- Author:
- AnandR <a.rampadarath@auckland.ac.nz>
- Date:
- 2018-12-14 16:04:47+13:00
- Desc:
- Annotated models using Semgen
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/55c/rawfile/a471aae70edb5e9f955c60046d52c99d87e69b44/Niederer_et_al_2006.cellml
<?xml version="1.0"?>
<model xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xml:base="file:///H:/terkildsen_niederer_crampin_hunter_smith_2008/Niederer_et_al_2006.cellml" cmeta:id="Niederer_et_al_2006" name="Niederer_et_al_2006">
<units name="per_ms">
<unit exponent="-1" prefix="milli" units="second"/>
</units>
<units name="ms">
<unit prefix="milli" units="second"/>
</units>
<units name="mM">
<unit prefix="milli" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="N_per_mm2">
<unit units="newton"/>
<unit exponent="-2" prefix="milli" units="metre"/>
</units>
<units name="per_mM_per_ms">
<unit exponent="-1" units="mM"/>
<unit exponent="-1" prefix="milli" units="second"/>
</units>
<units name="mM_per_ms">
<unit units="mM"/>
<unit exponent="-1" prefix="milli" units="second"/>
</units>
<component name="environment">
<variable name="time" public_interface="out" units="ms"/>
</component>
<component cmeta:id="id_00003" name="intracellular_ion_concentrations">
<variable name="time" public_interface="in" units="ms"/>
<variable cmeta:id="id_00001" name="Ca_i" public_interface="out" units="mM"/>
<variable cmeta:id="id_00002" name="Ca_b" public_interface="out" units="mM"/>
<variable cmeta:id="id_00004" initial_value="0.067593139865" name="TRPN" public_interface="out" units="mM"/>
<variable cmeta:id="id_00005" name="Ca_TRPN_Max" public_interface="in" units="mM"/>
<variable cmeta:id="id_00006" name="J_TRPN" public_interface="in" units="mM_per_ms"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Ca_b</ci>
<apply>
<minus/>
<ci>Ca_TRPN_Max</ci>
<ci>TRPN</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>TRPN</ci>
</apply>
<ci>J_TRPN</ci>
</apply>
<apply>
<eq/>
<ci>Ca_i</ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="dimensionless">1000</cn>
<cn type="e-notation" cellml:units="mM">1.8433<sep/>-7</cn>
</apply>
<apply>
<lt/>
<ci>time</ci>
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</apply>
</piece>
<piece>
<apply>
<times/>
<cn cellml:units="dimensionless">1000</cn>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="mM">1.055</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>time</ci>
<cn cellml:units="ms">1000</cn>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="mM">0.03507</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>time</ci>
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</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
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<times/>
<cn cellml:units="mM">0.0003992</cn>
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</apply>
<cn cellml:units="ms">1000</cn>
</apply>
</apply>
<cn type="e-notation" cellml:units="mM">1.356<sep/>-6</cn>
</apply>
</apply>
<apply>
<and/>
<apply>
<geq/>
<ci>time</ci>
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</apply>
<apply>
<lt/>
<ci>time</ci>
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</apply>
</apply>
</piece>
<piece>
<apply>
<times/>
<cn cellml:units="dimensionless">1000</cn>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="mM">0.014</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>time</ci>
<cn cellml:units="ms">1000</cn>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="mM">0.002555</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>time</ci>
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</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="mM">0.0001494</cn>
<ci>time</ci>
</apply>
<cn cellml:units="ms">1000</cn>
</apply>
</apply>
<cn type="e-notation" cellml:units="mM">1.428<sep/>-6</cn>
</apply>
</apply>
<apply>
<and/>
<apply>
<geq/>
<ci>time</ci>
<cn cellml:units="ms">15</cn>
</apply>
<apply>
<lt/>
<ci>time</ci>
<cn cellml:units="ms">55</cn>
</apply>
</apply>
</piece>
<piece>
<apply>
<times/>
<cn cellml:units="dimensionless">1000</cn>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<cn type="e-notation" cellml:units="mM">1.739<sep/>-5</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>time</ci>
<cn cellml:units="ms">1000</cn>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<times/>
<cn type="e-notation" cellml:units="mM">3.209<sep/>-6</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>time</ci>
<cn cellml:units="ms">1000</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn type="e-notation" cellml:units="mM">5.689<sep/>-6</cn>
<ci>time</ci>
</apply>
<cn cellml:units="ms">1000</cn>
</apply>
</apply>
<cn type="e-notation" cellml:units="mM">1.719<sep/>-6</cn>
</apply>
</apply>
<apply>
<and/>
<apply>
<geq/>
<ci>time</ci>
<cn cellml:units="ms">55</cn>
</apply>
<apply>
<lt/>
<ci>time</ci>
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</apply>
</apply>
</piece>
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<apply>
<times/>
<cn cellml:units="dimensionless">1000</cn>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="mM">0.0001321</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>time</ci>
<cn cellml:units="ms">1000</cn>
</apply>
<cn cellml:units="dimensionless">4</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="mM">0.0002197</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>time</ci>
<cn cellml:units="ms">1000</cn>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
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<apply>
<power/>
<apply>
<divide/>
<ci>time</ci>
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</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
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<ci>time</ci>
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</apply>
</apply>
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</apply>
</apply>
<apply>
<and/>
<apply>
<geq/>
<ci>time</ci>
<cn cellml:units="ms">250</cn>
</apply>
<apply>
<lt/>
<ci>time</ci>
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</apply>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<cn cellml:units="dimensionless">1000</cn>
<cn type="e-notation" cellml:units="mM">1.2148<sep/>-7</cn>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component cmeta:id="id_00007" name="thinfilaments"/>
<component cmeta:id="id_00008" name="tropomyosin">
<variable initial_value="0.014417937837" name="z" public_interface="out" units="dimensionless"/>
<variable name="z_max" public_interface="out" units="dimensionless"/>
<variable name="time" public_interface="in" units="ms"/>
<variable name="k_on" public_interface="in" units="per_mM_per_ms"/>
<variable name="k_Ref_off" public_interface="in" units="per_ms"/>
<variable cmeta:id="id_00009" name="gamma_trpn" public_interface="in" units="dimensionless"/>
<variable cmeta:id="id_00011" name="Ca_TRPN_Max" public_interface="in" units="mM"/>
<variable initial_value="8e-3" name="alpha_0" units="per_ms"/>
<variable initial_value="2e-3" name="alpha_r1" units="per_ms"/>
<variable initial_value="1.75e-3" name="alpha_r2" units="per_ms"/>
<variable initial_value="3" name="n_Rel" units="dimensionless"/>
<variable initial_value="0.15" name="K_z" units="dimensionless"/>
<variable initial_value="3" name="n_Hill" units="dimensionless"/>
<variable initial_value="1.05e-3" name="Ca_50ref" units="mM"/>
<variable initial_value="0.85" name="z_p" units="dimensionless"/>
<variable initial_value="-4" name="beta_1" units="dimensionless"/>
<variable name="Ca_50" units="mM"/>
<variable cmeta:id="id_00010" name="Ca_TRPN_50" units="mM"/>
<variable name="K_2" units="per_ms"/>
<variable name="K_1" units="per_ms"/>
<variable name="alpha_Tm" units="per_ms"/>
<variable name="beta_Tm" units="per_ms"/>
<variable name="beta_0" public_interface="in" units="dimensionless"/>
<variable name="Ca_b" public_interface="in" units="mM"/>
<variable name="lambda" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>K_2</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>alpha_r2</ci>
<apply>
<power/>
<ci>z_p</ci>
<ci>n_Rel</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>z_p</ci>
<ci>n_Rel</ci>
</apply>
<apply>
<power/>
<ci>K_z</ci>
<ci>n_Rel</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>n_Rel</ci>
<apply>
<power/>
<ci>K_z</ci>
<ci>n_Rel</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>z_p</ci>
<ci>n_Rel</ci>
</apply>
<apply>
<power/>
<ci>K_z</ci>
<ci>n_Rel</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>K_1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>alpha_r2</ci>
<apply>
<power/>
<ci>z_p</ci>
<apply>
<minus/>
<ci>n_Rel</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
<ci>n_Rel</ci>
<apply>
<power/>
<ci>K_z</ci>
<ci>n_Rel</ci>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<apply>
<power/>
<ci>z_p</ci>
<ci>n_Rel</ci>
</apply>
<apply>
<power/>
<ci>K_z</ci>
<ci>n_Rel</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>z_max</ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<divide/>
<ci>alpha_0</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_TRPN_50</ci>
<ci>Ca_TRPN_Max</ci>
</apply>
<ci>n_Hill</ci>
</apply>
</apply>
<ci>K_2</ci>
</apply>
<apply>
<plus/>
<ci>alpha_r1</ci>
<ci>K_1</ci>
<apply>
<divide/>
<ci>alpha_0</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_TRPN_50</ci>
<ci>Ca_TRPN_Max</ci>
</apply>
<ci>n_Hill</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ca_50</ci>
<apply>
<times/>
<ci>Ca_50ref</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>beta_1</ci>
<apply>
<minus/>
<ci>lambda</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ca_TRPN_50</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Ca_50</ci>
<ci>Ca_TRPN_Max</ci>
</apply>
<apply>
<plus/>
<ci>Ca_50</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>k_Ref_off</ci>
<ci>k_on</ci>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>beta_0</ci>
<apply>
<minus/>
<ci>lambda</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">0.5</cn>
</apply>
<ci>gamma_trpn</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_Tm</ci>
<apply>
<times/>
<ci>alpha_0</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_b</ci>
<ci>Ca_TRPN_50</ci>
</apply>
<ci>n_Hill</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_Tm</ci>
<apply>
<plus/>
<ci>alpha_r1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>alpha_r2</ci>
<apply>
<power/>
<ci>z</ci>
<apply>
<minus/>
<ci>n_Rel</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>z</ci>
<ci>n_Rel</ci>
</apply>
<apply>
<power/>
<ci>K_z</ci>
<ci>n_Rel</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>z</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_Tm</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>z</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_Tm</ci>
<ci>z</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00012" name="troponin">
<variable cmeta:id="id_00013" name="J_TRPN" public_interface="out" units="mM_per_ms"/>
<variable cmeta:id="id_00014" initial_value="70e-3" name="Ca_TRPN_Max" public_interface="out" units="mM"/>
<variable cmeta:id="id_00015" name="TRPN" public_interface="in" units="mM"/>
<variable name="Ca_i" public_interface="in" units="mM"/>
<variable name="k_off" units="per_ms"/>
<variable initial_value="100" name="k_on" public_interface="out" units="per_mM_per_ms"/>
<variable initial_value="0.2" name="k_Ref_off" public_interface="out" units="per_ms"/>
<variable initial_value="2" name="gamma_trpn" public_interface="out" units="dimensionless"/>
<variable name="Tension" public_interface="in" units="N_per_mm2"/>
<variable name="T_ref" public_interface="in" units="N_per_mm2"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>k_off</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>k_Ref_off</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Tension</ci>
<apply>
<times/>
<ci>gamma_trpn</ci>
<ci>T_ref</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<gt/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Tension</ci>
<apply>
<times/>
<ci>gamma_trpn</ci>
<ci>T_ref</ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">0.1</cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<ci>k_Ref_off</ci>
<cn cellml:units="dimensionless">0.1</cn>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>J_TRPN</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<ci>Ca_TRPN_Max</ci>
<ci>TRPN</ci>
</apply>
<ci>k_off</ci>
</apply>
<apply>
<times/>
<ci>Ca_i</ci>
<ci>TRPN</ci>
<ci>k_on</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00016" name="Myofilaments">
<variable name="time" public_interface="in" units="ms"/>
<variable name="lambda" public_interface="out" units="dimensionless"/>
<variable name="ExtensionRatio" public_interface="out" units="dimensionless"/>
<variable name="dExtensionRatiodt" public_interface="out" units="per_ms"/>
<variable name="lambda_prev" public_interface="out" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>ExtensionRatio</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">1</cn>
<apply>
<gt/>
<ci>time</ci>
<cn type="e-notation" cellml:units="ms">3<sep/>5</cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless">1</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>lambda_prev</ci>
<ci>ExtensionRatio</ci>
</apply>
<apply>
<eq/>
<ci>dExtensionRatiodt</ci>
<cn cellml:units="per_ms">0</cn>
</apply>
<apply>
<eq/>
<ci>lambda</ci>
<piecewise>
<piece>
<ci>ExtensionRatio</ci>
<apply>
<and/>
<apply>
<gt/>
<ci>ExtensionRatio</ci>
<cn cellml:units="dimensionless">0.8</cn>
</apply>
<apply>
<leq/>
<ci>ExtensionRatio</ci>
<cn cellml:units="dimensionless">1.15</cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="dimensionless">1.15</cn>
<apply>
<gt/>
<ci>ExtensionRatio</ci>
<cn cellml:units="dimensionless">1.15</cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless">0.8</cn>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component cmeta:id="id_00017" name="filament_overlap">
<variable name="lambda" public_interface="in" units="dimensionless"/>
<variable name="overlap" public_interface="out" units="dimensionless"/>
<variable initial_value="4.9" name="beta_0" public_interface="out" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>overlap</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>beta_0</ci>
<apply>
<minus/>
<ci>lambda</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="length_independent_tension">
<variable initial_value="56.2" name="T_ref" public_interface="out" units="N_per_mm2"/>
<variable name="T_Base" public_interface="out" units="N_per_mm2"/>
<variable name="z" public_interface="in" units="dimensionless"/>
<variable name="z_max" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>T_Base</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>T_ref</ci>
<ci>z</ci>
</apply>
<ci>z_max</ci>
</apply>
</apply>
</math>
</component>
<component name="isometric_tension">
<variable name="T_0" public_interface="out" units="N_per_mm2"/>
<variable name="T_Base" public_interface="in" units="N_per_mm2"/>
<variable name="overlap" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>T_0</ci>
<apply>
<times/>
<ci>T_Base</ci>
<ci>overlap</ci>
</apply>
</apply>
</math>
</component>
<component name="Cross_Bridges">
<variable name="time" public_interface="in" units="ms"/>
<variable name="dExtensionRatiodt" public_interface="in" units="per_ms"/>
<variable name="Q" units="dimensionless"/>
<variable initial_value="0.35" name="a" units="dimensionless"/>
<variable initial_value="0" name="Q_1" units="dimensionless"/>
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<variable initial_value="129" name="A_3" units="dimensionless"/>
<variable initial_value="0.03" name="alpha_1" units="per_ms"/>
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<variable name="T_0" public_interface="in" units="N_per_mm2"/>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<ci>Q</ci>
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<apply>
<eq/>
<ci>Tension</ci>
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<piece>
<apply>
<divide/>
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<ci>T_0</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>a</ci>
<ci>Q</ci>
</apply>
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<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>Q</ci>
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<apply>
<lt/>
<ci>Q</ci>
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<divide/>
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<ci>T_0</ci>
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<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<apply>
<plus/>
<ci>a</ci>
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<ci>Q</ci>
</apply>
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<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>Q</ci>
</apply>
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<bvar>
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<ci>Q_1</ci>
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<apply>
<minus/>
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<ci>A_1</ci>
<ci>dExtensionRatiodt</ci>
</apply>
<apply>
<times/>
<ci>alpha_1</ci>
<ci>Q_1</ci>
</apply>
</apply>
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<apply>
<eq/>
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<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Q_2</ci>
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<apply>
<minus/>
<apply>
<times/>
<ci>A_2</ci>
<ci>dExtensionRatiodt</ci>
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<apply>
<times/>
<ci>alpha_2</ci>
<ci>Q_2</ci>
</apply>
</apply>
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<apply>
<eq/>
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<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Q_3</ci>
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<apply>
<minus/>
<apply>
<times/>
<ci>A_3</ci>
<ci>dExtensionRatiodt</ci>
</apply>
<apply>
<times/>
<ci>alpha_3</ci>
<ci>Q_3</ci>
</apply>
</apply>
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</math>
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