Rendering of the source text

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		<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">
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								<title>model diagram</title>
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							<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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                                <abs/>
                                <ci>xXBprer</ci>
                            </apply>
                        </apply>
                        <ci>hfmdc</ci>
                        <apply>
                            <power/>
                            <apply>
                                <divide/>
                                <ci>xXBprer</ci>
                                <ci>x_0</ci>
                            </apply>
                            <cn cellml:units="dimensionless">2</cn>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <!-- hbmd = exp((xXBpostr-x_0)/abs(xXBpostr-x_0)*hbmdc*sqr((xXBpostr-x_0)/x_0));-->
            <apply>
                <eq/>
                <ci>hbmd</ci>
                <cn cellml:units="dimensionless">1</cn>
            </apply>
            <apply>
                <eq/>
                <ci>hfT</ci>
                <apply>
                    <times/>
                    <ci>hf</ci>
                    <ci>hfmd</ci>
                    <ci>xbmodsp</ci>
                    <apply>
                        <power/>
                        <ci>Qhf</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>
            <apply>
                <eq/>
                <ci>hbT</ci>
                <apply>
                    <times/>
                    <ci>hb</ci>
                    <ci>hbmd</ci>
                    <ci>xbmodsp</ci>
                    <apply>
                        <power/>
                        <ci>Qhb</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>
            <apply>
                <eq/>
                <ci>gxbmd</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <exp/>
                            <apply>
                                <times/>
                                <ci>sigmap</ci>
                                <apply>
                                    <power/>
                                    <apply>
                                        <divide/>
                                        <apply>
                                            <minus/>
                                            <ci>x_0</ci>
                                            <ci>xXBpostr</ci>
                                        </apply>
                                        <ci>x_0</ci>
                                    </apply>
                                    <cn cellml:units="dimensionless">2</cn>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <lt/>
                            <ci>xXBpostr</ci>
                            <ci>x_0</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <exp/>
                            <apply>
                                <times/>
                                <ci>sigman</ci>
                                <apply>
                                    <power/>
                                    <apply>
                                        <divide/>
                                        <apply>
                                            <minus/>
                                            <ci>xXBpostr</ci>
                                            <ci>x_0</ci>
                                        </apply>
                                        <ci>x_0</ci>
                                    </apply>
                                    <cn cellml:units="dimensionless">2</cn>
                                </apply>
                            </apply>
                        </apply>
                    </otherwise>
                </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/>
                <ci>ppforce_t</ci>
                <apply>
                    <times/>
                    <apply>
                        <divide/>
                        <apply>
                            <minus/>
                            <ci>SL</ci>
                            <ci>SLrest</ci>
                        </apply>
                        <apply>
                            <abs/>
                            <apply>
                                <minus/>
                                <ci>SL</ci>
                                <ci>SLrest</ci>
                            </apply>
                        </apply>
                    </apply>
                    <ci>PCon_t</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <times/>
                                <ci>PExp_t</ci>
                                <apply>
                                    <abs/>
                                    <apply>
                                        <minus/>
                                        <ci>SL</ci>
                                        <ci>SLrest</ci>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                        <cn cellml:units="dimensionless">1</cn>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>ppforce_c</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <ci>PCon_c</ci>
                            <apply>
                                <minus/>
                                <apply>
                                    <exp/>
                                    <apply>
                                        <times/>
                                        <ci>PExp_c</ci>
                                        <apply>
                                            <abs/>
                                            <apply>
                                                <minus/>
                                                <ci>SL</ci>
                                                <ci>SL_c</ci>
                                            </apply>
                                        </apply>
                                    </apply>
                                </apply>
                                <cn cellml:units="dimensionless">1</cn>
                            </apply>
                        </apply>
                        <apply>
                            <gt/>
                            <ci>SL</ci>
                            <ci>SL_c</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="unit_normalised_force">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <ci>ppforce</ci>
                <apply>
                    <plus/>
                    <ci>ppforce_t</ci>
                    <ci>ppforce_c</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>preload</ci>
                <apply>
                    <times/>
                    <apply>
                        <divide/>
                        <apply>
                            <abs/>
                            <apply>
                                <minus/>
                                <ci>SLset</ci>
                                <ci>SLrest</ci>
                            </apply>
                        </apply>
                        <apply>
                            <minus/>
                            <ci>SLset</ci>
                            <ci>SLrest</ci>
                        </apply>
                    </apply>
                    <ci>PCon_t</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <times/>
                                <ci>PExp_t</ci>
                                <apply>
                                    <abs/>
                                    <apply>
                                        <minus/>
                                        <ci>SLset</ci>
                                        <ci>SLrest</ci>
                                    </apply>
                                </apply>
                            </apply>
                        </apply>
                        <cn cellml:units="dimensionless">1</cn>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>afterload</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <ci>KSE</ci>
                            <apply>
                                <minus/>
                                <ci>SLset</ci>
                                <ci>SL</ci>
                            </apply>
                        </apply>
                        <apply>
                            <eq/>
                            <ci>SEon</ci>
                            <cn cellml:units="dimensionless">1</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="unit_normalised_force">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>SL</ci>
                </apply>
                <ci>dSL</ci>
            </apply>
            <apply>
                <eq/>
                <ci>dSL</ci>
                <cn cellml:units="micrometre_per_millisecond">0</cn>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>intf</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <plus/>
                        <ci>preload</ci>
                        <ci>afterload</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>ppforce</ci>
                        <ci>F_active</ci>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="calculation_of_micromolar_per_millisecondes_of_Ca_for_apparent_Ca_binding">
        <variable name="FrSBXB" units="dimensionless"/>
        <variable name="dFrSBXB" units="first_order_rate_constant"/>
        <variable name="dsovr_ze" units="micrometre_per_millisecond"/>
        <variable name="dsovr_cle" units="micrometre_per_millisecond"/>
        <variable name="dlen_sovr" units="micrometre_per_millisecond"/>
        <variable name="dSOVFThick" units="first_order_rate_constant"/>
        <variable name="dSOVFThin" units="first_order_rate_constant"/>
        <variable initial_value="70" name="Trop_conc" units="micromolar"/>
        <variable name="TropTot" units="micromolar"/>
        <variable name="dTropTot" units="micromolar_per_millisecond"/>
        <variable name="dSL" public_interface="in" units="micrometre_per_millisecond"/>
        <variable name="SL" public_interface="in" units="micrometre"/>
        <variable name="dXBpostr" public_interface="in" units="first_order_rate_constant"/>
        <variable name="dXBprer" public_interface="in" units="first_order_rate_constant"/>
        <variable name="dxXBpostr" public_interface="in" units="micrometre_per_millisecond"/>
        <variable name="dxXBprer" public_interface="in" units="micrometre_per_millisecond"/>
        <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="SSXBpostr" public_interface="in" units="dimensionless"/>
        <variable name="SSXBprer" public_interface="in" units="dimensionless"/>
        <variable name="SOVFThick" public_interface="in" units="dimensionless"/>
        <variable name="SOVFThin" public_interface="in" units="dimensionless"/>
        <variable name="len_thin" public_interface="in" units="micrometre"/>
        <variable name="len_thick" public_interface="in" units="micrometre"/>
        <variable name="len_hbare" public_interface="in" units="micrometre"/>
        <variable name="TRPNCaL" public_interface="in" units="dimensionless"/>
        <variable name="TRPNCaH" public_interface="in" units="dimensionless"/>
        <variable name="dTRPNCaL" public_interface="in" units="first_order_rate_constant"/>
        <variable name="dTRPNCaH" public_interface="in" units="first_order_rate_constant"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>FrSBXB</ci>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <ci>XBpostr</ci>
                        <ci>XBprer</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>SSXBpostr</ci>
                        <ci>SSXBprer</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>dFrSBXB</ci>
                <apply>
                    <divide/>
                    <apply>
                        <plus/>
                        <ci>dXBpostr</ci>
                        <ci>dXBprer</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <ci>SSXBpostr</ci>
                        <ci>SSXBprer</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>dsovr_ze</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                            <ci>dSL</ci>
                        </apply>
                        <apply>
                            <lt/>
                            <ci>SL</ci>
                            <ci>len_thick</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="micrometre_per_millisecond">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <ci>dsovr_cle</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">0.5</cn>
                            </apply>
                            <ci>dSL</ci>
                        </apply>
                        <apply>
                            <gt/>
                            <apply>
                                <minus/>
                                <apply>
                                    <times/>
                                    <cn cellml:units="dimensionless">2</cn>
                                    <ci>len_thin</ci>
                                </apply>
                                <ci>SL</ci>
                            </apply>
                            <ci>len_hbare</ci>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="micrometre_per_millisecond">0</cn>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <ci>dlen_sovr</ci>
                <apply>
                    <minus/>
                    <ci>dsovr_ze</ci>
                    <ci>dsovr_cle</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>dSOVFThin</ci>
                <apply>
                    <divide/>
                    <ci>dlen_sovr</ci>
                    <ci>len_thin</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>dSOVFThick</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>dlen_sovr</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>len_thick</ci>
                        <ci>len_hbare</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>TropTot</ci>
                <apply>
                    <times/>
                    <ci>Trop_conc</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>SOVFThin</ci>
                            </apply>
                            <ci>TRPNCaL</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>SOVFThin</ci>
                            <apply>
                                <plus/>
                                <apply>
                                    <times/>
                                    <ci>FrSBXB</ci>
                                    <ci>TRPNCaH</ci>
                                </apply>
                                <apply>
                                    <times/>
                                    <apply>
                                        <minus/>
                                        <cn cellml:units="dimensionless">1</cn>
                                        <ci>FrSBXB</ci>
                                    </apply>
                                    <ci>TRPNCaL</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>dTropTot</ci>
                <apply>
                    <times/>
                    <ci>Trop_conc</ci>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <ci>dSOVFThin</ci>
                            </apply>
                            <ci>TRPNCaL</ci>
                        </apply>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>SOVFThin</ci>
                            </apply>
                            <ci>dTRPNCaL</ci>
                        </apply>
                        <apply>
                            <times/>
                            <ci>dSOVFThin</ci>
                            <apply>
                                <plus/>
                                <apply>
                                    <times/>
                                    <ci>FrSBXB</ci>
                                    <ci>TRPNCaH</ci>
                                </apply>
                                <apply>
                                    <times/>
                                    <apply>
                                        <minus/>
                                        <cn cellml:units="dimensionless">1</cn>
                                        <ci>FrSBXB</ci>
                                    </apply>
                                    <ci>TRPNCaL</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <times/>
                            <ci>SOVFThin</ci>
                            <apply>
                                <minus/>
                                <apply>
                                    <plus/>
                                    <apply>
                                        <times/>
                                        <ci>dFrSBXB</ci>
                                        <ci>TRPNCaH</ci>
                                    </apply>
                                    <apply>
                                        <times/>
                                        <ci>FrSBXB</ci>
                                        <ci>dTRPNCaH</ci>
                                    </apply>
                                    <apply>
                                        <times/>
                                        <apply>
                                            <minus/>
                                            <cn cellml:units="dimensionless">1</cn>
                                            <ci>FrSBXB</ci>
                                        </apply>
                                        <ci>dTRPNCaL</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>dFrSBXB</ci>
                                    <ci>TRPNCaL</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
    </component>
    <component name="model_parameters">
        <variable initial_value="200.0" name="Cai" public_interface="out" units="micromolar"/>
        <variable initial_value="1.2" name="len_thin" public_interface="out" units="micrometre"/>
        <variable initial_value="1.65" name="len_thick" public_interface="out" units="micrometre"/>
        <variable initial_value="0.1" name="len_hbare" public_interface="out" units="micrometre"/>
        <variable initial_value="299" name="TmpC" public_interface="out" units="kelvin"/>
        <variable initial_value="0.007" name="x_0" public_interface="out" units="micrometre"/>
    </component>
    <connection>
        <map_components component_1="Ca_binding_to_troponin_to_thin_filament_regulation" component_2="environment"/>
        <map_variables variable_1="time" variable_2="time"/>
    </connection>
    <connection>
        <map_components component_1="regulation_and_crossbridge_cycling_state_equations" component_2="environment"/>
        <map_variables variable_1="time" variable_2="time"/>
    </connection>
    <connection>
        <map_components component_1="mean_strain_of_strongly_bound_states" component_2="environment"/>
        <map_variables variable_1="time" variable_2="time"/>
    </connection>
    <connection>
        <map_components component_1="normalised_active_and_passive_force" component_2="environment"/>
        <map_variables variable_1="time" variable_2="time"/>
    </connection>
    <connection>
        <map_components component_1="sarcomere_geometry" component_2="normalised_active_and_passive_force"/>
        <map_variables variable_1="SL" variable_2="SL"/>
        <map_variables variable_1="SOVFThick" variable_2="SOVFThick"/>
    </connection>
    <connection>
        <map_components component_1="sarcomere_geometry" component_2="model_parameters"/>
        <map_variables variable_1="len_thin" variable_2="len_thin"/>
        <map_variables variable_1="len_thick" variable_2="len_thick"/>
        <map_variables variable_1="len_hbare" variable_2="len_hbare"/>
    </connection>
    <connection>
        <map_components component_1="Ca_binding_to_troponin_to_thin_filament_regulation" component_2="model_parameters"/>
        <map_variables variable_1="TmpC" variable_2="TmpC"/>
        <map_variables variable_1="Cai" variable_2="Cai"/>
    </connection>
    <connection>
        <map_components component_1="Ca_binding_to_troponin_to_thin_filament_regulation" component_2="sarcomere_geometry"/>
        <map_variables variable_1="SOVFThin" variable_2="SOVFThin"/>
    </connection>
    <connection>
        <map_components component_1="thin_filament_regulation_and_crossbridge_cycling_rates" component_2="model_parameters"/>
        <map_variables variable_1="x_0" variable_2="x_0"/>
        <map_variables variable_1="TmpC" variable_2="TmpC"/>
    </connection>
    <connection>
        <map_components component_1="thin_filament_regulation_and_crossbridge_cycling_rates" component_2="sarcomere_geometry"/>
        <map_variables variable_1="SOVFThick" variable_2="SOVFThick"/>
    </connection>
    <connection>
        <map_components component_1="thin_filament_regulation_and_crossbridge_cycling_rates" component_2="mean_strain_of_strongly_bound_states"/>
        <map_variables variable_1="xXBpostr" variable_2="xXBpostr"/>
        <map_variables variable_1="xXBprer" variable_2="xXBprer"/>
        <map_variables variable_1="fappT" variable_2="fappT"/>
        <map_variables variable_1="gappT" variable_2="gappT"/>
        <map_variables variable_1="hfT" variable_2="hfT"/>
        <map_variables variable_1="hbT" variable_2="hbT"/>
        <map_variables variable_1="gxbT" variable_2="gxbT"/>
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    <connection>
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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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