- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-09-04 02:01:39+12:00
- Desc:
- committing version01 of rice_winslow_hunter_1999
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/rice_winslow_hunter_1999/rawfile/51ba5fd28b2c93c03c9c5479f1d5650bc6da8a7c/rice_winslow_hunter_1999_a.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : rice_model1_1999_raw.xml
CREATED : 20th June 2002
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 Rice et al's 1999 1st
model of isometric force generation in cardiac myofilaments.
CHANGES:
18/07/2002 - CML - Added more metadata.
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:pathway_editor="http://www.physiome.com/pathway_editor/1.0#" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" pathway_editor:rendering_config_file="rice_model1_1999_CellMLrender.xml" cmeta:id="rice_winslow_hunter_1999_version01" name="rice_winslow_hunter_1999_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Cooperative Mechanisms in Cardiac Muscle</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>
In cardiac muscle, steady-state force-Ca<superscript>2+</superscript> (F-Ca) relations exhibit more cooperativity than that predicted by the single Ca<superscript>2+</superscript> binding site on troponin. The exact mechanisms underlying this high cooperativity are unknown. In their 1999 paper, J. Jeremy Rice, Raimond L. Winslow and William C. Hunter present five potential models for force generation in cardiac muscle (see <xref linkend="fig_reaction_diagrams"/> below). These models were constructed by assuming different subsets of three possible cooperative mechanisms:
<itemizedlist>
<listitem>
<para>
<emphasis role="bold">Cooperative mechanism 1</emphasis>
â
is based on the theory that cross bridge formation between actin and myosin increases the affinity of troponin for Ca<superscript>2+</superscript>.</para>
</listitem>
<listitem>
<para>
<emphasis role="bold">Cooperative mechanism 2</emphasis>
â
assumes that the binding of a cross bridge increases the rate of formation of neighbouring cross bridges and that multiple cross bridges can actin activation even in the absence of Ca<superscript>2+</superscript>.</para>
</listitem>
<listitem>
<para>
<emphasis role="bold">Cooperative mechanism 2</emphasis>
â
simulates end-to-end interactions between adjacent troponin and tropomyosin.</para>
</listitem>
</itemizedlist>
</para>
<para>
<ulink url="http://ajpheart.physiology.org/cgi/content/abstract/276/5/H1734">Comparison of putative cooperative mechanisms in cardiac muscle: length dependence and dynamic responses</ulink> J. Jeremy Rice, Raimond L. Winslow and William C. Hunter, 1999, <ulink url="http://ajpheart.physiology.org/">
<emphasis>American Journal of Physiology</emphasis>
</ulink>, 276, H1734-H1754. (<ulink url="http://ajpheart.physiology.org/cgi/content/full/276/5/H1734">Full text</ulink> and <ulink url="http://ajpheart.physiology.org/cgi/reprint/276/5/H1734.pdf">PDF</ulink> versions of the article are available for Journal Members on the American Journal of Physiology website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10330260&dopt=Abstract">PubMed ID: 10330260</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagrams">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction_diagrams</title>
</objectinfo>
<imagedata fileref="rice_hunter_1999.png"/>
</imageobject>
</mediaobject>
<caption>State diagrams for the five models of isometric force generation in cardiac muscle. T represents tropomyosin, TCa is Ca<superscript>2+</superscript> bound tropomyosin, N0, N1, P0 and P1 are the non-permissive and permissive tropomyosin states.</caption>
</informalfigure>
<para>
All the models are similar in that they are structured around a functional unit of troponin, tropomyosin and actin. Tropomyosin can exist in four states, two permissive or two non-permissive (referring to whether or not the actin sites are available for binding to myosin and hence cross bridge formation). Depending on the model, one or more cross bridges exist, and these are either weakly-bound (non-force generating) or strongly bound (force generating).
</para>
<para>
The paper (cited below) tests the behaviours of the five models of force generation in cardiac myocytes. The first two models provide a baseline of performance for comparison. Models 3 to 5 are developed to incorporate more cooperative mechanisms. From the results of these simulations, which were compared to and consistent with experimental data, it is hypothesised that multiple mechanisms of cooperativity may coexist and contribute to the responses of cardiac muscle.
</para>
</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="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="flux">
<unit units="micromolar"/>
<unit units="second" exponent="-1"/>
</units>
<units name="first_order_rate_constant">
<unit units="second" exponent="-1"/>
</units>
<units name="second_order_rate_constant">
<unit units="micromolar" exponent="-1"/>
<unit units="second" exponent="-1"/>
</units>
<!--
The "environment" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
<component name="environment">
<variable units="second" public_interface="out" name="time"/>
</component>
<!--
The following components describe all the reactants and products involved in
the reactions.
-->
<component cmeta:id="N0" name="N0">
<variable units="micromolar" public_interface="out" name="N0" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_N0_rxn2"/>
<variable units="flux" public_interface="in" name="delta_N0_rxn0"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>N0</ci>
</apply>
<apply>
<plus/>
<ci>delta_N0_rxn2</ci>
<ci>delta_N0_rxn0</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="N1" name="N1">
<variable units="micromolar" public_interface="out" name="N1" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_N1_rxn1"/>
<variable units="flux" public_interface="in" name="delta_N1_rxn2"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>N1</ci>
</apply>
<apply>
<plus/>
<ci>delta_N1_rxn1</ci>
<ci>delta_N1_rxn2</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="P0" name="P0">
<variable units="micromolar" public_interface="out" name="P0" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_P0_rxn0"/>
<variable units="flux" public_interface="in" name="delta_P0_rxn3"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P0</ci>
</apply>
<apply>
<plus/>
<ci>delta_P0_rxn0</ci>
<ci>delta_P0_rxn3</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="P1" name="P1">
<variable units="micromolar" public_interface="out" name="P1" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_P1_rxn1"/>
<variable units="flux" public_interface="in" name="delta_P1_rxn3"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P1</ci>
</apply>
<apply>
<plus/>
<ci>delta_P1_rxn1</ci>
<ci>delta_P1_rxn3</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Ca" name="Ca">
<variable units="micromolar" public_interface="out" name="Ca" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_Ca_rxn0"/>
<variable units="flux" public_interface="in" name="delta_Ca_rxn1"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca</ci>
</apply>
<apply>
<plus/>
<ci>delta_Ca_rxn0</ci>
<ci>delta_Ca_rxn1</ci>
</apply>
</apply>
</math>
</component>
<!--
The following components describe the reactions of the model.
-->
<component name="reaction0">
<variable units="micromolar" public_interface="in" name="N0"/>
<variable units="micromolar" public_interface="in" name="Ca"/>
<variable units="micromolar" public_interface="in" name="P0"/>
<variable units="flux" public_interface="out" name="delta_N0_rxn0"/>
<variable units="flux" public_interface="out" name="delta_Ca_rxn0"/>
<variable units="flux" public_interface="out" name="delta_P0_rxn0"/>
<variable units="second_order_rate_constant" public_interface="out" name="k0" initial_value="39.0"/>
<variable units="first_order_rate_constant" name="k0_" initial_value="19.6"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="N0">
<role stoichiometry="1" direction="forward" delta_variable="delta_N0_rxn0" role="reactant"/>
</variable_ref>
<variable_ref variable="Ca">
<role stoichiometry="1" direction="forward" delta_variable="delta_Ca_rxn0" role="reactant"/>
</variable_ref>
<variable_ref variable="P0">
<role stoichiometry="1" direction="forward" delta_variable="delta_P0_rxn0" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>rate</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>k0</ci>
<ci>N0</ci>
<ci>Ca</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k0_</ci>
<ci>P0</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction1">
<variable units="micromolar" public_interface="in" name="N1"/>
<variable units="micromolar" public_interface="in" name="Ca"/>
<variable units="micromolar" public_interface="in" name="P1"/>
<variable units="flux" public_interface="out" name="delta_N1_rxn1"/>
<variable units="flux" public_interface="out" name="delta_Ca_rxn1"/>
<variable units="flux" public_interface="out" name="delta_P1_rxn1"/>
<variable units="second_order_rate_constant" name="k1" initial_value="1560.0"/>
<variable units="first_order_rate_constant" name="k1_" initial_value="19.6"/>
<variable units="second_order_rate_constant" public_interface="in" name="k0"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="N1">
<role stoichiometry="1" direction="forward" delta_variable="delta_N1_rxn1" role="reactant"/>
</variable_ref>
<variable_ref variable="Ca">
<role stoichiometry="1" direction="forward" delta_variable="delta_Ca_rxn1" role="reactant"/>
</variable_ref>
<variable_ref variable="P1">
<role stoichiometry="1" direction="forward" delta_variable="delta_P1_rxn1" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>rate</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>k1</ci>
<ci>N1</ci>
<ci>Ca</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k1_</ci>
<ci>P1</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="k1_calculation">
<eq/>
<ci> k1 </ci>
<apply>
<times/>
<ci> k0 </ci>
<cn cellml:units="dimensionless"> 40.0 </cn>
</apply>
</apply>
</math>
</component>
<component name="reaction2">
<variable units="micromolar" public_interface="in" name="N1"/>
<variable units="micromolar" public_interface="in" name="N0"/>
<variable units="flux" public_interface="out" name="delta_N1_rxn2"/>
<variable units="flux" public_interface="out" name="delta_N0_rxn2"/>
<variable units="first_order_rate_constant" name="k2" initial_value="15.0"/>
<variable units="flux" name="rate"/>
<reaction reversible="no">
<variable_ref variable="N1">
<role stoichiometry="1" delta_variable="delta_N1_rxn2" role="reactant"/>
</variable_ref>
<variable_ref variable="N0">
<role stoichiometry="1" delta_variable="delta_N0_rxn2" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>rate</ci>
<apply>
<times/>
<ci>k2</ci>
<ci>N1</ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction3">
<variable units="micromolar" public_interface="in" name="P0"/>
<variable units="micromolar" public_interface="in" name="P1"/>
<variable units="flux" public_interface="out" name="delta_P0_rxn3"/>
<variable units="flux" public_interface="out" name="delta_P1_rxn3"/>
<variable units="first_order_rate_constant" public_interface="out" name="k3" initial_value="0.95"/>
<variable units="first_order_rate_constant" public_interface="out" name="k3_" initial_value="2.04"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="P0">
<role stoichiometry="1" direction="forward" delta_variable="delta_P0_rxn3" role="reactant"/>
</variable_ref>
<variable_ref variable="P1">
<role stoichiometry="1" direction="forward" delta_variable="delta_P1_rxn3" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>rate</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>k3</ci>
<ci>P0</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k3_</ci>
<ci>P1</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<!--
The following component contains the equations to calculate the normalised
force of muscle contraction.
-->
<component name="force">
<variable units="dimensionless" public_interface="out" name="F" initial_value="0.0"/>
<variable units="dimensionless" name="alpha" initial_value="0.79"/>
<variable units="dimensionless" name="Fmax" initial_value="0.769"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="P1"/>
<variable units="micromolar" public_interface="in" name="N1"/>
<variable units="first_order_rate_constant" public_interface="in" name="k3"/>
<variable units="first_order_rate_constant" public_interface="in" name="k3_"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="F_calculation">
<eq/>
<ci> F </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> alpha </ci>
<apply>
<plus/>
<ci> P1 </ci>
<ci> N1 </ci>
</apply>
</apply>
<ci> Fmax </ci>
</apply>
</apply>
<apply id="Fmax_calculation">
<eq/>
<ci> Fmax </ci>
<apply>
<divide/>
<ci> k3 </ci>
<apply>
<plus/>
<ci> k3 </ci>
<ci> k3_ </ci>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_2="reaction2" component_1="N0"/>
<map_variables variable_2="N0" variable_1="N0"/>
<map_variables variable_2="delta_N0_rxn2" variable_1="delta_N0_rxn2"/>
</connection>
<connection>
<map_components component_2="reaction0" component_1="N0"/>
<map_variables variable_2="N0" variable_1="N0"/>
<map_variables variable_2="delta_N0_rxn0" variable_1="delta_N0_rxn0"/>
</connection>
<connection>
<map_components component_2="reaction1" component_1="N1"/>
<map_variables variable_2="N1" variable_1="N1"/>
<map_variables variable_2="delta_N1_rxn1" variable_1="delta_N1_rxn1"/>
</connection>
<connection>
<map_components component_2="reaction1" component_1="reaction0"/>
<map_variables variable_2="k0" variable_1="k0"/>
</connection>
<connection>
<map_components component_2="reaction2" component_1="N1"/>
<map_variables variable_2="N1" variable_1="N1"/>
<map_variables variable_2="delta_N1_rxn2" variable_1="delta_N1_rxn2"/>
</connection>
<connection>
<map_components component_2="reaction0" component_1="P0"/>
<map_variables variable_2="P0" variable_1="P0"/>
<map_variables variable_2="delta_P0_rxn0" variable_1="delta_P0_rxn0"/>
</connection>
<connection>
<map_components component_2="reaction3" component_1="P0"/>
<map_variables variable_2="P0" variable_1="P0"/>
<map_variables variable_2="delta_P0_rxn3" variable_1="delta_P0_rxn3"/>
</connection>
<connection>
<map_components component_2="reaction1" component_1="P1"/>
<map_variables variable_2="P1" variable_1="P1"/>
<map_variables variable_2="delta_P1_rxn1" variable_1="delta_P1_rxn1"/>
</connection>
<connection>
<map_components component_2="reaction3" component_1="P1"/>
<map_variables variable_2="P1" variable_1="P1"/>
<map_variables variable_2="delta_P1_rxn3" variable_1="delta_P1_rxn3"/>
</connection>
<connection>
<map_components component_2="reaction0" component_1="Ca"/>
<map_variables variable_2="Ca" variable_1="Ca"/>
<map_variables variable_2="delta_Ca_rxn0" variable_1="delta_Ca_rxn0"/>
</connection>
<connection>
<map_components component_2="reaction1" component_1="Ca"/>
<map_variables variable_2="Ca" variable_1="Ca"/>
<map_variables variable_2="delta_Ca_rxn1" variable_1="delta_Ca_rxn1"/>
</connection>
<connection>
<map_components component_2="environment" component_1="N0"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="N1"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="P0"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="P1"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Ca"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="force"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="P1" component_1="force"/>
<map_variables variable_2="P1" variable_1="P1"/>
</connection>
<connection>
<map_components component_2="N1" component_1="force"/>
<map_variables variable_2="N1" variable_1="N1"/>
</connection>
<connection>
<map_components component_2="force" component_1="reaction3"/>
<map_variables variable_2="k3" variable_1="k3"/>
<map_variables variable_2="k3_" variable_1="k3_"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#340cf943-77b7-47c6-b6ed-a4d4ef9c3d06">
<rdf:li>Cardiac Myocyte</rdf:li>
<rdf:li>cooperative mechanisms</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#citationAuthorsSeq">
<rdf:li rdf:resource="rdf:#author1Vcard"/>
<rdf:li rdf:resource="rdf:#author2Vcard"/>
<rdf:li rdf:resource="rdf:#author3Vcard"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#7592bcd5-dcf3-4124-81bb-e470f5b6b16a">
<dcterms:modified rdf:resource="rdf:#87757f55-6e42-4cbc-8bae-51993481a114"/>
<rdf:value>
Added more metadata.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#09d238b6-5101-4dcb-b821-53c6dc4adefa"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#735fa2e2-2e80-46f4-9c32-b851e6e16709">
<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#323527f1-9e64-46c5-83a5-68a5f085660f">
<dc:title>American Journal of Physiology</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author1Vcard">
<rdf:type>http://www.cellml.org/bqs/1.0#Person</rdf:type>
<vCard:N rdf:resource="rdf:#author1VcardN"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author3VcardN">
<vCard:Given>William</vCard:Given>
<vCard:Family>Hunter</vCard:Family>
<vCard:Other>C</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d0d9dbf3-3824-4bad-9931-8accd87e3b56">
<vCard:ORG rdf:resource="rdf:#434c1482-667f-4664-bac4-758a8b8e4b6b"/>
<vCard:EMAIL rdf:resource="rdf:#9efd9d03-e792-4865-9adb-cd18a6262d70"/>
<vCard:N rdf:resource="rdf:#97cfe28c-f5b4-44c4-9a85-6d3a65c6d630"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author2VcardN">
<vCard:Given>Raimond</vCard:Given>
<vCard:Family>Winslow</vCard:Family>
<vCard:Other>L</vCard:Other>
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The University of Auckland, Bioengineering Institute
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The Rice et al. 1999 1st model of isometric force generation in cardiac
myofilaments
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