MODEL}">Friel, 1995</ulink>). Analysis of a detailed mathematical model developed by Plant in 1981 reveals that the structure of this bursting oscillator is different from that in the beta-cell model. Where the beta-cell model has bistability, in Plant's model, oscillations arise from the autonomous activity of two slow variables. The bursting period is almost a parabolic function of time, which has lead to the name <emphasis>parabolic</emphasis> bursting.
</para>
<para>
Plant's model is similar to the beta-cell model in that it has a Ca<superscript>2+</superscript>-activated K<superscript>+</superscript> channel and a voltage-gated K<superscript>+</superscript> channel. However, it is distinct by having a voltage gated Na<superscript>+</superscript> channel and a slowly activating Ca<superscript>2+</superscript> current. The Na<superscript>+</superscript>, K<superscript>+</superscript>, and leak currents form the fast subsystem, while the Ca<superscript>2+</superscript> current forms the slow subsystem (see the figure below for a description of the model).
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Bifurcation and resonance in a model for bursting nerve cells, R.E. Plant, 1981, <ulink url="http://link.springer.de/link/service/journals/00285/index.htm">
<emphasis>Journal of Mathematical Biology</emphasis>
</ulink>, 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>Na</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>
<!--
Below, we define some additional units for association with variables and
constants within the model.
-->
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="per_millivolt">
<unit units="volt" prefix="milli" exponent="-1"/>
</units>
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="per_millivolt_millisecond">
<unit units="volt" prefix="milli" exponent="-1"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="per_millisecond">
<unit units="millisecond" exponent="-1"/>
</units>
<units name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="microA_per_cm2">
<unit units="ampere" prefix="micro"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="microF_per_cm2">
<unit units="farad" prefix="micro"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="milliS_per_cm2">
<unit units="siemens" prefix="milli"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<component name="environment">
<variable units="millisecond" public_interface="out" name="time"/>
</component>
<component name="membrane">
<variable units="millivolt" public_interface="out" name="V"/>
<variable units="microF_per_cm2" name="Cm" initial_value="1.0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="microA_per_cm2" public_interface="in" name="i_Na"/>
<variable units="microA_per_cm2" public_interface="in" name="i_Ca"/>
<variable units="microA_per_cm2" public_interface="in" name="i_K"/>
<variable units="microA_per_cm2" public_interface="in" name="i_K_Ca"/>
<variable units="microA_per_cm2" public_interface="in" name="i_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="membrane_voltage_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> V </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_Ca </ci>
<ci> i_K </ci>
<ci> i_K_Ca </ci>
<ci> i_L </ci>
</apply>
</apply>
<ci> Cm </ci>
</apply>
</apply>
</math>
</component>
<component name="sodium_current">
<variable units="microA_per_cm2" public_interface="out" name="i_Na"/>
<variable units="milliS_per_cm2" name="g_Na" initial_value="4.0"/>
<variable units="millivolt" name="V_Na" initial_value="30.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="m_infinity"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Na_calculation">
<eq/>
<ci> i_Na </ci>
<apply>
<times/>
<ci> g_Na </ci>
<apply>
<power/>
<ci> m_infinity </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> h </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_Na </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m_infinity"/>
<variable units="per_millisecond" name="alpha_m"/>
<variable units="per_millisecond" name="beta_m"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_m_calculation">
<eq/>
<ci> alpha_m </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.1 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<cn cellml:units="millivolt"> -10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_m_calculation">
<eq/>
<ci> beta_m </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 4.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
<cn cellml:units="millivolt"> -18.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="m_infinity_calculation">
<eq/>
<ci> m_infinity </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> alpha_m </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 1.21 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="dimensionless"> 78.71 </cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> alpha_m </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 1.21 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="dimensionless"> 78.71 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> beta_m </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 1.21 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="dimensionless"> 78.71 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_current_h_gate">
<variable units="dimensionless" public_interface="out" name="h"/>
<variable units="dimensionless" name="h_infinity"/>
<variable units="per_millisecond" name="alpha_h"/>
<variable units="per_millisecond" name="beta_h"/>
<variable units="millisecond" name="tau_h"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_h_calculation">
<eq/>
<ci> alpha_h </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.07 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
<cn cellml:units="millivolt"> -20.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_h_calculation">
<eq/>
<ci> beta_h </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.07 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 55.0 </cn>
</apply>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 55.0 </cn>
</apply>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dh_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> h </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> h_infinity </ci>
<ci> h </ci>
</apply>
<ci> tau_h </ci>
</apply>
</apply>
<apply id="h_infinity_calculation">
<eq/>
<ci> h_infinity </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> alpha_h </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 1.21 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="dimensionless"> 78.71 </cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> alpha_h </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 1.21 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="dimensionless"> 78.71 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> beta_h </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 1.21 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="dimensionless"> 78.71 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_h_calculation">
<eq/>
<ci> tau_h </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.08 </cn>
<apply>
<plus/>
<apply>
<times/>
<ci> alpha_h </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 1.21 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="dimensionless"> 78.71 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> beta_h </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 1.21 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="dimensionless"> 78.71 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_current">
<variable units="microA_per_cm2" public_interface="out" name="i_Ca"/>
<variable units="millimolar" public_interface="out" name="c"/>
<variable units="millivolt" name="V_Ca" initial_value="140.0"/>
<variable units="milliS_per_cm2" name="g_Ca" initial_value="0.004"/>
<variable units="per_millisecond" name="f" initial_value="0.0003"/>
<variable units="per_millivolt" name="k1" initial_value="0.0085"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="x"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ca_calculation">
<eq/>
<ci> i_Ca </ci>
<apply>
<times/>
<ci> g_Ca </ci>
<ci> x </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_Ca </ci>
</apply>
</apply>
</apply>
<apply id="dc_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> c </ci>
</apply>
<apply>
<times/>
<ci> f </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> k1 </ci>
<ci> x </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_Ca </ci>
</apply>
</apply>
<ci> c </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_current_x_gate">
<variable units="dimensionless" public_interface="out" name="x"/>
<variable units="dimensionless" name="x_infinity"/>
<variable units="millisecond" name="tau_x" initial_value="235.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="dx_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> x </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> x_infinity </ci>
<ci> x </ci>
</apply>
<ci> tau_x </ci>
</apply>
</apply>
<apply id="x_infinity_calculation">
<eq/>
<ci> x_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.15 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="potassium_current">
<variable units="microA_per_cm2" public_interface="out" name="i_K"/>
<variable units="millivolt" public_interface="out" name="V_K" initial_value="-75.0"/>
<variable units="milliS_per_cm2" name="g_K" initial_value="0.3"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="n"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_calculation">
<eq/>
<ci> i_K </ci>
<apply>
<times/>
<apply>
<times/>
<ci> g_K </ci>
<apply>
<power/>
<ci> n </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<ci> V </ci>
<ci> V_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="potassium_current_n_gate">
<variable units="dimensionless" public_interface="out" name="n"/>
<variable units="dimensionless" name="n_infinity"/>
<variable units="per_millisecond" name="alpha_n"/>
<variable units="per_millisecond" name="beta_n"/>
<variable units="millisecond" name="tau_n"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_n_calculation">
<eq/>
<ci> alpha_n </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.07 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 55.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 55.0 </cn>
</apply>
<cn cellml:units="millivolt"> -10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_n_calculation">
<eq/>
<ci> beta_n </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.125 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 45.0 </cn>
</apply>
<cn cellml:units="millivolt"> -80.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="dn_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> n </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> n_infinity </ci>
<ci> n </ci>
</apply>
<ci> tau_n </ci>
</apply>
</apply>
<apply id="n_infinity_calculation">
<eq/>
<ci> n_infinity </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> alpha_n </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 1.21 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="dimensionless"> 78.71 </cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> alpha_n </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 1.21 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="dimensionless"> 78.71 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> beta_n </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 1.21 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="dimensionless"> 78.71 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_n_calculation">
<eq/>
<ci> tau_n </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.08 </cn>
<apply>
<plus/>
<apply>
<times/>
<ci> alpha_n </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 1.21 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="dimensionless"> 78.71 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> beta_n </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 1.21 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="dimensionless"> 78.71 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_activated_potassium_current">
<variable units="microA_per_cm2" public_interface="out" name="i_K_Ca"/>
<variable units="milliS_per_cm2" name="g_K_Ca" initial_value="0.03"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="V_K"/>
<variable units="millimolar" public_interface="in" name="c"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_Ca_calculation">
<eq/>
<ci> i_K_Ca </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<power/>
<ci> g_K_Ca </ci>
<ci> c </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="millimolar"> 0.5 </cn>
<ci> c </ci>
</apply>
</apply>
<apply>
<minus/>
<ci> V </ci>
<ci> V_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="leak_current">
<variable units="microA_per_cm2" public_interface="out" name="i_L"/>
<variable units="milliS_per_cm2" name="g_L" initial_value="0.003"/>
<variable units="millivolt" name="V_L" initial_value="-40.0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_L_calculation">
<eq/>
<ci> i_L </ci>
<apply>
<times/>
<ci> g_L </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_L </ci>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="sodium_current">
<component_ref component="sodium_current_m_gate"/>
<component_ref component="sodium_current_h_gate"/>
</component_ref>
<component_ref component="calcium_current">
<component_ref component="calcium_current_x_gate"/>
</component_ref>
<component_ref component="potassium_current">
<component_ref component="potassium_current_n_gate"/>
</component_ref>
<component_ref component="calcium_activated_potassium_current"/>
<component_ref component="leak_current"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="sodium_current">
<component_ref component="sodium_current_m_gate"/>
<component_ref component="sodium_current_h_gate"/>
</component_ref>
<component_ref component="calcium_current">
<component_ref component="calcium_current_x_gate"/>
</component_ref>
<component_ref component="potassium_current">
<component_ref component="potassium_current_n_gate"/>
</component_ref>
</group>
<connection>
<map_components component_2="environment" component_1="membrane"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_activated_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="leak_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="sodium_current" component_1="membrane"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="calcium_current" component_1="membrane"/>
<map_variables variable_2="i_Ca" variable_1="i_Ca"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="potassium_current" component_1="membrane"/>
<map_variables variable_2="i_K" variable_1="i_K"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="calcium_activated_potassium_current" component_1="membrane"/>
<map_variables variable_2="i_K_Ca" variable_1="i_K_Ca"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="leak_current" component_1="membrane"/>
<map_variables variable_2="i_L" variable_1="i_L"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="calcium_activated_potassium_current" component_1="calcium_current"/>
<map_variables variable_2="c" variable_1="c"/>
</connection>
<connection>
<map_components component_2="calcium_activated_potassium_current" component_1="potassium_current"/>
<map_variables variable_2="V_K" variable_1="V_K"/>
</connection>
<connection>
<map_components component_2="sodium_current_m_gate" component_1="sodium_current"/>
<map_variables variable_2="m_infinity" variable_1="m_infinity"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="sodium_current_h_gate" component_1="sodium_current"/>
<map_variables variable_2="h" variable_1="h"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="potassium_current_n_gate" component_1="potassium_current"/>
<map_variables variable_2="n" variable_1="n"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="calcium_current_x_gate" component_1="calcium_current"/>
<map_variables variable_2="x" variable_1="x"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<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>resonance</rdf:li>
<rdf:li>Neuron</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"/>
</rdf:Description>
<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>
<rdf:Description rdf:about="rdf:#1eb4e357-be88-4699-9b7b-b8d4cd44205d">
<bqs:Person rdf:resource="rdf:#13e07285-3aef-4270-9276-9311c76944f1"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#14d6d6e9-0411-4e21-8511-0d36d2d78643">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<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>The Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#06b07339-1939-4452-a744-fe6c137bb2d8">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#13e07285-3aef-4270-9276-9311c76944f1">
<vCard:N rdf:resource="rdf:#95c5f101-c265-4a85-a692-85301c3fad6b"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ed2bb4fd-9de6-409e-8c88-c3aa03dee589">
<bqs:Pubmed_id>7252375</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#4f40d2cd-751b-49df-a628-9bec8a7075bd"/>
</rdf:Description>
<rdf:Description rdf:about="#plant_1981_version01">
<dc:title>
Plant's 1981 mathematical model of bursting nerve cells.
</dc:title>
<cmeta:bio_entity>Neuron</cmeta:bio_entity>
<cmeta:comment rdf:resource="rdf:#83361748-1756-4463-8274-ac189c377aff"/>
<bqs:reference rdf:resource="rdf:#a6d0ca3a-fb23-4fe5-a274-ba09d110c4d0"/>
<bqs:reference rdf:resource="rdf:#ed2bb4fd-9de6-409e-8c88-c3aa03dee589"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4f40d2cd-751b-49df-a628-9bec8a7075bd">
<dc:creator rdf:resource="rdf:#1eb4e357-be88-4699-9b7b-b8d4cd44205d"/>
<dc:title>
Bifurcation and resonance in a model for bursting nerve cells
</dc:title>
<bqs:volume>11</bqs:volume>
<bqs:first_page>15</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#c38b3aa7-f0c0-4d8e-b9d0-3f16309b7d2d"/>
<dcterms:issued rdf:resource="rdf:#ee3b1dcf-52dd-4258-82ca-7b54b8508dac"/>
<bqs:last_page>32</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c4c1528a-31e0-4580-bcd6-7ab8828af612">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value rdf:resource="rdf:#9ac2a308-5989-44a7-af3b-64ce9a902fd9"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#31023f1a-7f9e-4bb2-b98b-7f9368b8755d">
<vCard:ORG rdf:resource="rdf:#8b00a725-39ca-4964-9d32-942b8d230dc4"/>
<vCard:EMAIL rdf:resource="rdf:#b90e6ce7-c250-4b5b-84b4-fc35547e56d2"/>
<vCard:N rdf:resource="rdf:#06b07339-1939-4452-a744-fe6c137bb2d8"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c38b3aa7-f0c0-4d8e-b9d0-3f16309b7d2d">
<dc:title>Journal of Mathematical Biology</dc:title>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher>
The University of Auckland, Bioengineering Institute
</dc:publisher>
<cmeta:modification rdf:resource="rdf:#9c17c301-92c9-40ad-bd30-e798734cd182"/>
<dcterms:created rdf:resource="rdf:#e86ab73d-5fc3-4d65-9467-d67755a84827"/>
<dc:creator rdf:resource="rdf:#31023f1a-7f9e-4bb2-b98b-7f9368b8755d"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b90e6ce7-c250-4b5b-84b4-fc35547e56d2">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e86ab73d-5fc3-4d65-9467-d67755a84827">
<dcterms:W3CDTF>2003-01-23</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ee3b1dcf-52dd-4258-82ca-7b54b8508dac">
<dcterms:W3CDTF>1981-01</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9c17c301-92c9-40ad-bd30-e798734cd182">
<dcterms:modified rdf:resource="rdf:#55e44aa9-1736-4efa-946f-b28068974d81"/>
<rdf:value>
Added publication date information.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#09155c89-f797-4141-81fb-a1de9e85262b"/>
</rdf:Description>
</rdf:RDF>
</model>
