- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-06-17 16:27:03+12:00
- Desc:
- committing version01 of yang_clark_bryan_robertson_2003
- Permanent Source URI:
- https://models.cellml.org/workspace/yang_clark_bryan_robertson_2003/rawfile/95463ee23e548a2edffb41609d9b8914e792fadb/yang_clark_bryan_robertson_2003.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : yang_model_2003.xml
CREATED : 10th September 2003
LAST MODIFIED : 16th September 2003
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the CellML Metadata 1.0 Specification released on 16th
January, 2002.
DESCRIPTION : This file contains a CellML description of Yang et al's 2003 model; of the myogenic response in a smooth muscle cell.
CHANGES
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="yang_clark_bryan_robertson_2003_version01" name="yang_clark_bryan_robertson_2003_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>The myogenic response in isolated rat cerebrovascular arteries: a smooth muscle cell model</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Contraction in vascular smooth muscle cells can be triggered by mechanical, electrical and chemical stimuli. Several different signal transduction pathways can initiate the contraction, but they all share the common intermediate step of increasing the intracellular calcium concentration ([Ca<superscript>2+</superscript>]<subscript>i</subscript>). This increase is either due to a Ca<superscript>2+</superscript> influx through voltage-gated sarcolemmal Ca<superscript>2+</superscript> channels, or a Ca<superscript>2+</superscript> release from internal sarcoplasmic reticulum stores. In the cytosol, Ca<superscript>2+</superscript> binds to the buffer calmodulin, and the resulting complex (CaCM) activates myosin light chain kinase (MLCK), which in turn phosphorylates myosin light chains in the presence of ATP. This leads to cross-bridge formation and cycling between the myosin heads and the binding sites on the actin filaments, generating the active force needed for muscle contraction. Actin filaments are coupled to the sarcolemma via a viscoelastic system, resulting in changes in cell length. These macroscopic contractile properties of the cell are measured in terms of length-force and force-velocity relationships.
</para>
<para>
Several mathematical models of cerebrovascular smooth muscle cell function have been previously published; however, each of these has dealt with a single particular aspect of smooth muscle activity: electrophysiology; cytosolic calcium regulation; myosin phosphorylation; and mechanical behaviour have all been considered separately. In this study, Yang <emphasis>et al.</emphasis> combine electrophysiological, biochemical and mechanical experimental data and develop an integrated model of smooth muscle cell function (see the figure below).
</para>
<para>
The electrochemical model combines a Hodgkin-Huxley type membrane model which captures ionic membrane currents and transmembrane potential, together with a fluid compartment model which describes ionic fluxes, Ca<superscript>2+</superscript> buffering and Ca<superscript>2+</superscript> handling by the sarcoplasmic reticulum.
</para>
<para>
The second subsystem model is a chemomechanical model with two coupled units: a model of CaCM-dependent myosin phosphorylation and attached cross-bridge kinetics, and a mechanical model of force generation and mechanical coupling within the cell. A multiple-state kinetic model of myosin phosphorylation represents cross-bridge attachment, and a mechanical model describes active force generation by the contractile actin and myosin filaments and the viscoelastic properties of their coupling to the cell membrane.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T9K-492730C-1&_user=140507&_coverDate=10%2F31%2F2003&_alid=113377510&_rdoc=1&_fmt=summary&_orig=search&_qd=1&_cdi=5117&_sort=d&_docanchor=&view=c&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=542bea09ecdac9adeb440a62c3c01fcf">The myogenic response in isolated rat cerebrovascular arteries: smooth muscle cell model</ulink>, Jin Yang, John W. Clark Jr., Robert M. Bryan, and Claudia Robertson, 2003, <ulink url="http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=5117&_auth=y&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=fe63c517f063507236b489d7ac8a3f7b">
<emphasis>Medical Engineering and Physics</emphasis>
</ulink>, 25, 691-709. (<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T9K-492730C-1&_user=140507&_coverDate=10%2F31%2F2003&_alid=113377510&_rdoc=1&_fmt=full&_orig=search&_qd=1&_cdi=5117&_sort=d&_docanchor=&view=c&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=7fc3eff5b0bf03d8bfa720f16dde76f9">Full text (HTML)</ulink> and PDF versions of the article are available on the <emphasis>Medical Engineering and Physics</emphasis> website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=12900184&dopt=Abstract">PubMed ID: 12900184</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="yang_2003.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagrams of: A) the electrochemical model; B) the multi-state kinetic model of CaCM dependent myosin phosphorylation and cross-bridge formation; and C) functional block diagram of the whole integrated smooth muscle cell model.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
constants within the model.
-->
<units base_units="yes" name="mmHg"/>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units base_units="yes" name="mV_per_logmM"/>
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="nanoS">
<unit units="siemens" prefix="nano"/>
</units>
<units name="picoF">
<unit units="farad" prefix="pico"/>
</units>
<units name="picoA">
<unit units="ampere" prefix="pico"/>
</units>
<units name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="nanomolar">
<unit units="mole" prefix="nano"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="micrometre">
<unit units="metre" prefix="micro"/>
</units>
<units name="micrometre_per_ms">
<unit units="metre" prefix="micro"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="microN">
<unit units="newton" prefix="micro"/>
</units>
<units name="microN_per_micrometre">
<unit units="newton" prefix="micro"/>
<unit units="metre" prefix="micro" exponent="-1"/>
</units>
<units name="microN_ms_per_micrometre">
<unit units="newton" prefix="micro"/>
<unit units="millisecond"/>
<unit units="metre" prefix="micro" exponent="-1"/>
</units>
<units name="first_order_rate_constant">
<unit units="millisecond" exponent="-1"/>
</units>
<units name="second_order_rate_constant">
<unit units="millimolar"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="third_order_rate_constant">
<unit units="millimolar" exponent="-2"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="millijoule_per_mole_kelvin">
<unit units="joule" prefix="milli"/>
<unit units="mole" exponent="-1"/>
<unit units="kelvin" exponent="-1"/>
</units>
<units name="joule_per_kilomole_kelvin">
<unit units="joule"/>
<unit units="mole" prefix="kilo" exponent="-1"/>
<unit units="kelvin" exponent="-1"/>
</units>
<units name="coulomb_per_mole">
<unit units="coulomb"/>
<unit units="mole" exponent="-1"/>
</units>
<units name="cm2">
<unit units="metre" prefix="centi" exponent="2"/>
</units>
<units name="picol">
<unit units="litre" prefix="pico"/>
</units>
<component name="environment">
<variable units="millisecond" public_interface="out" name="time"/>
</component>
<component name="membrane">
<variable units="millivolt" public_interface="out" name="V" initial_value="-56.1257"/>
<variable units="millijoule_per_mole_kelvin" public_interface="out" name="R" initial_value="8314.0"/>
<variable units="kelvin" public_interface="out" name="T" initial_value="293.0"/>
<variable units="coulomb_per_mole" public_interface="out" name="F" initial_value="96487.0"/>
<variable units="picoF" name="Cm"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="picoA" public_interface="in" name="i_Ca_L"/>
<variable units="picoA" public_interface="in" name="i_K"/>
<variable units="picoA" public_interface="in" name="i_K_Ca"/>
<variable units="picoA" public_interface="in" name="i_Ki"/>
<variable units="picoA" public_interface="in" name="i_M"/>
<variable units="picoA" public_interface="in" name="i_NaCa"/>
<variable units="picoA" public_interface="in" name="i_NaK"/>
<variable units="picoA" public_interface="in" name="i_CaP"/>
<variable units="picoA" public_interface="in" name="i_B"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="membrane_voltage_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> V </ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> Cm </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> i_Ca_L </ci>
<ci> i_K </ci>
<ci> i_K_Ca </ci>
<ci> i_Ki </ci>
<ci> i_M </ci>
<ci> i_NaCa </ci>
<ci> i_NaK </ci>
<ci> i_CaP </ci>
<ci> i_B </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_calcium_current">
<variable units="picoA" public_interface="out" name="i_Ca_L"/>
<variable units="millivolt" name="E_Ca_L"/>
<variable units="nanoS" name="g_Ca_L" initial_value="1.4151"/>
<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="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="d"/>
<variable units="dimensionless" private_interface="in" name="f"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ca_L_calculation">
<eq/>
<ci> i_Ca_L </ci>
<apply>
<times/>
<ci> g_Ca_L </ci>
<ci> d </ci>
<ci> f </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Ca_L </ci>
</apply>
</apply>
</apply>
<apply id="E_Ca_L_calculation">
<eq/>
<ci> E_Ca_L </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Ca_o </ci>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_calcium_current_d_gate">
<variable units="dimensionless" public_interface="out" name="d" initial_value="0.00046"/>
<variable units="dimensionless" name="d_infinity"/>
<variable units="millisecond" name="tau_d"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="d_infinity_calculation">
<eq/>
<ci> d_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 1.878 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 7.5704 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_d_calculation">
<eq/>
<ci> tau_d </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond"> 2.8928 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 8.6344 </cn>
</apply>
<cn cellml:units="millivolt"> 12.3884 </cn>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond"> 2.4343 </cn>
</apply>
</apply>
<apply id="dd_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> d </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> d_infinity </ci>
<ci> d </ci>
</apply>
<ci> tau_d </ci>
</apply>
</apply>
</math>
</component>
<component name="L_type_calcium_current_f_gate">
<variable units="dimensionless" public_interface="out" name="f" initial_value="1.0"/>
<variable units="dimensionless" name="f_infinity"/>
<variable units="millisecond" name="tau_ff"/>
<variable units="dimensionless" name="ff" initial_value="1.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="f_infinity_calculation">
<eq/>
<ci> f_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 29.3188 </cn>
</apply>
<cn cellml:units="millivolt"> 1.5389 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_ff_calculation">
<eq/>
<ci> tau_ff </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond"> 295.5937 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 4.7187 </cn>
</apply>
<cn cellml:units="millivolt"> 112.545 </cn>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond"> 23.1907 </cn>
</apply>
</apply>
<apply id="dff_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> ff </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> f_infinity </ci>
<ci> ff </ci>
</apply>
<ci> tau_ff </ci>
</apply>
</apply>
<apply id="f_calculation">
<eq/>
<ci> f </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.74 </cn>
<ci> ff </ci>
</apply>
<cn cellml:units="dimensionless"> 0.26 </cn>
</apply>
</apply>
</math>
</component>
<component name="calcium_activated_potassium_current">
<variable units="picoA" public_interface="out" name="i_K_Ca"/>
<variable units="millivolt" public_interface="out" name="E_K"/>
<variable units="nanoS" name="g_K_Ca" initial_value="0.5"/>
<variable units="millimolar" public_interface="in" private_interface="out" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="K_i"/>
<variable units="millimolar" public_interface="in" name="K_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="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="P_K_Ca"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_Ca_calculation">
<eq/>
<ci> i_K_Ca </ci>
<apply>
<times/>
<ci> g_K_Ca </ci>
<ci> P_K_Ca </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
<apply id="E_K_calculation">
<eq/>
<ci> E_K </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> K_o </ci>
<ci> K_i </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="calcium_activated_potassium_current_P_K_Ca_gate">
<variable units="dimensionless" public_interface="out" name="P_K_Ca"/>
<variable units="dimensionless" name="Ps" initial_value="0.00032"/>
<variable units="dimensionless" name="Pf" initial_value="0.00032"/>
<variable units="dimensionless" name="Ps_infinity"/>
<variable units="dimensionless" name="Pf_infinity"/>
<variable units="dimensionless" name="Po_infinity"/>
<variable units="millisecond" name="tau_Ps" initial_value="11.5"/>
<variable units="millisecond" name="tau_Pf" initial_value="0.5"/>
<variable units="millivolt" name="V_1_2_K_Ca" initial_value="20.5"/>
<variable units="millimolar" public_interface="in" name="Ca_i"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Po_infinity_calculation">
<eq/>
<ci> Po_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci> V </ci>
<ci> V_1_2_K_Ca </ci>
</apply>
</apply>
<cn cellml:units="millivolt"> 21.70 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="V_1_2_K_Ca_calculation">
<eq/>
<ci> V_1_2_K_Ca </ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="millivolt"> 45.0 </cn>
<apply>
<log/>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
<cn cellml:units="millivolt"> 198.55 </cn>
</apply>
</apply>
<apply id="Pf_infinity_calculation">
<eq/>
<ci> Pf_infinity </ci>
<apply>
<minus/>
<ci> Ps_infinity </ci>
<ci> Po_infinity </ci>
</apply>
</apply>
<apply id="dPf_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Pf </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> Pf_infinity </ci>
<ci> Pf </ci>
</apply>
<ci> tau_Pf </ci>
</apply>
</apply>
<apply id="dPs_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ps </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> Ps_infinity </ci>
<ci> Ps </ci>
</apply>
<ci> tau_Ps </ci>
</apply>
</apply>
<apply id="P_K_Ca_calculation">
<eq/>
<ci> P_K_Ca </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.65 </cn>
<ci> Pf </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.35 </cn>
<ci> Ps </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_current">
<variable units="picoA" public_interface="out" name="i_K"/>
<variable units="nanoS" name="g_K" initial_value="9.8325"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="Pk"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_calculation">
<eq/>
<ci> i_K </ci>
<apply>
<times/>
<ci> g_K </ci>
<apply>
<power/>
<ci> Pk </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_current_Pk_gate">
<variable units="dimensionless" public_interface="out" name="Pk"/>
<variable units="dimensionless" name="P1" initial_value="0.0159"/>
<variable units="dimensionless" name="P2" initial_value="0.0159"/>
<variable units="dimensionless" name="P1_infinity"/>
<variable units="dimensionless" name="P2_infinity"/>
<variable units="dimensionless" name="Pk_infinity"/>
<variable units="millisecond" name="tau_P1"/>
<variable units="millisecond" name="tau_P2"/>
<variable units="millivolt" name="V_1_2" initial_value="-1.77"/>
<variable units="dimensionless" name="k" initial_value="14.52"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Pk_infinity_calculation">
<eq/>
<ci> Pk_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci> V </ci>
<ci> V_1_2 </ci>
</apply>
</apply>
<ci> k </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_P1_calculation">
<eq/>
<ci> tau_P1 </ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="millisecond"> 210.9873 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 214.3355 </cn>
</apply>
<cn cellml:units="millivolt"> 195.3502 </cn>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond"> 20.5866 </cn>
</apply>
</apply>
<apply id="tau_P2_calculation">
<eq/>
<ci> tau_P2 </ci>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="millisecond"> 821.3949 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 31.5891 </cn>
</apply>
<cn cellml:units="millivolt"> 27.4568 </cn>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond"> 0.1892 </cn>
</apply>
</apply>
<apply id="dP2_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P2 </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> Pk_infinity </ci>
<ci> P2 </ci>
</apply>
<ci> tau_P2 </ci>
</apply>
</apply>
<apply id="dP1_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P1 </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> Pk_infinity </ci>
<ci> P1 </ci>
</apply>
<ci> tau_P1 </ci>
</apply>
</apply>
<apply id="Pk_calculation">
<eq/>
<ci> Pk </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.58 </cn>
<ci> P1 </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.42 </cn>
<ci> P2 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="stretch_sensitive_current">
<variable units="picoA" public_interface="out" name="i_M"/>
<variable units="picoA" public_interface="out" name="i_M_K"/>
<variable units="picoA" public_interface="out" name="i_M_Na"/>
<variable units="picoA" public_interface="out" name="i_M_Ca"/>
<variable units="cm2" name="Am"/>
<variable units="dimensionless" name="Pm"/>
<variable units="dimensionless" name="P_Na"/>
<variable units="dimensionless" name="P_Ca"/>
<variable units="dimensionless" name="P_K"/>
<variable units="mmHg" name="sigma_1_2" initial_value="204.0"/>
<variable units="dimensionless" name="sigma"/>
<variable units="mmHg" name="k_sigma" initial_value="2.03"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<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="K_i"/>
<variable units="millimolar" public_interface="in" name="K_o"/>
<variable units="micromolar" public_interface="in" name="Ca_i"/>
<variable units="millimolar" public_interface="in" name="Ca_o"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_M_calculation">
<eq/>
<ci> i_M </ci>
<apply>
<plus/>
<ci> i_M_K </ci>
<ci> i_M_Na </ci>
<ci> i_M_Ca </ci>
</apply>
</apply>
<apply id="i_M_K_calculation">
<eq/>
<ci> i_M_K </ci>
<apply>
<times/>
<ci> Am </ci>
<ci> Pm </ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<ci> P_K</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> K_o </ci>
<apply>
<times/>
<ci> K_i </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_M_Na_calculation">
<eq/>
<ci> i_M_Na </ci>
<apply>
<times/>
<ci> Am </ci>
<ci> Pm </ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<ci> P_Na </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Na_o </ci>
<apply>
<times/>
<ci> Na_i </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_M_Ca_calculation">
<eq/>
<ci> i_M_Ca </ci>
<apply>
<times/>
<ci> Am </ci>
<ci> Pm </ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<power/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> P_Ca </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Ca_o </ci>
<apply>
<times/>
<ci> Ca_i </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> F </ci>
<ci> V </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="Pm_calculation">
<eq/>
<ci> Pm </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci> sigma </ci>
<ci> sigma_1_2 </ci>
</apply>
</apply>
<ci> k_sigma </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="inward_rectifier_current">
<variable units="picoA" public_interface="out" name="i_Ki"/>
<variable units="nanoS" name="g_max_Ki"/>
<variable units="dimensionless" name="G_Ki" initial_value="0.145"/>
<variable units="millivolt" name="V_1_2_Ki" initial_value="31.5"/>
<variable units="dimensionless" name="n_Ki" initial_value="0.5"/>
<variable units="mV_per_logmM" name="A" initial_value="25.19"/>
<variable units="millivolt" name="B" initial_value="112.29"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millimolar" public_interface="in" name="K_o"/>
<variable units="millimolar" public_interface="in" name="K_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ki_calculation">
<eq/>
<ci> i_Ki </ci>
<apply>
<times/>
<ci> g_max_Ki </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci> V </ci>
<ci> V_1_2_Ki </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> 28.89 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="g_max_Ki_calculation">
<eq/>
<ci> g_max_Ki </ci>
<apply>
<times/>
<ci> G_Ki </ci>
<ci> K_o </ci>
<ci> n_Ki</ci>
</apply>
</apply>
<apply id="V_1_2_Ki_calculation">
<eq/>
<ci> V_1_2_Ki </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> A </ci>
<apply>
<log/>
<ci> K_i </ci>
</apply>
</apply>
<ci> B </ci>
</apply>
</apply>
</math>
</component>
<component name="calcium_pump">
<variable units="picoA" public_interface="out" name="i_CaP"/>
<variable units="picoA" name="I_Ca_P"/>
<variable units="dimensionless" public_interface="in" name="K_CaCM"/>
<variable units="millimolar" public_interface="in" name="CaCM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_CaP_calculation">
<eq/>
<ci> i_CaP </ci>
<apply>
<times/>
<ci> I_Ca_P </ci>
<apply>
<divide/>
<ci> CaCM </ci>
<apply>
<plus/>
<ci> CaCM </ci>
<ci> K_CaCM </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_potassium_pump">
<variable units="picoA" public_interface="out" name="i_NaK"/>
<variable units="picoA" name="I_NaK"/>
<variable units="millimolar" name="Km_Nai"/>
<variable units="millimolar" name="Km_Ko"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millimolar" public_interface="in" name="K_o"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_NaK_calculation">
<eq/>
<ci> i_NaK </ci>
<apply>
<times/>
<ci> I_NaK </ci>
<apply>
<divide/>
<ci> K_o </ci>
<apply>
<plus/>
<ci> K_o </ci>
<ci> Km_Ko </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci> Na_i </ci>
<cn cellml:units="dimensionless"> 1.5 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> Na_i </ci>
<cn cellml:units="dimensionless"> 1.5 </cn>
</apply>
<apply>
<power/>
<ci> Km_Nai </ci>
<cn cellml:units="dimensionless"> 1.5 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 150.0 </cn>
</apply>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 200.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_calcium_exchanger">
<variable units="picoA" public_interface="out" name="i_NaCa"/>
<variable units="nanoS" name="g_NaCa"/>
<variable units="millimolar" name="d_NaCa"/>
<variable units="dimensionless" name="phi_R"/>
<variable units="dimensionless" name="phi_F"/>
<variable units="dimensionless" name="gamma"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<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"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Na_Ca_exchanger_calculation">
<eq/>
<ci> i_NaCa </ci>
<apply>
<times/>
<ci> g_NaCa </ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<ci> Na_i </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Ca_o </ci>
<ci> phi_F </ci>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci> Na_o </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Ca_i </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<apply>
<power/>
<ci> Na_o </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Ca_i </ci>
<ci> phi_R </ci>
</apply>
<apply>
<times/>
<apply>
<power/>
<ci> Na_i </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Ca_o </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="phi_F_calculation">
<eq/>
<ci> phi_F </ci>
<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>
<apply id="phi_R_calculation">
<eq/>
<ci> phi_R </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> gamma </ci>
</apply>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="background_currents">
<variable units="picoA" public_interface="out" name="i_B"/>
<variable units="picoA" public_interface="out" name="i_B_Na"/>
<variable units="picoA" public_interface="out" name="i_B_Ca"/>
<variable units="picoA" public_interface="out" name="i_B_K"/>
<variable units="nanoS" name="g_Nab" initial_value="0.01"/>
<variable units="nanoS" name="g_Cab" initial_value="0.012"/>
<variable units="nanoS" name="g_Kb" initial_value="0.01"/>
<variable units="millivolt" name="E_Na"/>
<variable units="millivolt" name="E_Ca"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_kilomole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<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"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_B_calculation">
<eq/>
<ci> i_B </ci>
<apply>
<plus/>
<ci> i_B_Na </ci>
<ci> i_B_Ca </ci>
<ci> i_B_K </ci>
</apply>
</apply>
<apply id="i_B_Na_calculation">
<eq/>
<ci> i_B_Na </ci>
<apply>
<times/>
<ci> g_Nab </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
<apply id="i_B_Ca_calculation">
<eq/>
<ci> i_B_Ca </ci>
<apply>
<times/>
<ci> g_Cab </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Ca </ci>
</apply>
</apply>
</apply>
<apply id="i_B_K_calculation">
<eq/>
<ci> i_B_K </ci>
<apply>
<times/>
<ci> g_Kb </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
<apply id="E_Na_calculation">
<eq/>
<ci> E_Na </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Na_o </ci>
<ci> Na_i </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="E_Ca_calculation">
<eq/>
<ci> E_Ca </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Ca_o </ci>
<ci> Ca_i </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="extracellular_ionic_concentrations">
<variable units="millimolar" public_interface="out" name="Na_o" initial_value="140.0"/>
<variable units="millimolar" public_interface="out" name="Ca_o" initial_value="2.0"/>
<variable units="millimolar" public_interface="out" name="K_o" initial_value="5.0"/>
</component>
<component name="intracellular_ionic_concentrations">
<variable units="millimolar" public_interface="out" name="Na_i" initial_value="5.06"/>
<variable units="nanomolar" public_interface="out" name="Ca_i" initial_value="100.92"/>
<variable units="millimolar" public_interface="out" name="K_i" initial_value="91.03"/>
<variable units="millimolar" public_interface="out" name="CaCM"/>
<variable units="millimolar" name="S_CM_Ca" initial_value="0.1"/>
<variable units="millimolar" name="S_CM_cal" initial_value="0.072"/>
<variable units="millimolar" name="CaS_CM"/>
<variable units="millimolar" name="B_F_Ca" initial_value="0.4"/>
<variable units="millimolar" name="B_F_cal" initial_value="0.336"/>
<variable units="millimolar" name="CaB_F"/>
<variable units="second_order_rate_constant" name="k1"/>
<variable units="first_order_rate_constant" name="k_1"/>
<variable units="second_order_rate_constant" name="kd"/>
<variable units="first_order_rate_constant" name="k_d"/>
<variable units="picol" name="Vol_Ca" initial_value="0.7"/>
<variable units="picol" name="Vol_i" initial_value="1.0"/>
<variable units="second_order_rate_constant" name="delta_S_CM_cal"/>
<variable units="second_order_rate_constant" name="delta_B_F_cal"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<variable units="picoA" public_interface="in" name="i_B_Na"/>
<variable units="picoA" public_interface="in" name="i_M_Na"/>
<variable units="picoA" public_interface="in" name="i_NaCa"/>
<variable units="picoA" public_interface="in" name="i_NaK"/>
<variable units="picoA" public_interface="in" name="i_Ca_L"/>
<variable units="picoA" public_interface="in" name="i_K_Ca"/>
<variable units="picoA" public_interface="in" name="i_K"/>
<variable units="picoA" public_interface="in" name="i_Ki"/>
<variable units="picoA" public_interface="in" name="i_B_K"/>
<variable units="picoA" public_interface="in" name="i_M_K"/>
<variable units="picoA" public_interface="in" name="i_CaP"/>
<variable units="picoA" public_interface="in" name="i_B_Ca"/>
<variable units="picoA" public_interface="in" name="i_M_Ca"/>
<variable units="picoA" public_interface="in" name="i_up"/>
<variable units="picoA" public_interface="in" name="i_rel"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="dNa_i_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Na_i </ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> i_NaK </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> i_NaCa </ci>
</apply>
<ci> i_B_Na </ci>
<ci> i_M_Na </ci>
</apply>
<apply>
<times/>
<ci> F </ci>
<ci> Vol_i </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="dK_i_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> K_i </ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_K </ci>
<ci> i_K_Ca </ci>
<ci> i_Ki </ci>
<ci> i_B_K </ci>
<ci> i_M_K </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> i_NaK </ci>
</apply>
</apply>
<apply>
<times/>
<ci> F </ci>
<ci> Vol_i </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="dCa_i_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_i </ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_Ca_L </ci>
<ci> i_CaP </ci>
<ci> i_B_Ca </ci>
<ci> i_M_Ca </ci>
<ci> i_up </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> i_NaCa </ci>
</apply>
<ci> i_rel </ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
<ci> Vol_Ca </ci>
</apply>
</apply>
</apply>
<ci> delta_S_CM_cal </ci>
<ci> delta_B_F_cal </ci>
</apply>
</apply>
<apply id="dS_CM_cal_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> S_CM_cal </ci>
</apply>
<ci> delta_S_CM_cal </ci>
</apply>
<apply id="delta_S_CM_cal_calulation">
<eq/>
<ci> delta_S_CM_cal </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> k_1 </ci>
<ci> CaS_CM </ci>
</apply>
<apply>
<times/>
<ci> k1 </ci>
<ci> Ca_i </ci>
<ci> S_CM_cal </ci>
</apply>
</apply>
</apply>
<apply id="CaS_CM_calculation">
<eq/>
<ci> CaS_CM </ci>
<ci> CaCM </ci>
</apply>
<apply id="CaCM_calculation">
<eq/>
<ci> CaCM </ci>
<apply>
<minus/>
<ci> S_CM_Ca </ci>
<ci> S_CM_cal </ci>
</apply>
</apply>
<apply id="dB_F_cal_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> B_F_cal </ci>
</apply>
<ci> delta_B_F_cal </ci>
</apply>
<apply id="delta_B_F_cal_calulation">
<eq/>
<ci> delta_B_F_cal </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> k_d </ci>
<ci> CaB_F </ci>
</apply>
<apply>
<times/>
<ci> kd </ci>
<ci> Ca_i </ci>
<ci> B_F_cal </ci>
</apply>
</apply>
</apply>
<apply id="CaB_F_calculation">
<eq/>
<ci> CaB_F </ci>
<apply>
<minus/>
<ci> B_F_Ca </ci>
<ci> B_F_cal </ci>
</apply>
</apply>
</math>
</component>
<component name="calcium_fluxes_in_the_SR">
<variable units="picoA" public_interface="out" name="i_rel"/>
<variable units="picoA" public_interface="out" name="i_up"/>
<variable units="millimolar" name="Ca_up" initial_value="0.5687"/>
<variable units="picoA" name="i_tr"/>
<variable units="picoA" name="I_up" initial_value="200.0"/>
<variable units="millisecond" name="tau_rel" initial_value="0.0333"/>
<variable units="millisecond" name="tau_tr" initial_value="1000.0"/>
<variable units="millimolar" name="Ca_u"/>
<variable units="millimolar" name="Ca_r"/>
<variable units="picol" name="Vol_u" initial_value="0.07"/>
<variable units="picol" name="Vol_r" initial_value="0.07"/>
<variable units="micromolar" name="Km_up" initial_value="0.08"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="micromolar" public_interface="in" name="Ca_i"/>
<variable units="dimensionless" public_interface="in" name="R10"/>
<variable units="coulomb_per_mole" public_interface="in" name="F"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_up_calculation">
<eq/>
<ci> i_up </ci>
<apply>
<times/>
<ci> I_up </ci>
<apply>
<divide/>
<ci> Ca_i </ci>
<apply>
<plus/>
<ci> Ca_i </ci>
<ci> Km_up </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_tr_calculation">
<eq/>
<ci> i_tr </ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci> Ca_u </ci>
<ci> Ca_r </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
<ci> Vol_u </ci>
</apply>
</apply>
<ci> tau_tr </ci>
</apply>
</apply>
<apply id="i_rel_calculation">
<eq/>
<ci> i_rel </ci>
<apply>
<times/>
<apply>
<power/>
<ci> R10 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<minus/>
<ci> Ca_u </ci>
<ci> Ca_r </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
<ci> Vol_r </ci>
</apply>
<ci> tau_rel </ci>
</apply>
</apply>
</apply>
<apply id="dCa_up_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_up </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> i_up </ci>
<ci> i_tr </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
<ci> Vol_u </ci>
</apply>
</apply>
</apply>
<apply id="dCa_r_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_r </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> i_tr </ci>
<ci> i_rel </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
<ci> Vol_r </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="CICR_mechanism_of_the_SR">
<variable units="dimensionless" public_interface="out" name="R10" initial_value="0.0033"/>
<variable units="dimensionless" name="R00" initial_value="0.001196"/>
<variable units="dimensionless" name="R01" initial_value="0.9955"/>
<variable units="dimensionless" name="R11" initial_value="4.0E-6"/>
<variable units="third_order_rate_constant" name="Kr1" initial_value="2500.0"/>
<variable units="second_order_rate_constant" name="Kr2" initial_value="1.05"/>
<variable units="first_order_rate_constant" name="Kr1_" initial_value="0.0076"/>
<variable units="first_order_rate_constant" name="Kr2_" initial_value="0.084"/>
<variable units="micromolar" public_interface="in" name="Ca_i"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="R00_calculation">
<eq/>
<ci> R00 </ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> Kr1_ </ci>
<ci> R10 </ci>
</apply>
<apply>
<times/>
<ci> Kr2_ </ci>
<ci> R01 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> Kr1 </ci>
<apply>
<power/>
<ci> Ca_i </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> Kr2 </ci>
<ci> Ca_i </ci>
</apply>
</apply>
<ci> R00 </ci>
</apply>
</apply>
</apply>
<apply id="R10_calculation">
<eq/>
<ci> R10 </ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> Kr1 </ci>
<apply>
<power/>
<ci> Ca_i </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> R00 </ci>
</apply>
<apply>
<times/>
<ci> Kr2_ </ci>
<ci> R11 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> Kr2 </ci>
<ci> Ca_i </ci>
</apply>
<ci> Kr1_ </ci>
</apply>
<ci> R10 </ci>
</apply>
</apply>
</apply>
<apply id="R11_calculation">
<eq/>
<ci> R11 </ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> Kr1 </ci>
<apply>
<power/>
<ci> Ca_i </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> R01 </ci>
</apply>
<apply>
<times/>
<ci> Kr2 </ci>
<ci> Ca_i </ci>
<ci> R10 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> Kr2_ </ci>
<ci> Kr1_ </ci>
</apply>
<ci> R11 </ci>
</apply>
</apply>
</apply>
<apply id="R01_calculation">
<eq/>
<ci> R01 </ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> Kr1_ </ci>
<ci> R11 </ci>
</apply>
<apply>
<times/>
<ci> Kr2 </ci>
<ci> Ca_i </ci>
<ci> R00 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> Kr1 </ci>
<apply>
<power/>
<ci> Ca_i </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<ci> Kr2_ </ci>
</apply>
<ci> R01 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="smooth_muscle_contraction">
<variable units="dimensionless" public_interface="out" name="K_CaCM" initial_value="1.78E-7"/>
<variable units="dimensionless" public_interface="out" name="AM" initial_value="0.2798"/>
<variable units="dimensionless" public_interface="out" name="AMp" initial_value="0.0627"/>
<variable units="dimensionless" name="Mp" initial_value="0.0476"/>
<variable units="dimensionless" name="M" initial_value="0.6099"/>
<variable units="first_order_rate_constant" name="K1"/>
<variable units="first_order_rate_constant" name="K2" initial_value="0.4"/>
<variable units="first_order_rate_constant" name="K3" initial_value="1.8"/>
<variable units="first_order_rate_constant" name="K4" initial_value="0.1"/>
<variable units="first_order_rate_constant" name="K5" initial_value="0.4"/>
<variable units="first_order_rate_constant" name="K6"/>
<variable units="first_order_rate_constant" name="K7" initial_value="0.045"/>
<variable units="millimolar" public_interface="in" name="CaCM"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="M_calculation">
<eq/>
<ci> M </ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> K2 </ci>
<ci> Mp </ci>
</apply>
<apply>
<times/>
<ci> K7 </ci>
<ci> AM </ci>
</apply>
</apply>
<apply>
<times/>
<ci> K1 </ci>
<ci> M </ci>
</apply>
</apply>
</apply>
<apply id="Mp_calculation">
<eq/>
<ci> Mp </ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> K1 </ci>
<ci> M </ci>
</apply>
<apply>
<times/>
<ci> K4 </ci>
<ci> AMp </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> K2 </ci>
<ci> K3 </ci>
</apply>
<ci> Mp </ci>
</apply>
</apply>
</apply>
<apply id="AMp_calculation">
<eq/>
<ci> AMp </ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> K6 </ci>
<ci> AM </ci>
</apply>
<apply>
<times/>
<ci> K3 </ci>
<ci> Mp </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> K5 </ci>
<ci> K4 </ci>
</apply>
<ci> AMp </ci>
</apply>
</apply>
</apply>
<apply id="AM_calculation">
<eq/>
<ci> AM </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> K5 </ci>
<ci> AMp </ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> K7 </ci>
<ci> K6 </ci>
</apply>
<ci> AM </ci>
</apply>
</apply>
</apply>
<apply id="K1_calculation">
<eq/>
<ci> K1 </ci>
<ci> K6 </ci>
</apply>
<apply id="K6_calculation">
<eq/>
<ci> K6 </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> CaCM </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> CaCM </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> K_CaCM </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="passive_force">
<variable units="microN" name="Fp"/>
<variable units="microN" name="kp" initial_value="0.1"/>
<variable units="dimensionless" name="alpha_p" initial_value="0.1"/>
<variable units="micrometre" name="l0" initial_value="40.0"/>
<variable units="micrometre" name="lc"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Fp_calculation">
<eq/>
<ci> Fp </ci>
<apply>
<times/>
<ci> kp </ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<ci> alpha_p </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> lc </ci>
<ci> l0 </ci>
</apply>
<ci> l0 </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="cross_bridge_elasticity">
<variable units="dimensionless" public_interface="out" name="beta" initial_value="7.5"/>
<variable units="micrometre" public_interface="out" name="la"/>
<variable units="micrometre" public_interface="out" name="lopt" initial_value="100.0"/>
<variable units="microN" name="Fx"/>
<variable units="microN_per_micrometre" name="kx1" initial_value="12.5"/>
<variable units="microN_per_micrometre" name="kx2" initial_value="8.8"/>
<variable units="micrometre" name="lx" initial_value="89.60"/>
<variable units="dimensionless" public_interface="in" name="AM"/>
<variable units="dimensionless" public_interface="in" name="AMp"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Fx_calculation">
<eq/>
<ci> Fx </ci>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> kx1 </ci>
<ci> AMp </ci>
</apply>
<apply>
<times/>
<ci> kx2 </ci>
<ci> AM </ci>
</apply>
</apply>
<ci> lx </ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci> beta </ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<apply>
<minus/>
<ci> la </ci>
<ci> lopt </ci>
</apply>
<ci> lopt </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="active_force_generation">
<variable units="microN" name="Fa"/>
<variable units="micrometre_per_ms" name="vx" initial_value="5.0"/>
<variable units="micrometre_per_ms" name="ia"/>
<variable units="microN_ms_per_micrometre" name="fAMp" initial_value="1.3"/>
<variable units="microN_per_micrometre" name="fAM" initial_value="85.5"/>
<variable units="dimensionless" public_interface="in" name="beta"/>
<variable units="micrometre" public_interface="in" name="la"/>
<variable units="micrometre" public_interface="in" name="lopt"/>
<variable units="dimensionless" public_interface="in" name="AM"/>
<variable units="dimensionless" public_interface="in" name="AMp"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Fa_calculation">
<eq/>
<ci> Fa </ci>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> fAMp </ci>
<ci> AMp </ci>
<apply>
<plus/>
<ci> vx </ci>
<ci> ia </ci>
</apply>
</apply>
<apply>
<times/>
<ci> fAM </ci>
<ci> AM </ci>
<ci> ia </ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci> beta </ci>
</apply>
<apply>
<power/>
<apply>
<divide/>
<apply>
<minus/>
<ci> la </ci>
<ci> lopt </ci>
</apply>
<ci> lopt </ci>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="series_viscoelastic_force">
<variable units="microN" name="Fs"/>
<variable units="microN" name="ks" initial_value="0.2"/>
<variable units="dimensionless" name="alpha_s" initial_value="4.5"/>
<variable units="micrometre" name="ls" initial_value="37.05"/>
<variable units="micrometre_per_ms" name="delta_ls"/>
<variable units="micrometre" name="ls0" initial_value="30.0"/>
<variable units="microN_ms_per_micrometre" name="mu_s" initial_value="0.01"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Fs_calculation">
<eq/>
<ci> Fs </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> mu_s </ci>
<ci> delta_ls </ci>
</apply>
<apply>
<times/>
<ci> ks </ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<ci> alpha_s </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> ls </ci>
<ci> ls0 </ci>
</apply>
<ci> ls0 </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="dls_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> ls </ci>
</apply>
<ci> delta_ls </ci>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="L_type_calcium_current">
<component_ref component="L_type_calcium_current_d_gate"/>
<component_ref component="L_type_calcium_current_f_gate"/>
</component_ref>
<component_ref component="calcium_activated_potassium_current">
<component_ref component="calcium_activated_potassium_current_P_K_Ca_gate"/>
</component_ref>
<component_ref component="delayed_rectifier_current">
<component_ref component="delayed_rectifier_current_Pk_gate"/>
</component_ref>
<component_ref component="stretch_sensitive_current"/>
<component_ref component="inward_rectifier_current"/>
<component_ref component="calcium_pump"/>
<component_ref component="sodium_potassium_pump"/>
<component_ref component="sodium_calcium_exchanger"/>
<component_ref component="background_currents"/>
<component_ref component="extracellular_ionic_concentrations"/>
<component_ref component="intracellular_ionic_concentrations"/>
<component_ref component="calcium_fluxes_in_the_SR"/>
<component_ref component="CICR_mechanism_of_the_SR"/>
<component_ref component="smooth_muscle_contraction"/>
<component_ref component="passive_force"/>
<component_ref component="cross_bridge_elasticity"/>
<component_ref component="active_force_generation"/>
<component_ref component="series_viscoelastic_force"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="L_type_calcium_current">
<component_ref component="L_type_calcium_current_d_gate"/>
<component_ref component="L_type_calcium_current_f_gate"/>
</component_ref>
<component_ref component="calcium_activated_potassium_current">
<component_ref component="calcium_activated_potassium_current_P_K_Ca_gate"/>
</component_ref>
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The myogenic response in isolated rat cerebrovascular arteries:
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Yang et al's 2003 model of the myogenic response in a smooth muscle
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The University of Auckland, Bioengineering Institute
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