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Modeling beta-adrenergic control of cardiac myocyte contractility in silico.
The CellML code.
<!-- FILE : saucerman_model_2003.xml
CREATED : 18th November 2003
LAST MODIFIED : 18th November 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 16/1/02 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Saucerman et al.'s 2003 mathematical model of beta-adrenergic control of cardiac myocyte contractility.
CHANGES:
-->
<model xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:rdf="http://www.w3.org/1999/0P/PP-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns="http://www.cellml.org/cellml/1.0#" cmeta:id="saucerman_model_2003" name="saucerman_2003_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modelling Beta-adrenergic Control of Cardiac Myocyte Contractility in Silico</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 CellML version of the model can not be run in either PCEnv or COR at the moment due to the presence of circular arguments.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
In cardiac myocytes, the beta-adrenergic signalling network is triggered in response to norepinephrine and epinephrine binding to the Gs-protein coupled beta-adrenergic receptor. Receptor-ligand binding activates the coupled Gs-protein, which in turn activates adenylate cyclase. ATP is converted into the secondary messenger cyclic AMP (cAMP). cAMP promotes dissociation of the protein kinase A (PKA) holoenzyme, whose catalytic subunits go on to phosphorylate a wide range of target proteins, two of which are the L-type calcium channel and phospholamban - which both play essential roles in the regulation of calcium dynamics and transport. In healthy cardiac myocytes, the end result of this signal transduction pathway is to provide coordinated control of contractility, metabolism and gene regulation. However, altered beta-adrenergic signalling may also play a role in the progression of heart failure.
</para>
<para>
Molecular components of this signalling pathway have been studied in detail as potential therapeutic targets in heart failure. However, the situation is complex, with intracellular compartmentation and functional integration of pathways being suggested as playing an important role in the signalling outcome. Systems level mathematical modelling will help make sense of large quantities of experimental data. Since the Hodgkin-Huxley Squid Axon Model was published in 1952, many ionic models of cell electrophysiology have been developed. Recently systems modelling has been identified as a potential method for improving understanding of signaling networks and the response to genetic and pharmaceutical perturbations.
</para>
<para>
While to date portions of the mammalian beta-adrenergic signalling network have been described by mathematical models of neuron and HEK-293 cells, no analysis has modelled and validated an entire pathway from ligand to effectors such that neuro-hormonal regulation of cell physiology can be predicted. In the publication described here, Jeffrey Saucerman <emphasis>et al.</emphasis> have developed a systems biology model to investigate the molecular mechanisms underlying the control of the beta-adrenergic signalling network over cardiac myocyte contractility (see figure below). The model was validated using a wide range of experimental data, and model simulations were used to investigate quantitatively the effects of specific molecular perturbations (with potential for pharmaceutical testing). By performing systems analysis the effects of molecular perturbations in the beta-adrenergic signalling network may be understood within the context of integrative physiology.
</para>
<para>
The model of the signal transduction pathway was embedded within an extension of the Luo-Rudy Ventricular Model II (dynamic), 1994, which was modified for the rabbit ventricular myocyte (Puglisi-Bers Rabbit Ventricular Myocyte Model, 2001). The model was further adapted by inserting the equations for the L-type calcium channel from the Jafri-Rice-Winslow Ventricular Model, 1998, and also the steady-state potassium currents from the Pandit <emphasis>et al.</emphasis> Adult Rat Left Ventricular Myocyte Model, 2001.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.jbc.org/cgi/content/abstract/278/48/47997">Modeling beta-adrenergic control of cardiac myocyte contractility <emphasis>in silico</emphasis>
</ulink>, Jeffrey J. Saucerman, Laurence L. Brunton, Anushka P. Michailova, and Andrew D. McCulloch, 2003, <ulink url="http://www.jbc.org/">
<emphasis>Journal of Biological Chemistry</emphasis>
</ulink>, 48, 47997-48003. (<ulink url="http://www.jbc.org/cgi/content/full/278/48/47997">Full text (HTML)</ulink> and <ulink url="http://www.jbc.org/cgi/reprint/278/48/47997.pdf">PDF</ulink> versions of the article are available on the <emphasis>Journal of Biological Chemistry</emphasis> website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=12972422&dopt=Abstract">PubMed ID: 12972422</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="../images/saucerman_model_2003/saucerman_mcculloch_2003.png" />
</imageobject>
</mediaobject>
<caption>Schematic diagram of the integrated model components, including the beta-adrenergic network, calcium handling, and the electrophysiology of the rat ventricular myocyte.</caption>
</informalfigure>
<informalfigure float="0" id="fig_pathway_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>pathway diagram</title>
</objectinfo>
<imagedata fileref="../images/saucerman_model_2003/saucerman_2003.png" />
</imageobject>
</mediaobject>
<caption>Schematic diagram highlighting the signalling network component of the model.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
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<unit units="litre" exponent="-1" />
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<units name="millimolar">
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</units>
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<unit units="millimolar" exponent="-4" />
<unit units="second" exponent="-1" />
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<units name="millimolar_4">
<unit units="millimolar" exponent="-4" />
</units>
<units name="joule_per_kilomole_kelvin">
<unit units="joule" />
<unit units="mole" prefix="kilo" exponent="-1" />
<unit units="kelvin" exponent="-1" />
</units>
<units name="coulomb_per_mole">
<unit units="coulomb" exponent="-1" />
<unit units="mole" />
</units>
<units name="pico_litre">
<unit units="litre" prefix="pico" />
</units>
<component name="environment">
<variable units="second" public_interface="out" name="time" />
</component>
<!-- Signal transduction pathway component of the model from the Saucerman et al. 2003 paper -->
<component name="beta_adrenergic_receptor_module">
<variable units="micromolar" public_interface="out" name="LRG" />
<variable units="micromolar" public_interface="out" name="RG" />
<variable units="micromolar" name="LR" />
<variable units="micromolar" name="beta1_AR" initial_value="0.01205" />
<variable units="micromolar" name="Gs" initial_value="3.829" />
<variable units="micromolar" name="beta1_ARact" initial_value="0.01205" />
<variable units="micromolar" name="beta1_AR_S464" initial_value="0.0" />
<variable units="micromolar" name="beta1_AR_S301" initial_value="1.154E-3" />
<variable units="micromolar" name="L" initial_value="10.0" />
<variable units="micromolar" name="Ltotmax" initial_value="1.0" />
<variable units="micromolar" name="KL" initial_value="0.285" />
<variable units="micromolar" name="KR" initial_value="0.062" />
<variable units="micromolar" name="KC" initial_value="33.0" />
<variable units="micromolar" name="Gstot" initial_value="3.83" />
<variable units="first_order_rate_constant" name="k_betaARK_plus" initial_value="1.1E-3" />
<variable units="first_order_rate_constant" name="k_betaARK_minus" initial_value="2.2E-3" />
<variable units="second_order_rate_constant" name="k_PKA_plus" initial_value="3.6E-3" />
<variable units="first_order_rate_constant" name="k_PKA_minus" initial_value="2.2E-3" />
<variable units="second" public_interface="in" name="time" />
<variable units="micromolar" public_interface="in" name="Gs_beta_gamma" />
<variable units="micromolar" public_interface="in" name="PKACI" />
<math xmlns="http://www.w3.org/1998/Math/MathML" id="1">
<apply>
<eq />
<apply>
<diff />
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</bvar>
<ci> L </ci>
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<apply>
<minus />
<ci> Ltotmax </ci>
<apply>
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<ci> LRG </ci>
<ci> L </ci>
</apply>
</apply>
</apply>
<apply>
<eq />
<ci>LR</ci>
<apply>
<divide />
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<times />
<ci> L </ci>
<ci> beta1_AR </ci>
</apply>
<ci> KL </ci>
</apply>
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<apply>
<eq />
<ci>LRG</ci>
<apply>
<divide />
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<times />
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<ci> beta1_AR </ci>
<ci> Gs </ci>
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<apply>
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<ci> KR </ci>
</apply>
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<eq />
<ci>RG</ci>
<apply>
<divide />
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<times />
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<ci> Gs </ci>
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<ci> KC </ci>
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<apply>
<eq />
<apply>
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<apply>
<eq />
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<diff />
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<ci> beta1_AR </ci>
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<apply>
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<ci> LR </ci>
<ci> LRG </ci>
<ci> RG </ci>
<ci> beta1_AR </ci>
</apply>
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</apply>
<apply>
<eq />
<apply>
<diff />
<bvar>
<ci>time</ci>
</bvar>
<ci>beta1_ARact</ci>
</apply>
<apply>
<plus />
<apply>
<minus />
<apply>
<times />
<ci> k_betaARK_minus </ci>
<ci> beta1_AR_S464 </ci>
</apply>
<apply>
<times />
<ci> k_betaARK_plus </ci>
<apply>
<plus />
<ci> LR </ci>
<ci> LRG </ci>
</apply>
</apply>
</apply>
<apply>
<minus />
<apply>
<times />
<ci> k_PKA_minus </ci>
<ci> beta1_AR_S301 </ci>
</apply>
<apply>
<times />
<ci> k_PKA_plus </ci>
<ci> PKACI </ci>
<ci> beta1_ARact </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq />
<apply>
<diff />
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</bvar>
<ci>beta1_AR_S464</ci>
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<apply>
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<apply>
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<ci> LR </ci>
<ci> LRG </ci>
</apply>
</apply>
<apply>
<times />
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<ci> beta1_AR_S464 </ci>
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<apply>
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</bvar>
<ci>beta1_AR_S301</ci>
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<times />
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<ci> PKACI </ci>
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<apply>
<times />
<ci> k_PKA_minus </ci>
<ci> beta1_AR_S301 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Gs_activation_module">
<variable units="micromolar" public_interface="out" name="Gs_beta_gamma" initial_value="0.02569" />
<variable units="micromolar" public_interface="out" name="Gs_alpha_GTPtot" initial_value="0.02505" />
<variable units="micromolar" name="Gs_alpha_GDP" initial_value="6.44E-4" />
<variable units="first_order_rate_constant" name="k_gact" initial_value="16.0" />
<variable units="first_order_rate_constant" name="k_hyd" initial_value="0.8" />
<variable units="second_order_rate_constant" name="k_reassoc" initial_value="1.21E3" />
<variable units="micromolar" public_interface="in" name="RG" />
<variable units="micromolar" public_interface="in" name="LRG" />
<variable units="second" public_interface="in" name="time" />
<math xmlns="http://www.w3.org/1998/Math/MathML" id="2">
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<times />
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<ci> Gs_beta_gamma </ci>
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<apply>
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<times />
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<ci> Gs_alpha_GTPtot </ci>
</apply>
<apply>
<times />
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<ci> Gs_alpha_GDP </ci>
<ci> Gs_beta_gamma </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="cyclic_AMP_metabolism_module">
<variable units="micromolar" public_interface="out" name="cAMPtot" initial_value="0.8453" />
<variable units="micromolar" name="AC" initial_value="0.04706" />
<variable units="micromolar" name="Gs_alpha_GTP" initial_value="0.02241" />
<variable units="micromolar" name="Gs_alpha_GTP_AC" />
<variable units="micromolar" name="PDE" initial_value="0.0389" />
<!-- <variable units="micromolar" name="PDE_ACT"/> -->
<variable units="micromolar" name="ACtot" initial_value="49.7E-3" />
<variable units="micromolar" name="ATP" initial_value="5.0E3" />
<variable units="micromolar" name="PDEtot" initial_value="38.9E-3" />
<variable units="micromolar" name="PDEinhib" />
<variable units="micromolar" name="IBMXtot" initial_value="0.0" />
<variable units="micromolar" name="IBMX" initial_value="0.0" />
<variable units="micromolar" name="fsktot" initial_value="0.0" />
<variable units="micromolar" name="fsk" initial_value="0.0" />
<variable units="micromolar" name="fsk_AC" />
<variable units="first_order_rate_constant" name="kAC_basal" initial_value="0.2" />
<variable units="first_order_rate_constant" name="kAC_fsk" initial_value="7.3" />
<variable units="first_order_rate_constant" name="k_PDE" initial_value="5.0" />
<variable units="first_order_rate_constant" name="kAC_Gs_alpha" initial_value="8.5" />
<variable units="micromolar" name="Km_basal" initial_value="1.03E3" />
<variable units="micromolar" name="Km_PDE" initial_value="1.3" />
<variable units="micromolar" name="Km_fsk" initial_value="860.0" />
<variable units="micromolar" name="K_fsk" initial_value="44.0" />
<variable units="micromolar" name="Km_Gs_alpha_GTP" initial_value="0.4" />
<variable units="micromolar" name="K_Gs_alpha" initial_value="0.4" />
<variable units="micromolar" name="K_IBMX" initial_value="30.0" />
<variable units="micromolar" public_interface="in" name="Gs_alpha_GTPtot" />
<variable units="second" public_interface="in" name="time" />
<variable units="micromolar" public_interface="in" name="cAMP" />
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<ci> PDE </ci>
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<diff />
<bvar>
<ci> time </ci>
</bvar>
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<ci> IBMX </ci>
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<!--
<apply><eq/>
<apply><diff/>
<bvar><ci> time </ci></bvar>
<ci> PDE_ACT </ci>
</apply>
<apply><divide/>
<apply><times/>
<ci> k_PDE </ci>
<ci> PDE </ci>
<ci> cAMP </ci>
</apply>
<apply><plus/>
<ci> Km_PDE </ci>
<ci> cAMP </ci>
</apply>
</apply>
</apply>
-->
<apply>
<eq />
<ci>Gs_alpha_
CREATED : 18th November 2003
LAST MODIFIED : 18th November 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 16/1/02 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Saucerman et al.'s 2003 mathematical model of beta-adrenergic control of cardiac myocyte contractility.
CHANGES:
-->
<model xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:rdf="http://www.w3.org/1999/0P/PP-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns="http://www.cellml.org/cellml/1.0#" cmeta:id="saucerman_model_2003" name="saucerman_2003_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modelling Beta-adrenergic Control of Cardiac Myocyte Contractility in Silico</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 CellML version of the model can not be run in either PCEnv or COR at the moment due to the presence of circular arguments.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
In cardiac myocytes, the beta-adrenergic signalling network is triggered in response to norepinephrine and epinephrine binding to the Gs-protein coupled beta-adrenergic receptor. Receptor-ligand binding activates the coupled Gs-protein, which in turn activates adenylate cyclase. ATP is converted into the secondary messenger cyclic AMP (cAMP). cAMP promotes dissociation of the protein kinase A (PKA) holoenzyme, whose catalytic subunits go on to phosphorylate a wide range of target proteins, two of which are the L-type calcium channel and phospholamban - which both play essential roles in the regulation of calcium dynamics and transport. In healthy cardiac myocytes, the end result of this signal transduction pathway is to provide coordinated control of contractility, metabolism and gene regulation. However, altered beta-adrenergic signalling may also play a role in the progression of heart failure.
</para>
<para>
Molecular components of this signalling pathway have been studied in detail as potential therapeutic targets in heart failure. However, the situation is complex, with intracellular compartmentation and functional integration of pathways being suggested as playing an important role in the signalling outcome. Systems level mathematical modelling will help make sense of large quantities of experimental data. Since the Hodgkin-Huxley Squid Axon Model was published in 1952, many ionic models of cell electrophysiology have been developed. Recently systems modelling has been identified as a potential method for improving understanding of signaling networks and the response to genetic and pharmaceutical perturbations.
</para>
<para>
While to date portions of the mammalian beta-adrenergic signalling network have been described by mathematical models of neuron and HEK-293 cells, no analysis has modelled and validated an entire pathway from ligand to effectors such that neuro-hormonal regulation of cell physiology can be predicted. In the publication described here, Jeffrey Saucerman <emphasis>et al.</emphasis> have developed a systems biology model to investigate the molecular mechanisms underlying the control of the beta-adrenergic signalling network over cardiac myocyte contractility (see figure below). The model was validated using a wide range of experimental data, and model simulations were used to investigate quantitatively the effects of specific molecular perturbations (with potential for pharmaceutical testing). By performing systems analysis the effects of molecular perturbations in the beta-adrenergic signalling network may be understood within the context of integrative physiology.
</para>
<para>
The model of the signal transduction pathway was embedded within an extension of the Luo-Rudy Ventricular Model II (dynamic), 1994, which was modified for the rabbit ventricular myocyte (Puglisi-Bers Rabbit Ventricular Myocyte Model, 2001). The model was further adapted by inserting the equations for the L-type calcium channel from the Jafri-Rice-Winslow Ventricular Model, 1998, and also the steady-state potassium currents from the Pandit <emphasis>et al.</emphasis> Adult Rat Left Ventricular Myocyte Model, 2001.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.jbc.org/cgi/content/abstract/278/48/47997">Modeling beta-adrenergic control of cardiac myocyte contractility <emphasis>in silico</emphasis>
</ulink>, Jeffrey J. Saucerman, Laurence L. Brunton, Anushka P. Michailova, and Andrew D. McCulloch, 2003, <ulink url="http://www.jbc.org/">
<emphasis>Journal of Biological Chemistry</emphasis>
</ulink>, 48, 47997-48003. (<ulink url="http://www.jbc.org/cgi/content/full/278/48/47997">Full text (HTML)</ulink> and <ulink url="http://www.jbc.org/cgi/reprint/278/48/47997.pdf">PDF</ulink> versions of the article are available on the <emphasis>Journal of Biological Chemistry</emphasis> website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=12972422&dopt=Abstract">PubMed ID: 12972422</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="../images/saucerman_model_2003/saucerman_mcculloch_2003.png" />
</imageobject>
</mediaobject>
<caption>Schematic diagram of the integrated model components, including the beta-adrenergic network, calcium handling, and the electrophysiology of the rat ventricular myocyte.</caption>
</informalfigure>
<informalfigure float="0" id="fig_pathway_diagram">
<mediaobject>
<imageobject>
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<title>pathway diagram</title>
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<imagedata fileref="../images/saucerman_model_2003/saucerman_2003.png" />
</imageobject>
</mediaobject>
<caption>Schematic diagram highlighting the signalling network component of the model.</caption>
</informalfigure>
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