- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:25:44+12:00
- Desc:
- committing version01 of mlcek_neumann_kittnar_novak_2001
- Permanent Source URI:
- http://models.cellml.org/workspace/mlcek_neumann_kittnar_novak_2001/rawfile/98af4be61d7ab1e2229119d3d7b00a3139607415/mlcek_neumann_kittnar_novak_2001.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : mlcek_model_2001_raw.xml
CREATED : 19th June 2002
LAST MODIFIED : 18th July 2002
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 Mlcek et al's
mathematical model of the electromechanical heart contractile
system.
CHANGES:
18/07/2002 - CML - Added more metadata.
--><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="mlcek_model_2001_CellMLrender.xml" cmeta:id="mlcek_neumann_kittnar_novak_2001_version01" name="mlcek_neumann_kittnar_novak_2001_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Mathematical Model of the Electromechanical Heart Contractile System</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>
Computational modelling in molecular cardiology has recently focused on simulating subsets of myocardial excitation-contraction processes. As people try to improve their understanding of myocardial function, there is an increasing interest in excitation-contraction coupling and mechanical events in cardiac muscle. It is hoped that these computer simulations will also help explain the pathophysiological mechanisms of heart failure.
</para>
<para>
In their 2001 paper, Mlcek, Neumann, Kittnar and Novak concentrate on the molecular level of electromechanical events in cardiac muscle. They introduce an actomyosin subsystem accompanied by a simple regulatory subsystem involving calcium binding to troponin C (see <xref linkend="fig_reaction_diagram"/> below). They performed many simulations to prove the stability of their model and they then used the simulation results to help interpret experimental and clinical data.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.biomed.cas.cz/physiolres/2001/issue4/mlcek.htm">Mathematical Model of the Electromechanical Heart Contractile System - Regulatory Subsystem Physiological Considerations</ulink>, M. Mlcek, J. Neumann, O. Kittnar and V. Novak, 2001, <ulink url="http://www.biomed.cas.cz/physiolres/">
<emphasis>Physiological Research</emphasis>
</ulink>, 50, 425-432. (A PDF version of the article is also available on the Physiological Research journal website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11551150&dopt=Abstract">PubMed ID: 11551150</ulink>
</para>
<para>
The raw CellML descriptions of the model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>.
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction_diagram</title>
</objectinfo>
<imagedata fileref="mlcek_2001.png"/>
</imageobject>
</mediaobject>
<caption>Diagram of the regulatory subsystem scheme and the actomyosin subsystem scheme.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
We start the model definition with a definition of some named
sets of units for use throughout the model.
-->
<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 following component is defined for modelling convenience. It contains
all the universal variables, in this case, only time.
-->
<component name="global_variables">
<variable units="second" public_interface="out" name="time"/>
</component>
<!--
The following components describe all the metabolites - both reactants and
products - involved in the elctromechanical heart contractile system.
-->
<component cmeta:id="Actin" name="Actin">
<variable units="micromolar" public_interface="out" name="Actin" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_Actin_rxn1"/>
<variable units="flux" public_interface="in" name="delta_Actin_rxn5"/>
<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>Actin</ci>
</apply>
<apply>
<plus/>
<ci>delta_Actin_rxn1</ci>
<ci>delta_Actin_rxn5</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Myosin" name="Myosin">
<variable units="micromolar" public_interface="out" name="Myosin" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_Myosin_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>Myosin</ci>
</apply>
<ci>delta_Myosin_rxn0</ci>
</apply>
</math>
</component>
<component cmeta:id="ATP" name="ATP">
<variable units="micromolar" public_interface="out" name="ATP" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_ATP_rxn0"/>
<variable units="flux" public_interface="in" name="delta_ATP_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>ATP</ci>
</apply>
<apply>
<plus/>
<ci>delta_ATP_rxn0</ci>
<ci>delta_ATP_rxn2</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="ADP" name="ADP">
<variable units="micromolar" public_interface="out" name="ADP" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_ADP_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>ADP</ci>
</apply>
<ci>delta_ADP_rxn3</ci>
</apply>
</math>
</component>
<component cmeta:id="Myosin_ATP" name="Myosin_ATP">
<variable units="micromolar" public_interface="out" name="Myosin_ATP" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_Myosin_ATP_rxn0"/>
<variable units="flux" public_interface="in" name="delta_Myosin_ATP_rxn1"/>
<variable units="flux" public_interface="in" name="delta_Myosin_ATP_rxn7"/>
<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>Myosin_ATP</ci>
</apply>
<apply>
<plus/>
<ci>delta_Myosin_ATP_rxn0</ci>
<ci>delta_Myosin_ATP_rxn1</ci>
<ci>delta_Myosin_ATP_rxn7</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Actomyosin_ATP" name="Actomyosin_ATP">
<variable units="micromolar" public_interface="out" name="Actomyosin_ATP" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_Actomyosin_ATP_rxn1"/>
<variable units="flux" public_interface="in" name="delta_Actomyosin_ATP_rxn2"/>
<variable units="flux" public_interface="in" name="delta_Actomyosin_ATP_rxn6"/>
<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>Actomyosin_ATP</ci>
</apply>
<apply>
<plus/>
<ci>delta_Actomyosin_ATP_rxn1</ci>
<ci>delta_Actomyosin_ATP_rxn2</ci>
<ci>delta_Actomyosin_ATP_rxn6</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Actomyosin" name="Actomyosin">
<variable units="micromolar" public_interface="out" name="Actomyosin" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_Actomyosin_rxn3"/>
<variable units="flux" public_interface="in" name="delta_Actomyosin_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>Actomyosin</ci>
</apply>
<apply>
<plus/>
<ci>delta_Actomyosin_rxn3</ci>
<ci>delta_Actomyosin_rxn2</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Actomyosin_ADP" name="Actomyosin_ADP">
<variable units="micromolar" public_interface="out" name="Actomyosin_ADP" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_Actomyosin_ADP_rxn4"/>
<variable units="flux" public_interface="in" name="delta_Actomyosin_ADP_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>Actomyosin_ADP</ci>
</apply>
<apply>
<plus/>
<ci>delta_Actomyosin_ADP_rxn4</ci>
<ci>delta_Actomyosin_ADP_rxn3</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Pi" name="Pi">
<variable units="micromolar" public_interface="out" name="Pi" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_Pi_rxn4"/>
<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>Pi</ci>
</apply>
<ci>delta_Pi_rxn4</ci>
</apply>
</math>
</component>
<component cmeta:id="Actomyosin_ADP_Pi" name="Actomyosin_ADP_Pi">
<variable units="micromolar" public_interface="out" name="Actomyosin_ADP_Pi" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_Actomyosin_ADP_Pi_rxn5"/>
<variable units="flux" public_interface="in" name="delta_Actomyosin_ADP_Pi_rxn6"/>
<variable units="flux" public_interface="in" name="delta_Actomyosin_ADP_Pi_rxn4"/>
<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>Actomyosin_ADP_Pi</ci>
</apply>
<apply>
<plus/>
<ci>delta_Actomyosin_ADP_Pi_rxn5</ci>
<ci>delta_Actomyosin_ADP_Pi_rxn6</ci>
<ci>delta_Actomyosin_ADP_Pi_rxn4</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Myosin_ADP_Pi" name="Myosin_ADP_Pi">
<variable units="micromolar" public_interface="out" name="Myosin_ADP_Pi" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_Myosin_ADP_Pi_rxn7"/>
<variable units="flux" public_interface="in" name="delta_Myosin_ADP_Pi_rxn5"/>
<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>Myosin_ADP_Pi</ci>
</apply>
<apply>
<plus/>
<ci>delta_Myosin_ADP_Pi_rxn7</ci>
<ci>delta_Myosin_ADP_Pi_rxn5</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="Troponin_C" name="Troponin_C">
<variable units="micromolar" public_interface="out" name="Troponin_C" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_Troponin_C_rxn8"/>
<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>Troponin_C</ci>
</apply>
<ci>delta_Troponin_C_rxn8</ci>
</apply>
</math>
</component>
<component cmeta:id="Troponin_C_Ca" name="Troponin_C_Ca">
<variable units="micromolar" public_interface="out" name="Troponin_C_Ca" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="delta_Troponin_C_Ca_rxn8"/>
<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>Troponin_C_Ca</ci>
</apply>
<ci>delta_Troponin_C_Ca_rxn8</ci>
</apply>
</math>
</component>
<component cmeta:id="Ca_i" name="Ca_i">
<variable units="micromolar" public_interface="out" name="Ca_i" initial_value="1.0"/>
<variable units="flux" public_interface="in" name="kr"/>
<variable units="flux" public_interface="in" name="delta_Ca_i_rxn8"/>
<variable units="flux" public_interface="in" name="delta_Ca_F"/>
<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_i</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>delta_Ca_i_rxn8</ci>
<ci>delta_Ca_F</ci>
</apply>
<apply>
<times/>
<ci>kr</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="delta_Ca_F" name="delta_Ca_F">
<variable units="flux" public_interface="out" name="delta_Ca_F" initial_value="480.0"/>
<variable units="second" public_interface="in" name="time"/>
</component>
<!--
The following component represents a calcium pump in the sarcoplasmic
reticulum.
-->
<component cmeta:id="Ca_pump" name="Ca_pump">
<variable units="flux" public_interface="out" name="kr" initial_value="1.0"/>
<variable units="micromolar" name="Ca_SR" initial_value="1.0"/>
<variable units="second" name="tau_kr" initial_value="1.0"/>
<variable units="micromolar" public_interface="in" name="Ca_i"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="kr_calculation">
<eq/>
<ci> kr </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Ca_i </ci>
<ci> Ca_SR </ci>
</apply>
<ci> tau_kr </ci>
</apply>
</apply>
</math>
</component>
<!--
The following components represent the reaction steps of the
elctromechanical heart contractile system.
-->
<component name="reaction0">
<variable units="micromolar" public_interface="in" name="Myosin"/>
<variable units="micromolar" public_interface="in" name="ATP"/>
<variable units="micromolar" public_interface="in" name="Myosin_ATP"/>
<variable units="flux" public_interface="out" name="delta_Myosin_rxn0"/>
<variable units="flux" public_interface="out" name="delta_ATP_rxn0"/>
<variable units="flux" public_interface="out" name="delta_Myosin_ATP_rxn0"/>
<variable units="second_order_rate_constant" name="k0" initial_value="1.0"/>
<variable units="first_order_rate_constant" name="k0_" initial_value="1.0"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="Myosin">
<role stoichiometry="1" direction="forward" delta_variable="delta_Myosin_rxn0" role="reactant"/>
</variable_ref>
<variable_ref variable="ATP">
<role stoichiometry="1" direction="forward" delta_variable="delta_ATP_rxn0" role="reactant"/>
</variable_ref>
<variable_ref variable="Myosin_ATP">
<role stoichiometry="1" direction="forward" delta_variable="delta_Myosin_ATP_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>Myosin</ci>
<ci>ATP</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k0_</ci>
<ci>Myosin_ATP</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction1">
<variable units="micromolar" public_interface="in" name="Actin"/>
<variable units="micromolar" public_interface="in" name="Myosin_ATP"/>
<variable units="micromolar" public_interface="in" name="Actomyosin_ATP"/>
<variable units="flux" public_interface="out" name="delta_Actin_rxn1"/>
<variable units="flux" public_interface="out" name="delta_Myosin_ATP_rxn1"/>
<variable units="flux" public_interface="out" name="delta_Actomyosin_ATP_rxn1"/>
<variable units="second_order_rate_constant" name="k1" initial_value="1.0"/>
<variable units="first_order_rate_constant" name="k1_" initial_value="1.0"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="Actin">
<role stoichiometry="1" direction="forward" delta_variable="delta_Actin_rxn1" role="reactant"/>
</variable_ref>
<variable_ref variable="Myosin_ATP">
<role stoichiometry="1" direction="forward" delta_variable="delta_Myosin_ATP_rxn1" role="reactant"/>
</variable_ref>
<variable_ref variable="Actomyosin_ATP">
<role stoichiometry="1" direction="forward" delta_variable="delta_Actomyosin_ATP_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>Actin</ci>
<ci>Myosin_ATP</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k1_</ci>
<ci>Actomyosin_ATP</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction2">
<variable units="micromolar" public_interface="in" name="ATP"/>
<variable units="micromolar" public_interface="in" name="Actomyosin"/>
<variable units="micromolar" public_interface="in" name="Actomyosin_ATP"/>
<variable units="flux" public_interface="out" name="delta_ATP_rxn2"/>
<variable units="flux" public_interface="out" name="delta_Actomyosin_rxn2"/>
<variable units="flux" public_interface="out" name="delta_Actomyosin_ATP_rxn2"/>
<variable units="second_order_rate_constant" name="k2" initial_value="1.0"/>
<variable units="first_order_rate_constant" name="k2_" initial_value="1.0"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="ATP">
<role stoichiometry="1" direction="forward" delta_variable="delta_ATP_rxn2" role="reactant"/>
</variable_ref>
<variable_ref variable="Actomyosin">
<role stoichiometry="1" direction="forward" delta_variable="delta_Actomyosin_rxn2" role="reactant"/>
</variable_ref>
<variable_ref variable="Actomyosin_ATP">
<role stoichiometry="1" direction="forward" delta_variable="delta_Actomyosin_ATP_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>
<plus/>
<apply>
<times/>
<ci>k2</ci>
<ci>ATP</ci>
<ci>Actomyosin</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k2_</ci>
<ci>Actomyosin_ATP</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction3">
<variable units="micromolar" public_interface="in" name="Actomyosin_ADP"/>
<variable units="micromolar" public_interface="in" name="ADP"/>
<variable units="micromolar" public_interface="in" name="Actomyosin"/>
<variable units="flux" public_interface="out" name="delta_Actomyosin_ADP_rxn3"/>
<variable units="flux" public_interface="out" name="delta_ADP_rxn3"/>
<variable units="flux" public_interface="out" name="delta_Actomyosin_rxn3"/>
<variable units="first_order_rate_constant" name="k3" initial_value="1.0"/>
<variable units="flux" name="rate"/>
<reaction reversible="no">
<variable_ref variable="Actomyosin_ADP">
<role stoichiometry="1" delta_variable="delta_Actomyosin_ADP_rxn3" role="reactant"/>
</variable_ref>
<variable_ref variable="ADP">
<role stoichiometry="1" delta_variable="delta_ADP_rxn3" role="product"/>
</variable_ref>
<variable_ref variable="Actomyosin">
<role stoichiometry="1" delta_variable="delta_Actomyosin_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>
<times/>
<ci>k3</ci>
<ci>Actomyosin_ADP</ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction4">
<variable units="micromolar" public_interface="in" name="Actomyosin_ADP_Pi"/>
<variable units="micromolar" public_interface="in" name="Pi"/>
<variable units="micromolar" public_interface="in" name="Actomyosin_ADP"/>
<variable units="flux" public_interface="out" name="delta_Actomyosin_ADP_Pi_rxn4"/>
<variable units="flux" public_interface="out" name="delta_Pi_rxn4"/>
<variable units="flux" public_interface="out" name="delta_Actomyosin_ADP_rxn4"/>
<variable units="first_order_rate_constant" name="k4" initial_value="1.0"/>
<variable units="flux" name="rate"/>
<reaction reversible="no">
<variable_ref variable="Actomyosin_ADP_Pi">
<role stoichiometry="1" delta_variable="delta_Actomyosin_ADP_Pi_rxn4" role="reactant"/>
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<variable_ref variable="Pi">
<role stoichiometry="1" delta_variable="delta_Pi_rxn4" role="product"/>
</variable_ref>
<variable_ref variable="Actomyosin_ADP">
<role stoichiometry="1" delta_variable="delta_Actomyosin_ADP_rxn4" 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>k4</ci>
<ci>Actomyosin_ADP_Pi</ci>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction5">
<variable units="micromolar" public_interface="in" name="Myosin_ADP_Pi"/>
<variable units="micromolar" public_interface="in" name="Actin"/>
<variable units="micromolar" public_interface="in" name="Actomyosin_ADP_Pi"/>
<variable units="flux" public_interface="out" name="delta_Myosin_ADP_Pi_rxn5"/>
<variable units="flux" public_interface="out" name="delta_Actin_rxn5"/>
<variable units="flux" public_interface="out" name="delta_Actomyosin_ADP_Pi_rxn5"/>
<variable units="second_order_rate_constant" name="k5" initial_value="1.0"/>
<variable units="first_order_rate_constant" name="k5_" initial_value="1.0"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="Myosin_ADP_Pi">
<role stoichiometry="1" direction="forward" delta_variable="delta_Myosin_ADP_Pi_rxn5" role="reactant"/>
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<variable_ref variable="Actin">
<role stoichiometry="1" direction="forward" delta_variable="delta_Actin_rxn5" role="reactant"/>
</variable_ref>
<variable_ref variable="Actomyosin_ADP_Pi">
<role stoichiometry="1" direction="forward" delta_variable="delta_Actomyosin_ADP_Pi_rxn5" 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>k5</ci>
<ci>Myosin_ADP_Pi</ci>
<ci>Actin</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
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<ci>Actomyosin_ADP_Pi</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction6">
<variable units="micromolar" public_interface="in" name="Actomyosin_ATP"/>
<variable units="micromolar" public_interface="in" name="Actomyosin_ADP_Pi"/>
<variable units="flux" public_interface="out" name="delta_Actomyosin_ATP_rxn6"/>
<variable units="flux" public_interface="out" name="delta_Actomyosin_ADP_Pi_rxn6"/>
<variable units="first_order_rate_constant" name="k6" initial_value="1.0"/>
<variable units="first_order_rate_constant" name="k6_" initial_value="1.0"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="Actomyosin_ATP">
<role stoichiometry="1" direction="forward" delta_variable="delta_Actomyosin_ATP_rxn6" role="reactant"/>
</variable_ref>
<variable_ref variable="Actomyosin_ADP_Pi">
<role stoichiometry="1" direction="forward" delta_variable="delta_Actomyosin_ADP_Pi_rxn6" role="product"/>
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<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>k6</ci>
<ci>Actomyosin_ATP</ci>
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<apply>
<minus/>
<apply>
<times/>
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<ci>Actomyosin_ADP_Pi</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction7">
<variable units="micromolar" public_interface="in" name="Myosin_ATP"/>
<variable units="micromolar" public_interface="in" name="Myosin_ADP_Pi"/>
<variable units="flux" public_interface="out" name="delta_Myosin_ATP_rxn7"/>
<variable units="flux" public_interface="out" name="delta_Myosin_ADP_Pi_rxn7"/>
<variable units="first_order_rate_constant" name="k7" initial_value="1.0"/>
<variable units="first_order_rate_constant" name="k7_" initial_value="1.0"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="Myosin_ATP">
<role stoichiometry="1" direction="forward" delta_variable="delta_Myosin_ATP_rxn7" role="reactant"/>
</variable_ref>
<variable_ref variable="Myosin_ADP_Pi">
<role stoichiometry="1" direction="forward" delta_variable="delta_Myosin_ADP_Pi_rxn7" 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>k7</ci>
<ci>Myosin_ATP</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k7_</ci>
<ci>Myosin_ADP_Pi</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction8">
<variable units="micromolar" public_interface="in" name="Troponin_C"/>
<variable units="micromolar" public_interface="in" name="Ca_i"/>
<variable units="micromolar" public_interface="in" name="Troponin_C_Ca"/>
<variable units="flux" public_interface="out" name="delta_Troponin_C_rxn8"/>
<variable units="flux" public_interface="out" name="delta_Ca_i_rxn8"/>
<variable units="flux" public_interface="out" name="delta_Troponin_C_Ca_rxn8"/>
<variable units="second_order_rate_constant" name="k8" initial_value="1.0"/>
<variable units="first_order_rate_constant" name="k8_" initial_value="1.0"/>
<variable units="flux" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="Troponin_C">
<role stoichiometry="1" direction="forward" delta_variable="delta_Troponin_C_rxn8" role="reactant"/>
</variable_ref>
<variable_ref variable="Ca_i">
<role stoichiometry="1" direction="forward" delta_variable="delta_Ca_i_rxn8" role="reactant"/>
</variable_ref>
<variable_ref variable="Troponin_C_Ca">
<role stoichiometry="1" direction="forward" delta_variable="delta_Troponin_C_Ca_rxn8" 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>k8</ci>
<ci>Troponin_C</ci>
<ci>Ca_i</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k8_</ci>
<ci>Troponin_C_Ca</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<connection>
<map_components component_2="reaction1" component_1="Actin"/>
<map_variables variable_2="Actin" variable_1="Actin"/>
<map_variables variable_2="delta_Actin_rxn1" variable_1="delta_Actin_rxn1"/>
</connection>
<connection>
<map_components component_2="reaction5" component_1="Actin"/>
<map_variables variable_2="Actin" variable_1="Actin"/>
<map_variables variable_2="delta_Actin_rxn5" variable_1="delta_Actin_rxn5"/>
</connection>
<connection>
<map_components component_2="reaction0" component_1="Myosin"/>
<map_variables variable_2="Myosin" variable_1="Myosin"/>
<map_variables variable_2="delta_Myosin_rxn0" variable_1="delta_Myosin_rxn0"/>
</connection>
<connection>
<map_components component_2="reaction0" component_1="ATP"/>
<map_variables variable_2="ATP" variable_1="ATP"/>
<map_variables variable_2="delta_ATP_rxn0" variable_1="delta_ATP_rxn0"/>
</connection>
<connection>
<map_components component_2="reaction2" component_1="ATP"/>
<map_variables variable_2="ATP" variable_1="ATP"/>
<map_variables variable_2="delta_ATP_rxn2" variable_1="delta_ATP_rxn2"/>
</connection>
<connection>
<map_components component_2="reaction3" component_1="ADP"/>
<map_variables variable_2="ADP" variable_1="ADP"/>
<map_variables variable_2="delta_ADP_rxn3" variable_1="delta_ADP_rxn3"/>
</connection>
<connection>
<map_components component_2="reaction0" component_1="Myosin_ATP"/>
<map_variables variable_2="Myosin_ATP" variable_1="Myosin_ATP"/>
<map_variables variable_2="delta_Myosin_ATP_rxn0" variable_1="delta_Myosin_ATP_rxn0"/>
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<connection>
<map_components component_2="reaction1" component_1="Myosin_ATP"/>
<map_variables variable_2="Myosin_ATP" variable_1="Myosin_ATP"/>
<map_variables variable_2="delta_Myosin_ATP_rxn1" variable_1="delta_Myosin_ATP_rxn1"/>
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<connection>
<map_components component_2="reaction7" component_1="Myosin_ATP"/>
<map_variables variable_2="Myosin_ATP" variable_1="Myosin_ATP"/>
<map_variables variable_2="delta_Myosin_ATP_rxn7" variable_1="delta_Myosin_ATP_rxn7"/>
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<connection>
<map_components component_2="reaction1" component_1="Actomyosin_ATP"/>
<map_variables variable_2="Actomyosin_ATP" variable_1="Actomyosin_ATP"/>
<map_variables variable_2="delta_Actomyosin_ATP_rxn1" variable_1="delta_Actomyosin_ATP_rxn1"/>
</connection>
<connection>
<map_components component_2="reaction2" component_1="Actomyosin_ATP"/>
<map_variables variable_2="Actomyosin_ATP" variable_1="Actomyosin_ATP"/>
<map_variables variable_2="delta_Actomyosin_ATP_rxn2" variable_1="delta_Actomyosin_ATP_rxn2"/>
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<connection>
<map_components component_2="reaction6" component_1="Actomyosin_ATP"/>
<map_variables variable_2="Actomyosin_ATP" variable_1="Actomyosin_ATP"/>
<map_variables variable_2="delta_Actomyosin_ATP_rxn6" variable_1="delta_Actomyosin_ATP_rxn6"/>
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<connection>
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<map_variables variable_2="Actomyosin" variable_1="Actomyosin"/>
<map_variables variable_2="delta_Actomyosin_rxn3" variable_1="delta_Actomyosin_rxn3"/>
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<map_variables variable_2="Actomyosin" variable_1="Actomyosin"/>
<map_variables variable_2="delta_Actomyosin_rxn2" variable_1="delta_Actomyosin_rxn2"/>
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<connection>
<map_components component_2="reaction4" component_1="Actomyosin_ADP"/>
<map_variables variable_2="Actomyosin_ADP" variable_1="Actomyosin_ADP"/>
<map_variables variable_2="delta_Actomyosin_ADP_rxn4" variable_1="delta_Actomyosin_ADP_rxn4"/>
</connection>
<connection>
<map_components component_2="reaction3" component_1="Actomyosin_ADP"/>
<map_variables variable_2="Actomyosin_ADP" variable_1="Actomyosin_ADP"/>
<map_variables variable_2="delta_Actomyosin_ADP_rxn3" variable_1="delta_Actomyosin_ADP_rxn3"/>
</connection>
<connection>
<map_components component_2="reaction4" component_1="Pi"/>
<map_variables variable_2="Pi" variable_1="Pi"/>
<map_variables variable_2="delta_Pi_rxn4" variable_1="delta_Pi_rxn4"/>
</connection>
<connection>
<map_components component_2="reaction5" component_1="Actomyosin_ADP_Pi"/>
<map_variables variable_2="Actomyosin_ADP_Pi" variable_1="Actomyosin_ADP_Pi"/>
<map_variables variable_2="delta_Actomyosin_ADP_Pi_rxn5" variable_1="delta_Actomyosin_ADP_Pi_rxn5"/>
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<map_components component_2="reaction6" component_1="Actomyosin_ADP_Pi"/>
<map_variables variable_2="Actomyosin_ADP_Pi" variable_1="Actomyosin_ADP_Pi"/>
<map_variables variable_2="delta_Actomyosin_ADP_Pi_rxn6" variable_1="delta_Actomyosin_ADP_Pi_rxn6"/>
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<map_variables variable_2="delta_Actomyosin_ADP_Pi_rxn4" variable_1="delta_Actomyosin_ADP_Pi_rxn4"/>
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<map_variables variable_2="Myosin_ADP_Pi" variable_1="Myosin_ADP_Pi"/>
<map_variables variable_2="delta_Myosin_ADP_Pi_rxn7" variable_1="delta_Myosin_ADP_Pi_rxn7"/>
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<map_components component_2="reaction5" component_1="Myosin_ADP_Pi"/>
<map_variables variable_2="Myosin_ADP_Pi" variable_1="Myosin_ADP_Pi"/>
<map_variables variable_2="delta_Myosin_ADP_Pi_rxn5" variable_1="delta_Myosin_ADP_Pi_rxn5"/>
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<connection>
<map_components component_2="reaction8" component_1="Troponin_C"/>
<map_variables variable_2="Troponin_C" variable_1="Troponin_C"/>
<map_variables variable_2="delta_Troponin_C_rxn8" variable_1="delta_Troponin_C_rxn8"/>
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<map_components component_2="reaction8" component_1="Troponin_C_Ca"/>
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<map_variables variable_2="delta_Troponin_C_Ca_rxn8" variable_1="delta_Troponin_C_Ca_rxn8"/>
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<map_variables variable_2="time" variable_1="time"/>
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<connection>
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<connection>
<map_components component_2="global_variables" component_1="ATP"/>
<map_variables variable_2="time" variable_1="time"/>
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<map_variables variable_2="time" variable_1="time"/>
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<connection>
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Mathematical Model of the Electromechanical Heart Contractile System - Regulatory Subsystem Physiological Considerations
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<dc:title>Physiological Research</dc:title>
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Mlcek et al's 2001 mathematical model of the elctromechanical heart
contractile system
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Below is a CellML description of Mlcek et al's mathematical model of
the elctromechanical heart contractile system.
Rate constants for the reactions were not specified in the original
paper, therefore in the CellML description they have been set at a
default value of 1.0. Similarly, initial concentrations were not
defined so these have been set at a default value of 1 micromolar.
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<dcterms:W3CDTF>2001</dcterms:W3CDTF>
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<vCard:Given>J</vCard:Given>
<vCard:Family>Neumann</vCard:Family>
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<bqs:subject_type>keyword</bqs:subject_type>
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<rdf:Description rdf:about="rdf:#9a93b42d-b65f-4749-a99b-de238aceddff">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
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<dcterms:W3CDTF>2002-07-18</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b83356d0-8b14-4082-b653-b701c5205888">
<dcterms:W3CDTF>2002-06-19</dcterms:W3CDTF>
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Added more metadata.
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<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
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<rdf:Description rdf:about="">
<dc:publisher>
The University of Auckland, Bioengineering Institute
</dc:publisher>
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