<?xml version='1.0'?>
<model cmeta:id="tran_2009" name="tran_2009" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A metabolite-sensitive, thermodynamically-constrained model of cardiac cross-bridge cycling: Implications for force development during ischemia</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<sect1 id="sec_status">
<title>Model Status</title>
<para>
This CellML model has been curated, the units are consistent and the model runs in COR and OpenCell to replicate the published results.
</para>
</sect1>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Abstract: We present a metabolically regulated model of cardiac active force generation with which we investigate the effects of ischemia on maximum force production. Our model, based on the Rice et al. (2008) model of cross-bridge kinetics, reproduces many of the observed effects of MgATP, MgADP, Pi and H+ on force development while still retaining the force/length/Ca2+ properties of the original model. We introduce three new parameters to account for the competitive binding of H+ to the Ca2+ binding site on troponin C and the binding of MgADP within the cross-bridge cycle. These parameters along with the Pi and H+ regulatory steps within the cross-bridge cycle were constrained using data from the literature and validated using a range of metabolic and sinusoidal length perturbation protocols. The placement of the MgADP binding step between two strongly-bound and force-generating states leads to the emergence of an unexpected effect on the force-MgADP curve, where the trend of the relationship (positive or negative) depends on the concentrations of the other metabolites and [H+]. The model is used to investigate the sensitivity of maximum force production to changes in metabolite concentrations during the development of ischemia.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
A metabolite-sensitive, thermodynamically-constrained model of cardiac cross-bridge cycling: Implications for force development during ischemia, Kenneth Tran, Nicolas P. Smith, Denis S. Loiselle and Edmund J. Crampin, 2010,
<emphasis>Biophysical Journal</emphasis>, 98, 267-276. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/20338848">PubMed ID: 20338848</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="tran_2009.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the Tran et al. 2010 model. The original model from Rice et al. 2008 has been modified to include metabolite dependence</caption>
</informalfigure>
</sect1>
</article>
</documentation>
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<unit units="dimensionless"/>
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<unit units="unit_normalised_force"/>
<unit units="millisecond"/>
</units>
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<unit units="unit_normalised_force"/>
<unit units="millisecond"/>
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<variable name="len_thin" public_interface="in" units="micrometre"/>
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<variable initial_value="0.05" name="kp_n" units="first_order_rate_constant"/>
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<variable name="permtot" units="dimensionless"/>
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<variable initial_value="2e-2" name="kdHCa" units="micromolar"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="TmpC" public_interface="in" units="kelvin"/>
<variable name="Cai" public_interface="in" units="micromolar"/>
<variable name="SOVFThin" public_interface="in" units="dimensionless"/>
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</piecewise>
</apply>
<apply>
<eq/>
<ci>gxbT</ci>
<apply>
<times/>
<ci>gxb</ci>
<ci>gxbmd</ci>
<ci>xbmodsp</ci>
<apply>
<power/>
<ci>Qgxb</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>TmpC</ci>
<cn cellml:units="kelvin">310</cn>
</apply>
<cn cellml:units="kelvin">10</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="regulation_and_crossbridge_cycling_state_equations">
<variable initial_value="1.81017564383744e-6" name="XBpostr" public_interface="out" units="dimensionless"/>
<variable initial_value="3.0494964880038e-7" name="XBprer" public_interface="out" units="dimensionless"/>
<variable name="dXBpostr" public_interface="out" units="first_order_rate_constant"/>
<variable cmeta:id="regulation_and_crossbridge_cycling_state_equations_dXBprer" name="dXBprer" public_interface="out" units="first_order_rate_constant"/>
<variable name="alpha1_plus" public_interface="out" units="first_order_rate_constant"/>
<variable name="alpha2_plus" public_interface="out" units="first_order_rate_constant"/>
<variable name="alpha3_plus" public_interface="out" units="first_order_rate_constant"/>
<variable name="alpha1_minus" public_interface="out" units="first_order_rate_constant"/>
<variable name="alpha2_minus" public_interface="out" units="first_order_rate_constant"/>
<variable name="alpha3_minus" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="15400e6" name="kMgATP" public_interface="out" units="micromolar2"/>
<variable cmeta:id="regulation_and_crossbridge_cycling_state_equations_kdADP" initial_value="4" name="kdADP" public_interface="out" units="micromolar"/>
<variable initial_value="2e3" name="xPi_cons" public_interface="out" units="micromolar"/>
<variable initial_value="5e3" name="MgATP_cons" public_interface="out" units="micromolar"/>
<variable cmeta:id="regulation_and_crossbridge_cycling_state_equations_fxbT" name="fxbT" units="first_order_rate_constant"/>
<variable cmeta:id="regulation_and_crossbridge_cycling_state_equations_N_NoXB" initial_value="0.999999959256274" name="N_NoXB" units="dimensionless"/>
<variable cmeta:id="regulation_and_crossbridge_cycling_state_equations_P_NoXB" initial_value="4.07437173988636e-8" name="P_NoXB" units="dimensionless"/>
<variable cmeta:id="regulation_and_crossbridge_cycling_state_equations_P" initial_value="0.999997834540066" name="P" units="dimensionless"/>
<variable name="N" units="dimensionless"/>
<variable initial_value="36" name="MgADP_cons" units="micromolar"/>
<variable initial_value="2e3" name="xPi" units="micromolar"/>
<variable cmeta:id="regulation_and_crossbridge_cycling_state_equations_MgATP" initial_value="5e3" name="MgATP" units="micromolar"/>
<variable cmeta:id="regulation_and_crossbridge_cycling_state_equations_MgADP" initial_value="36.3" name="MgADP" units="micromolar"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="fappT" public_interface="in" units="first_order_rate_constant"/>
<variable name="gappT" public_interface="in" units="first_order_rate_constant"/>
<variable name="hfT" public_interface="in" units="first_order_rate_constant"/>
<variable name="hbT" public_interface="in" units="first_order_rate_constant"/>
<variable name="gxbT" public_interface="in" units="first_order_rate_constant"/>
<variable name="kn_pT" public_interface="in" units="first_order_rate_constant"/>
<variable name="kp_nT" public_interface="in" units="first_order_rate_constant"/>
<variable name="H" public_interface="in" units="micromolar"/>
<variable name="H_cons" public_interface="in" units="micromolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>N_NoXB</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>kp_nT</ci>
<ci>P_NoXB</ci>
</apply>
<apply>
<times/>
<ci>kn_pT</ci>
<ci>N_NoXB</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_NoXB</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>kn_pT</ci>
<ci>N_NoXB</ci>
</apply>
<apply>
<times/>
<ci>kp_nT</ci>
<ci>P_NoXB</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>N</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>P</ci>
<ci>XBprer</ci>
<ci>XBpostr</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>kn_pT</ci>
<ci>N</ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>kp_nT</ci>
<ci>alpha1_plus</ci>
</apply>
<ci>P</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>XBprer</ci>
</apply>
<ci>dXBprer</ci>
</apply>
<apply>
<eq/>
<ci>dXBprer</ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha1_plus</ci>
<ci>P</ci>
</apply>
<apply>
<times/>
<ci>alpha2_minus</ci>
<ci>XBpostr</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>alpha1_minus</ci>
<ci>alpha2_plus</ci>
</apply>
<ci>XBprer</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>XBpostr</ci>
</apply>
<ci>dXBpostr</ci>
</apply>
<apply>
<eq/>
<ci>dXBpostr</ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha3_minus</ci>
<ci>P</ci>
</apply>
<apply>
<times/>
<ci>alpha2_plus</ci>
<ci>XBprer</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>alpha2_minus</ci>
<ci>alpha3_plus</ci>
</apply>
<ci>XBpostr</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha1_plus</ci>
<ci>fappT</ci>
</apply>
<apply>
<eq/>
<ci>alpha2_plus</ci>
<ci>hfT</ci>
</apply>
<apply>
<eq/>
<ci>alpha3_plus</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>MgATP</ci>
<ci>gxbT</ci>
</apply>
<ci>MgATP_cons</ci>
</apply>
<apply>
<plus/>
<ci>kdADP</ci>
<ci>MgADP_cons</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>kdADP</ci>
<ci>MgADP</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha1_minus</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>xPi</ci>
<ci>gappT</ci>
</apply>
<ci>xPi_cons</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha2_minus</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>H</ci>
<ci>hbT</ci>
</apply>
<ci>H_cons</ci>
</apply>
<apply>
<plus/>
<ci>kdADP</ci>
<ci>MgADP_cons</ci>
</apply>
</apply>
<ci>MgADP_cons</ci>
</apply>
<ci>MgADP</ci>
</apply>
<apply>
<plus/>
<ci>kdADP</ci>
<ci>MgADP</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha3_minus</ci>
<ci>fxbT</ci>
</apply>
<apply>
<eq/>
<ci>fxbT</ci>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<ci>kdADP</ci>
<ci>fappT</ci>
<ci>hfT</ci>
<ci>gxbT</ci>
</apply>
<ci>MgATP_cons</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>gappT</ci>
<ci>xPi_cons</ci>
</apply>
<ci>hbT</ci>
</apply>
<ci>H_cons</ci>
</apply>
<ci>kMgATP</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="mean_strain_of_strongly_bound_states">
<variable initial_value="0.00700005394873882" name="xXBpostr" public_interface="out" units="micrometre"/>
<variable initial_value="3.41212828972468e-8" name="xXBprer" public_interface="out" units="micrometre"/>
<variable name="dxXBpostr" public_interface="out" units="micrometre_per_millisecond"/>
<variable name="dxXBprer" public_interface="out" units="micrometre_per_millisecond"/>
<variable initial_value="2" name="xPsi" units="dimensionless"/>
<variable name="dutyprer" units="dimensionless"/>
<variable name="dutypostr" units="dimensionless"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="alpha1_plus" public_interface="in" units="first_order_rate_constant"/>
<variable name="alpha2_plus" public_interface="in" units="first_order_rate_constant"/>
<variable name="alpha3_plus" public_interface="in" units="first_order_rate_constant"/>
<variable name="alpha1_minus" public_interface="in" units="first_order_rate_constant"/>
<variable name="alpha2_minus" public_interface="in" units="first_order_rate_constant"/>
<variable name="alpha3_minus" public_interface="in" units="first_order_rate_constant"/>
<variable name="dSL" public_interface="in" units="micrometre_per_millisecond"/>
<variable name="x_0" public_interface="in" units="micrometre"/>
<variable name="fappT" public_interface="in" units="first_order_rate_constant"/>
<variable name="gappT" public_interface="in" units="first_order_rate_constant"/>
<variable name="hfT" public_interface="in" units="first_order_rate_constant"/>
<variable name="hbT" public_interface="in" units="first_order_rate_constant"/>
<variable name="gxbT" public_interface="in" units="first_order_rate_constant"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>xXBprer</ci>
</apply>
<ci>dxXBprer</ci>
</apply>
<apply>
<eq/>
<ci>dxXBprer</ci>
<apply>
<plus/>
<apply>
<divide/>
<ci>dSL</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>xPsi</ci>
<ci>dutyprer</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>alpha1_plus</ci>
</apply>
<ci>xXBprer</ci>
</apply>
<apply>
<times/>
<ci>alpha2_minus</ci>
<apply>
<minus/>
<ci>xXBpostr</ci>
<apply>
<plus/>
<ci>x_0</ci>
<ci>xXBprer</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>xXBpostr</ci>
</apply>
<ci>dxXBpostr</ci>
</apply>
<apply>
<eq/>
<ci>dxXBpostr</ci>
<apply>
<plus/>
<apply>
<divide/>
<ci>dSL</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>xPsi</ci>
<ci>dutypostr</ci>
</apply>
<ci>alpha2_plus</ci>
<apply>
<minus/>
<apply>
<plus/>
<ci>xXBprer</ci>
<ci>x_0</ci>
</apply>
<ci>xXBpostr</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>dutyprer</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha3_minus</ci>
<ci>alpha2_minus</ci>
</apply>
<apply>
<times/>
<ci>alpha3_plus</ci>
<ci>alpha1_plus</ci>
</apply>
<apply>
<times/>
<ci>alpha2_minus</ci>
<ci>alpha1_plus</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha1_plus</ci>
<ci>alpha2_plus</ci>
</apply>
<apply>
<times/>
<ci>alpha3_minus</ci>
<ci>alpha1_minus</ci>
</apply>
<apply>
<times/>
<ci>alpha3_minus</ci>
<ci>alpha2_plus</ci>
</apply>
<apply>
<times/>
<ci>alpha3_minus</ci>
<ci>alpha2_minus</ci>
</apply>
<apply>
<times/>
<ci>alpha3_plus</ci>
<ci>alpha1_plus</ci>
</apply>
<apply>
<times/>
<ci>alpha2_minus</ci>
<ci>alpha1_plus</ci>
</apply>
<apply>
<times/>
<ci>alpha2_plus</ci>
<ci>alpha3_plus</ci>
</apply>
<apply>
<times/>
<ci>alpha3_minus</ci>
<ci>alpha1_minus</ci>
</apply>
<apply>
<times/>
<ci>alpha3_plus</ci>
<ci>alpha1_minus</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>dutypostr</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha1_plus</ci>
<ci>alpha2_plus</ci>
</apply>
<apply>
<times/>
<ci>alpha3_minus</ci>
<ci>alpha1_minus</ci>
</apply>
<apply>
<times/>
<ci>alpha3_minus</ci>
<ci>alpha2_plus</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha1_plus</ci>
<ci>alpha2_plus</ci>
</apply>
<apply>
<times/>
<ci>alpha3_minus</ci>
<ci>alpha1_minus</ci>
</apply>
<apply>
<times/>
<ci>alpha3_minus</ci>
<ci>alpha2_plus</ci>
</apply>
<apply>
<times/>
<ci>alpha3_minus</ci>
<ci>alpha2_minus</ci>
</apply>
<apply>
<times/>
<ci>alpha3_plus</ci>
<ci>alpha1_plus</ci>
</apply>
<apply>
<times/>
<ci>alpha2_minus</ci>
<ci>alpha1_plus</ci>
</apply>
<apply>
<times/>
<ci>alpha2_plus</ci>
<ci>alpha3_plus</ci>
</apply>
<apply>
<times/>
<ci>alpha3_minus</ci>
<ci>alpha1_minus</ci>
</apply>
<apply>
<times/>
<ci>alpha3_plus</ci>
<ci>alpha1_minus</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="normalised_active_and_passive_force">
<variable name="SSXBpostr" public_interface="out" units="dimensionless"/>
<variable name="SSXBprer" public_interface="out" units="dimensionless"/>
<variable name="dSL" public_interface="out" units="micrometre_per_millisecond"/>
<variable initial_value="2.2" name="SL" public_interface="out" units="micrometre"/>
<variable name="ppforce" units="unit_normalised_force"/>
<variable name="ppforce_t" units="unit_normalised_force"/>
<variable name="ppforce_c" units="unit_normalised_force"/>
<variable name="preload" units="unit_normalised_force"/>
<variable name="afterload" units="unit_normalised_force"/>
<variable initial_value="-4.5113452510363e-6" name="intf" units="unit_normalised_force_millisecond"/>
<variable initial_value="2.25" name="SL_c" units="micrometre"/>
<variable initial_value="1.85" name="SLrest" units="micrometre"/>
<variable initial_value="1.9" name="SLset" units="micrometre"/>
<variable initial_value="0.002" name="PCon_t" units="unit_normalised_force"/>
<variable initial_value="10" name="PExp_t" units="per_micrometre"/>
<variable initial_value="0.02" name="PCon_c" units="unit_normalised_force"/>
<variable initial_value="70" name="PExp_c" units="per_micrometre"/>
<variable initial_value="1" name="KSE" units="unit_normalised_force_per_micrometre"/>
<variable name="fxb" units="first_order_rate_constant"/>
<variable name="MgATP_cons" public_interface="in" units="micromolar"/>
<variable name="xPi_cons" public_interface="in" units="micromolar"/>
<variable name="H_cons" public_interface="in" units="micromolar"/>
<variable name="kMgATP" public_interface="in" units="micromolar2"/>
<variable name="kdADP" public_interface="in" units="micromolar"/>
<variable name="x_0" public_interface="in" units="micrometre"/>
<variable name="fapp" public_interface="in" units="first_order_rate_constant"/>
<variable name="gapp" public_interface="in" units="first_order_rate_constant"/>
<variable name="hf" public_interface="in" units="first_order_rate_constant"/>
<variable name="hb" public_interface="in" units="first_order_rate_constant"/>
<variable name="gxb" public_interface="in" units="first_order_rate_constant"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="fappT" public_interface="in" units="first_order_rate_constant"/>
<variable name="gappT" public_interface="in" units="first_order_rate_constant"/>
<variable name="hfT" public_interface="in" units="first_order_rate_constant"/>
<variable name="hbT" public_interface="in" units="first_order_rate_constant"/>
<variable name="gxbT" public_interface="in" units="first_order_rate_constant"/>
<variable name="XBpostr" public_interface="in" units="dimensionless"/>
<variable name="XBprer" public_interface="in" units="dimensionless"/>
<variable name="xXBpostr" public_interface="in" units="micrometre"/>
<variable name="xXBprer" public_interface="in" units="micrometre"/>
<variable name="SOVFThick" public_interface="in" units="dimensionless"/>
<variable initial_value="1" name="SEon" units="dimensionless"/>
<variable name="F_active" units="unit_normalised_force"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>fxb</ci>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<ci>kdADP</ci>
<ci>fapp</ci>
<ci>hf</ci>
<ci>gxb</ci>
</apply>
<ci>MgATP_cons</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci>gapp</ci>
<ci>xPi_cons</ci>
</apply>
<ci>hb</ci>
</apply>
<ci>H_cons</ci>
</apply>
<ci>kMgATP</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>SSXBprer</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>fxb</ci>
<ci>hb</ci>
</apply>
<apply>
<times/>
<ci>gxb</ci>
<ci>fapp</ci>
</apply>
<apply>
<times/>
<ci>hbT</ci>
<ci>fapp</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>hf</ci>
<ci>gxb</ci>
</apply>
<apply>
<times/>
<ci>hb</ci>
<ci>gapp</ci>
</apply>
<apply>
<times/>
<ci>gxb</ci>
<ci>gapp</ci>
</apply>
<apply>
<times/>
<ci>fxb</ci>
<ci>hb</ci>
</apply>
<apply>
<times/>
<ci>gxb</ci>
<ci>fapp</ci>
</apply>
<apply>
<times/>
<ci>hb</ci>
<ci>fapp</ci>
</apply>
<apply>
<times/>
<ci>fxb</ci>
<ci>gapp</ci>
</apply>
<apply>
<times/>
<ci>fapp</ci>
<ci>hf</ci>
</apply>
<apply>
<times/>
<ci>fxb</ci>
<ci>hb</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>SSXBpostr</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>fapp</ci>
<ci>hf</ci>
</apply>
<apply>
<times/>
<ci>fxb</ci>
<ci>gapp</ci>
</apply>
<apply>
<times/>
<ci>fxb</ci>
<ci>hb</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>hf</ci>
<ci>gxb</ci>
</apply>
<apply>
<times/>
<ci>hb</ci>
<ci>gapp</ci>
</apply>
<apply>
<times/>
<ci>gxb</ci>
<ci>gapp</ci>
</apply>
<apply>
<times/>
<ci>fxb</ci>
<ci>hb</ci>
</apply>
<apply>
<times/>
<ci>gxb</ci>
<ci>fapp</ci>
</apply>
<apply>
<times/>
<ci>hb</ci>
<ci>fapp</ci>
</apply>
<apply>
<times/>
<ci>fxb</ci>
<ci>gapp</ci>
</apply>
<apply>
<times/>
<ci>fapp</ci>
<ci>hf</ci>
</apply>
<apply>
<times/>
<ci>fxb</ci>
<ci>hb</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>F_active</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>SOVFThick</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>xXBpostr</ci>
<ci>XBpostr</ci>
</apply>
<apply>
<times/>
<ci>xXBprer</ci>
<ci>XBprer</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>x_0</ci>
<ci>SSXBpostr</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
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The Modification History metadata. This lists the changes that have been
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The following metadata refers to the model itself, as indicated by the
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The Tran et al. 2010 metabolite-sensitive, thermodynamically-constrained model of cardiac cross-bridge cycling
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This is the CellML description of Tran et al's 2010 metabolite-sensitive, thermodynamically-constrained model of cardiac cross-bridge cycling
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A metabolite-sensitive, thermodynamically-constrained model of cardiac cross-bridge cycling: Implications for force development during ischemia
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<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Biophysical Journal</dc:title>
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