- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-08-21 04:52:17+12:00
- Desc:
- committing version02 of luo_rudy_1991
- Permanent Source URI:
- http://models.cellml.org/workspace/luo_rudy_1991/rawfile/6b3f13b80911e99ae1d63f36b72d828d73883ef2/luo_rudy_1991.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : luo_rudy_I_model_1991.xml
CREATED : September 2001
LAST MODIFIED : 5th June 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 the 16th
January, 2002.
DESCRIPTION : This file contains a CellML description of the mammalian
ventricular action potential based on the Luo-Rudy I model, 1991. This model is
a significant update to the Beeler-Reuter mammalian ventricular model.
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 equations after checking with mathml validator.
04/01/2002 - CML - Added an ionic_concentrations and an
intracellular_calcium_concentrations components and altered
the public interfaces and connections appropriately.
21/01/2002 - AAC - Updated metadata to conform to the 16/1/02 CellML Metadata
1.0 Specification.
18/02/2002 - AAC - Corrected the beta_K1_calculation eqn.
20/02/2002 - CML - Corrected the Cai differential eqn. 06/05/2002 - CML - Added some initial values.
18/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
05/06/2003 - CML - Fixed MathML in a few components.
--><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="luo_rudy_1991_version02" name="luo_rudy_1991_version02">
<!--
Below, we define some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="ms">
<unit units="second" prefix="milli"/>
</units>
<units name="per_ms">
<unit units="second" prefix="milli" exponent="-1"/>
</units>
<units name="mV">
<unit units="volt" prefix="milli"/>
</units>
<units name="per_mV">
<unit units="volt" prefix="milli" exponent="-1"/>
</units>
<units name="per_mV_ms">
<unit units="mV" exponent="-1"/>
<unit units="ms" exponent="-1"/>
</units>
<units name="mS_per_mm2">
<unit units="siemens" prefix="milli"/>
<unit units="metre" prefix="milli" exponent="-2"/>
</units>
<units name="uF_per_mm2">
<unit units="farad" prefix="micro"/>
<unit units="metre" prefix="milli" exponent="-2"/>
</units>
<units name="uA_per_mm2">
<unit units="ampere" prefix="micro"/>
<unit units="metre" prefix="milli" exponent="-2"/>
</units>
<units name="concentration_units">
<unit units="mole" prefix="nano"/>
<unit units="metre" prefix="milli" exponent="-3"/>
</units>
<units name="gas_constant_units">
<unit units="joule" prefix="pico"/>
<unit units="mole" prefix="nano" exponent="-1"/>
<unit units="kelvin" exponent="-1"/>
</units>
<units name="faradays_constant_units">
<unit units="coulomb" prefix="nano"/>
<unit units="mole" prefix="nano" 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" cmeta:id="environment">
<variable units="ms" 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" cmeta:id="membrane">
<!-- These variables are defined here and used in other components. -->
<variable units="mV" public_interface="out" name="V" initial_value="-84.5"/>
<variable units="gas_constant_units" public_interface="out" name="R" initial_value="8.314e3"/>
<variable units="kelvin" public_interface="out" name="T" initial_value="310.0"/>
<variable units="faradays_constant_units" public_interface="out" name="F" initial_value="96845.0"/>
<!-- These variables are defined here and only used internally. -->
<variable units="uF_per_mm2" name="C" initial_value="1.0e-2"/>
<variable units="uA_per_mm2" name="I_stim"/>
<!-- These variables are imported from other components. -->
<variable units="ms" public_interface="in" name="time"/>
<variable units="uA_per_mm2" public_interface="in" name="i_Na"/>
<variable units="uA_per_mm2" public_interface="in" name="i_si"/>
<variable units="uA_per_mm2" public_interface="in" name="i_K"/>
<variable units="uA_per_mm2" public_interface="in" name="i_K1"/>
<variable units="uA_per_mm2" public_interface="in" name="i_Kp"/>
<variable units="uA_per_mm2" public_interface="in" name="i_b"/>
<!--
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" cmeta:id="membrane_voltage_diff_eq">
<apply id="membrane_voltage_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> V </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> I_stim </ci>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_si </ci>
<ci> i_K </ci>
<ci> i_K1 </ci>
<ci> i_Kp </ci>
<ci> i_b </ci>
</apply>
</apply>
<ci> C </ci>
</apply>
</apply>
</math>
<variable units="uA_per_mm2" public_interface="out" name="IStimC"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="IStim_for_cmiss_eq">
<apply id="IStim_for_cmiss">
<eq/>
<ci>IStimC</ci>
<ci>I_stim</ci>
</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" cmeta:id="fast_sodium_current">
<!-- This variable is defined here and used in other components. -->
<variable units="uA_per_mm2" public_interface="out" name="i_Na"/>
<!-- These variables are defined here and only used internally. -->
<variable units="mS_per_mm2" name="g_Na" initial_value="23.0e-2"/>
<variable units="mV" name="E_Na" initial_value="54.4"/>
<!--
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="ms" public_interface="in" private_interface="out" name="time"/>
<variable units="mV" public_interface="in" private_interface="out" name="V"/>
<!-- 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" cmeta:id="i_Na_calculation_eq">
<!--
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>
</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" cmeta:id="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="1.67e-3"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_ms" name="alpha_m"/>
<variable units="per_ms" name="beta_m"/>
<!--
These variables are imported from the "environment" and the "membrane" via
the "fast_sodium_current" component.
-->
<variable units="mV" public_interface="in" name="V"/>
<variable units="ms" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="alpha_m_calculation_eq">
<apply id="alpha_m_calculation">
<eq/>
<ci> alpha_m </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_mV_ms"> 0.32 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 47.13 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> -0.1 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 47.13 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="beta_m_calculation_eq">
<apply id="beta_m_calculation">
<eq/>
<ci> beta_m </ci>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.08 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="mV"> 11.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="dm_dt_eq">
<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="dimensionless"> 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" cmeta:id="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="9.38e-1"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_ms" name="alpha_h"/>
<variable units="per_ms" name="beta_h"/>
<!--
These variables are imported from the "environment" and the "membrane" via
the "fast_sodium_current" component.
-->
<variable units="mV" public_interface="in" name="V"/>
<variable units="ms" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="alpha_h_calculation_eq">
<apply id="alpha_h_calculation">
<eq/>
<ci> alpha_h </ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.135 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="mV"> -80.0 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="mV"> 6.8 </cn>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="mV"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_ms"> 0.0 </cn>
</otherwise>
</piecewise>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="beta_h_calculation_eq">
<apply id="beta_h_calculation">
<eq/>
<ci> beta_h </ci>
<piecewise>
<piece>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_ms"> 3.56 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="mV"> 0.079 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_ms"> 310000.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> 0.35 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="mV"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="ms"> 0.13 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 10.66 </cn>
</apply>
</apply>
<cn cellml:units="mV"> 11.1 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="dh_dt_eq">
<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" cmeta:id="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="1.0"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_ms" name="alpha_j"/>
<variable units="per_ms" name="beta_j"/>
<!--
These variables are imported from the "environment" and the "membrane" via
the "fast_sodium_current" component.
-->
<variable units="mV" public_interface="in" name="V"/>
<variable units="ms" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="alpha_j_calculation_eq">
<apply id="alpha_j_calculation">
<eq/>
<ci> alpha_j </ci>
<piecewise>
<piece>
<apply>
<times/>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="per_mV_ms"> -127140.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> 0.2444 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_mV_ms"> 0.00003474 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> -0.04391 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 37.78 </cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> 0.311 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 79.23 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="mV"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_ms"> 0.0 </cn>
</otherwise>
</piecewise>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="beta_j_calculation_eq">
<apply id="beta_j_calculation">
<eq/>
<ci> beta_j </ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.1212 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> -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_mV"> -0.1378 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 40.14 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci> V </ci>
<cn cellml:units="mV"> -40.0 </cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.3 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> -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_mV"> -0.1 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 32.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="dj_dt_eq">
<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 "slow_inward_current " component contains the differential
equations governing the transient inward ionic current.It has two
encapsulated gates; an activation d gate and an inactivation f gate.
-->
<component name="slow_inward_current" cmeta:id="slow_inward_current">
<!-- This variable is defined here and used in other components. -->
<variable units="uA_per_mm2" public_interface="out" name="i_si"/>
<!-- These variables are defined here and only used internally. -->
<variable units="mV" name="E_si"/>
<variable units="mS_per_mm2" name="g_si" initial_value="9.0e-4"/>
<!--
Time is imported from the "environment", and membrane potential is
imported from the "membrane" component. These variables are used in the
"slow_inward_current" parent component, which also acts as an interface,
passing the variables to its encapsulated gate component.
-->
<variable units="ms" public_interface="in" private_interface="out" name="time"/>
<variable units="mV" public_interface="in" private_interface="out" name="V"/>
<variable units="concentration_units" public_interface="in" name="Cai"/>
<!-- These variables are imported from encapsulated components. -->
<variable units="dimensionless" private_interface="in" name="d"/>
<variable units="dimensionless" private_interface="in" name="f"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="E_si_calculation_eq">
<apply id="E_si_calculation">
<eq/>
<ci> E_si </ci>
<apply>
<minus/>
<cn cellml:units="mV"> 7.7 </cn>
<apply>
<times/>
<cn cellml:units="mV"> 13.0287 </cn>
<apply>
<ln/>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_si_calculation_eq">
<apply id="i_si_calculation">
<eq/>
<ci> i_si </ci>
<apply>
<times/>
<ci> g_si </ci>
<ci> d </ci>
<ci> f </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_si </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "slow_inward_current_d_gate" component is the d gate encapsulated in
the slow inward current.
-->
<component name="slow_inward_current_d_gate" cmeta:id="slow_inward_current_d_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="d" initial_value="2.98e-3"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_ms" name="alpha_d"/>
<variable units="per_ms" name="beta_d"/>
<!--
These variables are imported from the "environment" and the "membrane" via
the "slow_inward_current" component.
-->
<variable units="mV" public_interface="in" name="V"/>
<variable units="ms" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="alpha_d_calculation_eq">
<apply id="alpha_d_calculation">
<eq/>
<ci> alpha_d </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.095 </cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 0.01 </cn>
</apply>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="mV"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 0.072 </cn>
</apply>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="mV"> 5.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="beta_d_calculation_eq">
<apply id="beta_d_calculation">
<eq/>
<ci> beta_d </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.07 </cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 0.017 </cn>
</apply>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 44.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.05 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 44.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="dd_dt_eq">
<apply id="dd_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> d </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_d </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> d </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_d </ci>
<ci> d </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "slow_inward_current_f_gate" component is the f gate encapsulated in
the slow inward current.
-->
<component name="slow_inward_current_f_gate" cmeta:id="slow_inward_current_f_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="f" initial_value="1.0"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_ms" name="alpha_f"/>
<variable units="per_ms" name="beta_f"/>
<!--
These variables are imported from the "environment" and the "membrane" via
the "slow_inward_current" component.
-->
<variable units="mV" public_interface="in" name="V"/>
<variable units="ms" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="alpha_f_calculation_eq">
<apply id="alpha_f_calculation">
<eq/>
<ci> alpha_f </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.012 </cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 0.008 </cn>
</apply>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 28.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.15 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 28.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="beta_f_calculation_eq">
<apply id="beta_f_calculation">
<eq/>
<ci> beta_f </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.0065 </cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 0.02 </cn>
</apply>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 30.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 0.2 </cn>
</apply>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 30.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="df_dt_eq">
<apply id="df_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> f </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_f </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> f </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_f </ci>
<ci> f </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "time_dependent_potassium_current" component contains a
time-dependent activation gate (X) and a time-independent inactivation
gate (Xi), neither of which are dependent on the extracellular
concentration of potassium ions ([K]o).
-->
<component name="time_dependent_potassium_current" cmeta:id="time_dependent_potassium_current">
<!-- This variable is defined here and used in other components. -->
<variable units="uA_per_mm2" public_interface="out" name="i_K"/>
<!-- These variables are defined here and only used internally. -->
<variable units="mS_per_mm2" name="g_K" initial_value="2.82e-3"/>
<variable units="mS_per_mm2" name="g_K_max"/>
<variable units="mV" name="E_K"/>
<variable units="dimensionless" name="PR_NaK" initial_value="0.01833"/>
<!--
Time is imported from the "environment", and membrane potential and
extracellular potassium concentration are imported from the membrane
component. These variables are used in the
"time_dependent_potassium_current" parent component, which also acts as an
interface, passing the variables to its encapsulated gate components.
-->
<variable units="ms" public_interface="in" private_interface="out" name="time"/>
<variable units="mV" public_interface="in" private_interface="out" name="V"/>
<variable units="gas_constant_units" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="faradays_constant_units" public_interface="in" name="F"/>
<variable units="concentration_units" public_interface="in" name="Ko"/>
<variable units="concentration_units" public_interface="in" name="Ki"/>
<variable units="concentration_units" public_interface="in" name="Nao"/>
<variable units="concentration_units" public_interface="in" name="Nai"/>
<!-- 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" cmeta:id="g_K_max_calculation_eq">
<apply id="g_K_max_calculation">
<eq/>
<ci> g_K_max </ci>
<apply>
<times/>
<ci> g_K </ci>
<apply>
<root/>
<apply>
<divide/>
<ci> Ko </ci>
<cn cellml:units="concentration_units"> 5.4 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="E_K_calculation_eq">
<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> PR_NaK </ci>
<ci> Nao </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> Ki </ci>
<apply>
<times/>
<ci> PR_NaK </ci>
<ci> Nai </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_K_calculation_eq">
<apply id="i_K_calculation">
<eq/>
<ci> i_K </ci>
<apply>
<times/>
<ci> g_K_max </ci>
<ci> X </ci>
<ci> Xi </ci>
<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 time-dependent
potassium current.
-->
<component name="time_dependent_potassium_current_X_gate" cmeta:id="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="6.02e-3"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_ms" name="alpha_X"/>
<variable units="per_ms" name="beta_X"/>
<!--
These variables are imported from the "environment" and the "membrane" via
the "time_dependent_potassium_current" component.
-->
<variable units="mV" public_interface="in" name="V"/>
<variable units="ms" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="alpha_X_calculation_eq">
<apply id="alpha_X_calculation">
<eq/>
<ci> alpha_X </ci>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.0005 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.083 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.057 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="beta_X_calculation_eq">
<apply id="beta_X_calculation">
<eq/>
<ci> beta_X </ci>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.0013 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.06 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 20.0 </cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.04 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 20.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="dx_dt_eq">
<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" cmeta:id="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="mV" public_interface="in" name="V"/>
<variable units="ms" 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" cmeta:id="Xi_calculation_eq">
<apply id="Xi_calculation">
<eq/>
<ci> Xi </ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_mV_ms"> 2.837 </cn>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> 0.04 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 77.0 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 77.0 </cn>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> 0.04 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 35.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<gt/>
<ci> V </ci>
<cn cellml:units="mV"> -100.0 </cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_ms"> 1.0 </cn>
</otherwise>
</piecewise>
</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" cmeta:id="time_independent_potassium_current">
<!-- These variables are defined here and used in other components. -->
<variable units="uA_per_mm2" public_interface="out" name="i_K1"/>
<variable units="mV" public_interface="out" private_interface="out" name="E_K1"/>
<!-- This variable is defined here and only used internally. -->
<variable units="mS_per_mm2" name="g_K1" initial_value="6.047e-3"/>
<variable units="mS_per_mm2" name="g_K1_max"/>
<!--
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="ms" public_interface="in" private_interface="out" name="time"/>
<variable units="mV" public_interface="in" private_interface="out" name="V"/>
<variable units="concentration_units" public_interface="in" name="Ko"/>
<variable units="concentration_units" public_interface="in" name="Ki"/>
<variable units="gas_constant_units" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="faradays_constant_units" 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" cmeta:id="g_K1_max_calculation_eq">
<apply id="g_K1_max_calculation">
<eq/>
<ci> g_K1_max </ci>
<apply>
<times/>
<ci> g_K1 </ci>
<apply>
<root/>
<apply>
<divide/>
<ci> Ko </ci>
<cn cellml:units="concentration_units"> 5.4 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="E_K1_max_calculation_eq">
<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>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_K1_max_calculation_eq">
<apply id="i_K1_calculation">
<eq/>
<ci> i_K1 </ci>
<apply>
<times/>
<ci> g_K1_max </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" cmeta:id="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_ms" name="alpha_K1"/>
<variable units="per_ms" name="beta_K1"/>
<!--
These variables are imported from the "environment", "membrane" and
"time_independent_potassium_current" components.
-->
<variable units="mV" public_interface="in" name="V"/>
<variable units="ms" public_interface="in" name="time"/>
<variable units="mV" public_interface="in" name="E_K1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="alpha_K1_calculation_eq">
<apply id="alpha_K1_calculation">
<eq/>
<ci> alpha_K1 </ci>
<apply>
<divide/>
<cn cellml:units="per_ms"> 1.02 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> 0.2385 </cn>
<apply>
<minus/>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K1 </ci>
</apply>
<cn cellml:units="mV"> 59.215 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="beta_K1_calculation_eq">
<apply id="beta_K1_calculation">
<eq/>
<ci> beta_K1 </ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.49124 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.08032 </cn>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 5.476 </cn>
</apply>
<ci> E_K1 </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.06175 </cn>
<apply>
<minus/>
<ci> V </ci>
<apply>
<plus/>
<ci> E_K1 </ci>
<cn cellml:units="mV"> 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_mV"> -0.5143 </cn>
<apply>
<plus/>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K1 </ci>
</apply>
<cn cellml:units="mV"> 4.753 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="K1_infinity_calculation_eq">
<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" cmeta:id="plateau_potassium_current">
<!-- This variable is defined here and used in other components. -->
<variable units="uA_per_mm2" public_interface="out" name="i_Kp"/>
<!-- These variables are defined here and only used internally. -->
<variable units="mV" name="E_Kp"/>
<variable units="mS_per_mm2" name="g_Kp" initial_value="1.83e-4"/>
<variable units="dimensionless" name="Kp"/>
<!-- These variables are imported from other components. -->
<variable units="ms" public_interface="in" name="time"/>
<variable units="mV" public_interface="in" name="V"/>
<variable units="mV" public_interface="in" name="E_K1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="E_Kp_calculation_eq">
<apply id="E_Kp_calculation">
<eq/>
<ci> E_Kp </ci>
<ci> E_K1 </ci>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Kp_calculation_eq">
<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="mV"> 7.488 </cn>
<ci> V </ci>
</apply>
<cn cellml:units="mV"> 5.98 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_Kp_calculation_eq">
<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 "background_current" component describes an additional current
which contributes at plateau potentials.
-->
<component name="background_current" cmeta:id="background_current">
<!-- This variable is defined here and used in other components. -->
<variable units="uA_per_mm2" public_interface="out" name="i_b"/>
<!-- These variables are defined here and only used internally. -->
<variable units="mV" name="E_b" initial_value="-59.87"/>
<variable units="mS_per_mm2" name="g_b" initial_value="3.921e-4"/>
<!--
Time and membrane potential are imported from the "environment" and
"membrane" components.
-->
<variable units="ms" public_interface="in" name="time"/>
<variable units="mV" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_b_calculation_eq">
<apply id="i_b_calculation">
<eq/>
<ci> i_b </ci>
<apply>
<times/>
<ci> g_b </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_b </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ionic_concentrations" cmeta:id="ionic_concentrations">
<!-- These variables are defined here and used in other components -->
<variable units="concentration_units" public_interface="out" name="Nao" initial_value="140.0"/>
<variable units="concentration_units" public_interface="out" name="Nai" initial_value="18.0"/>
<variable units="concentration_units" name="Cao" initial_value="1.8"/>
<variable units="concentration_units" public_interface="out" name="Ki" initial_value="145.0"/>
<variable units="concentration_units" public_interface="out" name="Ko" initial_value="5.4"/>
</component>
<component name="intracellular_calcium_concentration" cmeta:id="intracellular_calcium_concentration">
<!-- This variable is defined here and used in other components. -->
<variable units="concentration_units" public_interface="out" name="Cai" initial_value="0.0002"/>
<!-- These variables are imported from other components. -->
<variable units="ms" public_interface="in" name="time"/>
<variable units="uA_per_mm2" public_interface="in" name="i_si"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="dCai_dt_eq">
<apply id="dCai_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Cai </ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.01 </cn>
<ci> i_si </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.07 </cn>
<apply>
<minus/>
<cn cellml:units="concentration_units"> 0.0001 </cn>
<ci> Cai </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="slow_inward_current">
<component_ref component="slow_inward_current_d_gate"/>
<component_ref component="slow_inward_current_f_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>
<component_ref component="plateau_potassium_current"/>
<component_ref component="background_current"/>
<component_ref component="ionic_concentrations"/>
<component_ref component="intracellular_calcium_concentration"/>
</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="slow_inward_current">
<component_ref component="slow_inward_current_d_gate"/>
<component_ref component="slow_inward_current_f_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>
<!--
The connections hold the actual mappings between variables declared in
different components. When more than one variable is mapped between two
components, all variable mappings must be listed in the same connection
element (there can only be one connection between two components). The
variables are assumed to be listed in the same order within the two
<component_ref> elements. The modeler should NOT rely on matching the
names of the variables in the two components.
-->
<!--
"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="slow_inward_current"/>
<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="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="background_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_calcium_concentration"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<!--
A number of variables are passed between the "membrane" and its six
sub-components, the "fast_sodium_current", "slow_inward_current",
"time_dependent_potassium_current", time_independent_potassium_current",
"plateau_potassium_current" and the "background_current".
-->
<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"/>
</connection>
<connection>
<map_components component_2="slow_inward_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_si" variable_1="i_si"/>
</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="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="background_current" component_1="membrane"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_b" variable_1="i_b"/>
</connection>
<!-- A few variables are passed between the other components. -->
<connection>
<map_components component_2="intracellular_calcium_concentration" component_1="slow_inward_current"/>
<map_variables variable_2="i_si" variable_1="i_si"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="plateau_potassium_current" component_1="time_independent_potassium_current"/>
<map_variables variable_2="E_K1" variable_1="E_K1"/>
</connection>
<connection>
<map_components component_2="ionic_concentrations" component_1="time_independent_potassium_current"/>
<map_variables variable_2="Ko" variable_1="Ko"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
</connection>
<!--
Various gating variables are passed between the "fast_sodium_current",
"slow_inward_current", "time_dependent_potassium_current" and the
"time_independent_potassium_current" components and the encapsulated "gate"
components.
-->
<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"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current_h_gate" component_1="fast_sodium_current"/>
<map_variables variable_2="h" variable_1="h"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="fast_sodium_current_j_gate" component_1="fast_sodium_current"/>
<map_variables variable_2="j" variable_1="j"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="slow_inward_current_d_gate" component_1="slow_inward_current"/>
<map_variables variable_2="d" variable_1="d"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="slow_inward_current_f_gate" component_1="slow_inward_current"/>
<map_variables variable_2="f" variable_1="f"/>
<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="K1_infinity" variable_1="K1_infinity"/>
<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"/>
</connection>
<rdf:RDF>
<rdf:Seq rdf:about="rdf:#citationAuthorsSeq">
<rdf:li rdf:resource="rdf:#author1Vcard"/>
<rdf:li rdf:resource="rdf:#author2Vcard"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#381d34e2-a585-45b2-be34-df0bfcf6cdfe">
<dc:title>Circulation Research</dc:title>
</rdf:Description>
<rdf:Description rdf:about="#time_dependent_potassium_current">
<cmeta:comment rdf:resource="rdf:#63609e36-3944-44ae-aace-1615bf0a48e0"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6fe0f0f1-b4da-405f-a1b7-bc2d253798e3">
<rdf:value>
Calculation of the reversal potential of the potassium channel.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7feb362d-9f7f-4fd0-8d12-ece589c7a6b9">
<rdf:value>
The kinetics of the Xi gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#fast_sodium_current_j_gate">
<cmeta:comment rdf:resource="rdf:#7d019f80-0940-4dca-b545-0c3225c7c450"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author1Vcard">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#author1VcardN"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#90d0798d-a860-449f-97f2-2f19d8045cf3">
<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A.</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#095d2170-a4cd-456e-bb8c-aaf3ec538ca9">
<dcterms:modified rdf:resource="rdf:#63cdc7e6-6488-410a-b78d-5c1a30c6f9c8"/>
<rdf:value>
Added some initial values from Penny Noble's documentation.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#540008fc-6ec6-4f1a-950e-9ed5a355e268"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d1ad4b0e-71f3-4c97-ad92-344badf8e5bf">
<dcterms:modified rdf:resource="rdf:#05b85e8a-e301-4619-88b0-99c098b75caf"/>
<rdf:value>
Changed equations after checking with mathml validator.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#0c8f7f6a-6cc7-4851-95c7-ce93dd84b303"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7a62dcc5-e1ca-4507-ad88-61ce3f641797">
<rdf:value>
Calculation of the maximum conductance of the potassium channel.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#i_K1_max_calculation_eq">
<cmeta:comment rdf:resource="rdf:#491a9a5a-4151-4e74-b195-2fea149787b1"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#de3ec2ad-e742-42d9-b2bf-47ae3ec556ea">
<dcterms:W3CDTF>2002-02-18</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#alpha_m_calculation_eq">
<cmeta:comment rdf:resource="rdf:#0e6354d7-68f8-4f82-999c-b9fac194bce6"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#685941ad-68ac-497d-a00f-2377283e6d47">
<rdf:value>
The opening rate of the K1 gating variable.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#fast_sodium_current_m_gate">
<cmeta:comment rdf:resource="rdf:#8251b4c9-c7d7-4059-827d-89a4103f9db8"/>
</rdf:Description>
<rdf:Description rdf:about="#dh_dt_eq">
<cmeta:comment rdf:resource="rdf:#01c876f6-9412-43bb-99ab-7efb83140b4d"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0e6354d7-68f8-4f82-999c-b9fac194bce6">
<rdf:value>
The opening rate of the m gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b4ad2440-43fe-4a4f-9c3d-5a88b3fa097c">
<rdf:value>
The sole ionic concentration modelled is intracellular calcium,
using the same equation as that used in the original Beller Reuter
(1977) model.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#beta_f_calculation_eq">
<cmeta:comment rdf:resource="rdf:#445d088f-55d3-4a55-b10f-a9ecb3cbf4ea"/>
</rdf:Description>
<rdf:Description rdf:about="#fast_sodium_current">
<cmeta:comment rdf:resource="rdf:#a101e3de-839f-4f9e-b0fb-a16c5a86703e"/>
</rdf:Description>
<rdf:Description rdf:about="#beta_X_calculation_eq">
<cmeta:comment rdf:resource="rdf:#7fa07bf4-f4f0-4adf-88eb-3bc30f368f03"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7d019f80-0940-4dca-b545-0c3225c7c450">
<rdf:value>
The voltage-dependent slow inaction gate for the the fast sodium
channel - the j gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ionic_concentrations">
<cmeta:comment rdf:resource="rdf:#9d0a0247-5d5b-471d-94d3-dc964289d2fc"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#78b516a9-2f8a-4e96-a141-4bdf25630178">
<rdf:value>
The reversal potential for the slow inward current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#E_K1_max_calculation_eq">
<cmeta:comment rdf:resource="rdf:#6fe0f0f1-b4da-405f-a1b7-bc2d253798e3"/>
</rdf:Description>
<rdf:Description rdf:about="#K1_infinity_calculation_eq">
<cmeta:comment rdf:resource="rdf:#ca6d0fde-63d8-4899-a36b-e6c1e4efc479"/>
</rdf:Description>
<rdf:Description rdf:about="#luo_rudy_1991_version02">
<dc:title>
The Luo-Rudy I Model of Mammalian Ventricular Cardiac Action Potentials,
1991
</dc:title>
<cmeta:bio_entity>Ventricular Myocyte</cmeta:bio_entity>
<cmeta:comment rdf:resource="rdf:#16828c84-637e-45d6-8393-de5b4a7fe4de"/>
<bqs:reference rdf:resource="rdf:#12eca215-24e0-4ab4-97dd-73426d9758f5"/>
<cmeta:species>Mammalia</cmeta:species>
</rdf:Description>
<rdf:Description rdf:about="rdf:#63609e36-3944-44ae-aace-1615bf0a48e0">
<rdf:value>
The time dependent potassium current contains a
time-dependent activation gate (X) and a time-independent
inactivation gate (Xi), neither of which are dependent on the
extracellular concentration of potassium ions ([K]o).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1f0284fe-6eb8-4dc7-8158-e521acfbe51c">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="#g_K_max_calculation_eq">
<cmeta:comment rdf:resource="rdf:#907daad5-35cc-4d75-af14-f12daf788bad"/>
</rdf:Description>
<rdf:Description rdf:about="#alpha_X_calculation_eq">
<cmeta:comment rdf:resource="rdf:#99648026-63d0-402c-ae53-b5021a3b4a15"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#12509676-4c87-47be-a935-e2d784075d48">
<rdf:value>
The voltage-dependent inactivation gate for the fast sodium channel
- the h gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#30b15cfb-3cce-4290-86ed-2144fcb4bf22">
<rdf:value>
The gating variable for the Kp channel.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#alpha_K1_calculation_eq">
<cmeta:comment rdf:resource="rdf:#685941ad-68ac-497d-a00f-2377283e6d47"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c8e97d74-23a9-4ff3-adad-c64f2f26a948">
<vCard:N rdf:resource="rdf:#90d0798d-a860-449f-97f2-2f19d8045cf3"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e892c0bd-894b-4cb8-8617-71d672b322ec">
<rdf:value>
The reversal potential is the same as the K1 channel.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#03d2db10-cac6-4f23-9b24-02b6f1fa4e4b">
<rdf:value>
The background current describes an additional current which
contributes at plateau potentials.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1add83ec-0ab6-4dac-bdfc-cdaf997393f6">
<dcterms:W3CDTF>2001-09-15</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#670b6b68-7d7c-4bb0-9ea5-c3b7ae026deb">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="#E_K_calculation_eq">
<cmeta:comment rdf:resource="rdf:#f3a1eda4-b6d3-40d9-827b-a78b0a71ee53"/>
</rdf:Description>
<rdf:Description rdf:about="#dm_dt_eq">
<cmeta:comment rdf:resource="rdf:#658ef0f5-b532-488b-afb9-6feaa177770c"/>
</rdf:Description>
<rdf:Description rdf:about="#i_si_calculation_eq">
<cmeta:comment rdf:resource="rdf:#e7c2d1b9-dce6-4847-9d90-bf9e542788e3"/>
</rdf:Description>
<rdf:Description rdf:about="#membrane">
<cmeta:comment rdf:resource="rdf:#54d9ca6f-43be-4d97-945a-a42f2fdc5938"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#859b8edb-38bc-4ccf-a03a-0472318ba19e">
<rdf:value>
The kinetics of the f gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#fast_sodium_current_h_gate">
<cmeta:comment rdf:resource="rdf:#12509676-4c87-47be-a935-e2d784075d48"/>
</rdf:Description>
<rdf:Description rdf:about="#dd_dt_eq">
<cmeta:comment rdf:resource="rdf:#4460e075-5d2c-44ec-9749-7da1f6180332"/>
</rdf:Description>
<rdf:Description rdf:about="#beta_K1_calculation_eq">
<cmeta:comment rdf:resource="rdf:#91af650f-2e21-4768-b964-5882e46f3a35"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#01c876f6-9412-43bb-99ab-7efb83140b4d">
<rdf:value>
The kinetics of the h gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#alpha_f_calculation_eq">
<cmeta:comment rdf:resource="rdf:#5a0fe4ef-d7ad-47f1-b428-1dfe8bf87450"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#491a9a5a-4151-4e74-b195-2fea149787b1">
<rdf:value>
Calculation of the time-independent potassium current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d9a904ec-4b84-4158-a1f3-01f8c1163f70">
<dcterms:W3CDTF>2002-02-20</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#df_dt_eq">
<cmeta:comment rdf:resource="rdf:#859b8edb-38bc-4ccf-a03a-0472318ba19e"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5a0fe4ef-d7ad-47f1-b428-1dfe8bf87450">
<rdf:value>
The opening rate of the f gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4d35aaf2-ad4b-4501-acd2-fb44b50b718b">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2618aec2-740e-4c4c-81e8-2dd2c7635cef">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ccf06f32-5d8d-4cbd-88aa-a1ab4c62208e">
<vCard:N rdf:resource="rdf:#1f0284fe-6eb8-4dc7-8158-e521acfbe51c"/>
</rdf:Description>
<rdf:Description rdf:about="#dx_dt_eq">
<cmeta:comment rdf:resource="rdf:#93d9c6ac-6048-40a3-9ca9-15e5f0b23ae7"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a2067db7-8499-4ba0-a830-6c035dd66a7d">
<rdf:value>
The closing rate of the j gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5c840012-8c82-43a2-bfd6-c40138fc53cf">
<dcterms:W3CDTF>2003-06-05</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#time_independent_potassium_current_K1_gate">
<cmeta:comment rdf:resource="rdf:#fa0db71d-ead7-4671-8ef9-b7d19c0840cd"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6fc1a784-753d-46cf-aa29-92967ade0b3a">
<rdf:value>
The voltage-dependent inactivation gate of the slow inward channel -
the f gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9adf4b02-9f97-44e8-b92e-0aad001e0cb9">
<rdf:value>
Calculation of the background current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4eab473a-bf59-496f-b360-6dee5b8f17c2">
<rdf:value>
Voltage- and time-dependent activation gate for the time-dependent
potassium current - the X gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#901628c7-27a3-4557-a42d-bc513e4a869b">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#657d3ad4-0253-4195-8325-dc330d66adee">
<dcterms:W3CDTF>2002-01-21</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher>
The University of Auckland, Bioengineering Institute
</dc:publisher>
<cmeta:modification rdf:resource="rdf:#052eb862-e357-498e-8b22-7ece4c2c663b"/>
<cmeta:modification rdf:resource="rdf:#095d2170-a4cd-456e-bb8c-aaf3ec538ca9"/>
<cmeta:modification rdf:resource="rdf:#6e238f89-0573-4604-9d7d-0a6a6f28748c"/>
<cmeta:modification rdf:resource="rdf:#9700a99e-76c9-43ad-95fd-1b5b4c1e0fc6"/>
<cmeta:modification rdf:resource="rdf:#cf5981d3-f417-4e3d-ae43-d6f85c028f8d"/>
<cmeta:modification rdf:resource="rdf:#d1ad4b0e-71f3-4c97-ad92-344badf8e5bf"/>
<cmeta:modification rdf:resource="rdf:#de27c243-ef8a-4947-aa4b-aaa0b24b8b12"/>
<cmeta:modification rdf:resource="rdf:#f1ef79a8-cdde-42bf-b6bb-2009ba1424e8"/>
<dcterms:created rdf:resource="rdf:#1add83ec-0ab6-4dac-bdfc-cdaf997393f6"/>
<dc:creator rdf:resource="rdf:#03d8c2be-1d1c-4ec1-90b9-6dae4375b75d"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#27f39a6d-94c2-4e96-aaef-c19032665104">
<vCard:N rdf:resource="rdf:#f812bdf3-445f-49fe-8c42-aacc950f7448"/>
</rdf:Description>
<rdf:Description rdf:about="#membrane_voltage_diff_eq">
<cmeta:comment rdf:resource="rdf:#cbc7c902-9de1-499d-8564-25b3198ff908"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cbc7c902-9de1-499d-8564-25b3198ff908">
<rdf:value>
The membrane potential kinetic equation.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#g_K1_max_calculation_eq">
<cmeta:comment rdf:resource="rdf:#7a62dcc5-e1ca-4507-ad88-61ce3f641797"/>
</rdf:Description>
<rdf:Description rdf:about="#slow_inward_current_f_gate">
<cmeta:comment rdf:resource="rdf:#6fc1a784-753d-46cf-aa29-92967ade0b3a"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cf61b008-3481-48d4-bc01-66ff7d0cb963">
<vCard:N rdf:resource="rdf:#1a22b26b-7995-4f63-a919-7dfba24de7e7"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#93d9c6ac-6048-40a3-9ca9-15e5f0b23ae7">
<rdf:value>
The kinetics for the X gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#03c34e17-0641-4498-a91e-644bcd893590">
<rdf:value>
Calculation of the plateau potassium current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#63cdc7e6-6488-410a-b78d-5c1a30c6f9c8">
<dcterms:W3CDTF>2002-05-06</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#alpha_j_calculation_eq">
<cmeta:comment rdf:resource="rdf:#477082fc-5e05-4549-bfd3-6e879261f382"/>
</rdf:Description>
<rdf:Description rdf:about="#E_si_calculation_eq">
<cmeta:comment rdf:resource="rdf:#78b516a9-2f8a-4e96-a141-4bdf25630178"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#12eca215-24e0-4ab4-97dd-73426d9758f5">
<bqs:Pubmed_id>1709839</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#27ea269c-7412-4ffc-8e06-2c12d5805d36"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#16828c84-637e-45d6-8393-de5b4a7fe4de">
<dc:creator rdf:resource="rdf:#670b6b68-7d7c-4bb0-9ea5-c3b7ae026deb"/>
<rdf:value>This is the CellML description of Luo and Rudy's mathematical model of the membrane action potential of the mammalian ventricular cell. It describes six ionic currents and it is a development of the Beeler-Reuter 1977 mammalian ventricular model, using Hodgkin-Huxley type equations.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#slow_inward_current">
<cmeta:comment rdf:resource="rdf:#216b9fc1-c518-4591-a162-9cff00133c76"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author2VcardN">
<vCard:Given>Yoram</vCard:Given>
<vCard:Family>Rudy</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author2Vcard">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#author2VcardN"/>
</rdf:Description>
<rdf:Description rdf:about="#time_independent_potassium_current">
<cmeta:comment rdf:resource="rdf:#e9027d81-d9b2-4eb1-aea5-5c033c9baf39"/>
</rdf:Description>
<rdf:Description rdf:about="#beta_d_calculation_eq">
<cmeta:comment rdf:resource="rdf:#9e48337d-9e4f-44de-b887-f93c23154edf"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#52fe3282-11b2-48b3-b724-4ef47c029906">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Research Group</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f812bdf3-445f-49fe-8c42-aacc950f7448">
<vCard:Given>David</vCard:Given>
<vCard:Family>Nickerson</vCard:Family>
<vCard:Other>P</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cf5981d3-f417-4e3d-ae43-d6f85c028f8d">
<dcterms:modified rdf:resource="rdf:#de3ec2ad-e742-42d9-b2bf-47ae3ec556ea"/>
<rdf:value>
Corrected the beta_K1_calculation eqn.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#c8e97d74-23a9-4ff3-adad-c64f2f26a948"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4f713bf6-144a-442e-9b22-20ec8427343b">
<rdf:value>
The opening rate of the d gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e8ca335f-ea71-4e38-b13b-12424a002650">
<dcterms:W3CDTF>2001-10-19</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4bf6e4c1-12b3-4b6a-80be-8bc8752bde42">
<rdf:value>
The closing rate of the h gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9d0a0247-5d5b-471d-94d3-dc964289d2fc">
<rdf:value>
In their 1991 model for most ions, Luo and Rudy do not include
equations to calculate changes in their concentrations. Instead
they fix the variables and specify their values, as shown in this
component. The only exception is for intracellular calcium
concentrations which is defined by an equation. Extracellular
calcium concentration is defined here but is not included in any of
the ionic flux calculations. Therefore it has no public_interface.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#E_Kp_calculation_eq">
<cmeta:comment rdf:resource="rdf:#e892c0bd-894b-4cb8-8617-71d672b322ec"/>
</rdf:Description>
<rdf:Description rdf:about="#beta_j_calculation_eq">
<cmeta:comment rdf:resource="rdf:#a2067db7-8499-4ba0-a830-6c035dd66a7d"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f4a321ce-fb51-4cb2-bc62-dbd3b9f907f3">
<dcterms:W3CDTF>2003-07-30</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9700a99e-76c9-43ad-95fd-1b5b4c1e0fc6">
<dcterms:modified rdf:resource="rdf:#657d3ad4-0253-4195-8325-dc330d66adee"/>
<rdf:value>
Added an ionic_concentrations and an
intracellular_calcium_concentrations components and altered the public
interfaces and connections appropriately.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#cf61b008-3481-48d4-bc01-66ff7d0cb963"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f9516b7f-ab07-495d-b460-d580188619d8">
<vCard:N rdf:resource="rdf:#f7c50d7b-0e1d-4a1d-8c79-5cbf7eda8dc7"/>
</rdf:Description>
<rdf:Description rdf:about="#background_current">
<cmeta:comment rdf:resource="rdf:#03d2db10-cac6-4f23-9b24-02b6f1fa4e4b"/>
</rdf:Description>
<rdf:Description rdf:about="#beta_h_calculation_eq">
<cmeta:comment rdf:resource="rdf:#4bf6e4c1-12b3-4b6a-80be-8bc8752bde42"/>
</rdf:Description>
<rdf:Description rdf:about="#i_Na_calculation_eq">
<cmeta:comment rdf:resource="rdf:#6d8e9efa-8774-4afd-8f39-728c1d1dc72c"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0c8f7f6a-6cc7-4851-95c7-ce93dd84b303">
<rdf:type rdf:resource="http://www.w3.org/2001/vcard-rdf/3.0#N"/>
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="#Kp_calculation_eq">
<cmeta:comment rdf:resource="rdf:#30b15cfb-3cce-4290-86ed-2144fcb4bf22"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#191641ac-1e9b-458a-b652-7cae07228aec">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#27ea269c-7412-4ffc-8e06-2c12d5805d36">
<dc:creator rdf:resource="rdf:#citationAuthorsSeq"/>
<dc:title>A Model of the Ventricular Cardiac Action Potential</dc:title>
<bqs:volume>68</bqs:volume>
<bqs:first_page>1501</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#381d34e2-a585-45b2-be34-df0bfcf6cdfe"/>
<dcterms:issued rdf:resource="rdf:#a0ecc631-2d59-4b00-8295-784bd50ef60c"/>
<bqs:last_page>1526</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#54d9ca6f-43be-4d97-945a-a42f2fdc5938">
<rdf:value>
The parent component of the model - all other components are
`contained' in this one. Defines the transmembrane potential.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7fa07bf4-f4f0-4adf-88eb-3bc30f368f03">
<rdf:value>
The closing rate for the X gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ca6d0fde-63d8-4899-a36b-e6c1e4efc479">
<rdf:value>
The steady-state approximation for the kinetics of the K1 gating
variable.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6bd5cf07-7ce1-4de1-817f-9a851a81e32c">
<rdf:value>
The differential equation governing the intracellular calcium ion
concentration.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#03d8c2be-1d1c-4ec1-90b9-6dae4375b75d">
<vCard:ORG rdf:resource="rdf:#52fe3282-11b2-48b3-b724-4ef47c029906"/>
<vCard:EMAIL rdf:resource="rdf:#901628c7-27a3-4557-a42d-bc513e4a869b"/>
<vCard:N rdf:resource="rdf:#2618aec2-740e-4c4c-81e8-2dd2c7635cef"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4c5a9a57-e175-4fdc-a073-b521f4c18395">
<rdf:value>
This is a dummy equation that we simply use to make grabbing the
value in CMISS much easier.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a8ead419-f5ec-4e85-b5ad-7f07e494a4d0">
<rdf:value>
The kinetics of the j gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#91af650f-2e21-4768-b964-5882e46f3a35">
<rdf:value>
The closing rate of the K1 gating variable.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#dj_dt_eq">
<cmeta:comment rdf:resource="rdf:#a8ead419-f5ec-4e85-b5ad-7f07e494a4d0"/>
</rdf:Description>
<rdf:Description rdf:about="#intracellular_calcium_concentration">
<cmeta:comment rdf:resource="rdf:#b4ad2440-43fe-4a4f-9c3d-5a88b3fa097c"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#477082fc-5e05-4549-bfd3-6e879261f382">
<rdf:value>
The opening rate of the j gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6d8e9efa-8774-4afd-8f39-728c1d1dc72c">
<rdf:value>
Evaluation of the fast sodium current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#beta_m_calculation_eq">
<cmeta:comment rdf:resource="rdf:#882fc8b9-c7fc-4746-83c6-4c70e98321fc"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a101e3de-839f-4f9e-b0fb-a16c5a86703e">
<rdf:value>
The fast sodium current is primarily responsible for the upstroke of
the action potential.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#445d088f-55d3-4a55-b10f-a9ecb3cbf4ea">
<rdf:value>
The closing rate of the f gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#99648026-63d0-402c-ae53-b5021a3b4a15">
<rdf:value>
The opening rate for the X gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#alpha_h_calculation_eq">
<cmeta:comment rdf:resource="rdf:#6bac165d-d506-43f7-8d1f-9505af18ffe9"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6bac165d-d506-43f7-8d1f-9505af18ffe9">
<rdf:value>
The opening rate of the h gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4f751558-0df6-4840-934c-f4c7d2992eeb">
<rdf:value>
The voltage-dependent and time-independent gate for the
time-dependent potassium current - the Xi gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#540008fc-6ec6-4f1a-950e-9ed5a355e268">
<vCard:N rdf:resource="rdf:#191641ac-1e9b-458a-b652-7cae07228aec"/>
</rdf:Description>
<rdf:Description rdf:about="#time_dependent_potassium_current_Xi_gate">
<cmeta:comment rdf:resource="rdf:#4f751558-0df6-4840-934c-f4c7d2992eeb"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#052eb862-e357-498e-8b22-7ece4c2c663b">
<dcterms:modified rdf:resource="rdf:#e8ca335f-ea71-4e38-b13b-12424a002650"/>
<rdf:value>
Removed document type definition as this is declared as optional
according to the W3C recommendation.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#ccf06f32-5d8d-4cbd-88aa-a1ab4c62208e"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fa0db71d-ead7-4671-8ef9-b7d19c0840cd">
<rdf:value>
The voltage-dependent and time-independent gating variable for the
time independent potassium current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f1ef79a8-cdde-42bf-b6bb-2009ba1424e8">
<dcterms:modified rdf:resource="rdf:#5c840012-8c82-43a2-bfd6-c40138fc53cf"/>
<rdf:value>
Corrected equations: alpha_j_calculation and beta_j_calculation in
fast_sodium_current_j_gate, alpha_d_calculation and beta_d_calculation in slow_inward_current_d_gate, alpha_f_calculation and
beta_f_calculation in slow_inward_current_f_gate, alpha_X_calculation
and beta_X_calculation in time_dependent_potassium_current_X_gate, and beta_K1_calculation in time_independent_potassium_current_K1_gate.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#f9516b7f-ab07-495d-b460-d580188619d8"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#658ef0f5-b532-488b-afb9-6feaa177770c">
<rdf:value>
The kinetics of the m gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#i_Kp_calculation_eq">
<cmeta:comment rdf:resource="rdf:#03c34e17-0641-4498-a91e-644bcd893590"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6e238f89-0573-4604-9d7d-0a6a6f28748c">
<dcterms:modified rdf:resource="rdf:#d9a904ec-4b84-4158-a1f3-01f8c1163f70"/>
<rdf:value>
Corrected the Cai differential eqn.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#e1eeae9a-08b5-4b91-8920-87ce3c7a6075"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a0ecc631-2d59-4b00-8295-784bd50ef60c">
<dcterms:W3CDTF>1991-01-01</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f3a1eda4-b6d3-40d9-827b-a78b0a71ee53">
<rdf:value>
The reversal potential for the channel.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#alpha_d_calculation_eq">
<cmeta:comment rdf:resource="rdf:#4f713bf6-144a-442e-9b22-20ec8427343b"/>
</rdf:Description>
<rdf:Description rdf:about="#i_K_calculation_eq">
<cmeta:comment rdf:resource="rdf:#49ac69a2-eb0a-4afd-abb5-4874ea2f94a2"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#882fc8b9-c7fc-4746-83c6-4c70e98321fc">
<rdf:value>
The closing rate of the m gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#05b85e8a-e301-4619-88b0-99c098b75caf">
<rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
</rdf:Description>
<rdf:Description rdf:about="#plateau_potassium_current">
<cmeta:comment rdf:resource="rdf:#65d778ad-b79a-4004-a822-6a31dddc06ab"/>
</rdf:Description>
<rdf:Description rdf:about="#Xi_calculation_eq">
<cmeta:comment rdf:resource="rdf:#7feb362d-9f7f-4fd0-8d12-ece589c7a6b9"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#907daad5-35cc-4d75-af14-f12daf788bad">
<rdf:value>
The maximum conductance for the channel.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9e48337d-9e4f-44de-b887-f93c23154edf">
<rdf:value>
The closing rate of the d gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#49ac69a2-eb0a-4afd-abb5-4874ea2f94a2">
<rdf:value>
Calculates the time-dependent potassium current in terms of the
conductance, the membrane voltage and the gate variables.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e7c2d1b9-dce6-4847-9d90-bf9e542788e3">
<rdf:value>
Calculation of the slow inward current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4460e075-5d2c-44ec-9749-7da1f6180332">
<rdf:value>
The kinetics of the d gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author1VcardN">
<vCard:Given>Ching-hsing</vCard:Given>
<vCard:Family>Luo</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#de27c243-ef8a-4947-aa4b-aaa0b24b8b12">
<dcterms:modified rdf:resource="rdf:#f4a321ce-fb51-4cb2-bc62-dbd3b9f907f3"/>
<rdf:value>
Changing units and fixing up some of the equations and parameters.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#27f39a6d-94c2-4e96-aaef-c19032665104"/>
</rdf:Description>
<rdf:Description rdf:about="#slow_inward_current_d_gate">
<cmeta:comment rdf:resource="rdf:#a17f595d-2605-4c8e-b753-aabf93885ea8"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e9027d81-d9b2-4eb1-aea5-5c033c9baf39">
<rdf:value>
The time independent potassium current contains a single
inactivation gate (K1) whose time constant is small enough that it
can be approximated by its steady-state value K1_infinity.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#65d778ad-b79a-4004-a822-6a31dddc06ab">
<rdf:value>
The plateau potassium current component contains the equations which
describe the contribution of a time-independent [K]o-insensitive
channel at plateau potentials.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1a22b26b-7995-4f63-a919-7dfba24de7e7">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="#IStim_for_cmiss_eq">
<cmeta:comment rdf:resource="rdf:#4c5a9a57-e175-4fdc-a073-b521f4c18395"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e1eeae9a-08b5-4b91-8920-87ce3c7a6075">
<vCard:N rdf:resource="rdf:#4d35aaf2-ad4b-4501-acd2-fb44b50b718b"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a17f595d-2605-4c8e-b753-aabf93885ea8">
<rdf:value>
The voltage-dependent activation gate for the slow inward current -
the d gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#dCai_dt_eq">
<cmeta:comment rdf:resource="rdf:#6bd5cf07-7ce1-4de1-817f-9a851a81e32c"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8251b4c9-c7d7-4059-827d-89a4103f9db8">
<rdf:value>
The voltage-dependent activation gate for the fast sodium channel -
the m gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#time_dependent_potassium_current_X_gate">
<cmeta:comment rdf:resource="rdf:#4eab473a-bf59-496f-b360-6dee5b8f17c2"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#216b9fc1-c518-4591-a162-9cff00133c76">
<rdf:value>
The slow inward (calcium) current is primarily responsible for the
plateau pahse of the action potential.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f7c50d7b-0e1d-4a1d-8c79-5cbf7eda8dc7">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="#i_b_calculation_eq">
<cmeta:comment rdf:resource="rdf:#9adf4b02-9f97-44e8-b92e-0aad001e0cb9"/>
</rdf:Description>
</rdf:RDF>
</model>
