- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-09-04 02:09:00+12:00
- Desc:
- committing version01 of jafri_rice_winslow_1998
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/jafri_rice_winslow_1998/rawfile/f538484b59a41496e248254a7b1b12873d12360e/jafri_rice_winslow_1998.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : jafri_rice_winslow_model_1998.xml
CREATED : September 2001
LAST MODIFIED : 30th July 2003
AUTHOR : Catherine Lloyd
Department of Engineering Science
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 the mammalian
ventricular action potential based on the Jafri-Rice-Winslow model, 1998. This
model is a development of the LR-II model. In particular, it makes an accurate
model of the membrane currents and adds a more sophisticated model of calcium
ion handling.
CHANGES:
19/10/2001 - CML - Removed document type definition as this is declared as
optional according to the W3C recommendation.
24/10/2001 - CML - Made changes to some of the metadata, bringing them up to
date with the most recent working draft (26th September) of
the Metadata specification.
07/12/2001 - CML - Changed tau_y_calculation after checking mathml using the
validator.
04/01/2002 - CML - Altered some of the connections.
21/01/2002 - AAC - Updated metadata to conform to the 16/1/02 CellML Metadata
1.0 Specification.
25/02/2002 - CML - Corrected several equations.
28/02/2002 - CML - Corrected several equations, variable units and their
initial values.
06/05/2002 - CML - Added some initial values.
22/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
04/06/2003 - CML - Fixed MathML in a few components.
30/07/2003 - CML - Altered a few equations.
--><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="jafri_rice_winslow_1998_version01" name="jafri_rice_winslow_1998_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Jafri-Rice-Winslow Ventricular Model 1998</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>
In 1998, M. Saleet Jafri, J. Jeremy Rice and Raimond L. Winslow published a model describing the ventricular action potential. By adding a more sophisticated model of calcium handling, this model builds upon the <ulink url="${HTML_EXMPL_DFN_MODEL}">Di Francesco-Noble</ulink> and the Luo-Rudy models (see the <ulink url="${HTML_EXMPL_LR_I_MODEL}">Luo-Rudy I</ulink> and the <ulink url="${HTML_EXMPL_LR_II_MODEL}">Luo-Rudy II</ulink> models with their accurate descriptions of membrane currents (see <xref linkend="fig_cell_diagram"/> below). Prior to this paper, membrane currents and calcium subsystems had only been considered separately.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.biophysj.org/cgi/content/abstract/74/3/1149">Cardiac Calcium Dynamics: The Roles of Ryanodine Receptor Adaptation and Sarcoplasmic Reticulum Load</ulink>, M. Saleet Jafri, J. Jeremy Rice and Raimond L. Winslow, 1998, <ulink url="http://www.biophysj.org/">
<emphasis>Biophysical Journal</emphasis>
</ulink>, 74, 1149-1168. (<ulink url="http://www.biophysj.org/cgi/content/full/74/3/1149">Full text</ulink> and <ulink url="http://www.biophysj.org/cgi/reprint/74/3/1149.pdf">PDF</ulink> versions of the article are available for Journal Members on the Biophysical Journal website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=9512016&dopt=Abstract">PubMed ID: 9512016</ulink>
</para>
<para>
ABSTRACT
</para>
<para>
We construct a detailed mathematical model for Ca2+ regulation in the ventricular myocyte that includes novel descriptions of subcellular mechanisms based on recent experimental findings: 1) the Keizer-Levine model for the ryanodine receptor (RyR), which displays adaptation at elevated Ca2+; 2) a model for the L-type Ca2+ channel that inactivates by mode switching; and 3) a restricted subspace into which the RyRs and L-type Ca2+ channels empty and interact via Ca2+. We add membrane currents from the Luo-Rudy Phase II ventricular cell model to our description of Ca2+ handling to formulate a new model for ventricular action potentials and Ca2+ regulation. The model can simulate Ca2+ transients during an action potential similar to those seen experimentally. The subspace [Ca2+] rises more rapidly and reaches a higher level (10-30 µM) than the bulk myoplasmic Ca2+ (peak [Ca2+]i approx 1 µM). Termination of sarcoplasmic reticulum (SR) Ca2+ release is predominately due to emptying of the SR, but is influenced by RyR adaptation. Because force generation is roughly proportional to peak myoplasmic Ca2+, we use [Ca2+]i in the model to explore the effects of pacing rate on force generation. The model reproduces transitions seen in force generation due to changes in pacing that cannot be simulated by previous models. Simulation of such complex phenomena requires an interplay of both RyR adaptation and the degree of SR Ca2+ loading. This model, therefore, shows improved behavior over existing models that lack detailed descriptions of subcellular Ca2+ regulatory mechanisms.
</para>
<para>
The raw CellML description of the Jafri-Rice-Winslow model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>. For an example of a more complete documentation for an electrophysiological model, see <ulink url="${HTML_EXMPL_HHSA_INTRO}">The Hodgkin-Huxley Squid Axon Model, 1952</ulink>.
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram of the Jafri-Rice-Winslow model showing ionic currents, pumps and exchangers within the sarcolemma and the sarcoplasmic reticulum</title>
</objectinfo>
<imagedata fileref="cell_diagram.gif"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram describing the current flows across the cell membrane that are captured in the Jafri-Rice-Winslow model.</caption>
</informalfigure>
<informalfigure float="0" id="fig_cellml_rendering">
<mediaobject>
<imageobject>
<objectinfo>
<title>the cellml rendering of the Jafri-Rice-Winslow model</title>
</objectinfo>
<imagedata fileref="cellml_rendering.gif"/>
</imageobject>
</mediaobject>
<caption>The network defined in the CellML description of the Jafri-Rice-Winslow model. A key describing the significance of the shapes of the components and the colours of the connections between them is in the <ulink url="${HTML_EXMPL_GRAPHICAL_NOTATION}">notation guide</ulink>. For simplicity, not all the variables are shown.</caption>
</informalfigure>
<para>
The membrane physically contains the currents, exchangers and pumps, as indicated by the blue arrows in <xref linkend="fig_cellml_rendering"/>. The currents act independently and are not connected to each other. Several of the channels encapsulate <emphasis>and</emphasis> contain further components which represent activation and inactivation gates. The addition of an encapsulation relationship informs modellers and processing software that the gates are important parts of the current model. It also prevents any other components that aren't also encapsulated by the parent component from connecting to its gates, effectively hiding them from the rest of the model.
</para>
<para>
The breakdown of the model into components and the definition of encapsulation and containment relationships between them is somewhat arbitrary. When considering how a model should be broken into components, modellers are encouraged to consider which parts of a model might be re-used and how the physiological elements of the system being modelled are naturally bounded. Containment relationships should be used to provide simple rendering information for processing software (ideally, this will correspond to the layout of the physical system), and encapsulation should be used to group sets of components into sub-models.
</para>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="per_millisecond">
<unit units="second" prefix="milli" exponent="-1"/>
</units>
<units name="per_second">
<unit units="second" exponent="-1"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="per_millivolt">
<unit units="volt" prefix="milli" exponent="-1"/>
</units>
<units name="per_millivolt_millisecond">
<unit units="millivolt" exponent="-1"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="milliS_per_microF">
<unit units="siemens" prefix="milli"/>
<unit units="farad" prefix="micro" exponent="-1"/>
</units>
<units name="cm2">
<unit units="metre" prefix="centi" exponent="2"/>
</units>
<units name="micro_litre">
<unit units="litre" prefix="micro"/>
</units>
<units name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="micromolar">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="nanomolar">
<unit units="mole" prefix="nano"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="micromolar_per_second">
<unit units="micromolar"/>
<unit units="second" exponent="-1"/>
</units>
<units name="micromolar_per_millisecond">
<unit units="micromolar"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="per_micromolar_per_second">
<unit units="micromolar" exponent="-1"/>
<unit units="second" exponent="-1"/>
</units>
<units name="per_micromolar3_per_millisecond">
<unit units="micromolar" exponent="-3"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="per_micromolar4_per_millisecond">
<unit units="micromolar" exponent="-4"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="microF_per_cm2">
<unit units="farad" prefix="micro"/>
<unit units="metre" prefix="centi" exponent="-2"/>
</units>
<units name="microA_per_microF">
<unit units="ampere" prefix="micro"/>
<unit units="farad" prefix="micro" exponent="-1"/>
</units>
<units name="cm_per_second">
<unit units="metre" prefix="centi"/>
<unit units="second" exponent="-1"/>
</units>
<units name="cm_per_millisecond">
<unit units="metre" prefix="centi"/>
<unit units="millisecond" exponent="-1"/>
</units>
<units name="joule_per_mole_kelvin">
<unit units="joule"/>
<unit units="mole" exponent="-1"/>
<unit units="kelvin" exponent="-1"/>
</units>
<units name="coulomb_per_millimole">
<unit units="coulomb"/>
<unit units="mole" prefix="milli" exponent="-1"/>
</units>
<!--
The "environment" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
<component name="environment">
<variable units="millisecond" public_interface="out" name="time"/>
</component>
<!--
The "membrane" component is really the `root' node of our model.
It defines the action potential variable "V" among other things.
-->
<component name="membrane">
<!-- These variables are defined here and used in other components. -->
<variable units="millivolt" public_interface="out" name="V" initial_value="-84.1638"/>
<variable units="joule_per_mole_kelvin" public_interface="out" name="R" initial_value="8.314"/>
<variable units="kelvin" public_interface="out" name="T" initial_value="310.0"/>
<variable units="coulomb_per_millimole" public_interface="out" name="F" initial_value="96.5"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_L_Ca"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_L_K"/>
<variable units="microA_per_microF" public_interface="in" name="i_K"/>
<variable units="microA_per_microF" public_interface="in" name="i_K1"/>
<variable units="microA_per_microF" public_interface="in" name="i_NaCa"/>
<variable units="microA_per_microF" public_interface="in" name="i_Kp"/>
<variable units="microA_per_microF" public_interface="in" name="i_p_Ca"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na_b"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_b"/>
<variable units="microA_per_microF" public_interface="in" name="i_NaK"/>
<variable units="microA_per_microF" public_interface="in" name="i_ns_Ca"/>
<!--
The membrane voltage (V) is calculated as an ordinary
differential equation in terms of the currents.
-->
<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>
<plus/>
<ci> i_Na </ci>
<ci> i_Ca_L_Ca </ci>
<ci> i_Ca_L_K </ci>
<ci> i_K </ci>
<ci> i_NaCa </ci>
<ci> i_K1 </ci>
<ci> i_Kp </ci>
<ci> i_p_Ca </ci>
<ci> i_Na_b </ci>
<ci> i_Ca_b </ci>
<ci> i_NaK </ci>
<ci> i_ns_Ca </ci>
</apply>
</apply>
</math>
</component>
<!--
The "fast_sodium_current" component contains the differential equations
governing the influx of sodium ions through the cell surface membrane
into the cell. Note that no initial values are needed on many
variables as they are all directly dependent on membrane voltage.
-->
<component name="fast_sodium_current">
<!-- These variables are defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_Na"/>
<variable units="millivolt" public_interface="out" name="E_Na"/>
<!-- This variable is defined here and only used internally. -->
<variable units="milliS_per_microF" name="g_Na" initial_value="1.96352"/>
<!--
Time is imported from the environment, and membrane potential is
imported from the membrane component. These variables are used in the
"sodium_current" parent component, which also acts as an interface,
passing the variables to its encapsulated gate components.
-->
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<!-- These variables are imported from encapsulated components. -->
<variable units="dimensionless" private_interface="in" name="m"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<variable units="dimensionless" private_interface="in" name="j"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The following equation calculates the sodium current in terms
of the conductance, the membrane voltage, and the gate variables.
-->
<apply id="i_Na_calculation">
<eq/>
<ci> i_Na </ci>
<apply>
<times/>
<ci> g_Na </ci>
<apply>
<power/>
<ci> m </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> h </ci>
<ci> j </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Na </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> Nao </ci>
<ci> Nai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "fast_sodium_current_m_gate" is the m gate encapsulated inside the fast
sodium current.
-->
<component name="fast_sodium_current_m_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="m" initial_value="0.0328302"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_m"/>
<variable units="per_millisecond" name="beta_m"/>
<!--
These variables are imported from the environment and the membrane via
the "fast_sodium_current" component.
-->
<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">
<!--
The rate constants on the m, h and j gates are functions
of membrane voltage.
-->
<apply id="alpha_m_calculation">
<eq/>
<ci> alpha_m </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.32 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 47.13 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.1 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 47.13 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_m_calculation">
<eq/>
<ci> beta_m </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.08 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 11.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="dm_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> m </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_m </ci>
<apply>
<minus/>
<cn cellml:units="per_millivolt"> 1.0 </cn>
<ci> m </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_m </ci>
<ci> m </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "fast_sodium_current_h_gate" component is the h gate encapsulated in
the fast sodium current.
-->
<component name="fast_sodium_current_h_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="h" initial_value="0.988354"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_h"/>
<variable units="per_millisecond" name="beta_h"/>
<!--
These variables are imported from the environment and the membrane via
the "fast_sodium_current" component.
-->
<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">
<!--
The equations for the rate constant coefficients of the inactivation
gates h and j are dependent on the value of the membrane potential.
-->
<apply id="alpha_h_calculation">
<eq/>
<ci> alpha_h </ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.135 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt"> 80.0 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> -6.8 </cn>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="millivolt"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_millisecond"> 0.0 </cn>
</otherwise>
</piecewise>
</apply>
<apply id="beta_h_calculation">
<eq/>
<ci> beta_h </ci>
<piecewise>
<piece>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 3.56 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="millivolt"> 0.079 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 310000.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.35 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="millivolt"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="millisecond"> 0.13 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 10.66 </cn>
</apply>
<cn cellml:units="millivolt"> -11.1 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply id="dh_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> h </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_h </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> h </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_h </ci>
<ci> h </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "fast_sodium_current_j_gate" component is the j gate encapsulated in
the fast sodium current.
-->
<component name="fast_sodium_current_j_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="j" initial_value="0.992540"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_j"/>
<variable units="per_millisecond" name="beta_j"/>
<!--
These variables are imported from the environment and the membrane via
the "fast_sodium_current" component.
-->
<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="alpha_j_calculation">
<eq/>
<ci> alpha_j </ci>
<piecewise>
<piece>
<apply>
<times/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> -127140.0
</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.2444 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.00003474 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.04391 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 37.78 </cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.311 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 79.23 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="millivolt"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_millisecond"> 0.0 </cn>
</otherwise>
</piecewise>
</apply>
<apply id="beta_j_calculation">
<eq/>
<ci> beta_j </ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.1212 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.01052 </cn>
<ci> V </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.1378 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 40.14 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="millivolt"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.3 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.0000002535 </cn>
<ci> V </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.1 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 32.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply id="dj_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> j </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_j </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> j </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_j </ci>
<ci> j </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The JWR model creates a new mathematical model to describe the L-type
calcium channel that is based on the experimentally observed mode-switching
behaviour of the channel. Inactivation occurs as calcium ion binding
induces the channel to switch (from mode normal) to a mode in which
transitions to open states are extremely slow (mode Ca). The channel has
one voltage inactivation gate, y.
-->
<component name="L_type_Ca_channel">
<!-- These variables are defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_Ca_L_Ca"/>
<variable units="microA_per_microF" public_interface="out" name="i_Ca_L_K"/>
<!-- These variables are defined here and only used internally. -->
<variable units="cm_per_second" name="P_Ca" initial_value="0.00054"/>
<variable units="cm_per_second" name="P_K" initial_value="0.0000001"/>
<variable units="cm_per_second" name="p_k"/>
<variable units="microA_per_microF" name="i_Ca_L_Ca_half" initial_value="-0.458"/>
<variable units="microA_per_microF" name="i_Ca_L_Ca_max"/>
<variable units="dimensionless" name="O" initial_value="0.00000000000000000000984546"/>
<variable units="dimensionless" name="O_Ca" initial_value="0.0"/>
<variable units="per_millisecond" name="alpha"/>
<variable units="per_millisecond" name="beta"/>
<variable units="per_millisecond" name="gamma"/>
<variable units="per_millisecond" name="alpha_a"/>
<variable units="per_millisecond" name="beta_b"/>
<variable units="dimensionless" name="a" initial_value="2.0"/>
<variable units="dimensionless" name="b" initial_value="2.0"/>
<variable units="per_millisecond" name="g" initial_value="2.0"/>
<variable units="per_millisecond" name="f" initial_value="0.3"/>
<variable units="per_millisecond" name="g_" initial_value="0.0"/>
<variable units="per_millisecond" name="f_" initial_value="0.0"/>
<variable units="per_millisecond" name="omega" initial_value="0.01"/>
<variable units="dimensionless" name="C0" initial_value="0.997208"/>
<variable units="dimensionless" name="C1" initial_value="0.0000638897"/>
<variable units="dimensionless" name="C2" initial_value="0.00000000153500"/>
<variable units="dimensionless" name="C3" initial_value="0.0000000000000163909"/>
<variable units="dimensionless" name="C4" initial_value="0.0000000000000000000656337"/>
<variable units="dimensionless" name="C_Ca0" initial_value="0.00272826"/>
<variable units="dimensionless" name="C_Ca1" initial_value="0.000000699215"/>
<variable units="dimensionless" name="C_Ca2" initial_value="0.0000000000671989"/>
<variable units="dimensionless" name="C_Ca3" initial_value="0.00000000000000287031"/>
<variable units="dimensionless" name="C_Ca4" initial_value="0.000000000000000000459752"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millimolar" public_interface="in" name="Ca_SS"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<!-- These variables are imported from encapsulated components. -->
<variable units="dimensionless" private_interface="in" name="y"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The following equation calculates the calcium current through the L-type
Ca channel.
-->
<apply id="i_Ca_L_Ca_calculation">
<eq/>
<ci> i_Ca_L_Ca </ci>
<apply>
<times/>
<ci> P_Ca </ci>
<ci> y </ci>
<apply>
<plus/>
<ci> O </ci>
<ci> O_Ca </ci>
</apply>
<cn cellml:units="dimensionless"> 4.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.001 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.341 </cn>
<ci> Cao </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<!--
The following equation calculates the potassium current through the
L-type Ca channel.
-->
<apply id="i_Ca_L_K_calculation">
<eq/>
<ci> i_Ca_L_K </ci>
<apply>
<times/>
<ci> p_k </ci>
<ci> y </ci>
<apply>
<plus/>
<ci> O </ci>
<ci> O_Ca </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> Ki </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<ci> Ko </ci>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="p_k_calculation">
<eq/>
<ci> p_k </ci>
<apply>
<divide/>
<ci> P_K </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> i_Ca_L_Ca_max </ci>
<ci> i_Ca_L_Ca_half </ci>
</apply>
</apply>
</apply>
</apply>
<!--
The following equation calculates the maximal L-type calcium current.
-->
<apply id="i_Ca_L_Ca_max_calculation">
<eq/>
<ci> i_Ca_L_Ca_max </ci>
<apply>
<times/>
<ci> P_Ca </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.001 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.341 </cn>
<ci> Cao </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<!--
The rate constants for the L-type calcium channel depend on material
parameters and the equations below.
-->
<apply id="alpha_calculation">
<eq/>
<ci> alpha </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.4 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 12.0 </cn>
</apply>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_calculation">
<eq/>
<ci> beta </ci>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.05 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 12.0 </cn>
</apply>
<cn cellml:units="millivolt"> 13.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="alpha_a_calculation">
<eq/>
<ci> alpha_a </ci>
<apply>
<times/>
<ci> alpha </ci>
<ci> a </ci>
</apply>
</apply>
<apply id="beta_b_calculation">
<eq/>
<ci> beta_b </ci>
<apply>
<divide/>
<ci> beta </ci>
<ci> b </ci>
</apply>
</apply>
<apply id="gamma_calculation">
<eq/>
<ci> gamma </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.1875 </cn>
<ci> Ca_SS </ci>
</apply>
</apply>
<!--
In the normal mode, the calcium channel is able to make the transition
to the open, conducting state (o) from the closed state (C) at a normal
rate.
-->
<apply id="C0_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C0 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> beta </ci>
<ci> C1 </ci>
</apply>
<apply>
<times/>
<ci> omega </ci>
<ci> C_Ca0 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> alpha </ci>
</apply>
<ci> gamma </ci>
</apply>
<ci> C0 </ci>
</apply>
</apply>
</apply>
<apply id="C1_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C1 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> alpha </ci>
<ci> C0 </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> beta </ci>
<ci> C2 </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> omega </ci>
<ci> b </ci>
</apply>
<ci> C_Ca1 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> beta </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> alpha </ci>
</apply>
<apply>
<times/>
<ci> gamma </ci>
<ci> a </ci>
</apply>
</apply>
<ci> C1 </ci>
</apply>
</apply>
</apply>
<apply id="C2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C2 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> alpha </ci>
<ci> C1 </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> beta </ci>
<ci> C3 </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> omega </ci>
<apply>
<power/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<ci> C_Ca2 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> beta </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> alpha </ci>
</apply>
<apply>
<times/>
<ci> gamma </ci>
<apply>
<power/>
<ci> a </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<ci> C2 </ci>
</apply>
</apply>
</apply>
<apply id="C3_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C3 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> alpha </ci>
<ci> C2 </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> beta </ci>
<ci> C4 </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> omega </ci>
<apply>
<power/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
<ci> C_Ca3 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> beta </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> alpha </ci>
<apply>
<times/>
<ci> gamma </ci>
<apply>
<power/>
<ci> a </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<ci> C3 </ci>
</apply>
</apply>
</apply>
<apply id="C4_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C4 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> alpha </ci>
<ci> C3 </ci>
</apply>
<apply>
<times/>
<ci> g </ci>
<ci> O </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> omega </ci>
<apply>
<power/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
</apply>
<ci> C_Ca4 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> beta </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<ci> f </ci>
<apply>
<times/>
<ci> gamma </ci>
<apply>
<power/>
<ci> a </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
</apply>
</apply>
<ci> C4 </ci>
</apply>
</apply>
</apply>
<apply id="O_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> O </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> f </ci>
<ci> C4 </ci>
</apply>
<apply>
<times/>
<ci> g </ci>
<ci> O </ci>
</apply>
</apply>
</apply>
<!--
Calcium binding to the Ca channel induces a conformational change from
normal mode to mode Ca. This effectively inhibits the conduction of
calcium ions because in mode Ca, the calcium channel makes the
transition to the open, conducting state (O) extremely slowly.
-->
<apply id="C_Ca0_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C_Ca0 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> beta_b </ci>
<ci> C_Ca1 </ci>
</apply>
<apply>
<times/>
<ci> gamma </ci>
<ci> C_Ca0 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> alpha_a </ci>
</apply>
<ci> omega </ci>
</apply>
<ci> C_Ca0 </ci>
</apply>
</apply>
</apply>
<apply id="C_Ca1_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C_Ca1 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> alpha_a </ci>
<ci> C_Ca0 </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> beta_b </ci>
<ci> C_Ca2 </ci>
</apply>
<apply>
<times/>
<ci> gamma </ci>
<ci> a </ci>
<ci> C1 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> beta_b </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> alpha_a </ci>
</apply>
<apply>
<divide/>
<ci> omega </ci>
<ci> b </ci>
</apply>
</apply>
<ci> C_Ca1 </ci>
</apply>
</apply>
</apply>
<apply id="C_Ca2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C_Ca2 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> alpha_a </ci>
<ci> C_Ca1 </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> beta_b </ci>
<ci> C_Ca3 </ci>
</apply>
<apply>
<times/>
<ci> gamma </ci>
<apply>
<power/>
<ci> a </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> C2 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> beta_b </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> alpha_a </ci>
</apply>
<apply>
<divide/>
<ci> omega </ci>
<apply>
<power/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<ci> C_Ca2 </ci>
</apply>
</apply>
</apply>
<apply id="C_Ca3_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C_Ca3 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> alpha_a </ci>
<ci> C_Ca2 </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> beta_b </ci>
<ci> C_Ca4 </ci>
</apply>
<apply>
<times/>
<ci> gamma </ci>
<apply>
<power/>
<ci> a </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> C3 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> beta_b </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> alpha_a </ci>
<apply>
<divide/>
<ci> omega </ci>
<apply>
<power/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<ci> C_Ca3 </ci>
</apply>
</apply>
</apply>
<apply id="C_Ca4_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> C_Ca4 </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci> alpha_a </ci>
<ci> C_Ca3 </ci>
</apply>
<apply>
<times/>
<ci> g_ </ci>
<ci> O_Ca </ci>
</apply>
<apply>
<times/>
<ci> gamma </ci>
<apply>
<power/>
<ci> a </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<ci> C4 </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> beta_b </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<ci> f_ </ci>
<apply>
<divide/>
<ci> omega </ci>
<apply>
<power/>
<ci> b </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
</apply>
</apply>
<ci> C_Ca4 </ci>
</apply>
</apply>
</apply>
<apply id="O_Ca_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> O_Ca </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> f_ </ci>
<ci> C_Ca4 </ci>
</apply>
<apply>
<times/>
<ci> g_ </ci>
<ci> O_Ca </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "L_type_Ca_channel" component has an encapsulated voltage inactivation
gate, y.
-->
<component name="L_type_Ca_channel_y_gate">
<!-- this variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="y" initial_value="0.998983"/>
<!-- These variables are defined here and only used internally. -->
<variable units="dimensionless" name="y_infinity"/>
<variable units="dimensionless" name="tau_y"/>
<!--
These variables are imported from the environment and the membrane via
the "L_type_Ca_channel" component.
-->
<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="y_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> y </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> y_infinity </ci>
<ci> y </ci>
</apply>
<ci> tau_y </ci>
</apply>
</apply>
<apply id="y_infinity_calculation">
<eq/>
<ci> y_infinity </ci>
<apply>
<plus/>
<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"> 55.0 </cn>
</apply>
<cn cellml:units="millivolt"> 7.5 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 0.1 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 21.0 </cn>
</apply>
<cn cellml:units="millivolt"> 6.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_y_calculation">
<eq/>
<ci> tau_y </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 20.0 </cn>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 600.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
<cn cellml:units="millivolt"> 9.5 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The time-dependent potassium current has an X^2 dependence on it's
activation gate, and an Xi inactivation gate. These are encapsulated in the
parent "time_dependent_potassium_current" component.
-->
<component name="time_dependent_potassium_current">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_K"/>
<!-- These variables are defined here and only used internally. -->
<variable units="milliS_per_microF" name="g_K"/>
<variable units="millivolt" name="E_K"/>
<variable units="dimensionless" name="P_NaK" initial_value="0.01833"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<!-- These variables are imported from encapsulated components. -->
<variable units="dimensionless" private_interface="in" name="X"/>
<variable units="dimensionless" private_interface="in" name="Xi"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The following equation calculates the maximum conductance of the
potassium channel (gK).
-->
<apply id="g_K_calculation">
<eq/>
<ci> g_K </ci>
<apply>
<times/>
<cn cellml:units="milliS_per_microF"> 0.1128 </cn>
<apply>
<root/>
<apply>
<divide/>
<ci> Ko </ci>
<cn cellml:units="millimolar"> 5.4 </cn>
</apply>
</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/>
<apply>
<plus/>
<ci> Ko </ci>
<apply>
<times/>
<ci> P_NaK </ci>
<ci> Nao </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> Ki </ci>
<apply>
<times/>
<ci> P_NaK </ci>
<ci> Nai </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<!--
The following equation calculates the time-dependent potassium
current in terms of the conductance, the membrane voltage and the
gate variables.
-->
<apply id="i_K_calculation">
<eq/>
<ci> i_K </ci>
<apply>
<times/>
<ci> g_K </ci>
<ci> Xi </ci>
<apply>
<power/>
<ci> X </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "time_dependent_potassium_current_X_gate" component is the
time-dependent activation gate encapsulated in the rapid_time-dependent
potassium current.
-->
<component name="time_dependent_potassium_current_X_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="X" initial_value="0.000928836"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_X"/>
<variable units="per_millisecond" name="beta_X"/>
<!--
These variables are imported from the environment and the membrane via
the "time_dependent_potassium_current" component. -->
<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">
<!-- The rate constants for X are governed by the following equations. -->
<apply id="alpha_X_calculation">
<eq/>
<ci> alpha_X </ci>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.0000719 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.148 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_X_calculation">
<eq/>
<ci> beta_X </ci>
<apply>
<times/>
<cn cellml:units="per_millivolt_millisecond"> 0.000131 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.0687 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dX_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> X </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_X </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> X </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_X </ci>
<ci> X </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "time_dependent_potassium_current_Xi_gate" component is the
time-independent inactivation gate encapsulated in the time-dependent
potassium current.
-->
<component name="time_dependent_potassium_current_Xi_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="Xi"/>
<!--
These variables are imported from the "environment" and the "membrane" via
the "time_dependent_potassium_current" component.
-->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<!--
Xi is the inward rectification parameter and is given by the following
equation.
-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Xi_calculation">
<eq/>
<ci> Xi </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/>
<ci> V </ci>
<cn cellml:units="millivolt"> 56.26 </cn>
</apply>
<cn cellml:units="millivolt"> 32.1 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "time_independent_potassium_current" component contains a single
inactivation gate (K1) whose time constant is small enough that it
can be approximated by its steady-state value K1_infinity.
-->
<component name="time_independent_potassium_current">
<!-- These variables are defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_K1"/>
<variable units="millivolt" public_interface="out" private_interface="out" name="E_K1"/>
<!-- This variable is defined here and only used internally. -->
<variable units="milliS_per_microF" name="g_K1"/>
<!--
These variables are imported from other components. They are all used in
the parent "time_independent_potassium_current" component and some are
also passed via this interface to the encapsulated gates.
-->
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<!-- This variable is imported from an encapsulated component. -->
<variable units="dimensionless" private_interface="in" name="K1_infinity"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The following equation determines the maximum conductance of the
potassium channel.
-->
<apply id="g_K1_calculation">
<eq/>
<ci> g_K1 </ci>
<apply>
<times/>
<cn cellml:units="milliS_per_microF"> 0.75 </cn>
<apply>
<root/>
<apply>
<divide/>
<ci> Ko </ci>
<cn cellml:units="millimolar"> 5.4 </cn>
</apply>
</apply>
</apply>
</apply>
<!--
The following equation calculates the reversal potential of the
time-independent potassium current.
-->
<apply id="E_K1_calculation">
<eq/>
<ci> E_K1 </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Ko </ci>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</apply>
<!--
The following equation calculates the time-independent potassium
current in terms of the conductance, the membrane voltage and the
gate variables.
-->
<apply id="i_K1_calculation">
<eq/>
<ci> i_K1 </ci>
<apply>
<times/>
<ci> g_K1 </ci>
<ci> K1_infinity </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "time_independent_potassium_current_K1_gate" component is the K1 gate
encapsulated in the time-independent potassium current.
-->
<component name="time_independent_potassium_current_K1_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="K1_infinity"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_millisecond" name="alpha_K1"/>
<variable units="per_millisecond" name="beta_K1"/>
<!--
These variables are imported from the "environment", "membrane" and
"time_independent_potassium_current" components.
-->
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="E_K1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The rate constants on the K1 gate are functions of membrane voltage.
-->
<apply id="alpha_K1_calculation">
<eq/>
<ci> alpha_K1 </ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond"> 1.02 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.2385 </cn>
<apply>
<minus/>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K1 </ci>
</apply>
<cn cellml:units="millivolt"> 59.215 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_K1_calculation">
<eq/>
<ci> beta_K1 </ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millisecond"> 0.49124 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.08032 </cn>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 5.476 </cn>
</apply>
<ci> E_K1 </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.06175 </cn>
<apply>
<minus/>
<ci> V </ci>
<apply>
<plus/>
<ci> E_K1 </ci>
<cn cellml:units="millivolt"> 594.31 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt"> -0.5143 </cn>
<apply>
<minus/>
<ci> V </ci>
<apply>
<plus/>
<ci> E_K1 </ci>
<cn cellml:units="millivolt"> 4.753 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<!--
The steady-state value K1_infinity is given by the following
equation.
-->
<apply id="K1_infinity_calculation">
<eq/>
<ci> K1_infinity </ci>
<apply>
<divide/>
<ci> alpha_K1 </ci>
<apply>
<plus/>
<ci> alpha_K1 </ci>
<ci> beta_K1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "plateau_potassium_current" component contains the equations
which describe the contribution of a time independent
[K]o-insensitive channel at plateau potentials.
-->
<component name="plateau_potassium_current">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_Kp"/>
<!-- These variables are defined here and only used internally. -->
<variable units="millivolt" name="E_Kp"/>
<variable units="milliS_per_microF" name="g_Kp" initial_value="0.00828"/>
<variable units="dimensionless" name="Kp"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="E_K1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!--
The following equation calculates the plateau potassium current
reversal potential.
-->
<apply id="E_Kp_calculation">
<eq/>
<ci> E_Kp </ci>
<ci> E_K1 </ci>
</apply>
<!-- The following equation calculates the constant Kp. -->
<apply id="Kp_calculation">
<eq/>
<ci> Kp </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/>
<cn cellml:units="millivolt"> 7.488 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="millivolt"> 5.98 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<!--
The following equation determines the plateau potassium current in terms of the membrane voltage.
-->
<apply id="i_Kp_calculation">
<eq/>
<ci> i_Kp </ci>
<apply>
<times/>
<ci> g_Kp </ci>
<ci> Kp </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Kp </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "Na_Ca_exchanger" component describes how a protein molecule in the cell
surface membrane transports Na ions into the cytosol and exports Ca ions
into the extracellular matrix, in a ratio of 3:1 respectively.
-->
<component name="Na_Ca_exchanger">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_NaCa"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microA_per_microF" name="K_NaCa" initial_value="767.0"/>
<variable units="millimolar" name="K_mNa" initial_value="87.5"/>
<variable units="millimolar" name="K_mCa" initial_value="1.38"/>
<variable units="dimensionless" name="K_sat" initial_value="0.1"/>
<variable units="dimensionless" name="gamma" initial_value="0.35"/>
<!-- These variables are imported in from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="nanomolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<!-- The current is given as: -->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Na_Ca_exchanger">
<eq/>
<ci> i_NaCa </ci>
<apply>
<times/>
<ci> K_NaCa </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<apply>
<power/>
<ci> K_mNa </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<power/>
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<ci> K_mCa </ci>
<ci> Cao </ci>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> K_sat </ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci> gamma </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<times/>
<ci> gamma </ci>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci> Nai </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Cao </ci>
</apply>
<apply>
<times/>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci> gamma </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
<ci> V </ci>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "sarcolemmal_calcium_pump" is an additional mechanism for removing Ca
ions from the myoplasm to help maintain a low intracellular calcium
concentration when at rest.
-->
<component name="sarcolemmal_calcium_pump">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_p_Ca"/>
<!-- These variables are defined here and only used internally. -->
<variable units="micromolar" name="K_mpCa" initial_value="0.5"/>
<variable units="microA_per_microF" name="I_pCa" initial_value="1.15"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="nanomolar" public_interface="in" name="Cai"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_p_Ca_calculation">
<eq/>
<ci> i_p_Ca </ci>
<apply>
<times/>
<ci> I_pCa </ci>
<apply>
<divide/>
<ci> Cai </ci>
<apply>
<plus/>
<ci> K_mpCa </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "sodium_background_current" is a time-independent diffusion of Na ions
down their electrochemical gradient, through the cell surface membrane into
the cytosol.
-->
<component name="sodium_background_current">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_Na_b"/>
<!-- These variables are defined here and only used internally. -->
<variable units="milliS_per_microF" name="g_Nab" initial_value="0.00141"/>
<variable units="millivolt" name="E_NaN"/>
<!--
Time and membrane potential are imported from the "environment" and the
"membrane" components. The reversal potential is imported from the
"fast_sodium_current" component.
-->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="E_NaN_calculation">
<eq/>
<ci> E_NaN </ci>
<ci> E_Na </ci>
</apply>
<apply id="i_Na_b_calculation">
<eq/>
<ci> i_Na_b </ci>
<apply>
<times/>
<ci> g_Nab </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_NaN </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "calcium_background_current" describes a time-independent diffusion of
Ca ions down their electrochemical gradient through the cell surface
membrane into the cytosol. However, calcium is not allowed to accumulate to
high intracellular concentrations. This influx is balanced by the Ca ion
extrusion through the Na-Ca exchanger and the sarcolemmal Ca pump.
-->
<component name="calcium_background_current">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_Ca_b"/>
<!-- These variables are defined here and only used internally. -->
<variable units="milliS_per_microF" name="g_Cab" initial_value="0.006032"/>
<variable units="millivolt" name="E_CaN"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="nanomolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="E_CaN_calculation">
<eq/>
<ci> E_CaN </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> Cao </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="i_Ca_b_calculation">
<eq/>
<ci> i_Ca_b </ci>
<apply>
<times/>
<ci> g_Cab </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_CaN </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "sodium_potassium_pump" is an active protein in the cell membrane which
couples the free energy released by the hydrolysis of ATP to the movement of
Na and K ions against their electrochemical gradients through the cell
surface membrane.
-->
<component name="sodium_potassium_pump">
<!-- This variable is defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_NaK"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microA_per_microF" name="I_NaK" initial_value="1.3"/>
<variable units="dimensionless" name="f_NaK"/>
<variable units="millimolar" name="K_mNai" initial_value="10.0"/>
<variable units="millimolar" name="K_mKo" initial_value="1.5"/>
<variable units="dimensionless" name="sigma"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="f_NaK_calculation">
<eq/>
<ci> f_NaK </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.1245 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.1 </cn>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0365 </cn>
<ci> sigma </ci>
<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>
<apply id="sigma_calculation">
<eq/>
<ci> sigma </ci>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 7.0 </cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 67.3 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
<apply id="i_NaK_calculation">
<eq/>
<ci> i_NaK </ci>
<apply>
<times/>
<ci> I_NaK </ci>
<ci> f_NaK </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> K_mNai </ci>
<ci> Nai </ci>
</apply>
<cn cellml:units="dimensionless"> 1.5 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> Ko </ci>
<apply>
<plus/>
<ci> Ko </ci>
<ci> K_mKo </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "non_specific_calcium_activated_current" describes a channel which is activated by calcium ions, but is permeable to only sodium and potassium
ions.
-->
<component name="non_specific_calcium_activated_current">
<!-- These variables are defined here and used in other components. -->
<variable units="microA_per_microF" public_interface="out" name="i_ns_Ca"/>
<variable units="microA_per_microF" public_interface="out" name="i_ns_Na"/>
<variable units="microA_per_microF" public_interface="out" name="i_ns_K"/>
<!-- These variables are defined here and only used internally. -->
<variable units="microA_per_microF" name="I_ns_Ca"/>
<variable units="microA_per_microF" name="I_ns_Na"/>
<variable units="microA_per_microF" name="I_ns_K"/>
<variable units="micromolar" name="K_m_ns_Ca" initial_value="1.2"/>
<variable units="cm_per_second" name="P_ns_Ca" initial_value="1.75E-7"/>
<!--
Time and membrane potential are imported from the "environment" and the
"membrane" components. Intracellular calcium concentration is imported
from the "ionic_concentrations" component.
-->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="nanomolar" public_interface="in" name="Cai"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_ns_Na_calculation">
<eq/>
<ci> i_ns_Na </ci>
<apply>
<times/>
<ci> I_ns_Na </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> K_m_ns_Ca </ci>
<ci> Cai </ci>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_ns_K_calculation">
<eq/>
<ci> i_ns_K </ci>
<apply>
<times/>
<ci> I_ns_K </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> K_m_ns_Ca </ci>
<ci> Cai </ci>
</apply>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_ns_Ca_calculation">
<eq/>
<ci> i_ns_Ca </ci>
<apply>
<plus/>
<ci> i_ns_Na </ci>
<ci> i_ns_K </ci>
</apply>
</apply>
<apply id="I_ns_Na_calculation">
<eq/>
<ci> I_ns_Na </ci>
<apply>
<times/>
<ci> P_ns_Ca </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.75 </cn>
<ci> Nai </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<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"> 0.75 </cn>
<ci> Nao </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="I_ns_K_calculation">
<eq/>
<ci> I_ns_K </ci>
<apply>
<times/>
<ci> P_ns_Ca </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<apply>
<power/>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.75 </cn>
<ci> Ki </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<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"> 0.75 </cn>
<ci> Ko </ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
In the JRW model, subcellular calcium regulatory mechanisms are described in
detail. There are six calcium fluxes to consider; J_rel, J_leak, J_up,
J_tr, J_xfer and J_trpn. In addition, three membrane current fluxes are
also necessary for the formulation of calcium regulation; i_p_Ca, i_Ca_L_Ca
and i_NaCa. The equations to calculate these fluxes are contained within
the "calcium_subsystem" component.
-->
<component name="calcium_subsystem">
<!-- These variables are defined here and used in other components. -->
<variable units="nanomolar" public_interface="out" name="Cai" initial_value="0.0000994893"/>
<variable units="millimolar" public_interface="out" name="Ca_SS" initial_value="0.000136058"/>
<variable units="cm2" public_interface="out" name="A_cap" initial_value="0.0001534"/>
<variable units="micro_litre" public_interface="out" name="V_myo" initial_value="0.00002584"/>
<!-- These variables are defined here and only used internally. -->
<variable units="dimensionless" name="RyR_open"/>
<variable units="dimensionless" name="P_O1" initial_value="0.00119168"/>
<variable units="dimensionless" name="P_O2" initial_value="0.00000000630613"/>
<variable units="dimensionless" name="P_C1" initial_value="0.762527"/>
<variable units="dimensionless" name="P_C2" initial_value="0.236283"/>
<variable units="per_second" name="v1" initial_value="1.8"/>
<variable units="per_second" name="v2" initial_value="0.000058"/>
<variable units="micromolar_per_second" name="v3" initial_value="1.8"/>
<variable units="dimensionless" name="n" initial_value="4.0"/>
<variable units="dimensionless" name="m" initial_value="3.0"/>
<variable units="per_micromolar4_per_millisecond" name="k_a_plus" initial_value="0.01215"/>
<variable units="per_millisecond" name="k_a_minus" initial_value="0.1425"/>
<variable units="per_micromolar3_per_millisecond" name="k_b_plus" initial_value="0.00405"/>
<variable units="per_millisecond" name="k_b_minus" initial_value="1.930"/>
<variable units="per_millisecond" name="k_c_plus" initial_value="0.018"/>
<variable units="per_millisecond" name="k_c_minus" initial_value="0.0008"/>
<variable units="per_micromolar_per_second" name="k_htrpn_plus" initial_value="20000000.0"/>
<variable units="per_second" name="k_htrpn_minus" initial_value="0.066"/>
<variable units="per_micromolar_per_second" name="k_ltrpn_plus" initial_value="40000000.0"/>
<variable units="per_micromolar_per_second" name="k_ltrpn_minus" initial_value="40.0"/>
<variable units="millisecond" name="tau_tr" initial_value="34.48"/>
<variable units="millimolar" name="Ca_JSR" initial_value="1.17504"/>
<variable units="millimolar" name="Ca_NSR" initial_value="1.243891"/>
<variable units="micro_litre" name="V_JSR" initial_value="0.00000012"/>
<variable units="micro_litre" name="V_NSR" initial_value="0.000002098"/>
<variable units="micro_litre" name="V_SS" initial_value="0.000000001485"/>
<variable units="micromolar" name="K_mup" initial_value="0.5"/>
<variable units="micromolar" name="K_mCMDN" initial_value="2.38"/>
<variable units="millimolar" name="K_mCSQN" initial_value="0.8"/>
<variable units="millisecond" name="tau_xfer" initial_value="3.125"/>
<variable units="micromolar" name="HTRPN_tot" initial_value="140.0"/>
<variable units="micromolar" name="LTRPN_tot" initial_value="70.0"/>
<variable units="millimolar" name="HTRPNCa" initial_value="0.971295"/>
<variable units="millimolar" name="LTRPNCa" initial_value="907.139"/>
<variable units="millimolar" name="CSQN_tot" initial_value="15.0"/>
<variable units="micromolar" name="CMDN_tot" initial_value="50.0"/>
<variable units="dimensionless" name="Bi"/>
<variable units="dimensionless" name="B_SS"/>
<variable units="dimensionless" name="B_JSR"/>
<variable units="micromolar_per_millisecond" name="J_rel"/>
<variable units="micromolar_per_millisecond" name="J_leak"/>
<variable units="micromolar_per_millisecond" name="J_up"/>
<variable units="micromolar_per_millisecond" name="J_tr"/>
<variable units="micromolar_per_millisecond" name="J_xfer"/>
<variable units="micromolar_per_millisecond" name="J_trpn"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_b"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_L_Ca"/>
<variable units="microA_per_microF" public_interface="in" name="i_NaCa"/>
<variable units="microA_per_microF" public_interface="in" name="i_p_Ca"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<!-- The RyR channel flux is calculated by the following equation. -->
<apply id="J_rel_calculation">
<eq/>
<ci> J_rel </ci>
<apply>
<times/>
<ci> v1 </ci>
<ci> RyR_open </ci>
<apply>
<minus/>
<ci> Ca_JSR </ci>
<ci> Ca_SS </ci>
</apply>
</apply>
</apply>
<apply id="RyR_open_calculation">
<eq/>
<ci> RyR_open </ci>
<apply>
<plus/>
<ci> P_O1 </ci>
<ci> P_O2 </ci>
</apply>
</apply>
<apply id="P_C1_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_C1 </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci> k_a_plus </ci>
</apply>
<apply>
<power/>
<ci> Ca_SS </ci>
<ci> n </ci>
</apply>
<ci> P_C1 </ci>
</apply>
<apply>
<times/>
<ci> k_a_minus </ci>
<ci> P_O1 </ci>
</apply>
</apply>
</apply>
<apply id="P_O1_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_O1 </ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci> k_a_plus </ci>
<apply>
<power/>
<ci> Ca_SS </ci>
<ci> n </ci>
</apply>
<ci> P_C1 </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci> k_a_minus </ci>
<ci> P_O1 </ci>
</apply>
<apply>
<times/>
<ci> k_b_plus </ci>
<apply>
<power/>
<ci> Ca_SS </ci>
<ci> m </ci>
</apply>
<ci> P_O1 </ci>
</apply>
<apply>
<times/>
<ci> k_c_plus </ci>
<ci> P_O1 </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k_b_minus </ci>
<ci> P_O2 </ci>
</apply>
<apply>
<times/>
<ci> k_c_minus </ci>
<ci> P_C2 </ci>
</apply>
</apply>
</apply>
<apply id="P_O2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_O2 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_b_plus </ci>
<apply>
<power/>
<ci> Ca_SS </ci>
<ci> m </ci>
</apply>
<ci> P_O1 </ci>
</apply>
<apply>
<times/>
<ci> k_b_minus </ci>
<ci> P_O2 </ci>
</apply>
</apply>
</apply>
<apply id="P_C2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> P_C2 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_c_plus </ci>
<ci> P_O1 </ci>
</apply>
<apply>
<times/>
<ci> k_c_minus </ci>
<ci> P_C2 </ci>
</apply>
</apply>
</apply>
<!--
The leak from the NSR into the myoplasm is given by the following
equation.
-->
<apply id="J_leak_calculation">
<eq/>
<ci> J_leak </ci>
<apply>
<times/>
<ci> v2 </ci>
<apply>
<minus/>
<ci> Ca_NSR </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
<!--
Calcium uptake into the NSR by the sarcolemmal calcium pump is given by
the following equation.
-->
<apply id="J_up_calculation">
<eq/>
<ci> J_up </ci>
<apply>
<times/>
<ci> v3 </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Cai </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> K_mup </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> Cai </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<!--
The transfer flux of calcium from the NSR to the JSR is described by the
following equation.
-->
<apply id="J_tr_calculation">
<eq/>
<ci> J_tr </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Ca_NSR </ci>
<ci> Ca_JSR </ci>
</apply>
<ci> tau_tr </ci>
</apply>
</apply>
<!--
The transfer flux of calcium from the subspace to the myoplasm is
described by the following equation.
-->
<apply id="J_xfer_calculation">
<eq/>
<ci> J_xfer </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Ca_SS </ci>
<ci> Cai </ci>
</apply>
<ci> tau_xfer </ci>
</apply>
</apply>
<!--
Calcium buffering in the myoplasm by troponin (Tn) is described by the
following equation.
-->
<apply id="J_trpn_calculation">
<eq/>
<ci> J_trpn </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> k_htrpn_plus </ci>
<ci> Cai </ci>
<apply>
<minus/>
<apply>
<minus/>
<ci> HTRPN_tot </ci>
<ci> HTRPNCa </ci>
</apply>
<apply>
<times/>
<ci> k_htrpn_minus </ci>
<ci> HTRPNCa </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k_ltrpn_plus </ci>
<ci> Cai </ci>
<apply>
<minus/>
<apply>
<minus/>
<ci> LTRPN_tot </ci>
<ci> LTRPNCa </ci>
</apply>
<apply>
<times/>
<ci> k_ltrpn_minus </ci>
<ci> LTRPNCa </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<!--
The concentration of calcium bound to high affinity Tn is given by:
-->
<apply id="HTRPNCa_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> HTRPNCa </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_htrpn_plus </ci>
<ci> Cai </ci>
<apply>
<minus/>
<ci> HTRPN_tot </ci>
<ci> HTRPNCa </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_htrpn_minus </ci>
<ci> HTRPNCa </ci>
</apply>
</apply>
</apply>
<!--
The concentration of calcium bound to low affinity Tn is given by:
-->
<apply id="LTRPNCa_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> LTRPNCa </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k_ltrpn_plus </ci>
<ci> Cai </ci>
<apply>
<minus/>
<ci> LTRPN_tot </ci>
<ci> LTRPNCa </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k_ltrpn_minus </ci>
<ci> LTRPNCa </ci>
</apply>
</apply>
</apply>
<!--
Calcium is buffered by calmodulin (CMDN) in the subspace and myoplasm,
and by calsequestrin (CSQN) in the JSR.
-->
<apply id="Bi_calculation">
<eq/>
<ci> Bi </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> CMDN_tot </ci>
<ci> K_mCMDN </ci>
</apply>
<apply>
<plus/>
<ci> K_mCMDN </ci>
<apply>
<power/>
<ci> Cai </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="B_SS_calculation">
<eq/>
<ci> B_SS </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> CMDN_tot </ci>
<ci> K_mCMDN </ci>
</apply>
<apply>
<plus/>
<ci> K_mCMDN </ci>
<apply>
<power/>
<ci> Ca_SS </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="B_JSR_calculation">
<eq/>
<ci> B_JSR </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<apply>
<times/>
<ci> CSQN_tot </ci>
<ci> K_mCSQN </ci>
</apply>
<apply>
<plus/>
<ci> K_mCSQN </ci>
<apply>
<power/>
<ci> Ca_JSR </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="calcium_internal_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Cai </ci>
</apply>
<apply>
<times/>
<ci> Bi </ci>
<apply>
<minus/>
<apply>
<plus/>
<ci> J_leak </ci>
<ci> J_xfer </ci>
</apply>
<apply>
<plus/>
<ci> J_up </ci>
<ci> J_trpn </ci>
<apply>
<times/>
<apply>
<plus/>
<apply>
<minus/>
<ci> i_Ca_b </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> i_NaCa </ci>
</apply>
</apply>
<ci> i_p_Ca </ci>
</apply>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="calcium_subspace_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_SS </ci>
</apply>
<apply>
<times/>
<ci> B_SS </ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci> J_rel </ci>
<apply>
<divide/>
<ci> V_JSR </ci>
<ci> V_SS </ci>
</apply>
</apply>
<apply>
<times/>
<ci> J_xfer </ci>
<apply>
<divide/>
<ci> V_myo </ci>
<ci> V_SS </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> i_Ca_L_Ca </ci>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_SS </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="calcium_JSR_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_JSR </ci>
</apply>
<apply>
<times/>
<ci> B_JSR </ci>
<apply>
<minus/>
<ci> J_tr </ci>
<ci> J_rel </ci>
</apply>
</apply>
</apply>
<apply id="calcium_NSR_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_NSR </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<ci> J_up </ci>
<ci> J_leak </ci>
</apply>
<apply>
<divide/>
<ci> V_myo </ci>
<ci> V_NSR </ci>
</apply>
</apply>
<apply>
<times/>
<ci> J_tr </ci>
<apply>
<divide/>
<ci> V_JSR </ci>
<ci> V_NSR </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The descriptions of the rate of change of [Na]i and [K]i are the same as the
LR-II model. In addition to the LR-II model, both high and low affinity
calcium binding sites are included for troponin (Tn).
-->
<component name="ionic_concentrations">
<!-- these variables are defined here and used in other components -->
<variable units="millimolar" public_interface="out" name="Nai" initial_value="10.2042"/>
<variable units="millimolar" public_interface="out" name="Nao" initial_value="140.0"/>
<variable units="millimolar" public_interface="out" name="Ki" initial_value="143.727"/>
<variable units="millimolar" public_interface="out" name="Ko" initial_value="5.4"/>
<variable units="millimolar" public_interface="out" name="Cao" initial_value="1.8"/>
<!-- These variables are imported from other components. -->
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na"/>
<variable units="microA_per_microF" public_interface="in" name="i_Na_b"/>
<variable units="microA_per_microF" public_interface="in" name="i_ns_Na"/> <variable units="microA_per_microF" public_interface="in" name="i_NaCa"/>
<variable units="microA_per_microF" public_interface="in" name="i_NaK"/>
<variable units="microA_per_microF" public_interface="in" name="i_Ca_L_K"/> <variable units="microA_per_microF" public_interface="in" name="i_K"/>
<variable units="microA_per_microF" public_interface="in" name="i_K1"/>
<variable units="microA_per_microF" public_interface="in" name="i_Kp"/>
<variable units="microA_per_microF" public_interface="in" name="i_ns_K"/>
<variable units="cm2" public_interface="in" name="A_cap"/>
<variable units="micro_litre" public_interface="in" name="V_myo"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="sodium_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Nai </ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_Na_b </ci>
<ci> i_ns_Na </ci>
<apply>
<times/>
<ci> i_NaCa </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<times/>
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="potassium_internal_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ki </ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_Ca_L_K </ci>
<ci> i_K </ci>
<ci> i_K1 </ci>
<ci> i_Kp </ci>
<ci> i_ns_K </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="potassium_external_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ko </ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> i_Ca_L_K </ci>
<ci> i_K </ci>
<ci> i_K1 </ci>
<ci> i_Kp </ci>
<ci> i_ns_K </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> A_cap </ci>
<apply>
<times/>
<ci> V_myo </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The following <group> element specifies a single containment hierarchy
that encompasses all of the components in the model, with the exception of
the "environment" component. The "containment" relationship is used to
describe geometric hierarchies - or how components are physically arranged
in relation to eachother.
-->
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<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="fast_sodium_current_j_gate"/>
</component_ref>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_y_gate"/>
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_X_gate"/>
<component_ref component="time_dependent_potassium_current_Xi_gate"/>
</component_ref>
<component_ref component="Na_Ca_exchanger"/>
<component_ref component="time_independent_potassium_current">
<component_ref component="time_independent_potassium_current_K1_gate"/>
</component_ref>
<component_ref component="plateau_potassium_current"/>
<component_ref component="sarcolemmal_calcium_pump"/>
<component_ref component="sodium_background_current"/>
<component_ref component="calcium_background_current"/>
<component_ref component="sodium_potassium_pump"/>
<component_ref component="non_specific_calcium_activated_current"/>
<component_ref component="calcium_subsystem"/>
<component_ref component="ionic_concentrations"/>
</component_ref>
</group>
<!--
The following <group> element specifies how the components
representing activation and inactivation coefficients are
encapsulated inside the sodium and potassium channel components.
Encapsulation describes the logical hierarchy of components in a network,
and may or may not reflect their physical arrangement.
-->
<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="fast_sodium_current_j_gate"/>
</component_ref>
<component_ref component="L_type_Ca_channel">
<component_ref component="L_type_Ca_channel_y_gate"/>
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_X_gate"/>
<component_ref component="time_dependent_potassium_current_Xi_gate"/>
</component_ref>
<component_ref component="time_independent_potassium_current">
<component_ref component="time_independent_potassium_current_K1_gate"/>
</component_ref>
</group>
<!--
"Time" is passed from the "environment" component into the
"membrane" and current components.
-->
<connection>
<map_components component_2="environment" component_1="membrane"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="fast_sodium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="L_type_Ca_channel"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="time_independent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="plateau_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sarcolemmal_calcium_pump"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_background_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_background_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_potassium_pump"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="non_specific_calcium_activated_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="calcium_subsystem"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="ionic_concentrations"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<!--
Several variables are passed between the "membrane" and its sub-components.
-->
<connection>
<map_components component_2="fast_sodium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="L_type_Ca_channel" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Ca_L_Ca" variable_1="i_Ca_L_Ca"/>
<map_variables variable_2="i_Ca_L_K" variable_1="i_Ca_L_K"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="time_dependent_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K" variable_1="i_K"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="Na_Ca_exchanger" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="time_independent_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="plateau_potassium_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Kp" variable_1="i_Kp"/>
</connection>
<connection>
<map_components component_2="sarcolemmal_calcium_pump" component_1="membrane"/>
<map_variables variable_2="i_p_Ca" variable_1="i_p_Ca"/>
</connection>
<connection>
<map_components component_2="sodium_background_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Na_b" variable_1="i_Na_b"/>
</connection>
<connection>
<map_components component_2="calcium_background_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_Ca_b" variable_1="i_Ca_b"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="sodium_potassium_pump" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_NaK" variable_1="i_NaK"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="non_specific_calcium_activated_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_ns_Ca" variable_1="i_ns_Ca"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="calcium_subsystem" component_1="membrane"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="membrane"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<!-- Several variables are passed between the sibling components. -->
<connection>
<map_components component_2="ionic_concentrations" component_1="fast_sodium_current"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
</connection>
<connection>
<map_components component_2="sodium_background_current" component_1="fast_sodium_current"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<connection>
<map_components component_2="calcium_subsystem" component_1="L_type_Ca_channel"/>
<map_variables variable_2="Ca_SS" variable_1="Ca_SS"/>
<map_variables variable_2="i_Ca_L_Ca" variable_1="i_Ca_L_Ca"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="L_type_Ca_channel"/>
<map_variables variable_2="i_Ca_L_K" variable_1="i_Ca_L_K"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
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<connection>
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<map_variables variable_2="Ki" variable_1="Ki"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
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<map_variables variable_2="Nai" variable_1="Nai"/>
<map_variables variable_2="i_K" variable_1="i_K"/>
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<connection>
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<map_variables variable_2="Cao" variable_1="Cao"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
</connection>
<connection>
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<map_variables variable_2="Cai" variable_1="Cai"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
</connection>
<connection>
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<map_variables variable_2="Ki" variable_1="Ki"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
</connection>
<connection>
<map_components component_2="time_independent_potassium_current" component_1="plateau_potassium_current"/>
<map_variables variable_2="E_K1" variable_1="E_K1"/>
</connection>
<connection>
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<map_variables variable_2="i_Kp" variable_1="i_Kp"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="sodium_background_current"/>
<map_variables variable_2="i_Na_b" variable_1="i_Na_b"/>
</connection>
<connection>
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<map_variables variable_2="i_p_Ca" variable_1="i_p_Ca"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
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<connection>
<map_components component_2="calcium_subsystem" component_1="calcium_background_current"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
<map_variables variable_2="i_Ca_b" variable_1="i_Ca_b"/>
</connection>
<connection>
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<map_variables variable_2="Cao" variable_1="Cao"/>
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<connection>
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<map_variables variable_2="Nai" variable_1="Nai"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
<map_variables variable_2="i_NaK" variable_1="i_NaK"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="non_specific_calcium_activated_current"/>
<map_variables variable_2="i_ns_Na" variable_1="i_ns_Na"/>
<map_variables variable_2="i_ns_K" variable_1="i_ns_K"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
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<connection>
<map_components component_2="calcium_subsystem" component_1="non_specific_calcium_activated_current"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
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<map_variables variable_2="A_cap" variable_1="A_cap"/>
<map_variables variable_2="V_myo" variable_1="V_myo"/>
</connection>
<!--
Various variables are passed between parent components and their
encapsulated gates.
-->
<connection>
<map_components component_2="fast_sodium_current_m_gate" component_1="fast_sodium_current"/>
<map_variables variable_2="m" variable_1="m"/>
<map_variables variable_2="time" variable_1="time"/>
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<connection>
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<map_variables variable_2="h" variable_1="h"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
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<map_variables variable_2="j" variable_1="j"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
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<connection>
<map_components component_2="L_type_Ca_channel_y_gate" component_1="L_type_Ca_channel"/>
<map_variables variable_2="y" variable_1="y"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="time_dependent_potassium_current_X_gate" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="X" variable_1="X"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="time_dependent_potassium_current_Xi_gate" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="Xi" variable_1="Xi"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="time_independent_potassium_current_K1_gate" component_1="time_independent_potassium_current"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="E_K1" variable_1="E_K1"/>
<map_variables variable_2="K1_infinity" variable_1="K1_infinity"/>
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Changed tau_y_calculation after checking mathml using the validator.
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The University of Auckland, Bioengineering Research Group
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<rdf:value>This is the CellML description of Jafri, Rice and Winslow's mathematical model for calcium regulation in the ventricular myocyte. It is based on an accurate model of the membrane currents and adds a more sophisticated model of calcium handling. The JRW model is based on the LR-II model for ventricular action potentials, with several modifications.</rdf:value>
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Corrected equations: alpha_j_calculation and beta_j_calculation in
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The Jafri-Rice-Winslow Model for Calcium Regulation in the Ventricular
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Corrected equations.
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<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#45ac2334-f6c8-426c-a7b1-a2d5f542a8e1">
<dcterms:W3CDTF>2001-10-19</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a0b69316-40ba-4e1b-bcb3-192afe6f213b">
<dcterms:modified rdf:resource="rdf:#eb701aff-ce13-4bee-a7e3-17270a207fee"/>
<rdf:value>
Added some initial values from Penny Noble's documentation.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#03bd157e-3c1f-445b-ad02-962231683864"/>
</rdf:Description>
</rdf:RDF>
</model>
