- Author:
- David Nickerson <nickerso@users.sourceforge.net>
- Date:
- 2015-08-12 12:06:21+12:00
- Desc:
- corrections from Kenneth Tran. Removing incorrect scaling of hbT; removing unescessary spring constant to simplify force units
- Permanent Source URI:
- https://models.cellml.org/workspace/tran_2009/rawfile/404213ff066b2ef4a4bbfecacc4220746ec57faf/tran_2009.cellml
<?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#">
<units base_units="yes" name="unit_normalised_force"/>
<units name="unit_normalised_force_millisecond2_per_micrometre">
<unit units="unit_normalised_force"/>
<unit exponent="2" units="millisecond"/>
<unit exponent="-1" units="micrometre"/>
</units>
<units name="unit_normalised_force_millisecond">
<unit units="unit_normalised_force"/>
<unit units="millisecond"/>
</units>
<units name="unit_normalised_force_millisecond_per_micrometre">
<unit units="unit_normalised_force"/>
<unit units="millisecond"/>
<unit exponent="-1" units="micrometre"/>
</units>
<units name="unit_normalised_force_per_micrometre">
<unit units="unit_normalised_force"/>
<unit exponent="-1" units="micrometre"/>
</units>
<units name="micrometre">
<unit prefix="micro" units="metre"/>
</units>
<units name="per_micrometre">
<unit exponent="-1" units="micrometre"/>
</units>
<units name="micrometre_per_millisecond">
<unit units="micrometre"/>
<unit exponent="-1" units="millisecond"/>
</units>
<units name="millisecond_per_micrometre">
<unit units="millisecond"/>
<unit exponent="-1" units="micrometre"/>
</units>
<units name="millisecond">
<unit prefix="milli" units="second"/>
</units>
<units name="millisecond2_per_micrometre">
<unit exponent="2" units="millisecond"/>
<unit exponent="-1" units="micrometre"/>
</units>
<units name="micromolar">
<unit prefix="micro" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="micromolar2">
<unit exponent="2" units="micromolar"/>
</units>
<units name="micromolar_per_millisecond">
<unit units="micromolar"/>
<unit exponent="-1" units="millisecond"/>
</units>
<units name="first_order_rate_constant">
<unit exponent="-1" units="millisecond"/>
</units>
<units name="second_order_rate_constant">
<unit exponent="-1" units="micromolar"/>
<unit exponent="-1" units="millisecond"/>
</units>
<units name="millinewton_per_millimetre2">
<unit prefix="milli" units="newton"/>
<unit exponent="-2" prefix="milli" units="metre"/>
</units>
<units name="millinewton_per_millimetre2_per_millisecond">
<unit prefix="milli" units="newton"/>
<unit exponent="-2" prefix="milli" units="metre"/>
<unit exponent="-1" prefix="milli" units="second"/>
</units>
<component name="environment">
<variable cmeta:id="environment_time" name="time" public_interface="out" units="millisecond"/>
</component>
<component name="sarcomere_geometry">
<variable name="SOVFThick" public_interface="out" units="dimensionless"/>
<variable name="SOVFThin" public_interface="out" units="dimensionless"/>
<variable name="sovr_ze" units="micrometre"/>
<variable name="sovr_cle" units="micrometre"/>
<variable name="len_sovr" units="micrometre"/>
<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="SL" public_interface="in" units="micrometre"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>sovr_ze</ci>
<piecewise>
<piece>
<apply>
<divide/>
<ci>len_thick</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<lt/>
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<divide/>
<ci>len_thick</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<divide/>
<ci>SL</ci>
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</apply>
</apply>
</piece>
<otherwise>
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</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>sovr_cle</ci>
<piecewise>
<piece>
<apply>
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<apply>
<divide/>
<ci>SL</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<minus/>
<ci>SL</ci>
<ci>len_thin</ci>
</apply>
</apply>
<apply>
<gt/>
<apply>
<minus/>
<apply>
<divide/>
<ci>SL</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<minus/>
<ci>SL</ci>
<ci>len_thin</ci>
</apply>
</apply>
<apply>
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</apply>
</apply>
</piece>
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<divide/>
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</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>len_sovr</ci>
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<minus/>
<ci>sovr_ze</ci>
<ci>sovr_cle</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>SOVFThick</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>len_sovr</ci>
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<apply>
<minus/>
<ci>len_thick</ci>
<ci>len_hbare</ci>
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</apply>
</apply>
<apply>
<eq/>
<ci>SOVFThin</ci>
<apply>
<divide/>
<ci>len_sovr</ci>
<ci>len_thin</ci>
</apply>
</apply>
</math>
</component>
<component name="Ca_binding_to_troponin_to_thin_filament_regulation">
<variable initial_value="0.0147730085063734" name="TRPNCaL" public_interface="out" units="dimensionless"/>
<variable initial_value="0.13066096561522" name="TRPNCaH" public_interface="out" units="dimensionless"/>
<variable name="dTRPNCaL" public_interface="out" units="first_order_rate_constant"/>
<variable name="dTRPNCaH" public_interface="out" units="first_order_rate_constant"/>
<variable cmeta:id="Ca_binding_to_troponin_to_thin_filament_regulation_kn_pT" name="kn_pT" public_interface="out" units="first_order_rate_constant"/>
<variable cmeta:id="Ca_binding_to_troponin_to_thin_filament_regulation_kp_nT" name="kp_nT" public_interface="out" units="first_order_rate_constant"/>
<variable cmeta:id="Ca_binding_to_troponin_to_thin_filament_regulation_H" name="H" public_interface="out" units="micromolar"/>
<variable name="H_cons" public_interface="out" units="micromolar"/>
<variable name="konT" units="second_order_rate_constant"/>
<variable name="koffLT" units="first_order_rate_constant"/>
<variable name="koffHT" units="first_order_rate_constant"/>
<variable initial_value="1.5" name="Qkon" units="dimensionless"/>
<variable initial_value="1.3" name="Qkoff" units="dimensionless"/>
<variable initial_value="1.6" name="Qkn_p" units="dimensionless"/>
<variable initial_value="1.6" name="Qkp_n" units="dimensionless"/>
<variable initial_value="0.05" name="kon" units="second_order_rate_constant"/>
<variable initial_value="0.25" name="koffL" units="first_order_rate_constant"/>
<variable initial_value="0.025" name="koffH" units="first_order_rate_constant"/>
<variable initial_value="0.5" name="perm50" units="dimensionless"/>
<variable initial_value="15" name="nperm" units="dimensionless"/>
<variable initial_value="0.5" name="kn_p" units="first_order_rate_constant"/>
<variable initial_value="0.05" name="kp_n" units="first_order_rate_constant"/>
<variable initial_value="1" name="koffmod" units="dimensionless"/>
<variable name="Tropreg" units="dimensionless"/>
<variable name="permtot" units="dimensionless"/>
<variable name="inprmt" units="dimensionless"/>
<variable initial_value="7.15" name="pH" units="dimensionless"/>
<variable initial_value="1" name="m" units="dimensionless"/>
<variable initial_value="2e-2" name="kdHCa" units="micromolar"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="TmpC" public_interface="in" units="celsius"/>
<variable name="Cai" public_interface="in" units="micromolar"/>
<variable name="SOVFThin" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>konT</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<power/>
<ci>kdHCa</ci>
<ci>m</ci>
</apply>
<apply>
<power/>
<ci>H_cons</ci>
<ci>m</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>kdHCa</ci>
<ci>m</ci>
</apply>
<apply>
<power/>
<ci>H</ci>
<ci>m</ci>
</apply>
</apply>
</apply>
<ci>kon</ci>
<apply>
<power/>
<ci>Qkon</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>TmpC</ci>
<cn cellml:units="celsius">37</cn>
</apply>
<cn cellml:units="celsius">10</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>H</ci>
<apply>
<times/>
<cn cellml:units="micromolar">10e6</cn>
<apply>
<power/>
<cn cellml:units="dimensionless">10</cn>
<apply>
<minus/>
<ci>pH</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>H_cons</ci>
<apply>
<times/>
<cn cellml:units="micromolar">10e6</cn>
<apply>
<power/>
<cn cellml:units="dimensionless">10</cn>
<apply>
<minus/>
<cn cellml:units="dimensionless">7.15</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>koffLT</ci>
<apply>
<times/>
<ci>koffL</ci>
<ci>koffmod</ci>
<apply>
<power/>
<ci>Qkoff</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>TmpC</ci>
<cn cellml:units="celsius">37</cn>
</apply>
<cn cellml:units="celsius">10</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>koffHT</ci>
<apply>
<times/>
<ci>koffH</ci>
<ci>koffmod</ci>
<apply>
<power/>
<ci>Qkoff</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>TmpC</ci>
<cn cellml:units="celsius">37</cn>
</apply>
<cn cellml:units="celsius">10</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>kn_pT</ci>
<apply>
<times/>
<ci>kn_p</ci>
<ci>permtot</ci>
<apply>
<power/>
<ci>Qkn_p</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>TmpC</ci>
<cn cellml:units="celsius">37</cn>
</apply>
<cn cellml:units="celsius">10</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>kp_nT</ci>
<apply>
<times/>
<ci>kp_n</ci>
<ci>inprmt</ci>
<apply>
<power/>
<ci>Qkp_n</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>TmpC</ci>
<cn cellml:units="celsius">37</cn>
</apply>
<cn cellml:units="celsius">10</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>permtot</ci>
<apply>
<root/>
<apply>
<abs/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>perm50</ci>
<ci>Tropreg</ci>
</apply>
<ci>nperm</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>inprmt</ci>
<piecewise>
<piece>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<ci>permtot</ci>
</apply>
<apply>
<lt/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<ci>permtot</ci>
</apply>
<cn cellml:units="dimensionless">100</cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless">100</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>TRPNCaL</ci>
</apply>
<ci>dTRPNCaL</ci>
</apply>
<apply>
<eq/>
<ci>dTRPNCaL</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>konT</ci>
<ci>Cai</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>TRPNCaL</ci>
</apply>
</apply>
<apply>
<times/>
<ci>koffLT</ci>
<ci>TRPNCaL</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>TRPNCaH</ci>
</apply>
<ci>dTRPNCaH</ci>
</apply>
<apply>
<eq/>
<ci>dTRPNCaH</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>konT</ci>
<ci>Cai</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>TRPNCaH</ci>
</apply>
</apply>
<apply>
<times/>
<ci>koffHT</ci>
<ci>TRPNCaH</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Tropreg</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>
<ci>TRPNCaH</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="thin_filament_regulation_and_crossbridge_cycling_rates">
<variable cmeta:id="thin_filament_regulation_and_crossbridge_cycling_rates_fappT" name="fappT" public_interface="out" units="first_order_rate_constant"/>
<variable cmeta:id="thin_filament_regulation_and_crossbridge_cycling_rates_gappT" name="gappT" public_interface="out" units="first_order_rate_constant"/>
<variable cmeta:id="thin_filament_regulation_and_crossbridge_cycling_rates_hfT" name="hfT" public_interface="out" units="first_order_rate_constant"/>
<variable cmeta:id="thin_filament_regulation_and_crossbridge_cycling_rates_hbT" name="hbT" public_interface="out" units="first_order_rate_constant"/>
<variable cmeta:id="thin_filament_regulation_and_crossbridge_cycling_rates_gxbT" name="gxbT" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.5" name="fapp" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.07" name="gapp" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="2" name="hf" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.4" name="hb" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="0.07" name="gxb" public_interface="out" units="first_order_rate_constant"/>
<variable initial_value="6" name="gslmod" units="dimensionless"/>
<variable name="hfmd" units="dimensionless"/>
<variable name="hbmd" units="dimensionless"/>
<variable initial_value="5" name="hfmdc" units="dimensionless"/>
<variable initial_value="0" name="hbmdc" units="dimensionless"/>
<variable initial_value="8" name="sigmap" units="dimensionless"/>
<variable initial_value="1" name="sigman" units="dimensionless"/>
<variable initial_value="0.2" name="xbmodsp" units="dimensionless"/>
<variable initial_value="6.25" name="Qfapp" units="dimensionless"/>
<variable initial_value="2.5" name="Qgapp" units="dimensionless"/>
<variable initial_value="6.25" name="Qhf" units="dimensionless"/>
<variable initial_value="6.25" name="Qhb" units="dimensionless"/>
<variable initial_value="6.25" name="Qgxb" units="dimensionless"/>
<variable name="gxbmd" units="dimensionless"/>
<variable name="gapslmd" units="dimensionless"/>
<variable name="x_0" public_interface="in" units="micrometre"/>
<variable name="TmpC" public_interface="in" units="celsius"/>
<variable name="SOVFThick" public_interface="in" units="dimensionless"/>
<variable name="xXBpostr" public_interface="in" units="micrometre"/>
<variable name="xXBprer" public_interface="in" units="micrometre"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>fappT</ci>
<apply>
<times/>
<ci>fapp</ci>
<ci>xbmodsp</ci>
<apply>
<power/>
<ci>Qfapp</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>TmpC</ci>
<cn cellml:units="celsius">37</cn>
</apply>
<cn cellml:units="celsius">10</cn>
</apply>
</apply>
</apply>
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<apply>
<eq/>
<ci>gapslmd</ci>
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<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>SOVFThick</ci>
</apply>
<ci>gslmod</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>gappT</ci>
<apply>
<times/>
<ci>gapp</ci>
<ci>gapslmd</ci>
<ci>xbmodsp</ci>
<apply>
<power/>
<ci>Qgapp</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>TmpC</ci>
<cn cellml:units="celsius">37</cn>
</apply>
<cn cellml:units="celsius">10</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>hfmd</ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<minus/>
<ci>xXBprer</ci>
</apply>
<apply>
<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>
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<apply>
<eq/>
<ci>hfT</ci>
<apply>
<times/>
<ci>hf</ci>
<ci>hfmd</ci>
<ci>xbmodsp</ci>
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<power/>
<ci>Qhf</ci>
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<divide/>
<apply>
<minus/>
<ci>TmpC</ci>
<cn cellml:units="celsius">37</cn>
</apply>
<cn cellml:units="celsius">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="celsius">37</cn>
</apply>
<cn cellml:units="celsius">10</cn>
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</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>
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</apply>
</apply>
<apply>
<lt/>
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<ci>x_0</ci>
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</piece>
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<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="celsius">37</cn>
</apply>
<cn cellml:units="celsius">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="Fnordv" units="millinewton_per_millimetre2"/>
<variable name="force" units="millinewton_per_millimetre2"/>
<variable name="active" units="unit_normalised_force"/>
<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"/>
<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>Fnordv</ci>
<apply>
<times/>
<ci>x_0</ci>
<ci>SSXBpostr</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>force</ci>
<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>
<apply>
<eq/>
<ci>active</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="unit_normalised_force">1</cn>
<ci>force</ci>
</apply>
<ci>Fnordv</ci>
</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>
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The Creation Date metadata. This is the date on which the model
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The Tran et al. 2009 metabolite-sensitive, thermodynamically-constrained model of cardiac cross-bridge cycling
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This is the CellML description of Tran et al's 2009 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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