<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : snyder_model_2000.xml
CREATED : 18th March 2002
LAST MODIFIED : 22nd April 2005
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 2000, and the 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of snyder et al's 2000
mathematical model of cardiocyte Ca2+ dynamics.
CHANGES:
22/07/2002 - CML - Added more metadata.
22/04/2005 - PJV - Removed unnecessary type. Changed MathML id's to
make them unique.
--><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="snyder_palmer_moore_2000_version01" name="snyder_palmer_moore_2000_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A Mathematical Model Of Cardiocyte Ca2+ Dynamics</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>
The regulation of cytosolic Ca<superscript>2+</superscript> concentration, [Ca<superscript>2+</superscript>]<subscript>c</subscript>, in cardiac myocytes has been recognised to be the predominant determinant of cardiac contraction and relaxation dynamics. Several models have been developed to describe [Ca<superscript>2+</superscript>]<subscript>c</subscript> regulation in cardiac myocytes and these have evolved to the point where they are able to predict intracellular Ca<superscript>2+</superscript> dynamics under experimental conditions.
</para>
<para>
In their 2000 study, Steven M. Snyder, Bradley M. Palmer and Russell L. Moore published a detailed mathematical model describing cardiocyte Ca<superscript>2+</superscript> dynamics with a novel representation of sarcoplasmic reticular Ca<superscript>2+</superscript> control (see the figure below). The mathematical representation of the Ca<superscript>2+</superscript> regulatory mechanisms of a rat cardiac myocyte included a set of six differential equations.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.biophysj.org/cgi/content/abstract/79/1/94">A Mathematical Model of Cardiocyte Ca<superscript>2+</superscript> Dynamics with a Novel Representation of Sarcoplasmic Reticular Ca<superscript>2+</superscript> Control</ulink>, Steven M. Snyder, Bradley M. Palmer and Russell L. Moore, 2000, <ulink url="http://www.biophysj.org/">
<emphasis>Biophysical Journal</emphasis>
</ulink>, 79, 94-115. (<ulink url="http://www.biophysj.org/cgi/content/full/79/1/94">Full text</ulink> and <ulink url="http://www.biophysj.org/cgi/reprint/79/1/94.pdf">PDF</ulink> versions of the article are available for Journal Members on the Biophysical Journal website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10866940&dopt=Abstract">PubMed ID: 10866940</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell schematic for the model</title>
</objectinfo>
<imagedata fileref="snyder_2000.png"/>
</imageobject>
</mediaobject>
<caption>Cell schematic for the model representing three intracellular compartments with buffering, the extracellular space, and the related Ca<superscript>2+</superscript> movement processes.</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="molar">
<unit units="mole"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="flux">
<unit units="mole"/>
<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="molar" 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>
<component name="Ca_influx_across_the_SR">
<variable units="molar" public_interface="in" name="Ca_e"/>
<variable units="molar" public_interface="in" name="Ca_f"/>
<variable units="flux" public_interface="out" name="delta_Ca_e_rxn_1"/>
<variable units="first_order_rate_constant" name="k1" initial_value="0.2"/>
<variable units="flux" public_interface="out" name="r_rxn_1"/>
<reaction reversible="no">
<variable_ref variable="Ca_e">
<role stoichiometry="1" direction="forward" delta_variable="delta_Ca_e_rxn_1" role="reactant"/>
</variable_ref>
<variable_ref variable="Ca_f">
<role stoichiometry="1" direction="forward" role="product"/>
</variable_ref>
<variable_ref variable="r_rxn_1">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r_rxn_1 </ci>
<apply>
<times/>
<ci> k1 </ci>
<apply>
<minus/>
<ci> Ca_e </ci>
<ci> Ca_f </ci>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="Ca_movement_through_the_SRRC">
<variable units="molar" public_interface="in" name="Ca_2_S1"/>
<variable units="molar" public_interface="in" name="Ca_S2"/>
<variable units="molar" public_interface="in" name="S1"/>
<variable units="molar" public_interface="in" name="S2"/>
<variable units="molar" public_interface="in" name="Ca_f"/>
<variable units="molar" public_interface="in" name="Ca_s"/>
<variable units="flux" public_interface="out" name="delta_Ca_f_rxn_2"/>
<variable units="flux" public_interface="out" name="delta_S1_rxn_2"/>
<variable units="flux" public_interface="out" name="delta_Ca_2_S1_rxn_2"/>
<variable units="flux" public_interface="out" name="delta_Ca_f_rxn_3"/>
<variable units="flux" public_interface="out" name="delta_S2_rxn_3"/>
<variable units="flux" public_interface="out" name="delta_Ca_S2_rxn_3"/>
<variable units="second_order_rate_constant" name="k_on1" initial_value="2000000000.0"/>
<variable units="first_order_rate_constant" name="k_off1" initial_value="1400.0"/>
<variable units="second_order_rate_constant" name="k_on2" initial_value="13000000.0"/>
<variable units="first_order_rate_constant" name="k_off2" initial_value="3.9"/>
<variable units="first_order_rate_constant" name="k_s" initial_value="9.0"/>
<variable units="dimensionless" name="cas1"/>
<variable units="dimensionless" public_interface="out" name="dcas1_dt"/>
<variable units="dimensionless" name="cas2"/>
<variable units="dimensionless" public_interface="out" name="dcas2_dt"/>
<variable units="dimensionless" name="r_o"/>
<variable units="flux" name="r_rxn_2"/>
<variable units="flux" name="r_rxn_3"/>
<variable units="flux" public_interface="out" name="r_rxn_4"/>
<variable units="second" public_interface="in" name="time"/>
<reaction reversible="yes">
<variable_ref variable="Ca_f">
<role stoichiometry="1" direction="forward" delta_variable="delta_Ca_f_rxn_2" role="reactant"/>
</variable_ref>
<variable_ref variable="S1">
<role stoichiometry="1" direction="forward" delta_variable="delta_S1_rxn_2" role="reactant"/>
</variable_ref>
<variable_ref variable="Ca_2_S1">
<role stoichiometry="1" direction="forward" delta_variable="delta_Ca_2_S1_rxn_2" role="product"/>
</variable_ref>
<variable_ref variable="r_rxn_2">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r_rxn_2 </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> k_on1 </ci>
<ci> Ca_f </ci>
<ci> S1 </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<power/>
<ci> k_off1 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<ci> k_on1 </ci>
<ci> Ca_f </ci>
</apply>
</apply>
<ci> Ca_2_S1 </ci>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
<reaction reversible="yes">
<variable_ref variable="Ca_f">
<role stoichiometry="1" direction="forward" delta_variable="delta_Ca_f_rxn_3" role="reactant"/>
</variable_ref>
<variable_ref variable="S2">
<role stoichiometry="1" direction="forward" delta_variable="delta_S2_rxn_3" role="reactant"/>
</variable_ref>
<variable_ref variable="Ca_S2">
<role stoichiometry="1" direction="forward" delta_variable="delta_Ca_S2_rxn_3" role="product"/>
</variable_ref>
<variable_ref variable="r_rxn_3">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r_rxn_3 </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> k_on2 </ci>
<ci> Ca_f </ci>
<ci> S2 </ci>
</apply>
<apply>
<times/>
<ci> k_off2 </ci>
<ci> Ca_S2 </ci>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="r_o_calculation">
<eq/>
<ci> r_o </ci>
<apply>
<times/>
<ci> cas1 </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> cas2 </ci>
</apply>
</apply>
</apply>
<apply id="dcas1_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> cas1 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_on1 </ci>
<ci> Ca_f </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> cas1 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<power/>
<ci> k_off1 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<ci> k_on1 </ci>
<ci> Ca_f </ci>
</apply>
</apply>
<ci> cas1 </ci>
</apply>
</apply>
</apply>
<apply id="dcas2_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> cas2 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_on2 </ci>
<ci> Ca_f </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> cas2 </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_off2 </ci>
<ci> cas2 </ci>
</apply>
</apply>
</apply>
</math>
<reaction reversible="no">
<variable_ref variable="Ca_s">
<role stoichiometry="1" direction="forward" role="reactant"/>
</variable_ref>
<variable_ref variable="Ca_f">
<role stoichiometry="1" direction="forward" role="product"/>
</variable_ref>
<variable_ref variable="r_rxn_4">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r_rxn_4 </ci>
<apply>
<times/>
<ci> k_s </ci>
<ci> r_o </ci>
<apply>
<minus/>
<ci> Ca_s </ci>
<ci> Ca_f </ci>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="Ca_efflux_across_the_SR_by_NaCa_exchange">
<variable units="molar" public_interface="in" name="Ca_e"/>
<variable units="molar" public_interface="in" name="Ca_f"/>
<variable units="flux" public_interface="out" name="delta_Ca_e_rxn_5"/>
<variable units="molar" name="Km_NaCaX" initial_value="0.000036"/>
<variable units="flux" name="Vmax_NaCaX" initial_value="0.0012"/>
<variable units="flux" public_interface="out" name="r_rxn_5"/>
<reaction reversible="no">
<variable_ref variable="Ca_f">
<role stoichiometry="1" direction="forward" role="reactant"/>
</variable_ref>
<variable_ref variable="Ca_e">
<role stoichiometry="1" direction="forward" delta_variable="delta_Ca_e_rxn_5" role="product"/>
</variable_ref>
<variable_ref variable="r_rxn_5">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r_rxn_5 </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> Vmax_NaCaX </ci>
<ci> Ca_f </ci>
</apply>
<apply>
<plus/>
<ci> Km_NaCaX </ci>
<ci> Ca_f </ci>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="Ca_movement_between_the_fuzzy_space_and_cytosol">
<variable units="molar" public_interface="in" name="Ca_c"/>
<variable units="molar" public_interface="in" name="Ca_f"/>
<variable units="first_order_rate_constant" name="kf" initial_value="2500.0"/>
<variable units="flux" public_interface="out" name="r_rxn_6"/>
<reaction reversible="no">
<variable_ref variable="Ca_f">
<role stoichiometry="1" direction="forward" role="reactant"/>
</variable_ref>
<variable_ref variable="Ca_c">
<role stoichiometry="1" direction="forward" role="product"/>
</variable_ref>
<variable_ref variable="r_rxn_6">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r_rxn_6 </ci>
<apply>
<times/>
<ci> kf </ci>
<apply>
<minus/>
<ci> Ca_f </ci>
<ci> Ca_c </ci>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="Ca_uptake_by_SR_Ca_ATPase">
<variable units="molar" public_interface="in" name="Ca_c"/>
<variable units="molar" public_interface="in" name="Ca_s"/>
<variable units="molar" name="Km_s" initial_value="0.00000025"/>
<variable units="flux" name="Vmax_s" initial_value="0.000525"/>
<variable units="flux" public_interface="out" name="r_rxn_7"/>
<reaction reversible="no">
<variable_ref variable="Ca_c">
<role stoichiometry="1" direction="forward" role="reactant"/>
</variable_ref>
<variable_ref variable="Ca_s">
<role stoichiometry="1" direction="forward" role="product"/>
</variable_ref>
<variable_ref variable="r_rxn_7">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r_rxn_7 </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> Vmax_s </ci>
<apply>
<minus/>
<apply>
<power/>
<ci> Ca_c </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci> Ca_s </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<cn cellml:units="dimensionless"> 7000.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> Km_s </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> Ca_c </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci> Ca_s </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<cn cellml:units="dimensionless"> 7000.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="Ca_buffering_in_the_SR">
<variable units="molar" public_interface="in" name="Ca_CSQ"/>
<variable units="molar" public_interface="in" name="Ca_s"/>
<variable units="flux" public_interface="out" name="delta_Ca_CSQ_rxn_8"/>
<variable units="second_order_rate_constant" name="K_ons" initial_value="8772.0"/>
<variable units="first_order_rate_constant" name="K_offs" initial_value="5.596536"/>
<variable units="molar" name="Bmax_s" initial_value="0.008"/>
<variable units="flux" public_interface="out" name="r_rxn_8"/>
<reaction reversible="yes">
<variable_ref variable="Ca_s">
<role stoichiometry="1" direction="forward" role="reactant"/>
</variable_ref>
<variable_ref variable="Ca_CSQ">
<role stoichiometry="1" direction="forward" delta_variable="delta_Ca_CSQ_rxn_8" role="product"/>
</variable_ref>
<variable_ref variable="r_rxn_8">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> r_rxn_8 </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> K_ons </ci>
<ci> Ca_s </ci>
<apply>
<minus/>
<ci> Bmax_s </ci>
<ci> Ca_CSQ </ci>
</apply>
</apply>
<apply>
<times/>
<ci> K_offs </ci>
<ci> Ca_CSQ </ci>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="fuzzy_space_calcium">
<variable units="molar" public_interface="out" name="Ca_f"/>
<variable units="molar" name="Rt" initial_value="0.00000015"/>
<variable units="molar" name="Bmax_f1" initial_value="0.0002"/>
<variable units="molar" name="Bmax_f2" initial_value="0.0011"/>
<variable units="molar" name="Kb_f1" initial_value="0.000017"/>
<variable units="molar" name="Kb_f2" initial_value="0.000013"/>
<variable units="molar" name="Ca_f1"/>
<variable units="molar" name="Ca_f2"/>
<variable units="dimensionless" name="V_f" initial_value="0.0013"/>
<variable units="flux" public_interface="in" name="r_rxn_1"/>
<variable units="flux" public_interface="in" name="r_rxn_4"/>
<variable units="flux" public_interface="in" name="r_rxn_5"/>
<variable units="flux" public_interface="in" name="r_rxn_6"/>
<variable units="dimensionless" public_interface="in" name="dcas1_dt"/>
<variable units="dimensionless" public_interface="in" name="dcas2_dt"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_f_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_f </ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<minus/>
<ci> r_rxn_4 </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> Rt </ci>
<apply>
<plus/>
<ci> dcas1_dt </ci>
<ci> dcas2_dt </ci>
</apply>
</apply>
<ci> r_rxn_6 </ci>
<ci> r_rxn_5 </ci>
</apply>
</apply>
<ci> r_rxn_1 </ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<ci> Bmax_f1 </ci>
<ci> Kb_f1 </ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci> Ca_f1 </ci>
<ci> Kb_f1 </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> Bmax_f2 </ci>
<ci> Kb_f2 </ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci> Ca_f2 </ci>
<ci> Kb_f2 </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<ci> V_f </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="cytosolic_calcium">
<variable units="molar" public_interface="out" name="Ca_c" initial_value="1.0e-7"/>
<variable units="molar" name="Bmax_c" initial_value="0.00012"/>
<variable units="molar" name="dye_c"/>
<variable units="molar" name="Kb_c" initial_value="0.00000096"/>
<variable units="molar" name="Kb_dye"/>
<variable units="molar" name="Ca_f1"/>
<variable units="molar" name="Ca_f2"/>
<variable units="dimensionless" name="V_c" initial_value="0.9287"/>
<variable units="flux" public_interface="in" name="r_rxn_6"/>
<variable units="flux" public_interface="in" name="r_rxn_7"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_c_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_c </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> r_rxn_6 </ci>
<ci> r_rxn_7 </ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<ci> Bmax_c </ci>
<ci> Kb_c </ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci> Ca_c </ci>
<ci> Kb_c </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> dye_c </ci>
<ci> Kb_dye </ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci> Ca_c </ci>
<ci> Kb_dye </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<ci> V_c </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="SR_calcium">
<variable units="molar" public_interface="out" name="Ca_s"/>
<variable units="dimensionless" name="V_s" initial_value="0.07"/>
<variable units="flux" public_interface="in" name="r_rxn_4"/>
<variable units="flux" public_interface="in" name="r_rxn_7"/>
<variable units="flux" public_interface="in" name="r_rxn_8"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_s_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_s </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> r_rxn_7 </ci>
<ci> r_rxn_4 </ci>
</apply>
<apply>
<minus/>
<ci> V_s </ci>
<ci> r_rxn_8 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="extracellular_calcium">
<variable units="molar" public_interface="out" name="Ca_e"/>
<variable units="flux" public_interface="in" name="delta_Ca_e_rxn_1"/>
<variable units="flux" public_interface="in" name="delta_Ca_e_rxn_5"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="extracellular_calcium_Ca_e_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_e </ci>
</apply>
<apply>
<plus/>
<ci> delta_Ca_e_rxn_1 </ci>
<ci> delta_Ca_e_rxn_5 </ci>
</apply>
</apply>
</math>
</component>
<component name="calsequestrin_bound_calcium">
<variable units="molar" public_interface="out" name="Ca_CSQ"/>
<variable units="flux" public_interface="in" name="delta_Ca_CSQ_rxn_8"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="calsequestrin_bound_calcium_Ca_e_diff_eq">
<eq/>
<apply>
<diff/>
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<ci> time </ci>
</bvar>
<ci> Ca_CSQ </ci>
</apply>
<ci> delta_Ca_CSQ_rxn_8 </ci>
</apply>
</math>
</component>
<component name="SRRC_fast_activating_binding_site">
<variable units="molar" public_interface="out" name="S1"/>
<variable units="flux" public_interface="in" name="delta_S1_rxn_2"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<eq/>
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<diff/>
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<ci> time </ci>
</bvar>
<ci> S1 </ci>
</apply>
<ci> delta_S1_rxn_2 </ci>
</apply>
</math>
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<component name="SRRC_slow_inactivating_binding_site">
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<variable units="flux" public_interface="in" name="delta_S2_rxn_3"/>
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<eq/>
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<ci> time </ci>
</bvar>
<ci> S2 </ci>
</apply>
<ci> delta_S2_rxn_3 </ci>
</apply>
</math>
</component>
<component name="Ca_bound_to_the_SRRC_fast_activating_binding_site">
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<variable units="flux" public_interface="in" name="delta_Ca_2_S1_rxn_2"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_2_S1_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_2_S1 </ci>
</apply>
<ci> delta_Ca_2_S1_rxn_2 </ci>
</apply>
</math>
</component>
<component name="Ca_bound_to_the_SRRC_slow_inactivating_binding_site">
<variable units="molar" public_interface="out" name="Ca_S2"/>
<variable units="flux" public_interface="in" name="delta_Ca_S2_rxn_3"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Ca_S2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_S2 </ci>
</apply>
<ci> delta_Ca_S2_rxn_3 </ci>
</apply>
</math>
</component>
<connection>
<map_components component_2="extracellular_calcium" component_1="Ca_influx_across_the_SR"/>
<map_variables variable_2="Ca_e" variable_1="Ca_e"/>
<map_variables variable_2="delta_Ca_e_rxn_1" variable_1="delta_Ca_e_rxn_1"/>
</connection>
<connection>
<map_components component_2="fuzzy_space_calcium" component_1="Ca_influx_across_the_SR"/>
<map_variables variable_2="Ca_f" variable_1="Ca_f"/>
<map_variables variable_2="r_rxn_1" variable_1="r_rxn_1"/>
</connection>
<connection>
<map_components component_2="Ca_bound_to_the_SRRC_fast_activating_binding_site" component_1="Ca_movement_through_the_SRRC"/>
<map_variables variable_2="Ca_2_S1" variable_1="Ca_2_S1"/>
<map_variables variable_2="delta_Ca_2_S1_rxn_2" variable_1="delta_Ca_2_S1_rxn_2"/>
</connection>
<connection>
<map_components component_2="Ca_bound_to_the_SRRC_slow_inactivating_binding_site" component_1="Ca_movement_through_the_SRRC"/>
<map_variables variable_2="Ca_S2" variable_1="Ca_S2"/>
<map_variables variable_2="delta_Ca_S2_rxn_3" variable_1="delta_Ca_S2_rxn_3"/>
</connection>
<connection>
<map_components component_2="SRRC_fast_activating_binding_site" component_1="Ca_movement_through_the_SRRC"/>
<map_variables variable_2="S1" variable_1="S1"/>
<map_variables variable_2="delta_S1_rxn_2" variable_1="delta_S1_rxn_2"/>
</connection>
<connection>
<map_components component_2="SRRC_slow_inactivating_binding_site" component_1="Ca_movement_through_the_SRRC"/>
<map_variables variable_2="S2" variable_1="S2"/>
<map_variables variable_2="delta_S2_rxn_3" variable_1="delta_S2_rxn_3"/>
</connection>
<connection>
<map_components component_2="fuzzy_space_calcium" component_1="Ca_movement_through_the_SRRC"/>
<map_variables variable_2="Ca_f" variable_1="Ca_f"/>
<map_variables variable_2="dcas1_dt" variable_1="dcas1_dt"/>
<map_variables variable_2="dcas2_dt" variable_1="dcas2_dt"/>
<map_variables variable_2="r_rxn_4" variable_1="r_rxn_4"/>
</connection>
<connection>
<map_components component_2="SR_calcium" component_1="Ca_movement_through_the_SRRC"/>
<map_variables variable_2="Ca_s" variable_1="Ca_s"/>
<map_variables variable_2="r_rxn_4" variable_1="r_rxn_4"/>
</connection>
<connection>
<map_components component_2="fuzzy_space_calcium" component_1="Ca_efflux_across_the_SR_by_NaCa_exchange"/>
<map_variables variable_2="Ca_f" variable_1="Ca_f"/>
<map_variables variable_2="r_rxn_5" variable_1="r_rxn_5"/>
</connection>
<connection>
<map_components component_2="extracellular_calcium" component_1="Ca_efflux_across_the_SR_by_NaCa_exchange"/>
<map_variables variable_2="Ca_e" variable_1="Ca_e"/>
<map_variables variable_2="delta_Ca_e_rxn_5" variable_1="delta_Ca_e_rxn_5"/>
</connection>
<connection>
<map_components component_2="fuzzy_space_calcium" component_1="Ca_movement_between_the_fuzzy_space_and_cytosol"/>
<map_variables variable_2="Ca_f" variable_1="Ca_f"/>
<map_variables variable_2="r_rxn_6" variable_1="r_rxn_6"/>
</connection>
<connection>
<map_components component_2="cytosolic_calcium" component_1="Ca_movement_between_the_fuzzy_space_and_cytosol"/>
<map_variables variable_2="Ca_c" variable_1="Ca_c"/>
<map_variables variable_2="r_rxn_6" variable_1="r_rxn_6"/>
</connection>
<connection>
<map_components component_2="cytosolic_calcium" component_1="Ca_uptake_by_SR_Ca_ATPase"/>
<map_variables variable_2="Ca_c" variable_1="Ca_c"/>
<map_variables variable_2="r_rxn_7" variable_1="r_rxn_7"/>
</connection>
<connection>
<map_components component_2="SR_calcium" component_1="Ca_uptake_by_SR_Ca_ATPase"/>
<map_variables variable_2="Ca_s" variable_1="Ca_s"/>
<map_variables variable_2="r_rxn_7" variable_1="r_rxn_7"/>
</connection>
<connection>
<map_components component_2="SR_calcium" component_1="Ca_buffering_in_the_SR"/>
<map_variables variable_2="Ca_s" variable_1="Ca_s"/>
<map_variables variable_2="r_rxn_8" variable_1="r_rxn_8"/>
</connection>
<connection>
<map_components component_2="calsequestrin_bound_calcium" component_1="Ca_buffering_in_the_SR"/>
<map_variables variable_2="Ca_CSQ" variable_1="Ca_CSQ"/>
<map_variables variable_2="delta_Ca_CSQ_rxn_8" variable_1="delta_Ca_CSQ_rxn_8"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Ca_movement_through_the_SRRC"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="fuzzy_space_calcium"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="cytosolic_calcium"/>
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</connection>
<connection>
<map_components component_2="environment" component_1="SR_calcium"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="extracellular_calcium"/>
<map_variables variable_2="time" variable_1="time"/>
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<connection>
<map_components component_2="environment" component_1="calsequestrin_bound_calcium"/>
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<connection>
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<connection>
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</connection>
<connection>
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<connection>
<map_components component_2="environment" component_1="Ca_bound_to_the_SRRC_slow_inactivating_binding_site"/>
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Snyder et al's 2000 mathematical model of cardiocyte Ca2+ dynamics
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The University of Auckland, Bioengineering Institute
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Removed unnecessary type. Made MathML id's unique
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<dcterms:W3CDTF>2005-04-22</dcterms:W3CDTF>
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Below is a CellML description of snyder et al's 2000 mathematical
model of rat cardiocyte Ca2+ dynamics with a novel representation of
sarcoplasmic reticular Ca2+ control. The mathematical representations of the movement mechanisms and the influence of Ca2+ buffering are
based on experimental data taken from rat cardiac myocytes.
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<dcterms:W3CDTF>2000</dcterms:W3CDTF>
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<vCard:Given>Steven</vCard:Given>
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<vCard:Other>M</vCard:Other>
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<dc:title>
A Mathematical Model of Cardiocyte Ca2+ Dynamics with a Novel Representation of Sarcoplasmic Reticular Ca2+ Control
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<bqs:first_page>94</bqs:first_page>
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<dcterms:W3CDTF>2002-03-18</dcterms:W3CDTF>
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