- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2007-06-15 02:01:03+12:00
- Desc:
- committing version02 of iribe_kohl_noble_2006
- Permanent Source URI:
- https://models.cellml.org/workspace/iribe_kohl_noble_2006/rawfile/a9c9ef6570c7cb6283f7b7f975b4f946c0c6994d/iribe_kohl_noble_2006.cellml
<?xml version='1.0' encoding='utf-8'?>
<!--
This CellML file was generated on 2006/02/10 at 0:33:55 using:
COR (0.9.31.217)
Copyright 2002-2006 Oxford Cardiac Electrophysiology Group
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk
CellML 1.0 was used to generate this cellular model
http://www.CellML.org/
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<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<section id="sec_status">
<title>Model Status</title>
<para>
This model was created by Penny Noble of Oxford University. An unsupported predefined operator diff error in component intracellular_calcium_concentration was fixed to allow the model to run in PCEnv (19/04/07, James Lawson.) A stimulus protocol was then added to allow simulation of trains of action potentials (JL, 15/06/07.) This file is known to run COR and PCEnv. A PCEnv session file is also associated with this model.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
This model was based on the paper:
</para>
<para>
Modulatory effect of calmodulin-dependent kinase II (CaMKII) on sarcoplasmic reticulum Ca2+ handling and interval-force relations: a modelling study.
</para>
<para>
by Iribe G, Kohl P, Noble D
</para>
<para>
Philos Transact A Math Phys Eng Sci. 2006 May 15;364(1842):1107-33
</para>
<para>
ABSTRACT:
</para>
<para>
We hypothesize that slow inactivation of Ca2+/calmodulin-dependent kinase II (CaMKII) and its modulatory effect on sarcoplasmic reticulum (SR) Ca2+ handling are important for various interval-force (I-F) relations, in particular for the beat interval dependency in transient alternans during the decay of post-extrasystolic potentiation. We have developed a mathematical model of a single cardiomyocyte to integrate various I-F relations, including alternans, by incorporating a conceptual CaMKII kinetics model into the SR Ca2+ handling model. Our model integrates I-F relations, such as the beat interval-dependent twitch force duration, restitution and potentiation, positive staircase phenomenon and alternans. We found that CaMKII affects more or less all I-F relations, and it is a key factor for integration of the various I-F relations in our model. Alternans arises, in the model, out of a steep relation between SR Ca2+ load and release, owing to SR load-dependent changes in the releasability of Ca2+ via the ryanodine receptor. Beat interval-dependent CaMKII activity, owing to its kinetic properties and amplifying effect on SR Ca2+ load dependency of Ca2+ release, replicated the beat interval dependency of alternans, as observed experimentally. Additionally, our model enabled reproduction of the effects of various interventions on alternans, such as the slowing or accelerating of Ca2+ release and/or uptake. We conclude that a slow time-dependent factor, represented in the model by CaMKII, is important for the integration of I-F relations, including alternans, and that our model offers a useful tool for further analysis of the roles of integrative Ca2+ handling in myocardial I-F relations.
</para>
</sect1>
</article>
</documentation>
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<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_current">
<variable units="nanoA" public_interface="out" name="i_to"/>
<variable units="microS" name="g_to" initial_value="0.005"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="s"/>
<variable units="dimensionless" private_interface="in" name="r"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_to</ci>
<apply>
<times/>
<ci>g_to</ci>
<ci>s</ci>
<ci>r</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_current_s_gate">
<variable units="dimensionless" public_interface="out" name="s" initial_value="0.95854"/>
<variable units="per_second" name="alpha_s"/>
<variable units="per_second" name="beta_s"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_s</ci>
<apply>
<times/>
<cn cellml:units="per_second">0.033</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">17</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_s</ci>
<apply>
<divide/>
<cn cellml:units="per_second">33</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0.125</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>s</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_s</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>s</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_s</ci>
<ci>s</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="transient_outward_current_r_gate">
<variable units="dimensionless" public_interface="out" name="r" initial_value="1.5185e-8"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>r</ci>
</apply>
<apply>
<times/>
<cn cellml:units="per_second">333</cn>
<apply>
<minus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">4</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">5</cn>
</apply>
</apply>
</apply>
</apply>
<ci>r</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel">
<variable units="nanoA" public_interface="out" cmeta:id="L_type_Ca_channel_i_Ca_L" name="i_Ca_L"/>
<variable units="nanoA" public_interface="out" name="i_Ca_L_Na"/>
<variable units="nanoA" public_interface="out" name="i_Ca_L_K"/>
<variable units="nanoA" public_interface="out" name="i_Ca_L_Ca"/>
<variable units="nanoA_per_millimolar" name="P_Ca_L_Ca" initial_value="0.25"/>
<variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millimolar" public_interface="in" name="Ca_o"/>
<variable units="millimolar" public_interface="in" private_interface="out" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="K_o"/>
<variable units="millimolar" public_interface="in" name="K_i"/>
<variable units="millimolar" public_interface="in" name="Na_o"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="dimensionless" private_interface="in" name="d"/>
<variable units="dimensionless" private_interface="in" name="f"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Ca_L_Ca</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>d</ci>
<ci>f</ci>
<ci>P_Ca_L_Ca</ci>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>Ca_i</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">100</cn>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>Ca_o</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_Ca_L_K</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.002</cn>
<ci>d</ci>
<ci>f</ci>
<ci>P_Ca_L_Ca</ci>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>K_i</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">50</cn>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>K_o</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_Ca_L_Na</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.01</cn>
<ci>d</ci>
<ci>f</ci>
<ci>P_Ca_L_Ca</ci>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>Na_i</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">50</cn>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>Na_o</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_Ca_L</ci>
<apply>
<plus/>
<ci>i_Ca_L_Ca</ci>
<ci>i_Ca_L_K</ci>
<ci>i_Ca_L_Na</ci>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_d_gate">
<variable units="dimensionless" public_interface="out" name="d" initial_value="1.7908e-8"/>
<variable units="per_second" name="alpha_d"/>
<variable units="per_second" name="beta_d"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" name="E0_d"/>
<variable units="dimensionless" name="speed_d" initial_value="3"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E0_d</ci>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">24</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_d</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>speed_d</ci>
<cn cellml:units="per_second">120</cn>
</apply>
<apply>
<lt/>
<apply>
<abs/>
<ci>E0_d</ci>
</apply>
<cn cellml:units="millivolt">0.00001</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<ci>speed_d</ci>
<cn cellml:units="per_millivolt_second">30</cn>
<ci>E0_d</ci>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>E0_d</ci>
</apply>
<cn cellml:units="millivolt">4</cn>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>beta_d</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>speed_d</ci>
<cn cellml:units="per_second">120</cn>
</apply>
<apply>
<lt/>
<apply>
<abs/>
<ci>E0_d</ci>
</apply>
<cn cellml:units="millivolt">0.00001</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<ci>speed_d</ci>
<apply>
<minus/>
<cn cellml:units="per_millivolt_second">12</cn>
</apply>
<ci>E0_d</ci>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<ci>E0_d</ci>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>d</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_d</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>d</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_d</ci>
<ci>d</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_channel_f_gate">
<variable units="dimensionless" public_interface="out" name="f" initial_value="1"/>
<variable units="per_second" name="alpha_f"/>
<variable units="per_second" name="beta_f"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="dimensionless" name="speed_f" initial_value="0.5"/>
<variable units="millivolt" name="E0_f"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E0_f</ci>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">34</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_f</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>speed_f</ci>
<cn cellml:units="per_second">25</cn>
</apply>
<apply>
<lt/>
<apply>
<abs/>
<ci>E0_f</ci>
</apply>
<cn cellml:units="millivolt">0.00001</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<ci>speed_f</ci>
<cn cellml:units="per_millivolt_second">6.25</cn>
<ci>E0_f</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>E0_f</ci>
<cn cellml:units="millivolt">4</cn>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>beta_f</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>speed_f</ci>
<cn cellml:units="per_second">50</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>E0_f</ci>
</apply>
<cn cellml:units="millivolt">4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_f</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>f</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_f</ci>
<ci>f</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_calcium_exchanger">
<variable units="nanoA" public_interface="out" name="i_NaCa"/>
<variable units="nanoA" name="i_NaCa_max" initial_value="0.0005"/>
<variable units="dimensionless" name="gamma" initial_value="0.5"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millimolar" public_interface="in" name="Na_o"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_o"/>
<variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaCa</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>i_NaCa_max</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>gamma</ci>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_o</ci>
</apply>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>gamma</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci>Na_o</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Ca_i</ci>
<cn cellml:units="millimolar">0.0069</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_potassium_pump">
<variable units="nanoA" public_interface="out" name="i_NaK"/>
<variable units="nanoA" name="i_NaK_max" initial_value="1.36"/>
<variable units="millimolar" name="K_mK" initial_value="1"/>
<variable units="millimolar" name="K_mNa" initial_value="21.7"/>
<variable units="millimolar" public_interface="in" name="K_o"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaK</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>i_NaK_max</ci>
<ci>K_o</ci>
</apply>
<apply>
<plus/>
<ci>K_mK</ci>
<ci>K_o</ci>
</apply>
</apply>
<ci>Na_i</ci>
</apply>
<apply>
<plus/>
<ci>K_mNa</ci>
<ci>Na_i</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.1245</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0.1</cn>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.0353</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_background_current">
<variable units="nanoA" public_interface="out" name="i_b_Ca"/>
<variable units="microS" name="g_b_Ca" initial_value="0.00025"/>
<variable units="millivolt" public_interface="in" name="E_Ca"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_b_Ca</ci>
<apply>
<times/>
<ci>g_b_Ca</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ca</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="potassium_background_current">
<variable units="nanoA" public_interface="out" name="i_b_K"/>
<variable units="microS" name="g_b_K" initial_value="0.0006"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_b_K</ci>
<apply>
<times/>
<ci>g_b_K</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_background_current">
<variable units="nanoA" public_interface="out" name="i_b_Na"/>
<variable units="microS" name="g_b_Na" initial_value="0.0006"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_b_Na</ci>
<apply>
<times/>
<ci>g_b_Na</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="CaMKII_factor">
<variable units="dimensionless" public_interface="out" name="F_CaMK" initial_value="1.028"/>
<variable units="dimensionless" name="Inf_CaMK"/>
<variable units="second" name="Tau_CaMK" initial_value="0.8"/>
<variable units="millimolar" public_interface="in" name="Cmdn_Ca"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Inf_CaMK</ci>
<apply>
<divide/>
<ci>Cmdn_Ca</ci>
<cn cellml:units="dimensionless">0.00005</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>F_CaMK</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>Inf_CaMK</ci>
<ci>F_CaMK</ci>
</apply>
<ci>Tau_CaMK</ci>
</apply>
</apply>
</math>
</component>
<component name="RyR">
<variable units="millimolar_per_second" public_interface="out" name="j_rel"/>
<variable units="per_second" name="K_rel"/>
<variable units="dimensionless" name="F_rel"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_SR"/>
<variable units="nanoA" public_interface="in" name="i_Ca_L"/>
<variable units="dimensionless" public_interface="in" name="F_CaMK"/>
<variable units="per_second" name="K_rel_max" initial_value="500"/>
<variable units="dimensionless" name="F_SRCa_RyR" initial_value="0.25089"/>
<variable units="second" name="Tau_SRCa_RyR" initial_value="0.05"/>
<variable units="dimensionless" name="N_CaMK"/>
<variable units="dimensionless" name="gain_k1" initial_value="1"/>
<variable units="dimensionless" name="gain_k2" initial_value="1"/>
<variable units="dimensionless" name="gain_k3" initial_value="1"/>
<variable units="dimensionless" name="gain_k4" initial_value="1"/>
<variable units="per_second" name="k_1"/>
<variable units="per_second" name="k_2"/>
<variable units="per_second" name="k_3"/>
<variable units="per_second" name="k_4"/>
<variable units="dimensionless" name="F_1" initial_value="0.5268"/>
<variable units="dimensionless" name="F_2" initial_value="8.7508e-6"/>
<variable units="dimensionless" name="F_3"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>N_CaMK</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>F_CaMK</ci>
<cn cellml:units="dimensionless">0.7</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>k_1</ci>
<apply>
<times/>
<ci>gain_k1</ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless">30625000</cn>
<apply>
<power/>
<ci>Ca_i</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">245</cn>
<ci>i_Ca_L</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k_2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>gain_k2</ci>
<cn cellml:units="dimensionless">450</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.36</cn>
<ci>Ca_SR</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k_3</ci>
<apply>
<times/>
<ci>gain_k3</ci>
<cn cellml:units="dimensionless">1.885</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>F_SRCa_RyR</ci>
<cn cellml:units="dimensionless">0.22</cn>
</apply>
<ci>N_CaMK</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k_4</ci>
<apply>
<times/>
<ci>gain_k4</ci>
<cn cellml:units="dimensionless">1.8</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>F_1</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>k_3</ci>
<ci>F_3</ci>
</apply>
<apply>
<times/>
<ci>k_4</ci>
<ci>F_1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_1</ci>
<ci>F_1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>F_2</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_1</ci>
<ci>F_1</ci>
</apply>
<apply>
<times/>
<ci>k_2</ci>
<ci>F_2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>F_3</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>F_1</ci>
<ci>F_2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>F_rel</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>F_2</ci>
<apply>
<plus/>
<ci>F_2</ci>
<cn cellml:units="dimensionless">0.25</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>F_SRCa_RyR</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ca_SR</ci>
<ci>F_SRCa_RyR</ci>
</apply>
<ci>Tau_SRCa_RyR</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>K_rel</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>K_rel_max</ci>
<ci>F_SRCa_RyR</ci>
</apply>
<apply>
<plus/>
<ci>F_SRCa_RyR</ci>
<cn cellml:units="dimensionless">0.2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>j_rel</ci>
<apply>
<times/>
<ci>K_rel</ci>
<ci>F_rel</ci>
<apply>
<minus/>
<ci>Ca_SR</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="SERCA">
<variable units="millimolar_per_second" public_interface="out" name="j_up"/>
<variable units="dimensionless" public_interface="in" name="F_CaMK"/>
<variable units="millimolar_per_second" name="V_max_f" initial_value="0.292"/>
<variable units="millimolar_per_second" name="V_max_r" initial_value="0.391"/>
<variable units="dimensionless" name="f_b"/>
<variable units="dimensionless" name="r_b"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_SR"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f_b</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<cn cellml:units="dimensionless">0.00024</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>r_b</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_SR</ci>
<cn cellml:units="dimensionless">1.64</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>j_up</ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>F_CaMK</ci>
<ci>V_max_f</ci>
<ci>f_b</ci>
</apply>
<apply>
<times/>
<ci>V_max_r</ci>
<ci>r_b</ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<ci>f_b</ci>
<ci>r_b</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calmodulin">
<variable units="millimolar" public_interface="out" name="Cmdn_Ca" initial_value="3.9636e-6"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" name="Cmdn_tot" initial_value="0.02"/>
<variable units="per_millimolar_per_second" name="alpha_cmdn" initial_value="10000"/>
<variable units="per_second" name="beta_cmdn" initial_value="500"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>dCmdn_Ca_dtime</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_cmdn</ci>
<apply>
<minus/>
<ci>Cmdn_tot</ci>
<ci>Cmdn_Ca</ci>
</apply>
<ci>Ca_i</ci>
</apply>
<apply>
<times/>
<ci>beta_cmdn</ci>
<ci>Cmdn_Ca</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>dCmdn_Ca_dtime</ci>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Cmdn_Ca</ci>
</apply>
</apply>
</math>
<variable units="millimolar_per_second" public_interface="out" name="dCmdn_Ca_dtime"/>
</component>
<component name="troponin">
<variable units="millimolar" public_interface="out" name="Trpn_Ca" initial_value="2.7661e-4"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="out" name="Trpn_tot" initial_value="0.07"/>
<variable units="per_millimolar_per_second" public_interface="out" name="alpha_trpn" initial_value="80000"/>
<variable units="per_second" public_interface="out" name="beta_trpn" initial_value="200"/>
<variable units="dimensionless" public_interface="in" name="Force_norm"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>dTrpn_Ca_dtime</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_trpn</ci>
<apply>
<minus/>
<ci>Trpn_tot</ci>
<ci>Trpn_Ca</ci>
</apply>
<ci>Ca_i</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>beta_trpn</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>Force_norm</ci>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Trpn_Ca</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>dTrpn_Ca_dtime</ci>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Trpn_Ca</ci>
</apply>
</apply>
</math>
<variable units="millimolar_per_second" public_interface="out" name="dTrpn_Ca_dtime"/>
</component>
<component name="intracellular_calcium_concentration">
<variable units="millimolar" public_interface="out" name="Ca_i" initial_value="9.91e-6"/>
<variable units="nanoA" public_interface="in" name="i_Ca_L_Ca"/>
<variable units="nanoA" public_interface="in" name="i_b_Ca"/>
<variable units="nanoA" public_interface="in" name="i_NaCa"/>
<variable units="millimolar" public_interface="in" name="Cmdn_Ca"/>
<variable units="millimolar" public_interface="in" name="Trpn_Ca"/>
<variable units="millimolar_per_second" public_interface="in" name="j_rel"/>
<variable units="millimolar_per_second" public_interface="in" name="j_up"/>
<variable units="microlitre" public_interface="in" name="v_SR"/>
<variable units="microlitre" public_interface="in" name="v_i"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_i</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_Ca_L_Ca</ci>
<ci>i_b_Ca</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_NaCa</ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>v_i</ci>
<ci>F</ci>
</apply>
<ci>j_up</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>j_rel</ci>
<ci>v_SR</ci>
</apply>
<ci>v_i</ci>
</apply>
</apply>
<ci>dCmdn_Ca_dtime</ci>
</apply>
<ci>dTrpn_Ca_dtime</ci>
</apply>
</apply>
</math>
<variable units="millimolar_per_second" public_interface="in" name="dCmdn_Ca_dtime"/>
<variable units="millimolar_per_second" public_interface="in" name="dTrpn_Ca_dtime"/>
</component>
<component name="SR_calcium_concentration">
<variable units="millimolar" public_interface="out" name="Ca_SR" initial_value="0.24886"/>
<variable units="millimolar_per_second" public_interface="in" name="j_rel"/>
<variable units="millimolar_per_second" public_interface="in" name="j_up"/>
<variable units="microlitre" public_interface="in" name="v_SR"/>
<variable units="microlitre" public_interface="in" name="v_i"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_SR</ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>j_up</ci>
<ci>v_i</ci>
</apply>
<ci>v_SR</ci>
</apply>
<ci>j_rel</ci>
</apply>
</apply>
</math>
</component>
<component name="intracellular_sodium_concentration">
<variable units="millimolar" public_interface="out" name="Na_i" initial_value="5.8041"/>
<variable units="nanoA" public_interface="in" name="i_Na"/>
<variable units="nanoA" public_interface="in" name="i_b_Na"/>
<variable units="nanoA" public_interface="in" name="i_Ca_L_Na"/>
<variable units="nanoA" public_interface="in" name="i_NaCa"/>
<variable units="nanoA" public_interface="in" name="i_NaK"/>
<variable units="microlitre" public_interface="in" name="v_i"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Na_i</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_Na</ci>
<ci>i_b_Na</ci>
<ci>i_Ca_L_Na</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_NaCa</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_NaK</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>v_i</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_potassium_concentration">
<variable units="millimolar" public_interface="out" name="K_i" initial_value="138.22"/>
<variable units="nanoA" public_interface="in" name="i_K1"/>
<variable units="nanoA" public_interface="in" name="i_K"/>
<variable units="nanoA" public_interface="in" name="i_to"/>
<variable units="nanoA" public_interface="in" name="i_b_K"/>
<variable units="nanoA" public_interface="in" name="i_Ca_L_K"/>
<variable units="nanoA" public_interface="in" name="i_NaK"/>
<variable units="microlitre" public_interface="in" name="v_i"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K_i</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_K1</ci>
<ci>i_K</ci>
<ci>i_to</ci>
<ci>i_b_K</ci>
<ci>i_Ca_L_K</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_NaK</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>v_i</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="Force">
<variable units="N_per_mm2" cmeta:id="Force_Force" name="Force"/>
<variable units="N_per_mm2" name="zeta" initial_value="0.1"/>
<variable units="dimensionless" name="Force_max"/>
<variable units="dimensionless" name="phi_SL"/>
<variable units="dimensionless" name="P_1_max"/>
<variable units="dimensionless" name="P_2_max"/>
<variable units="dimensionless" name="P_3_max"/>
<variable units="dimensionless" name="sigma_paths"/>
<variable units="dimensionless" name="N_0" initial_value="0.99917"/>
<variable units="dimensionless" name="P_0" initial_value="9.8593e-5"/>
<variable units="dimensionless" name="P_1" initial_value="1.3331e-4"/>
<variable units="dimensionless" name="P_2" initial_value="2.3505e-4"/>
<variable units="dimensionless" name="P_3" initial_value="1.5349e-4"/>
<variable units="dimensionless" name="N_1"/>
<variable units="per_second" name="alpha_tm"/>
<variable units="per_second" name="beta_tm" initial_value="40"/>
<variable units="dimensionless" name="K_tm"/>
<variable units="dimensionless" name="N_tm"/>
<variable units="micrometre" name="SL" initial_value="2.15"/>
<variable units="dimensionless" name="SL_norm"/>
<variable units="per_second" name="f_01"/>
<variable units="per_second" name="f_12"/>
<variable units="per_second" name="f_23"/>
<variable units="per_second" name="g_01"/>
<variable units="per_second" name="g_12"/>
<variable units="per_second" name="g_23"/>
<variable units="per_second" name="f_XB" initial_value="10"/>
<variable units="per_second" name="g_XB" initial_value="30"/>
<variable units="millimolar" public_interface="in" name="Trpn_Ca"/>
<variable units="millimolar" public_interface="in" name="Trpn_tot"/>
<variable units="per_millimolar_per_second" public_interface="in" name="alpha_trpn"/>
<variable units="per_second" public_interface="in" name="beta_trpn"/>
<variable units="dimensionless" public_interface="out" name="Force_norm"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f_01</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>f_XB</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>f_12</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">10</cn>
<ci>f_XB</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>f_23</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">7</cn>
<ci>f_XB</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>g_01</ci>
<apply>
<times/>
<ci>g_XB</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
<ci>SL_norm</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>g_12</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>g_XB</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
<ci>SL_norm</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>g_23</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>g_XB</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">2</cn>
<ci>SL_norm</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>SL_norm</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>SL</ci>
<cn cellml:units="micrometre">1.7</cn>
</apply>
<cn cellml:units="micrometre">0.7</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>N_tm</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">3.5</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">2.5</cn>
<ci>SL_norm</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>K_tm</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<divide/>
<ci>beta_trpn</ci>
<ci>alpha_trpn</ci>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">0.0017</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.0009</cn>
<ci>SL_norm</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_tm</ci>
<apply>
<times/>
<ci>beta_tm</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Trpn_Ca</ci>
<apply>
<times/>
<ci>Trpn_tot</ci>
<ci>K_tm</ci>
</apply>
</apply>
<ci>N_tm</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>N_0</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>beta_tm</ci>
<ci>P_0</ci>
</apply>
<apply>
<times/>
<ci>alpha_tm</ci>
<ci>N_0</ci>
</apply>
</apply>
<apply>
<times/>
<ci>g_01</ci>
<ci>N_1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_0</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci>beta_tm</ci>
<ci>f_01</ci>
</apply>
</apply>
<ci>P_0</ci>
</apply>
<apply>
<times/>
<ci>alpha_tm</ci>
<ci>N_0</ci>
</apply>
<apply>
<times/>
<ci>g_01</ci>
<ci>P_1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_1</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci>beta_tm</ci>
<ci>f_12</ci>
<ci>g_01</ci>
</apply>
</apply>
<ci>P_1</ci>
</apply>
<apply>
<times/>
<ci>alpha_tm</ci>
<ci>N_1</ci>
</apply>
<apply>
<times/>
<ci>f_01</ci>
<ci>P_0</ci>
</apply>
<apply>
<times/>
<ci>g_12</ci>
<ci>P_2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_2</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci>f_23</ci>
<ci>g_12</ci>
</apply>
</apply>
<ci>P_2</ci>
</apply>
<apply>
<times/>
<ci>f_12</ci>
<ci>P_1</ci>
</apply>
<apply>
<times/>
<ci>g_23</ci>
<ci>P_3</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_3</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>g_23</ci>
</apply>
<ci>P_3</ci>
</apply>
<apply>
<times/>
<ci>f_23</ci>
<ci>P_2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>N_1</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>N_0</ci>
<ci>P_0</ci>
<ci>P_1</ci>
<ci>P_2</ci>
<ci>P_3</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>sigma_paths</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>g_XB</ci>
<cn cellml:units="dimensionless">2</cn>
<ci>g_XB</ci>
<cn cellml:units="dimensionless">3</cn>
<ci>g_XB</ci>
</apply>
<apply>
<times/>
<ci>f_01</ci>
<cn cellml:units="dimensionless">2</cn>
<ci>g_XB</ci>
<cn cellml:units="dimensionless">3</cn>
<ci>g_XB</ci>
</apply>
<apply>
<times/>
<ci>f_01</ci>
<ci>f_12</ci>
<cn cellml:units="dimensionless">3</cn>
<ci>g_XB</ci>
</apply>
<apply>
<times/>
<ci>f_01</ci>
<ci>f_12</ci>
<ci>f_23</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>P_1_max</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>f_01</ci>
<cn cellml:units="dimensionless">2</cn>
<ci>g_XB</ci>
<cn cellml:units="dimensionless">3</cn>
<ci>g_XB</ci>
</apply>
<ci>sigma_paths</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_2_max</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>f_01</ci>
<ci>f_12</ci>
<cn cellml:units="dimensionless">3</cn>
<ci>g_XB</ci>
</apply>
<ci>sigma_paths</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_3_max</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>f_01</ci>
<ci>f_12</ci>
<ci>f_23</ci>
</apply>
<ci>sigma_paths</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Force_max</ci>
<apply>
<plus/>
<ci>P_1_max</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>P_2_max</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>P_3_max</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>phi_SL</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<minus/>
<ci>SL</ci>
<cn cellml:units="micrometre">0.6</cn>
</apply>
<cn cellml:units="micrometre">1.4</cn>
</apply>
<apply>
<and/>
<apply>
<geq/>
<ci>SL</ci>
<cn cellml:units="micrometre">1.7</cn>
</apply>
<apply>
<leq/>
<ci>SL</ci>
<cn cellml:units="micrometre">2</cn>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="dimensionless">1</cn>
<apply>
<and/>
<apply>
<gt/>
<ci>SL</ci>
<cn cellml:units="micrometre">2</cn>
</apply>
<apply>
<leq/>
<ci>SL</ci>
<cn cellml:units="micrometre">2.2</cn>
</apply>
</apply>
</piece>
<piece>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="micrometre">3.6</cn>
<ci>SL</ci>
</apply>
<cn cellml:units="micrometre">1.4</cn>
</apply>
<apply>
<and/>
<apply>
<gt/>
<ci>SL</ci>
<cn cellml:units="micrometre">2.2</cn>
</apply>
<apply>
<leq/>
<ci>SL</ci>
<cn cellml:units="micrometre">2.3</cn>
</apply>
</apply>
</piece>
</piecewise>
</apply>
<apply>
<eq/>
<ci>Force_norm</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>phi_SL</ci>
<apply>
<plus/>
<ci>P_1</ci>
<ci>N_1</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>P_2</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>P_3</ci>
</apply>
</apply>
</apply>
<ci>Force_max</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Force</ci>
<apply>
<times/>
<ci>zeta</ci>
<ci>Force_norm</ci>
</apply>
</apply>
</math>
</component>
<component name="stimulus_protocol">
<variable units="nanoA" public_interface="out" cmeta:id="stimulus_protocol_Istim" name="Istim"/>
<variable units="second" cmeta:id="stimulus_protocol_IstimStart" name="IstimStart" initial_value="0.1"/>
<variable units="second" cmeta:id="stimulus_protocol_IstimEnd" name="IstimEnd" initial_value="50000"/>
<variable units="nanoA" cmeta:id="stimulus_protocol_IstimAmplitude" name="IstimAmplitude" initial_value="-4"/>
<variable units="second" cmeta:id="stimulus_protocol_IstimPeriod" name="IstimPeriod" initial_value="1"/>
<variable units="second" cmeta:id="stimulus_protocol_IstimPulseDuration" name="IstimPulseDuration" initial_value="0.002"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="Stimulus_Current_Equation">
<apply>
<eq/>
<ci>Istim</ci>
<piecewise>
<piece>
<ci>IstimAmplitude</ci>
<apply>
<and/>
<apply>
<geq/>
<ci>time</ci>
<ci>IstimStart</ci>
</apply>
<apply>
<leq/>
<ci>time</ci>
<ci>IstimEnd</ci>
</apply>
<apply>
<leq/>
<apply>
<minus/>
<apply>
<minus/>
<ci>time</ci>
<ci>IstimStart</ci>
</apply>
<apply>
<times/>
<apply>
<floor/>
<apply>
<divide/>
<apply>
<minus/>
<ci>time</ci>
<ci>IstimStart</ci>
</apply>
<ci>IstimPeriod</ci>
</apply>
</apply>
<ci>IstimPeriod</ci>
</apply>
</apply>
<ci>IstimPulseDuration</ci>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="nanoA">0</cn>
</otherwise>
</piecewise>
</apply>
</math>
<variable units="second" public_interface="in" name="time"/>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="Force">
<component_ref component="troponin"/>
</component_ref>
<component_ref component="CaMKII_factor">
<component_ref component="membrane_potential"/>
<component_ref component="RyR"/>
<component_ref component="SERCA"/>
</component_ref>
<component_ref component="intracellular_calcium_concentration">
<component_ref component="SR_calcium_concentration"/>
<component_ref component="intracellular_sodium_concentration"/>
<component_ref component="intracellular_potassium_concentration"/>
<component_ref component="calmodulin"/>
</component_ref>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_d_gate"/>
<component_ref component="L_type_Ca_channel_f_gate"/>
</component_ref>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
</component_ref>
<component_ref component="time_dependent_rectifier_potassium_current">
<component_ref component="time_dependent_rectifier_potassium_current_x_gate"/>
</component_ref>
<component_ref component="transient_outward_current">
<component_ref component="transient_outward_current_s_gate"/>
<component_ref component="transient_outward_current_r_gate"/>
</component_ref>
<component_ref component="sodium_background_current">
<component_ref component="calcium_background_current"/>
<component_ref component="potassium_background_current"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
</component_ref>
<component_ref component="time_dependent_rectifier_potassium_current">
<component_ref component="time_dependent_rectifier_potassium_current_x_gate"/>
</component_ref>
<component_ref component="transient_outward_current">
<component_ref component="transient_outward_current_s_gate"/>
<component_ref component="transient_outward_current_r_gate"/>
</component_ref>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_d_gate"/>
<component_ref component="L_type_Ca_channel_f_gate"/>
</component_ref>
</group>
<connection>
<map_components component_2="stimulus_protocol" component_1="membrane_potential"/>
<map_variables variable_2="Istim" variable_1="i_Stim"/>
</connection>
<connection>
<map_components component_2="stimulus_protocol" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="membrane_potential" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="time_dependent_rectifier_potassium_current" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="transient_outward_current" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="L_type_Ca_channel" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="CaMKII_factor" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="RyR" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="calmodulin" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="troponin" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="intracellular_calcium_concentration" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="SR_calcium_concentration" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="Force" component_1="environment"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="membrane_potential" component_1="cell_parameters"/>
<map_variables variable_2="Cm" variable_1="Cm"/>
</connection>
<connection>
<map_components component_2="reversal_potentials" component_1="cell_parameters"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="Na_o" variable_1="Na_o"/>
<map_variables variable_2="K_o" variable_1="K_o"/>
<map_variables variable_2="Ca_o" variable_1="Ca_o"/>
</connection>
<connection>
<map_components component_2="time_dependent_rectifier_potassium_current" component_1="cell_parameters"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="K_o" variable_1="K_o"/>
</connection>
<connection>
<map_components component_2="time_independent_potassium_current" component_1="cell_parameters"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="K_o" variable_1="K_o"/>
</connection>
<connection>
<map_components component_2="L_type_Ca_channel" component_1="cell_parameters"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="Na_o" variable_1="Na_o"/>
<map_variables variable_2="K_o" variable_1="K_o"/>
<map_variables variable_2="Ca_o" variable_1="Ca_o"/>
</connection>
<connection>
<map_components component_2="sodium_calcium_exchanger" component_1="cell_parameters"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="Na_o" variable_1="Na_o"/>
<map_variables variable_2="Ca_o" variable_1="Ca_o"/>
</connection>
<connection>
<map_components component_2="sodium_potassium_pump" component_1="cell_parameters"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="K_o" variable_1="K_o"/>
</connection>
<connection>
<map_components component_2="intracellular_calcium_concentration" component_1="cell_parameters"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="v_SR" variable_1="v_SR"/>
<map_variables variable_2="v_i" variable_1="v_i"/>
</connection>
<connection>
<map_components component_2="SR_calcium_concentration" component_1="cell_parameters"/>
<map_variables variable_2="v_SR" variable_1="v_SR"/>
<map_variables variable_2="v_i" variable_1="v_i"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="cell_parameters"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="v_i" variable_1="v_i"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="cell_parameters"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="v_i" variable_1="v_i"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current" component_1="membrane_potential"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
</connection>
<connection>
<map_components component_2="time_dependent_rectifier_potassium_current" component_1="membrane_potential"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K" variable_1="i_K"/>
</connection>
<connection>
<map_components component_2="time_independent_potassium_current" component_1="membrane_potential"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
</connection>
<connection>
<map_components component_2="transient_outward_current" component_1="membrane_potential"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_to" variable_1="i_to"/>
</connection>
<connection>
<map_components component_2="L_type_Ca_channel" component_1="membrane_potential"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Ca_L" variable_1="i_Ca_L"/>
</connection>
<connection>
<map_components component_2="sodium_calcium_exchanger" component_1="membrane_potential"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
</connection>
<connection>
<map_components component_2="sodium_potassium_pump" component_1="membrane_potential"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_NaK" variable_1="i_NaK"/>
</connection>
<connection>
<map_components component_2="calcium_background_current" component_1="membrane_potential"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_b_Ca" variable_1="i_b_Ca"/>
</connection>
<connection>
<map_components component_2="potassium_background_current" component_1="membrane_potential"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_b_K" variable_1="i_b_K"/>
</connection>
<connection>
<map_components component_2="sodium_background_current" component_1="membrane_potential"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_b_Na" variable_1="i_b_Na"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current" component_1="reversal_potentials"/>
<map_variables variable_2="E_mh" variable_1="E_mh"/>
</connection>
<connection>
<map_components component_2="time_independent_potassium_current" component_1="reversal_potentials"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="transient_outward_current" component_1="reversal_potentials"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="calcium_background_current" component_1="reversal_potentials"/>
<map_variables variable_2="E_Ca" variable_1="E_Ca"/>
</connection>
<connection>
<map_components component_2="potassium_background_current" component_1="reversal_potentials"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="sodium_background_current" component_1="reversal_potentials"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="reversal_potentials"/>
<map_variables variable_2="K_i" variable_1="K_i"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="reversal_potentials"/>
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