<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : surkis_model_1998.xml
CREATED : 5th December 2002
LAST MODIFIED : 9th September 2003
AUTHOR : Catherine Lloyd
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 Surkis et al's 1998 mathematical model of the cable properties of laterodorsal tegmental neurons.
CHANGES:
09/04/2003 - AAC - Added publication date information.
09/09/2003 - AAC - Changed units of Gm in membrane component from
microS_per_cm2.
--><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="surkis_peskin_tranchina_leonard_1998_version01" name="surkis_peskin_tranchina_leonard_1998_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modelling the Membrane Behaviour of LDT 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 model contains partial differentials and as such can not currently be solved by existing CellML tools.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
The laterodorsal tegmental nucleus (LDT) is located at the junction of the pons and the midbrain - regions of the brain. The neurons from this area are thought to play an essential role in the generation of the electroencephalographic (EEG)-desyncronised states of waking and rapid eye movement (REM) sleep. The neurons are heterogeneous, displaying different firing rates in waking, slow-wave (SW), and REM sleep. Different membrane properties, cell morphology and synaptic input signals are thought to underlie this firing heterogeneity. </para>
<para>
In order to evaluate the relative importance of these factors, Surkis <emphasis>et al.</emphasis> analysed the cable properties of the principal LDT neurons. (the complete original paper reference is cited below). Data from these experiments were then used to produce a biologically realistic mathematical model of these cells. Their study involved developing two cell models, one in which the membrane was assumed to be passive, and one in which it was assumed that voltage-dependent conductances were contributing to cell behaviour. They found that only the active membrane model could adequately describe the behaviour of the LDT cells, and it is this model which is described below.
</para>
<para>
<ulink url="http://jn.physiology.org/cgi/content/abstract/80/5/2593">Recovery of Cable Properties Through Active and Passive Modeling of Subthreshold Membrane Responses From Laterodorsal Tegmental Neurons</ulink>, A. Surkis, C.S. Peskin, D. Tranchina, and C.S. Leonard, 1998, <ulink url="http://jn.physiology.org/">
<emphasis>Journal of Neurophysiology</emphasis>
</ulink>, 80, 2593-2607. (<ulink url="http://jn.physiology.org/cgi/content/full/80/5/2593">Full text</ulink> and <ulink url="http://jn.physiology.org/cgi/reprint/80/5/2593.pdf">PDF</ulink> versions of the article are available for Journal Members on the Journal of Neurophysiology website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=9819266&dopt=Abstract">PubMed ID: 9819266</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell schematic for the model</title>
</objectinfo>
<imagedata fileref="surkis_1998.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the voltage-dependent conductances across the plasma membrane of a LDT neuron. <emphasis>I<subscript>A</subscript>
</emphasis> represents a transient subthreshold K<superscript>+</superscript> current. <emphasis>I<subscript>H</subscript>
</emphasis> is a cation current that has a depolarising influence and it is activated on hyperpolarisation of the cell.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="microF_per_cm2">
<unit units="farad" prefix="micro"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="ohms_per_cm">
<unit units="ohm"/>
<unit units="metre" prefix="centi" exponent="-1"/>
</units>
<units name="nanoS">
<unit units="siemens" prefix="nano"/>
</units>
<units name="picoA">
<unit units="ampere" prefix="pico"/>
</units>
<units name="micrometre">
<unit units="metre" prefix="micro"/>
</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="nanoS" name="Gm" initial_value="50.0"/>
<variable units="nanoS" name="Gsh" initial_value="3.2"/>
<variable units="ohms_per_cm" name="Ri" initial_value="400.0"/>
<variable units="dimensionless" name="v_x2"/>
<variable units="dimensionless" name="v_x"/>
<variable units="dimensionless" name="a_x"/>
<variable units="micrometre" name="a"/>
<variable units="micrometre" name="x"/>
<variable units="millivolt" name="Em" initial_value="-60.0"/>
<variable units="millivolt" name="Esh" initial_value="-70.0"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="picoA" public_interface="in" name="i_A"/>
<variable units="picoA" public_interface="in" name="i_H"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="membrane_voltage_partialdiff_eq">
<eq/>
<apply>
<partialdiff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> v </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<divide/>
<ci> a </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> Ri </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> v_x2 </ci>
<apply>
<times/>
<ci> v_x </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> a </ci>
</apply>
<ci> a_x </ci>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<ci> a_x </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 0.5 </cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> Gm </ci>
<apply>
<minus/>
<ci> v </ci>
<ci> Em </ci>
</apply>
</apply>
<apply>
<times/>
<ci> Gsh </ci>
<apply>
<minus/>
<ci> v </ci>
<ci> Esh </ci>
</apply>
</apply>
<ci> i_H </ci>
<ci> i_A </ci>
</apply>
</apply>
<ci> Cm </ci>
</apply>
</apply>
<apply id="v_x_partialdiff_eq">
<eq/>
<apply>
<partialdiff/>
<bvar>
<ci> x </ci>
</bvar>
<ci> v </ci>
</apply>
<ci> v_x </ci>
</apply>
<apply id="a_x_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> x </ci>
</bvar>
<ci> a </ci>
</apply>
<ci> a_x </ci>
</apply>
<apply id="v_x2_partialdiff_eq">
<eq/>
<apply>
<partialdiff/>
<bvar>
<ci> x </ci>
<degree>
<cn cellml:units="dimensionless"> 2.0 </cn>
</degree>
</bvar>
<degree>
<cn cellml:units="dimensionless"> 2.0 </cn>
</degree>
<ci> v </ci>
</apply>
<ci> v_x2 </ci>
</apply>
</math>
</component>
<component name="H_current">
<variable units="picoA" public_interface="out" name="i_H"/>
<variable units="nanoS" name="GH"/>
<variable units="millivolt" name="EH" initial_value="-40.0"/>
<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="mH"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_H_calculation">
<eq/>
<ci> i_H </ci>
<apply>
<times/>
<ci> GH </ci>
<ci> mH </ci>
<apply>
<minus/>
<ci> v </ci>
<ci> EH </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="H_current_m_gate">
<variable units="dimensionless" public_interface="out" name="mH"/>
<variable units="dimensionless" name="mH_infinity"/>
<variable units="millisecond" name="tau_mH"/>
<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="mH_partialdiff_eq"><eq />
<apply><partialdiff />
<bvar><ci> time </ci></bvar>
<ci> mH </ci>
</apply>
<apply><divide />
<apply><minus />
<ci> mH_infinity </ci>
<ci> mH </ci>
</apply>
<ci> tau_mH </ci>
</apply>
</apply>
-->
<apply id="mH_infinity_calculation">
<eq/>
<ci> mH_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> v </ci>
<cn cellml:units="millivolt"> 75.0 </cn>
</apply>
<cn cellml:units="millivolt"> 5.5 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_mH_calculation">
<eq/>
<ci> tau_mH </ci>
<apply>
<divide/>
<cn cellml:units="millisecond"> 1.0 </cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 14.06 </cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.86 </cn>
<ci> v </ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<plus/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.87 </cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.070 </cn>
<ci> v </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="A_current">
<variable units="picoA" public_interface="out" name="i_A"/>
<variable units="nanoS" name="GA"/>
<variable units="millivolt" name="EA" initial_value="-97.0"/>
<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="mA"/>
<variable units="dimensionless" private_interface="in" name="hA"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_A_calculation">
<eq/>
<ci> i_A </ci>
<apply>
<times/>
<ci> GA </ci>
<ci> mA </ci>
<ci> hA </ci>
<apply>
<minus/>
<ci> v </ci>
<ci> EA </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="A_current_m_gate">
<variable units="dimensionless" public_interface="out" name="mA"/>
<variable units="dimensionless" name="mA_infinity"/>
<variable units="millisecond" name="tau_mA" initial_value="0.7"/>
<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="mA_partialdiff_eq"><eq />
<apply><partialdiff />
<bvar><ci> time </ci></bvar>
<ci> mA </ci>
</apply>
<apply><divide />
<apply><minus />
<ci> mA_infinity </ci>
<ci> mA </ci>
</apply>
<ci> tau_mA </ci>
</apply>
</apply>
-->
<apply id="mA_infinity_calculation">
<eq/>
<ci> mA_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> v </ci>
<cn cellml:units="millivolt"> 39.0 </cn>
</apply>
<cn cellml:units="millivolt"> -5.6 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="A_current_h_gate">
<variable units="dimensionless" public_interface="out" name="hA"/>
<variable units="dimensionless" name="hA_infinity"/>
<variable units="millisecond" name="tau_hA" initial_value="18.0"/>
<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="hA_partialdiff_eq"><eq />
<apply><partialdiff />
<bvar><ci> time </ci></bvar>
<ci> hA </ci>
</apply>
<apply><divide />
<apply><minus />
<ci> hA_infinity </ci>
<ci> hA </ci>
</apply>
<ci> tau_hA </ci>
</apply>
</apply>
-->
<apply id="hA_infinity_calculation">
<eq/>
<ci> hA_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> v </ci>
<cn cellml:units="millivolt"> 57.0 </cn>
</apply>
<cn cellml:units="millivolt"> 4.8 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="H_current">
<component_ref component="H_current_m_gate"/>
</component_ref>
<component_ref component="A_current">
<component_ref component="A_current_m_gate"/>
<component_ref component="A_current_h_gate"/>
</component_ref>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="H_current">
<component_ref component="H_current_m_gate"/>
</component_ref>
<component_ref component="A_current">
<component_ref component="A_current_m_gate"/>
<component_ref component="A_current_h_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="H_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="A_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="H_current" component_1="membrane"/>
<map_variables variable_2="v" variable_1="v"/>
<map_variables variable_2="i_H" variable_1="i_H"/>
</connection>
<connection>
<map_components component_2="A_current" component_1="membrane"/>
<map_variables variable_2="v" variable_1="v"/>
<map_variables variable_2="i_A" variable_1="i_A"/>
</connection>
<connection>
<map_components component_2="H_current_m_gate" component_1="H_current"/>
<map_variables variable_2="mH" variable_1="mH"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="v" variable_1="v"/>
</connection>
<connection>
<map_components component_2="A_current_m_gate" component_1="A_current"/>
<map_variables variable_2="mA" variable_1="mA"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="v" variable_1="v"/>
</connection>
<connection>
<map_components component_2="A_current_h_gate" component_1="A_current"/>
<map_variables variable_2="hA" variable_1="hA"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="v" variable_1="v"/>
</connection>
<rdf:RDF>
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<rdf:li>mitochondria</rdf:li>
<rdf:li>energy transfer</rdf:li>
<rdf:li>neuron</rdf:li>
<rdf:li>cardiac myocyte</rdf:li>
<rdf:li>electrophysiology</rdf:li>
<rdf:li>cable properties</rdf:li>
<rdf:li>metabolism</rdf:li>
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<rdf:Seq rdf:about="rdf:#a3668e7b-27ad-402a-b1b9-498e519dad12">
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<dc:publisher>The University of Auckland, Bioengineering Institute</dc:publisher>
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<dcterms:W3CDTF>2003-09-09</dcterms:W3CDTF>
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<rdf:Description rdf:about="rdf:#756df6d5-1571-4744-88aa-1cd6781e5476">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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<vCard:Given>A</vCard:Given>
<vCard:Family>Surkis</vCard:Family>
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Changed units of Gm in membrane component from microS_per_cm2.
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<rdf:Description rdf:about="#surkis_peskin_tranchina_leonard_1998_version01">
<dc:title>
Surkis et al's 1998 mathematical model of the cable properties of
laterodorsal tegmental neurons.
</dc:title>
<cmeta:bio_entity>laterodorsal tegmental neurons</cmeta:bio_entity>
<cmeta:comment rdf:resource="rdf:#ea4b4c0c-f386-498a-9fbe-08806b0e4895"/>
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<dc:creator rdf:resource="rdf:#a3668e7b-27ad-402a-b1b9-498e519dad12"/>
<dc:title>Recovery of Cable Properties Through Active and Passive Modeling of Subthreshold Membrane Responses From Laterodorsal Tegmental Neurons</dc:title>
<bqs:volume>80</bqs:volume>
<bqs:first_page>2593</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#642eddc5-68ba-46d1-9ac0-45eedef06ac8"/>
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<bqs:last_page>2607</bqs:last_page>
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<vCard:Given>C</vCard:Given>
<vCard:Family>Peskin</vCard:Family>
<vCard:Other>S</vCard:Other>
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<rdf:Description rdf:about="rdf:#c0a66748-ad3d-4cb9-ae41-de412ec07c38">
<vCard:Given>D</vCard:Given>
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