- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-08-21 04:38:30+12:00
- Desc:
- committing version02 of difrancesco_noble_1985
- Permanent Source URI:
- http://models.cellml.org/workspace/difrancesco_noble_1985/rawfile/0e0a42d690abf54e1bd684813946b487ab1a0713/difrancesco_noble_1985.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : DFN_purkinje_fibre_model_1985.xml
CREATED : September 2001
LAST MODIFIED : 5th April 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 cardiac action
potentials in purkinje fibres, based on the Di Francesco-Noble model, 1985.
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 using mathml validator.
03/01/2002 - CML - Created two extra components for extracellular sodium and
extracellular calcium concentrations. Then changed the Nao
and Cao variable public interfaces and the connections
between components appropriately.
21/01/2002 - AAC - Updated metadata to conform with the 16/1/02 CellML
Metadata 1.0 Specification.
25/02/2002 - CML - Corrected several equations.
06/05/2002 - CML - Added some initial values.
19/07/2002 - CML - Added more metadata.
05/04/2003 - AAC - Changed the model name so the model loads in the database
easier.
--><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="DFN_purkinje_fibre_model_1985" name="difrancesco_noble_1985_version02">
<!--
Below, are defined some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="mm">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="per_mm">
<unit units="mole" prefix="micro"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="ms">
<unit units="second" prefix="milli"/>
</units>
<units name="per_ms">
<unit units="ms" exponent="-1"/>
</units>
<units name="mV">
<unit units="volt" prefix="milli"/>
</units>
<units name="per_mV">
<unit units="mV" 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="mm" exponent="-2"/>
</units>
<units name="uF_per_mm2">
<unit units="farad" prefix="micro"/>
<unit units="mm" exponent="-2"/>
</units>
<units name="uA_per_mm2">
<unit units="ampere" prefix="micro"/>
<unit units="mm" exponent="-2"/>
</units>
<units name="uA_per_mm2_per_mM">
<unit units="ampere" prefix="micro"/>
<unit units="mm" exponent="-2"/>
<unit units="mM" exponent="-1"/>
</units>
<units name="mM">
<unit units="mole" prefix="nano"/>
<unit units="mm" exponent="-3"/>
</units>
<units name="mM_per_ms">
<unit units="mM"/>
<unit units="ms" exponent="-1"/>
</units>
<units name="per_ms_per_mM">
<unit units="ms" exponent="-1"/>
<unit units="mM" exponent="-1"/>
</units>
<units name="mM2">
<unit units="mM" exponent="2"/>
</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 cmeta:id="environment" name="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 cmeta:id="membrane" name="membrane">
<!-- These variables are defined here and used in other components. -->
<variable units="mV" public_interface="out" name="V" initial_value="-87.0"/>
<variable units="gas_constant_units" public_interface="out" name="R" initial_value="8314.41"/>
<variable units="kelvin" public_interface="out" name="T" initial_value="310.0"/>
<variable units="faradays_constant_units" public_interface="out" name="F" initial_value="96485.3"/>
<!-- This variable is defined here and only used internally. -->
<variable units="uF_per_mm2" name="C" initial_value="0.08466"/>
<!-- 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_f"/>
<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_to"/>
<variable units="uA_per_mm2" public_interface="in" name="i_Na_b"/>
<variable units="uA_per_mm2" public_interface="in" name="i_Ca_b"/>
<variable units="uA_per_mm2" public_interface="in" name="i_NaK"/>
<variable units="uA_per_mm2" public_interface="in" name="i_NaCa"/>
<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" name="I_stim"/>
<!--
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_f </ci>
<ci> i_K </ci>
<ci> i_K1 </ci>
<ci> i_to </ci>
<ci> i_Na_b </ci>
<ci> i_Ca_b </ci>
<ci> i_NaK </ci>
<ci> i_NaCa </ci>
<ci> i_Na </ci>
<ci> i_si </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 hyperpolarising-activated current (i_f) is a Na-K current. -->
<component cmeta:id="hyperpolarising_activated_current" name="hyperpolarising_activated_current">
<!-- These variables are defined here and used in other components. -->
<variable units="uA_per_mm2" public_interface="out" name="i_f"/>
<variable units="uA_per_mm2" public_interface="out" name="i_fK"/>
<variable units="uA_per_mm2" public_interface="out" name="i_fNa"/>
<variable units="mV" public_interface="out" name="E_Na"/>
<variable units="mV" public_interface="out" name="E_K"/>
<!-- These variables are defined here and only used internally. -->
<variable units="mS_per_mm2" name="g_f_Na" initial_value="3.39e-3"/>
<variable units="mS_per_mm2" name="g_f_K" initial_value="3.39e-3"/>
<variable units="uA_per_mm2" name="I_fK"/>
<variable units="uA_per_mm2" name="I_fNa"/>
<variable units="mM" name="Km_f" initial_value="45.0"/>
<!-- These variables are imported from other 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="mM" public_interface="in" name="Kc"/>
<variable units="mM" public_interface="in" name="Ki"/>
<variable units="mM" public_interface="in" name="Nai"/>
<variable units="mM" public_interface="in" name="Nao"/>
<!-- These variables are imported from encapsulated components. -->
<variable units="dimensionless" private_interface="in" name="y"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_f_calculation_eq">
<apply id="i_f_calculation">
<eq/>
<ci> i_f </ci>
<apply>
<plus/>
<ci> i_fK </ci>
<ci> i_fNa </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_fK_calculation">
<eq/>
<ci> i_fK </ci>
<apply>
<times/>
<ci> y </ci>
<ci> I_fK </ci>
</apply>
</apply>
<apply id="i_fNa_calculation">
<eq/>
<ci> i_fNa </ci>
<apply>
<times/>
<ci> y </ci>
<ci> I_fNa </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="I_fK_calculation_eq">
<apply id="I_fK_calculation">
<eq/>
<ci> I_fK </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> Kc </ci>
<apply>
<plus/>
<ci> Kc </ci>
<ci> Km_f </ci>
</apply>
</apply>
<apply>
<times/>
<ci> g_f_K </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="I_fNa_calculation_eq">
<apply id="I_fNa_calculation">
<eq/>
<ci> I_fNa </ci>
<apply>
<times/>
<apply>
<divide/>
<ci> Kc </ci>
<apply>
<plus/>
<ci> Kc </ci>
<ci> Km_f </ci>
</apply>
</apply>
<apply>
<times/>
<ci> g_f_Na </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="E_f_calculation_eq">
<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>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="E_K_calculation">
<eq/>
<ci> E_K </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Kc </ci>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The y gate is encapsulated within the hyperpolarising-activated current.
-->
<component cmeta:id="hyperpolarising_activated_current_y_gate" name="hyperpolarising_activated_current_y_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="y" initial_value="0.2"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_ms" name="alpha_y"/>
<variable units="per_ms" name="beta_y"/>
<!-- These variables are imported from parent and sibling components. -->
<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_y_calculation_eq">
<apply id="alpha_y_calculation">
<eq/>
<ci> alpha_y </ci>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.05e-3 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> -0.067 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 42.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="beta_y_calculation_eq">
<apply id="beta_y_calculation">
<eq/>
<ci> beta_y </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_ms">1.0e-3</cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 42.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> -0.2 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 42.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="y_kinetics">
<apply id="dy_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> y </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_y </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> y </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_y </ci>
<ci> y </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The time-dependent (delayed) potassium current is equivalent to the plateau
potassium current (1) in the MNT model. It is controlled by a single gate,
x.
-->
<component cmeta:id="time_dependent_potassium_current" name="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="dimensionless" name="K"/>
<variable units="uA_per_mm2" name="I_K"/>
<variable units="uA_per_mm2" name="i_K_max" initial_value="0.2032"/>
<!-- These variables are imported from other 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="mM" public_interface="in" name="Ki"/>
<variable units="mM" public_interface="in" name="Kc"/>
<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="x"/>
<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> x </ci>
<ci> I_K </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="I_K_calculation">
<eq/>
<ci> I_K </ci>
<apply>
<times/>
<ci> i_K_max </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Ki </ci>
<apply>
<times/>
<ci> Kc </ci>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="mM"> 140.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<!-- The x gate encapsulated within the time-dependent potassium current. -->
<component cmeta:id="time_dependent_potassium_current_x_gate" 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="0.01"/>
<!-- 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 other 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="alpha_x_calculation_eq">
<apply id="alpha_x_calculation">
<eq/>
<ci> alpha_x </ci>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.5e-3 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<cn cellml:units="mV"> 12.1 </cn>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<cn cellml:units="mV"> 17.5 </cn>
</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"> 1.3e-3 </cn>
<apply>
<divide/>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 20.0 </cn>
</apply>
<cn cellml:units="mV"> 16.67 </cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 20.0 </cn>
</apply>
<cn cellml:units="mV"> 25.0 </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-independent (background) potassium current (i_K1). -->
<component cmeta:id="time_independent_potassium_current" name="time_independent_potassium_current">
<!-- This variable is defined here and used in other components. -->
<variable units="uA_per_mm2" public_interface="out" name="i_K1"/>
<!-- These variables are defined here and only used internally. -->
<variable units="mS_per_mm2" name="g_K1" initial_value="1.0385"/>
<variable units="mM" name="Km_K1" initial_value="210.0"/>
<!-- 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_K"/>
<variable units="mM" public_interface="in" name="Kc"/>
<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"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_K1_calculation_eq">
<apply id="i_K1_calculation">
<eq/>
<ci> i_K1 </ci>
<apply>
<times/>
<ci> g_K1 </ci>
<apply>
<divide/>
<ci> Kc </ci>
<apply>
<plus/>
<ci> Kc </ci>
<ci> Km_K1 </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
<ci> E_K </ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 10.0 </cn>
</apply>
<ci> E_K </ci>
</apply>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The transient outward current (i_to) replaces the i_qr chloride-based
current of the MNT model. This current is a calcium-activated, outward
rectifier. It has an inactivation gate, r.
-->
<component cmeta:id="transient_outward_current" name="transient_outward_current">
<!-- This variable is defined here and used in other components. -->
<variable units="uA_per_mm2" public_interface="out" name="i_to"/>
<!-- These variables are defined here and only used internally. -->
<variable units="mM" name="Km_to" initial_value="10.0"/>
<variable units="mM" name="Km_Ca" initial_value="0.5e-3"/>
<variable units="mS_per_mm2" name="g_to" initial_value="0.316e-3"/>
<!-- These variables are imported from other 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="mM" public_interface="in" name="Kc"/>
<variable units="mM" public_interface="in" name="Ki"/>
<variable units="mM" public_interface="in" name="Cai"/>
<!-- this variable is imported from an encapsulated component. -->
<variable units="dimensionless" private_interface="in" name="r"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_to_calculation_eq">
<apply id="i_to_calculation">
<eq/>
<ci> i_to </ci>
<apply>
<times/>
<ci> r </ci>
<ci> g_to </ci>
<apply>
<plus/>
<cn cellml:units="mM"> 0.2 </cn>
<apply>
<divide/>
<ci> Kc </ci>
<apply>
<plus/>
<ci> Km_to </ci>
<ci> Kc </ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> Cai </ci>
<apply>
<plus/>
<ci> Km_Ca </ci>
<ci> Cai </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 10.0 </cn>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> -0.2 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> Ki </ci>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> 0.02 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Kc </ci>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_mV"> -0.02 </cn>
<ci> V </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!-- The inactivation process is described by the following r component. -->
<component cmeta:id="transient_outward_current_r_gate" name="transient_outward_current_r_gate">
<!-- this variable is defined here and used in other components -->
<variable units="dimensionless" public_interface="out" name="r" initial_value="1.0"/>
<!-- these variables are defined here and only used internally -->
<variable units="per_ms" name="alpha_r"/>
<variable units="per_ms" name="beta_r"/>
<!-- these variables are imported from parent and sibling components -->
<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_r_calculation_eq">
<apply id="alpha_r_calculation">
<eq/>
<ci> alpha_r </ci>
<apply>
<times/>
<cn cellml:units="per_ms"> 0.033e-3 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci> V </ci>
</apply>
<cn cellml:units="mV"> 17.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="beta_r_calculation_eq">
<apply id="beta_r_calculation">
<eq/>
<ci> beta_r </ci>
<apply>
<divide/>
<cn cellml:units="per_ms"> 33.0e-3 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 10.0 </cn>
</apply>
<cn cellml:units="mV"> 8.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="dr_dt_eq">
<apply id="dr_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> r </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_r </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> r </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_r </ci>
<ci> r </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The sodium background current is a simple, time-independent current which
is similar to the i_Na_b of the MNT model. i_Ch_b is a background current
due to choline, or some other sodium substitute.
-->
<component cmeta:id="sodium_background_current" name="sodium_background_current">
<!-- This variable is defined here and used in other components. -->
<variable units="uA_per_mm2" public_interface="out" name="i_Na_b"/>
<!-- This variable is defined here and only used internally. -->
<variable units="mS_per_mm2" name="g_Nab" initial_value="0.203e-3"/>
<!-- 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_Na"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_Na_b_calculation_eq">
<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_Na </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The calcium background current is in the same form as the sodium background
current.
-->
<component cmeta:id="calcium_background_current" name="calcium_background_current">
<!-- These variables are defined here and used in other components. -->
<variable units="uA_per_mm2" public_interface="out" name="i_Ca_b"/>
<variable units="mV" public_interface="out" name="E_Ca"/>
<!-- This variable is defined here and only used internally. -->
<variable units="mS_per_mm2" name="g_Cab" initial_value="0.0226e-3"/>
<!-- 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="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="mM" public_interface="in" name="Cai"/>
<variable units="mM" public_interface="in" name="Cao"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_Ca_b_calculation_eq">
<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_Ca </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="E_Ca_calculation_eq">
<apply id="E_Ca_calculation">
<eq/>
<ci> E_Ca </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<apply>
<times/>
<ci> F </ci>
<cn cellml:units="dimensionless">2.0</cn>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Cao </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The Na-K exchange pump couples the free energy released by the hydrolysis of
ATP to transfer sodium and potassium ions across the cell membrane against
their electrochemical gradients. 3 Na ions are pumped out for every 2 K
ions pumped into the cell.
-->
<component cmeta:id="sodium_potassium_pump" name="sodium_potassium_pump">
<!-- This variable is defined here and used in other components. -->
<variable units="uA_per_mm2" public_interface="out" name="i_NaK"/>
<!-- This variable is defined here and only used internally. -->
<variable units="uA_per_mm2" name="I_NaK" initial_value="0.141"/>
<variable units="mM" name="K_mK" initial_value="1.0"/>
<variable units="mM" name="K_mNa" initial_value="40.0"/>
<!-- 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="mM" public_interface="in" name="Nai"/>
<variable units="mM" public_interface="in" name="Kc"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_NaK_calculation_eq">
<apply id="i_NaK_calculation">
<eq/>
<ci> i_NaK </ci>
<apply>
<times/>
<ci> I_NaK </ci>
<apply>
<divide/>
<ci> Kc </ci>
<apply>
<plus/>
<ci> K_mK </ci>
<ci> Kc </ci>
</apply>
</apply>
<apply>
<divide/>
<ci> Nai </ci>
<apply>
<plus/>
<ci> K_mNa </ci>
<ci> Nai </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The equation for the Na-Ca exchange current assumes that i_NaCa depends
soley on the sodium and calcium ion electrochemical gradients and the
transmembrane potential. The stoichiometry of the exchange is 3Na : 1Ca,
producing a net outward current.
-->
<component cmeta:id="Na_Ca_exchanger" name="Na_Ca_exchanger">
<!-- This variable is defined here and used in other components. -->
<variable units="uA_per_mm2" public_interface="out" name="i_NaCa"/>
<variable units="dimensionless" public_interface="out" name="n_NaCa" initial_value="3.0"/>
<!-- These variables are defined here and only used internally. -->
<variable units="uA_per_mm2" name="k_NaCa" initial_value="0.0226e-3"/>
<variable units="mV" name="E_NaCa"/>
<variable units="dimensionless" name="d_NaCa" initial_value="0.001"/>
<variable units="dimensionless" name="gamma" initial_value="0.5"/>
<variable units="dimensionless" name="n"/>
<!-- These variables are imported in from other components. -->
<variable units="ms" public_interface="in" name="time"/>
<variable units="mV" public_interface="in" 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="mM" public_interface="in" name="Cao"/>
<variable units="mM" public_interface="in" name="Cai"/>
<variable units="mV" public_interface="in" name="E_Na"/>
<variable units="mM" public_interface="in" name="Nai"/>
<variable units="mM" public_interface="in" name="Nao"/>
<variable units="mV" public_interface="in" name="E_Ca"/>
<!-- The current is given as: -->
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Na_Ca_exchanger_calculation2_eq">
<!--
<apply id="Na_Ca_exchanger_calculation1"><eq />
<ci> i_NaCa </ci>
<apply><times />
<ci> K_NaCa </ci>
<apply><sinh />
<apply><divide />
<apply><times />
<apply><minus />
<ci> V </ci>
<ci> E_NaCa </ci>
</apply>
<ci> F </ci>
</apply>
<apply><times />
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="E_NaCa_calculation"><eq />
<ci> E_NaCa </ci>
<apply><divide />
<apply><minus />
<apply><times />
<ci> n_NaCa </ci>
<ci> E_Na </ci>
</apply>
<apply><times />
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> E_Ca </ci>
</apply>
</apply>
<apply><minus />
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
-->
<apply id="Na_Ca_exchanger_calculation2">
<eq/>
<ci> i_NaCa </ci>
<apply>
<times/>
<ci> k_NaCa </ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> gamma </ci>
<apply>
<minus/>
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci> Nai </ci>
<ci> n_NaCa </ci>
</apply>
<ci> Cao </ci>
</apply>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> gamma </ci>
</apply>
<apply>
<minus/>
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> V </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci> Nao </ci>
<ci> n_NaCa </ci>
</apply>
<ci> Cai </ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> d_NaCa </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> Cai </ci>
<apply>
<power/>
<ci> Nao </ci>
<ci> n_NaCa </ci>
</apply>
</apply>
<apply>
<times/>
<ci> Cao </ci>
<apply>
<power/>
<ci> Nai </ci>
<ci> n_NaCa </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The DFN model retains a two-variable mode; of the sodium kinetics, with new
equations for the gates m and h. It is acknowledged however that the model
does not represent the slower components of Na inactivation and recovery.
It is also assumed that the sodium channel shows a 12% permeability to k
ions.
-->
<component cmeta:id="fast_sodium_current" name="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="0.846"/>
<variable units="mV" name="E_mh"/>
<!-- These variables are imported from other 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="mM" public_interface="in" name="Nao"/>
<variable units="mM" public_interface="in" name="Nai"/>
<variable units="mM" public_interface="in" name="Kc"/>
<variable units="mM" public_interface="in" name="Ki"/>
<!-- These variables are imported from encapsulated components. -->
<variable units="dimensionless" private_interface="in" name="m"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_Na_calculation_eq">
<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>
<apply>
<minus/>
<ci> V </ci>
<ci> E_mh </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="E_mh_calculation_eq">
<apply id="E_mh_calculation">
<eq/>
<ci> E_mh </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> Nao </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.12 </cn>
<ci> Kc </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> Nai </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.12 </cn>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "fast_sodium_current_m_gate" is the activation m gate encapsulated
inside the "fast sodium current" component.
-->
<component cmeta:id="fast_sodium_current_m_gate" 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="0.01"/>
<!-- 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"> 200.0e-3 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 41.0 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.1 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 41.0 </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"> 8000.0e-3 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.056 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 66.0 </cn>
</apply>
</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 inactivation h gate
encapsulated in the "fast sodium current" component.
-->
<component cmeta:id="fast_sodium_current_h_gate" 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="0.98"/>
<!-- 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>
<apply>
<times/>
<cn cellml:units="per_ms"> 20.0e-3 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.125 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 75.0 </cn>
</apply>
</apply>
</apply>
</apply>
</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>
<apply>
<divide/>
<cn cellml:units="per_ms"> 2000.0e-3 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 320.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.1 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 75.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</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>
<!--
Like the MNT model, the kinetics of the secondary inward current are still
described in terms of two gate variables d and f, but the time constants for
activation and inactivation processes are much shorter. The fast component,
i_si of this current has been divided into the individual ion movements of
Ca, K and Na.
-->
<component cmeta:id="secondary_inward_current" name="secondary_inward_current">
<!-- These variables are defined here and used in other components. -->
<variable units="uA_per_mm2" public_interface="out" name="i_si"/>
<variable units="uA_per_mm2" public_interface="out" name="i_siCa"/>
<variable units="uA_per_mm2" public_interface="out" name="i_siK"/>
<variable units="uA_per_mm2" public_interface="out" name="i_siNa"/>
<!-- This variable is defined here and only used internally. -->
<variable units="uA_per_mm2_per_mM" name="P_Ca" initial_value="16.93e-3"/>
<variable units="dimensionless" name="P_CaK" initial_value="0.01"/>
<variable units="dimensionless" name="P_CaNa" initial_value="0.01"/>
<!-- These variables are imported from other 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="mM" public_interface="in" name="Nao"/>
<variable units="mM" public_interface="in" name="Nai"/>
<variable units="mM" public_interface="in" name="Kc"/>
<variable units="mM" public_interface="in" name="Ki"/>
<variable units="mM" public_interface="in" name="Cao"/>
<variable units="mM" public_interface="in" private_interface="out" 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"/>
<variable units="dimensionless" private_interface="in" name="f2"/>
<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>
<plus/>
<ci> i_siCa </ci>
<ci> i_siK </ci>
<ci> i_siNa </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_siCa_calculation_eq">
<apply id="i_siCa_calculation">
<eq/>
<ci> i_siCa </ci>
<apply>
<times/>
<ci> d </ci>
<ci> f </ci>
<ci> f2 </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.0 </cn>
<ci> P_Ca </ci>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> Cai </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 50.0 </cn>
<ci> F </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Cao </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -2.0 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_siK_calculation_eq">
<apply id="i_siK_calculation">
<eq/>
<ci> i_siK </ci>
<apply>
<times/>
<ci> d </ci>
<ci> f </ci>
<ci> f2 </ci>
<apply>
<divide/>
<apply>
<times/>
<ci>P_CaK</ci>
<ci> P_Ca </ci>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> Ki </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 50.0 </cn>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Kc </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_siNa_calculation_eq">
<apply id="i_siNa_calculation">
<eq/>
<ci> i_siNa </ci>
<apply>
<times/>
<ci> d </ci>
<ci> f </ci>
<ci> f2 </ci>
<apply>
<divide/>
<apply>
<times/>
<ci>P_CaNa</ci>
<ci> P_Ca </ci>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<apply>
<divide/>
<ci> F </ci>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> Nai </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 50.0 </cn>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> Nao </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="mV"> 50.0 </cn>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The "secondary_inward_current_d_gate" component is the d gate encapsulated
in the "secondary inward current" component.
-->
<component cmeta:id="secondary_inward_current_d_gate" name="secondary_inward_current_d_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="d" initial_value="0.005"/>
<!-- 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 "secondary_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>
<times/>
<cn cellml:units="per_mV_ms"> 30.0e-3 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 19.0 </cn>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 19.0 </cn>
</apply>
</apply>
<cn cellml:units="mV"> 4.0 </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>
<times/>
<cn cellml:units="per_mV_ms"> 12.0e-3 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 19.0 </cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 19.0 </cn>
</apply>
<cn cellml:units="mV"> 10.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</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 "secondary_inward_current_f_gate" component is the f gate encapsulated
in the "secondary inward current" component.
-->
<component cmeta:id="secondary_inward_current_f_gate" name="secondary_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 parent and sibling components. -->
<variable units="mV" public_interface="in" name="V"/>
<variable units="ms" public_interface="in" name="time"/>
<variable units="mM" public_interface="in" name="Cai"/>
<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>
<times/>
<cn cellml:units="per_mV_ms"> 6.25e-3 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 34.0 </cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 34.0 </cn>
</apply>
<cn cellml:units="mV"> 4.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</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/>
<cn cellml:units="per_ms"> 50.0e-3 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 34.0 </cn>
</apply>
</apply>
<cn cellml:units="mV"> 4.0 </cn>
</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 DFN model also includes a description of Ca-dependent inactivation.
When calcium ions bind to a regulatory site on the channel protein, they
induce a conformational change such that the channel no longer conducts,
and the secondary current slows or ceases.
-->
<component cmeta:id="secondary_inward_current_f2_gate" name="secondary_inward_current_f2_gate">
<!-- This variable is defined here and used in other components. -->
<variable units="dimensionless" public_interface="out" name="f2" initial_value="1.0"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_ms" name="alpha_f2" initial_value="5.0e-3"/>
<variable units="per_ms" name="beta_f2"/>
<variable units="mM" name="K_mf2" initial_value="1.0e-3"/>
<!-- These variables are imported from parent and sibling components. -->
<variable units="mV" public_interface="in" name="V"/>
<variable units="ms" public_interface="in" name="time"/>
<variable units="mM" public_interface="in" name="Cai"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="df2_dt_eq">
<apply id="df2_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> f2 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_f2 </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> f2 </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_f2 </ci>
<ci> f2 </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="beta_f2_calculation">
<eq/>
<ci> beta_f2 </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> Cai </ci>
<ci> alpha_f2 </ci>
</apply>
<ci> K_mf2 </ci>
</apply>
</apply>
</math>
</component>
<!--
Additionally, the DFN model attempted to quantify the changes in several ion
concentrations, as well as the [Ca]i of earlier models.
-->
<component cmeta:id="extracellular_sodium_concentration" name="extracellular_sodium_concentration">
<!-- This variable is defined here and used in other components -->
<variable units="mM" public_interface="out" name="Nao" initial_value="140.0"/>
</component>
<component cmeta:id="intracellular_sodium_concentration" name="intracellular_sodium_concentration">
<!-- This variable is defined here and used in other components -->
<variable units="mM" public_interface="out" name="Nai" initial_value="8.0"/>
<!-- These variables are imported from other components. -->
<variable units="dimensionless" public_interface="in" name="V_i"/>
<variable units="per_mm" public_interface="in" name="Am"/>
<variable units="ms" public_interface="in" name="time"/>
<variable units="faradays_constant_units" public_interface="in" name="F"/>
<variable units="uA_per_mm2" public_interface="in" name="i_Na"/>
<variable units="uA_per_mm2" public_interface="in" name="i_Na_b"/>
<variable units="uA_per_mm2" public_interface="in" name="i_siNa"/>
<variable units="uA_per_mm2" public_interface="in" name="i_NaK"/>
<variable units="uA_per_mm2" public_interface="in" name="i_fNa"/>
<variable units="uA_per_mm2" public_interface="in" name="i_NaCa"/>
<variable units="dimensionless" public_interface="in" name="n_NaCa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="sodium_diff_eq">
<apply id="sodium_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Nai </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Am</ci>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_Na_b </ci>
<ci> i_fNa </ci>
<ci> i_siNa </ci>
<apply>
<times/>
<ci> i_NaK </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<times/>
<ci> i_NaCa </ci>
<apply>
<divide/>
<ci> n_NaCa </ci>
<apply>
<minus/>
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> V_i </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="extracellular_calcium_concentration" name="extracellular_calcium_concentration">
<!-- This variable is defined here and used in other components -->
<variable units="mM" public_interface="out" name="Cao" initial_value="2.0"/>
</component>
<!--
Changes in [Ca]i were first modelled in the BR model and has only been
slightly developed in the DFN model. Calcium is sequestered in the
sarcoplasmic reticulum ([Ca]up). A fraction is transferred to a release
store in the junctional SR ([Ca]rel) before being released into the
intracellular space. The Ca concentrations in each of these various
stores is modelled together with the transfer between the calcium sites
and the ca transfer across the cell membrane via the other ionic
currents.
-->
<component cmeta:id="intracellular_calcium_concentration" name="intracellular_calcium_concentration">
<!-- This variable is defined here and used in other components -->
<variable units="mM" public_interface="out" name="Cai" initial_value="0.00005"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_mm" public_interface="in" name="Am"/>
<variable units="dimensionless" public_interface="in" name="V_up"/>
<variable units="dimensionless" public_interface="in" name="V_rel"/>
<variable units="dimensionless" public_interface="in" name="V_i"/>
<variable units="mM_per_ms" name="i_up"/>
<variable units="mM_per_ms" name="i_tr"/>
<variable units="mM_per_ms" name="i_rel"/>
<variable units="per_ms_per_mM" name="alpha_up"/>
<variable units="per_ms" name="alpha_tr"/>
<variable units="per_ms" name="alpha_rel"/>
<variable units="mM" name="Ca_up" initial_value="2.0"/>
<variable units="mM" name="Ca_rel" initial_value="1.0"/>
<variable units="mM" name="Ca_up_max" initial_value="5.0"/>
<variable units="mM2" name="K_mCa" initial_value="1.0e-6"/>
<variable units="dimensionless" name="p" initial_value="1.0"/>
<variable units="per_ms" name="alpha_p"/>
<variable units="per_ms" name="beta_p"/>
<variable units="ms" name="tau_up" initial_value="25.0"/>
<variable units="ms" name="tau_rep" initial_value="2.0e+3"/>
<variable units="ms" name="tau_rel" initial_value="50.0"/>
<!-- 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="faradays_constant_units" public_interface="in" name="F"/>
<variable units="uA_per_mm2" public_interface="in" name="i_Ca_b"/>
<variable units="uA_per_mm2" public_interface="in" name="i_siCa"/>
<variable units="uA_per_mm2" public_interface="in" name="i_NaCa"/>
<variable units="dimensionless" public_interface="in" name="n_NaCa"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_up_calculation_eq">
<apply id="i_up_calculation">
<eq/>
<ci> i_up </ci>
<apply>
<times/>
<ci> alpha_up </ci>
<ci> Cai </ci>
<apply>
<minus/>
<ci> Ca_up_max </ci>
<ci> Ca_up </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="alpha_up_calculation_eq">
<apply id="alpha_up_calculation">
<eq/>
<ci> alpha_up </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<ci> tau_up </ci>
<ci> Ca_up_max </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_tr_calculation_eq">
<apply id="i_tr_calculation">
<eq/>
<ci> i_tr </ci>
<apply>
<times/>
<ci> alpha_tr </ci>
<ci> p </ci>
<apply>
<minus/>
<ci> Ca_up </ci>
<ci> Ca_rel </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_tr_calculation">
<eq/>
<ci> alpha_tr </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> tau_rep </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="alpha_p_calculation_eq">
<apply id="alpha_p_calculation">
<eq/>
<ci> alpha_p </ci>
<apply>
<times/>
<cn cellml:units="per_mV_ms"> 0.625e-3 </cn>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 34.0 </cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 34.0 </cn>
</apply>
<cn cellml:units="mV"> 4.0 </cn>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="beta_p_calculation_eq">
<apply id="beta_p_calculation">
<eq/>
<ci> beta_p </ci>
<apply>
<divide/>
<cn cellml:units="per_ms"> 5.0e-3 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="mV"> 34.0 </cn>
</apply>
</apply>
<cn cellml:units="mV"> 4.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="dp_dt_eq">
<apply id="dp_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> p </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_p </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> p </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_p </ci>
<ci> p </ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_rel_calculation_eq">
<apply id="i_rel_calculation">
<eq/>
<ci> i_rel </ci>
<apply>
<times/>
<ci> alpha_rel </ci>
<ci> Ca_rel </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Cai </ci>
<cn cellml:units="dimensionless">2.0</cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> Cai </ci>
<cn cellml:units="dimensionless">2.0</cn>
</apply>
<ci> K_mCa </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_rel_calculation">
<eq/>
<ci> alpha_rel </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> tau_rel </ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Ca_up_diff_eq">
<apply id="Ca_up_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_up </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>i_up</ci>
<apply>
<divide/>
<ci>V_i</ci>
<ci>V_up</ci>
</apply>
</apply>
<apply>
<times/>
<ci>i_tr</ci>
<apply>
<divide/>
<ci>V_rel</ci>
<ci>V_up</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Ca_rel_diff_eq">
<apply id="Ca_rel_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ca_rel </ci>
</apply>
<apply>
<minus/>
<ci>i_tr</ci>
<ci>i_rel</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Cai_diff_eq">
<apply id="Cai_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Cai </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>i_rel</ci>
<apply>
<divide/>
<ci>V_rel</ci>
<ci>V_i</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>i_up</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Am</ci>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_siCa </ci>
<ci> i_Ca_b </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> i_NaCa </ci>
</apply>
<apply>
<minus/>
<ci> n_NaCa </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_i </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The DFN model assumes that the potassium ion concentration is homogeneous
throughout the three-compartment model.
-->
<component cmeta:id="extracellular_potassium_concentration" name="extracellular_potassium_concentration">
<!-- This variable is defined here and used in other components -->
<variable units="mM" public_interface="out" name="Kc" initial_value="4.0"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_mm" public_interface="in" name="Am"/>
<variable units="dimensionless" public_interface="in" name="V_i"/>
<variable units="mM" name="Kb" initial_value="4.0"/>
<variable units="uA_per_mm2" public_interface="out" name="i_mK"/>
<variable units="dimensionless" name="P" initial_value="0.7"/>
<!-- These variables are imported from other components. -->
<variable units="ms" public_interface="in" name="time"/>
<variable units="faradays_constant_units" public_interface="in" name="F"/>
<variable units="uA_per_mm2" public_interface="in" name="i_K1"/>
<variable units="uA_per_mm2" public_interface="in" name="i_K"/>
<variable units="uA_per_mm2" public_interface="in" name="i_fK"/>
<variable units="uA_per_mm2" public_interface="in" name="i_siK"/>
<variable units="uA_per_mm2" public_interface="in" name="i_NaK"/>
<variable units="uA_per_mm2" public_interface="in" name="i_to"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Kc_diff_eq">
<apply id="Kc_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Kc </ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci> P </ci>
<apply>
<minus/>
<ci> Kc </ci>
<ci> Kb </ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Am</ci>
<ci> i_mK </ci>
</apply>
<apply>
<times/>
<ci> V_i </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="i_mK_calculation_eq">
<apply id="i_mK_calculation">
<eq/>
<ci> i_mK </ci>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_K1 </ci>
<ci> i_K </ci>
<ci> i_fK </ci>
<ci> i_siK </ci>
<ci> i_to </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> i_NaK </ci>
</apply>
</apply>
</apply>
</math>
</component>
<!--
The intracellular potassium concentration is related to the total potassium
ion membrane flux.
-->
<component cmeta:id="intracellular_potassium_concentration" name="intracellular_potassium_concentration">
<!-- This variable is defined here and used in other components -->
<variable units="mM" public_interface="out" name="Ki" initial_value="140.0"/>
<!-- These variables are defined here and only used internally. -->
<variable units="per_mm" public_interface="in" name="Am"/>
<variable units="dimensionless" public_interface="in" name="V_i"/>
<variable units="uA_per_mm2" public_interface="in" name="i_mK"/>
<!-- These variables are imported from other components. -->
<variable units="ms" public_interface="in" name="time"/>
<variable units="faradays_constant_units" public_interface="in" name="F"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Ki_diff_eq">
<apply id="Ki_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ki </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Am</ci>
<ci> i_mK </ci>
</apply>
</apply>
<apply>
<times/>
<ci> V_i </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="volumes" name="volumes">
<variable units="mm" name="radius" initial_value="50e-3"/>
<variable units="mm" name="length" initial_value="2"/>
<variable units="dimensionless" name="V_ecs" initial_value="0.1"/>
<variable units="per_mm" public_interface="out" name="Am" initial_value="40.0"/>
<variable units="dimensionless" public_interface="out" name="V_i"/>
<variable units="dimensionless" public_interface="out" name="V_e"/>
<variable units="dimensionless" public_interface="out" name="V_up"/>
<variable units="dimensionless" public_interface="out" name="V_rel"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="V_i_calculation_eq">
<apply id="V_i_calculation">
<eq/>
<ci>V_i</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1.0</cn>
<ci>V_ecs</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="V_e_calculation_eq">
<apply id="V_e_calculation">
<eq/>
<ci>V_e</ci>
<ci>V_ecs</ci>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="V_up_calculation_eq">
<apply id="V_up_calculation">
<eq/>
<ci>V_up</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.05</cn>
<ci>V_i</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="V_rel_calculation_eq">
<apply id="V_rel_calculation">
<eq/>
<ci>V_rel</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.02</cn>
<ci>V_i</ci>
</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.
-->
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="hyperpolarising_activated_current">
<component_ref component="hyperpolarising_activated_current_y_gate"/>
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_x_gate"/>
</component_ref>
<component_ref component="time_independent_potassium_current"/>
<component_ref component="transient_outward_current">
<component_ref component="transient_outward_current_r_gate"/>
</component_ref>
<component_ref component="sodium_background_current"/>
<component_ref component="calcium_background_current"/>
<component_ref component="sodium_potassium_pump"/>
<component_ref component="Na_Ca_exchanger"/>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
</component_ref>
<component_ref component="secondary_inward_current">
<component_ref component="secondary_inward_current_d_gate"/>
<component_ref component="secondary_inward_current_f_gate"/>
<component_ref component="secondary_inward_current_f2_gate"/>
</component_ref>
<component_ref component="intracellular_sodium_concentration"/>
<component_ref component="extracellular_sodium_concentration"/>
<component_ref component="intracellular_calcium_concentration"/>
<component_ref component="extracellular_calcium_concentration"/>
<component_ref component="extracellular_potassium_concentration"/>
<component_ref component="intracellular_potassium_concentration"/>
</component_ref>
</group>
<!--
The following <group> element specifies how the components representing
activation and inactivation gates are encapsulated inside their parent
currents.
-->
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="hyperpolarising_activated_current">
<component_ref component="hyperpolarising_activated_current_y_gate"/>
</component_ref>
<component_ref component="time_dependent_potassium_current">
<component_ref component="time_dependent_potassium_current_x_gate"/>
</component_ref>
<component_ref component="transient_outward_current">
<component_ref component="transient_outward_current_r_gate"/>
</component_ref>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
</component_ref>
<component_ref component="secondary_inward_current">
<component_ref component="secondary_inward_current_d_gate"/>
<component_ref component="secondary_inward_current_f_gate"/>
<component_ref component="secondary_inward_current_f2_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="hyperpolarising_activated_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="transient_outward_current"/>
<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="Na_Ca_exchanger"/>
<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="secondary_inward_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_sodium_concentration"/>
<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>
<connection>
<map_components component_2="environment" component_1="extracellular_potassium_concentration"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="transient_outward_current"/>
<map_variables variable_2="i_to" variable_1="i_to"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_potassium_concentration"/>
<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="membrane" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="i_f" variable_1="i_f"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="time_dependent_potassium_current"/>
<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="membrane" component_1="time_independent_potassium_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="transient_outward_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="i_to" variable_1="i_to"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="sodium_background_current"/>
<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="membrane" component_1="calcium_background_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="i_Ca_b" variable_1="i_Ca_b"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="sodium_potassium_pump"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_NaK" variable_1="i_NaK"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="Na_Ca_exchanger"/>
<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="F" variable_1="F"/>
<map_variables variable_2="T" variable_1="T"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="fast_sodium_current"/>
<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="F" variable_1="F"/>
<map_variables variable_2="T" variable_1="T"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="secondary_inward_current"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="i_si" variable_1="i_si"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="T" variable_1="T"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="intracellular_sodium_concentration"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="intracellular_calcium_concentration"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="extracellular_potassium_concentration"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="membrane" component_1="intracellular_potassium_concentration"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<!-- A few variables are passed between the other components. -->
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
<map_variables variable_2="i_fK" variable_1="i_fK"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
</connection>
<connection>
<map_components component_2="time_independent_potassium_current" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="E_K" variable_1="E_K"/>
</connection>
<connection>
<map_components component_2="sodium_background_current" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<connection>
<map_components component_2="Na_Ca_exchanger" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="E_Na" variable_1="E_Na"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="i_fNa" variable_1="i_fNa"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="extracellular_sodium_concentration" component_1="hyperpolarising_activated_current"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
</connection>
<connection>
<map_components component_2="Na_Ca_exchanger" component_1="calcium_background_current"/>
<map_variables variable_2="E_Ca" variable_1="E_Ca"/>
</connection>
<connection>
<map_components component_2="extracellular_calcium_concentration" component_1="calcium_background_current"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
<map_variables variable_2="i_K" variable_1="i_K"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="time_dependent_potassium_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="time_independent_potassium_current"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
<map_variables variable_2="i_K1" variable_1="i_K1"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="transient_outward_current"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="transient_outward_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
</connection>
<connection>
<map_components component_2="intracellular_calcium_concentration" component_1="transient_outward_current"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="sodium_background_current"/>
<map_variables variable_2="i_Na_b" variable_1="i_Na_b"/>
</connection>
<connection>
<map_components component_2="intracellular_calcium_concentration" component_1="calcium_background_current"/>
<map_variables variable_2="i_Ca_b" variable_1="i_Ca_b"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="sodium_potassium_pump"/>
<map_variables variable_2="i_NaK" variable_1="i_NaK"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="sodium_potassium_pump"/>
<map_variables variable_2="i_NaK" variable_1="i_NaK"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="extracellular_sodium_concentration" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
</connection>
<connection>
<map_components component_2="extracellular_calcium_concentration" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="n_NaCa" variable_1="n_NaCa"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="intracellular_calcium_concentration" component_1="Na_Ca_exchanger"/>
<map_variables variable_2="n_NaCa" variable_1="n_NaCa"/>
<map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="fast_sodium_current"/>
<map_variables variable_2="i_Na" variable_1="i_Na"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="extracellular_sodium_concentration" component_1="fast_sodium_current"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="fast_sodium_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="fast_sodium_current"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
</connection>
<connection>
<map_components component_2="intracellular_calcium_concentration" component_1="secondary_inward_current"/>
<map_variables variable_2="i_siCa" variable_1="i_siCa"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="extracellular_calcium_concentration" component_1="secondary_inward_current"/>
<map_variables variable_2="Cao" variable_1="Cao"/>
</connection>
<connection>
<map_components component_2="extracellular_sodium_concentration" component_1="secondary_inward_current"/>
<map_variables variable_2="Nao" variable_1="Nao"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="secondary_inward_current"/>
<map_variables variable_2="i_siK" variable_1="i_siK"/>
<map_variables variable_2="Kc" variable_1="Kc"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="secondary_inward_current"/>
<map_variables variable_2="i_siNa" variable_1="i_siNa"/>
<map_variables variable_2="Nai" variable_1="Nai"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="secondary_inward_current"/>
<map_variables variable_2="Ki" variable_1="Ki"/>
</connection>
<!--
Several variables are passed between parent components and their
encapsulated gates.
-->
<connection>
<map_components component_2="hyperpolarising_activated_current_y_gate" component_1="hyperpolarising_activated_current"/>
<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="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="secondary_inward_current_d_gate" component_1="secondary_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="secondary_inward_current_f_gate" component_1="secondary_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"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="secondary_inward_current_f2_gate" component_1="secondary_inward_current"/>
<map_variables variable_2="f2" variable_1="f2"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
<map_variables variable_2="Cai" variable_1="Cai"/>
</connection>
<connection>
<map_components component_2="transient_outward_current_r_gate" component_1="transient_outward_current"/>
<map_variables variable_2="r" variable_1="r"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="V" variable_1="V"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_concentration" component_1="volumes"/>
<map_variables variable_2="V_i" variable_1="V_i"/>
<map_variables variable_2="Am" variable_1="Am"/>
</connection>
<connection>
<map_components component_2="intracellular_calcium_concentration" component_1="volumes"/>
<map_variables variable_2="V_i" variable_1="V_i"/>
<map_variables variable_2="V_up" variable_1="V_up"/>
<map_variables variable_2="V_rel" variable_1="V_rel"/>
<map_variables variable_2="Am" variable_1="Am"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium_concentration" component_1="volumes"/>
<map_variables variable_2="V_i" variable_1="V_i"/>
<map_variables variable_2="Am" variable_1="Am"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="volumes"/>
<map_variables variable_2="V_i" variable_1="V_i"/>
<map_variables variable_2="Am" variable_1="Am"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_concentration" component_1="extracellular_potassium_concentration"/>
<map_variables variable_2="i_mK" variable_1="i_mK"/>
</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:#2d18a709-1932-4563-a513-070f7b94eb91">
<rdf:value>
The total i_si current is simply the sum of the component calcium,
potassium, and sodium currents.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#84d179ec-97d1-43dd-90fc-f8e63c7f5c30">
<bqs:Pubmed_id>2578676</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#34a13925-a376-4b19-990e-8cf88a8d43b8"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c5ad1e7c-63a8-44fd-b42e-5a72ffd7dc2e">
<vCard:N rdf:resource="rdf:#635f152b-6ce5-4566-b74a-f92a378bcb52"/>
</rdf:Description>
<rdf:Description rdf:about="#E_Ca_calculation_eq">
<cmeta:comment rdf:resource="rdf:#0ef6f6f7-7c1b-4814-8333-76f7bdf1b120"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#dc220893-b71e-4f76-b709-8d8115e56c5c">
<dc:creator rdf:resource="rdf:#a58339a3-a319-4bda-9bab-778341c0f154"/>
<rdf:value>This is the CellML description of Di Francesco and Noble's mathematical model of cardiac action potentials of Purkinje fibres. It is a significant development on the MNT model (1975), and it remains the most complete of all Purkinje fibre ionic current models to date. It is a complete replacement for the MNT model. In particular it considers changes in the interpretation of the i_K2 system, includes more accurate experimental data concerning the fast sodium current and it starts to account for fluctuations in ionic concentrations. In addition, a start is made on accounting for intracellular calcium movement between the sarcoplasmic reticulum and the myoplasm. Corrections for the model can be found in an appendix at the end of Earm & Noble, Proc. Roy. Soc. B, Vol 240(1297), 1990.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#beta_r_calculation_eq">
<cmeta:comment rdf:resource="rdf:#d8005836-cf90-469e-9d55-c5249a6f66ed"/>
</rdf:Description>
<rdf:Description rdf:about="#fast_sodium_current_h_gate">
<cmeta:comment rdf:resource="rdf:#3445a022-24ec-4c9c-a154-1e85673c664d"/>
</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:#c0b5323a-5f49-4844-9b6c-b1169e9e5ca2">
<vCard:N rdf:resource="rdf:#8ca0a76b-a8e1-479f-8fc9-33f9f3854303"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c62a8953-cf18-48c7-839f-dfa9fb274907">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Research Group</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#635f152b-6ce5-4566-b74a-f92a378bcb52">
<vCard:Given>David</vCard:Given>
<vCard:Family>Nickerson</vCard:Family>
<vCard:Other>P</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="#y_kinetics">
<cmeta:comment rdf:resource="rdf:#aa208dfc-32e7-4711-aa7a-18751e868d4f"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#46ebae0d-ed6a-4dcd-824a-5c93ac37fb0a">
<vCard:ORG rdf:resource="rdf:#c62a8953-cf18-48c7-839f-dfa9fb274907"/>
<vCard:EMAIL rdf:resource="rdf:#4a59262d-5f0f-4e23-aac4-7b4312a5972a"/>
<vCard:N rdf:resource="rdf:#6da50c07-5933-477f-89dd-122b76ba3ea7"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#62e1e8ad-28bf-424c-a560-24baacbfc3e1">
<dcterms:W3CDTF>2002-05-06</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#dd_dt_eq">
<cmeta:comment rdf:resource="rdf:#d5a072a4-1bec-496c-8370-c977aa5bdf37"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#794f2524-5754-43de-a925-f159c8de0e16">
<rdf:value>
The opening rate of the p gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#Ki_diff_eq">
<cmeta:comment rdf:resource="rdf:#812573b3-77b3-46f4-b17f-ee4aa1240259"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9e2932d2-2413-4c21-8ab7-202673d186f7">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#06d86784-8060-4a3f-b9d9-1768d41ae06a">
<rdf:value>
The extracellular volume fraction.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#hyperpolarising_activated_current">
<cmeta:comment rdf:resource="rdf:#407456dd-a7fb-419e-af64-53f85af923d9"/>
</rdf:Description>
<rdf:Description rdf:about="#dm_dt_eq">
<cmeta:comment rdf:resource="rdf:#8a8170bd-67b5-4625-8059-8a5a148592d4"/>
</rdf:Description>
<rdf:Description rdf:about="#sodium_diff_eq">
<cmeta:comment rdf:resource="rdf:#1c3657e8-d62f-49b6-a28e-d03e8d57350a"/>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher>
The University of Auckland, Bioengineering Research Group
</dc:publisher>
<cmeta:modification rdf:resource="rdf:#1a501ecc-efe1-449d-80e3-4e221c012e4a"/>
<cmeta:modification rdf:resource="rdf:#5b4f8059-5062-4181-a758-cdedce4b198f"/>
<cmeta:modification rdf:resource="rdf:#5d305ec1-520c-42ed-8997-7abc88a13dbc"/>
<cmeta:modification rdf:resource="rdf:#603a83dc-10cd-44ac-ab7d-fcee7671b093"/>
<cmeta:modification rdf:resource="rdf:#6930d4d1-4910-415e-9f82-980c33ed5535"/>
<cmeta:modification rdf:resource="rdf:#7b2bdbf3-5971-4f63-aa86-3cdd6a87187d"/>
<cmeta:modification rdf:resource="rdf:#80fa37d8-7539-423c-9317-8369aad86440"/>
<cmeta:modification rdf:resource="rdf:#976943ff-ab2d-4e67-b1c6-fc880123e22f"/>
<cmeta:modification rdf:resource="rdf:#bb377858-2621-4109-92d5-e7a1f13b20df"/>
<cmeta:modification rdf:resource="rdf:#e53a9547-95ba-4e3b-a637-04e369c1161d"/>
<dcterms:created rdf:resource="rdf:#8ea810f6-cfd6-46e5-bbc5-ff5dd893dd0b"/>
<dc:creator rdf:resource="rdf:#46ebae0d-ed6a-4dcd-824a-5c93ac37fb0a"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#96475617-de2f-45a5-a419-b12c4417d962">
<rdf:value>
The opening rate of the d gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#alpha_r_calculation_eq">
<cmeta:comment rdf:resource="rdf:#9a7c622e-0124-4904-838c-08268b4fe75a"/>
</rdf:Description>
<rdf:Description rdf:about="#extracellular_sodium_concentration">
<cmeta:comment rdf:resource="rdf:#b0d94a0d-e2ae-4d93-afb3-b0da683b4d75"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#34a13925-a376-4b19-990e-8cf88a8d43b8">
<dc:creator rdf:resource="rdf:#citationAuthorsSeq"/>
<dc:title>A model of cardiac electrical activity incorporating ionic pumps and concentration changes</dc:title>
<bqs:volume>307</bqs:volume>
<bqs:first_page>353</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#fcaaf623-d1ac-4264-8925-878e8325680b"/>
<dcterms:issued rdf:resource="rdf:#0591d415-448c-448a-9848-72ad9cb6772d"/>
<bqs:last_page>398</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#812573b3-77b3-46f4-b17f-ee4aa1240259">
<rdf:value>
The rate of change of intracellular potassium concentration is the
sum of the ions crossing the membrane.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1c538d2f-fb63-4e83-9766-e2065a9eeb5d">
<dcterms:W3CDTF>2003-04-05</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1598a8d2-1546-4076-a9af-869908e011e1">
<rdf:value>
The voltage-dependent activation variable for the time-dependent
potassium current, the x gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#76c5d36a-040c-4a42-bfa0-7631f1f074e6">
<rdf:value>
The calcium current between the uptake and release stores, which
uses a voltage-dependent activation variable - the p gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#alpha_x_calculation_eq">
<cmeta:comment rdf:resource="rdf:#8159b033-0e45-423d-956c-730a5ae34d11"/>
</rdf:Description>
<rdf:Description rdf:about="#Na_Ca_exchanger">
<cmeta:comment rdf:resource="rdf:#83092907-c0ec-42ac-aa48-5024a504acc8"/>
</rdf:Description>
<rdf:Description rdf:about="#dx_dt_eq">
<cmeta:comment rdf:resource="rdf:#3fc26de4-2666-4b21-bce4-e7e99b524bcb"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1c3657e8-d62f-49b6-a28e-d03e8d57350a">
<rdf:value>
The rate of change of intracellular sodium concentration is the sum
of the ions entering the intracellular volume via the sodium
transmembrane currents.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#Ca_up_diff_eq">
<cmeta:comment rdf:resource="rdf:#798fdc6d-dd13-4c15-8d5b-f208d54d4cc2"/>
</rdf:Description>
<rdf:Description rdf:about="#DFN_purkinje_fibre_model_1985">
<dc:title>
The Di Francesco-Noble Model of Cardiac Action Potentials in Purkinje
fibres, 1985
</dc:title>
<cmeta:bio_entity>Purkinje Fibre</cmeta:bio_entity>
<cmeta:comment rdf:resource="rdf:#dc220893-b71e-4f76-b709-8d8115e56c5c"/>
<bqs:reference rdf:resource="rdf:#84d179ec-97d1-43dd-90fc-f8e63c7f5c30"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9a99a950-45bd-4a01-b3cc-0e6763256194">
<rdf:value>
The Na-K exchange pump couples the free energy released by the
hydrolysis of ATP to transfer sodium and potassium ions across the
cell membrane against their electrochemical gradients. 3 Na ions are
pumped out for every 2 K ions pumped into the cell.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#membrane_voltage_diff_eq">
<cmeta:comment rdf:resource="rdf:#f30258b2-2322-45e3-9a57-512dca2127e0"/>
</rdf:Description>
<rdf:Description rdf:about="#time_independent_potassium_current">
<cmeta:comment rdf:resource="rdf:#9f8506d2-0b7d-4763-8c3a-e147d677e2c6"/>
</rdf:Description>
<rdf:Description rdf:about="#beta_x_calculation_eq">
<cmeta:comment rdf:resource="rdf:#955ec352-d962-46b6-bee4-2672130989b7"/>
</rdf:Description>
<rdf:Description rdf:about="#volumes">
<cmeta:comment rdf:resource="rdf:#78a86af3-fdac-4aea-ab7c-32d71904ae10"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4c1e8181-9d16-4ef9-8155-4568c1f6ead7">
<rdf:value>
Changes in [Ca]i were first modelled in the BR model and has only
been slightly developed in the DFN model. Calcium is sequestered in
the sarcoplasmic reticulum ([Ca]up). A fraction is transferred to a
release store in the junctional SR ([Ca]rel) before being released
into the intracellular space. The Ca concentrations in each of these
various stores is modelled together with the transfer between the
calcium sites and the Ca transfer across the cell membrane via the
other ionic currents.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f67a93d6-a45d-46ce-a7bc-07d950c78917">
<rdf:value>
The intracellular volume fraction.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4550554a-7a55-4e2c-a867-373fc995891f">
<rdf:value>
A resting background leakage calcium flux.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d2ba22fd-b8e7-40d0-a720-5e2a543f1712">
<rdf:value>
The calcium current into the uptake store.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#i_tr_calculation_eq">
<cmeta:comment rdf:resource="rdf:#76c5d36a-040c-4a42-bfa0-7631f1f074e6"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#955ec352-d962-46b6-bee4-2672130989b7">
<rdf:value>
The closing rate of the x gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#61055f63-82da-465c-a4a7-2a8cc52e2d08">
<rdf:value>
The calcium uptake store volume fraction.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#180ae7aa-fe54-48b4-b364-cccfeb8b834b">
<rdf:value>
The voltage-dependent inactivation gate for the second inward
current - the f gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7b2bdbf3-5971-4f63-aa86-3cdd6a87187d">
<dcterms:modified rdf:resource="rdf:#8beb535f-6ac6-4ce4-965f-63d94e121148"/>
<rdf:value>
Created two extra components for extracellular sodium and
extracellular calcium concentrations. Then changed the Nao and Cao
variable public interfaces and the connections between components
appropriately.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#a3bacf6a-bc7a-42cb-afec-30d1f5010e91"/>
</rdf:Description>
<rdf:Description rdf:about="#sodium_potassium_pump">
<cmeta:comment rdf:resource="rdf:#9a99a950-45bd-4a01-b3cc-0e6763256194"/>
</rdf:Description>
<rdf:Description rdf:about="#alpha_m_calculation_eq">
<cmeta:comment rdf:resource="rdf:#053c2996-caed-4f2c-82b4-b2330561e17b"/>
</rdf:Description>
<rdf:Description rdf:about="#i_Na_calculation_eq">
<cmeta:comment rdf:resource="rdf:#0e728f36-a6c1-4cdd-98ed-dfb8259e6147"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d8005836-cf90-469e-9d55-c5249a6f66ed">
<rdf:value>
The closing rate of the r gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#i_si_calculation_eq">
<cmeta:comment rdf:resource="rdf:#2d18a709-1932-4563-a513-070f7b94eb91"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fcaaf623-d1ac-4264-8925-878e8325680b">
<dc:title>Philosophical Transactions of the Royal Society of London Series B</dc:title>
</rdf:Description>
<rdf:Description rdf:about="#beta_h_calculation_eq">
<cmeta:comment rdf:resource="rdf:#0aa739ce-1712-45de-b219-487a363096cb"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#bdb535cb-a6b0-43d4-9189-54fe4bb4762e">
<rdf:value>
The kinetics of the p gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0ef6f6f7-7c1b-4814-8333-76f7bdf1b120">
<rdf:value>
The calcium reversal potential.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1d227c42-fee0-475d-a00a-4dab8a384e27">
<rdf:value>
Calculation of the transient outward current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#V_i_calculation_eq">
<cmeta:comment rdf:resource="rdf:#f67a93d6-a45d-46ce-a7bc-07d950c78917"/>
</rdf:Description>
<rdf:Description rdf:about="#i_K1_calculation_eq">
<cmeta:comment rdf:resource="rdf:#da651906-d6f0-4a03-91da-dfe23e0533e2"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cdbde3df-6de7-48fe-b3d1-7a231568db06">
<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="#fast_sodium_current">
<cmeta:comment rdf:resource="rdf:#9362883a-b547-4800-8af1-e1011afb8fab"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#34007ede-4a37-40ce-963c-6a4e2d4075dc">
<rdf:value>
Calculation of the Na/K-pump current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#bf2658ac-86f8-4e9c-884c-8df5b5a6ede0">
<rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#dc2ef87f-e792-47fa-b7af-5f4b014f5cce">
<rdf:value>
The calcium release store volume fraction.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4d0313ca-3112-42f8-9790-87e8ab3d6e40">
<rdf:value>
The membrane component is the main component for this model,
containing the differential equation for the transmembrane potential
(the action potential).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#34a14fcc-5e10-4f4e-a887-49b7a816d434">
<rdf:value>
The maximal potassium current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#55a0dac7-f3a3-4bdd-bb61-f12f09b2e6a8">
<rdf:value>
The calcium release current from the SR into the cytosol.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#143ecafb-b951-4ac5-abac-6a0473e75365">
<rdf:value>
A linear resting sodium flux.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f30258b2-2322-45e3-9a57-512dca2127e0">
<rdf:value>
The action potential equation consists of the sum of the
trans-sarcolemmal currents plus an applied stimulus, which may be
used to pace the cell model.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#686f6c68-4f59-43f8-96de-332b130c61da">
<rdf:value>
The rate of change of intracellular calcium concentration.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#dh_dt_eq">
<cmeta:comment rdf:resource="rdf:#72b44fc0-e154-4f7b-9e0b-3f1351e1f9b7"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#78a86af3-fdac-4aea-ab7c-32d71904ae10">
<rdf:value>
A component used to group the geometry parameters and calculations.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0f49519c-dc02-401d-823d-47270357a8d7">
<rdf:value>
Calculation of the potassium component of the second inward current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#Kc_diff_eq">
<cmeta:comment rdf:resource="rdf:#494dc7e9-d0ba-43d0-9d1d-431f789a9fbb"/>
</rdf:Description>
<rdf:Description rdf:about="#beta_d_calculation_eq">
<cmeta:comment rdf:resource="rdf:#2c86e1c5-ccd8-4241-b882-f7fb8fbce4a2"/>
</rdf:Description>
<rdf:Description rdf:about="#i_siNa_calculation_eq">
<cmeta:comment rdf:resource="rdf:#1c9542c7-aa80-43a8-8a67-35ade71b9581"/>
</rdf:Description>
<rdf:Description rdf:about="#i_siK_calculation_eq">
<cmeta:comment rdf:resource="rdf:#0f49519c-dc02-401d-823d-47270357a8d7"/>
</rdf:Description>
<rdf:Description rdf:about="#membrane">
<cmeta:comment rdf:resource="rdf:#4d0313ca-3112-42f8-9790-87e8ab3d6e40"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d9162a6e-4335-4946-90c0-3b78350eee8a">
<rdf:value>
The reversal potential of the fast sodium channel, assuming a 12%
permeability of potassium ions.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#15a82e9d-9e38-4b49-8d7c-06fa4e5769e8">
<rdf:value>
This component contains the description of intracellular sodium
concentration change.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a126323b-1fc6-4115-88f4-dfae86930a39">
<rdf:value>
The activation variable for the transient outward current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e53a9547-95ba-4e3b-a637-04e369c1161d">
<dcterms:modified rdf:resource="rdf:#62e1e8ad-28bf-424c-a560-24baacbfc3e1"/>
<rdf:value>
Added some initial values from Penny Noble's documentation.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#b6ebfd6a-35af-4cfd-81ab-96b7f655f831"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#46304604-af07-4550-8994-7ff18d5e56d0">
<rdf:value>
The kinetics for the r gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f746dff6-0f33-4111-83ee-27005b906ff1">
<rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#aa208dfc-32e7-4711-aa7a-18751e868d4f">
<rdf:value>
The Hodgkin-Huxley type kinetics for the y gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f92a4bb2-6906-4da6-8a8f-d5068f4b3f30">
<rdf:value>
Calculation of the calcium leakage current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d5a072a4-1bec-496c-8370-c977aa5bdf37">
<rdf:value>
The kinetics of the d gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5b4f8059-5062-4181-a758-cdedce4b198f">
<dcterms:modified rdf:resource="rdf:#4c65dfed-6de7-4222-b1e4-1373772e4cee"/>
<rdf:value>
Added more metadata.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#39331805-814f-46d2-81d1-e77cd6ad63fc"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e760219b-5864-41ce-9d7c-8585935e4a6b">
<rdf:value>
Calculation of the calcium component of the second inward current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#secondary_inward_current_f_gate">
<cmeta:comment rdf:resource="rdf:#180ae7aa-fe54-48b4-b364-cccfeb8b834b"/>
</rdf:Description>
<rdf:Description rdf:about="#Ca_rel_diff_eq">
<cmeta:comment rdf:resource="rdf:#ac6a7a29-5016-4710-8d08-ef329ab96c18"/>
</rdf:Description>
<rdf:Description rdf:about="#time_dependent_potassium_current">
<cmeta:comment rdf:resource="rdf:#71658202-fdcc-4b5b-9310-87815703b802"/>
</rdf:Description>
<rdf:Description rdf:about="#i_K_calculation_eq">
<cmeta:comment rdf:resource="rdf:#b3c13ef2-b42a-4349-9146-6e3633273aac"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0e728f36-a6c1-4cdd-98ed-dfb8259e6147">
<rdf:value>
Calculation of the fast sodium current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#alpha_h_calculation_eq">
<cmeta:comment rdf:resource="rdf:#be7b71bc-26c7-4e5a-9b78-1eb567c80dba"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#053c2996-caed-4f2c-82b4-b2330561e17b">
<rdf:value>
The opening rate of the m gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0335d59f-1a57-40b4-90db-d64b968856d8">
<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:#b0d94a0d-e2ae-4d93-afb3-b0da683b4d75">
<rdf:value>
A representation of extracellular sodium ion concentration, held
constant in this model.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#beta_y_calculation_eq">
<cmeta:comment rdf:resource="rdf:#0b3f99cd-122f-426b-b858-579803ab2aaf"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3445a022-24ec-4c9c-a154-1e85673c664d">
<rdf:value>
The voltage-dependent inactivation gate for the fast sodium current
- the h gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#98f188f7-4e21-4077-8abe-a4f2b5c83b0b">
<rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
</rdf:Description>
<rdf:Description rdf:about="#alpha_f_calculation_eq">
<cmeta:comment rdf:resource="rdf:#8ba60639-acf7-4e2b-ba00-6f853a100f36"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#603a83dc-10cd-44ac-ab7d-fcee7671b093">
<dcterms:modified rdf:resource="rdf:#bf2658ac-86f8-4e9c-884c-8df5b5a6ede0"/>
<rdf:value>
Made changes to some of the metadata, bringing them up to date with
the most recent working draft (26th September) of the Metadata
Specification.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#7a089597-5855-4cb2-8d0f-8f3f06346219"/>
</rdf:Description>
<rdf:Description rdf:about="#i_mK_calculation_eq">
<cmeta:comment rdf:resource="rdf:#70e02131-778a-4ea4-b5c2-fdc53409304b"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9362883a-b547-4800-8af1-e1011afb8fab">
<rdf:value>
The DFN model retains a two-variable model of the sodium kinetics,
with new equations for the gates m and h. It is acknowledged however
that the model does not represent the slower components of Na
inactivation and recovery. It is also assumed that the sodium
channel shows a 12% permeability to K ions.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9f8506d2-0b7d-4763-8c3a-e147d677e2c6">
<rdf:value>
The time-independent background potassium current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#i_up_calculation_eq">
<cmeta:comment rdf:resource="rdf:#d2ba22fd-b8e7-40d0-a720-5e2a543f1712"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1c9542c7-aa80-43a8-8a67-35ade71b9581">
<rdf:value>
Calculation of the sodium component of the second inward current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#09d3d8db-0618-4332-ad27-13c1baed848c">
<rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8beb535f-6ac6-4ce4-965f-63d94e121148">
<rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#54fcdd85-f255-4742-859f-4bcc330159f6">
<rdf:type rdf:resource="http://www.w3.org/2001/vcard-rdf/3.0#N"/>
<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A.</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="#df_dt_eq">
<cmeta:comment rdf:resource="rdf:#4da1457e-a3c8-42a0-af88-342d24366697"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0591d415-448c-448a-9848-72ad9cb6772d">
<dcterms:W3CDTF>1985-01-10</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#df2_dt_eq">
<cmeta:comment rdf:resource="rdf:#35835943-d78f-4d1f-9327-20785d4acdd3"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0b3f99cd-122f-426b-b858-579803ab2aaf">
<rdf:value>
The closing rate for the y gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#798fdc6d-dd13-4c15-8d5b-f208d54d4cc2">
<rdf:value>
The rate of change of calcium concentration in the uptake store.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#I_fNa_calculation_eq">
<cmeta:comment rdf:resource="rdf:#6a56d7ba-71dd-47d1-873d-ff1ee250e731"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e5f27d75-19f6-44b6-b523-41da86f7934c">
<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="rdf:#a58339a3-a319-4bda-9bab-778341c0f154">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1740055e-e69e-42e0-9710-a2e38aacb28b">
<rdf:value>
A representation of extracellular calcium ion concentration, held
constant in this model.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#dr_dt_eq">
<cmeta:comment rdf:resource="rdf:#46304604-af07-4550-8994-7ff18d5e56d0"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author2VcardN">
<vCard:Given>D</vCard:Given>
<vCard:Family>Noble</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="#secondary_inward_current_f2_gate">
<cmeta:comment rdf:resource="rdf:#19dbb93d-30d8-423f-93e0-c5d474b257dd"/>
</rdf:Description>
<rdf:Description rdf:about="#i_siCa_calculation_eq">
<cmeta:comment rdf:resource="rdf:#e760219b-5864-41ce-9d7c-8585935e4a6b"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#665ade67-693b-46ec-b530-042f40964617">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="#V_e_calculation_eq">
<cmeta:comment rdf:resource="rdf:#06d86784-8060-4a3f-b9d9-1768d41ae06a"/>
</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="rdf:#407456dd-a7fb-419e-af64-53f85af923d9">
<rdf:value>
The "funny" current - activated by hyperpolarisation rather than
depolarisation, and consisting of sodium and potassium components.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#IStim_for_cmiss_eq">
<cmeta:comment rdf:resource="rdf:#0335d59f-1a57-40b4-90db-d64b968856d8"/>
</rdf:Description>
<rdf:Description rdf:about="#extracellular_calcium_concentration">
<cmeta:comment rdf:resource="rdf:#1740055e-e69e-42e0-9710-a2e38aacb28b"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b6ebfd6a-35af-4cfd-81ab-96b7f655f831">
<vCard:N rdf:resource="rdf:#665ade67-693b-46ec-b530-042f40964617"/>
</rdf:Description>
<rdf:Description rdf:about="#intracellular_potassium_concentration">
<cmeta:comment rdf:resource="rdf:#5eafa933-52f5-4157-a01e-e3f7f457b70d"/>
</rdf:Description>
<rdf:Description rdf:about="#fast_sodium_current_m_gate">
<cmeta:comment rdf:resource="rdf:#6c2db4a6-7dcb-40a5-b2fd-f2401bf3976d"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#71658202-fdcc-4b5b-9310-87815703b802">
<rdf:value>
The time-dependent potassium current, a current dependent on both
potassium ion concentration and membrane potential.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#Cai_diff_eq">
<cmeta:comment rdf:resource="rdf:#686f6c68-4f59-43f8-96de-332b130c61da"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6c2db4a6-7dcb-40a5-b2fd-f2401bf3976d">
<rdf:value>
The voltage-dependent activation gate for the fast sodium channel -
the m gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#35835943-d78f-4d1f-9327-20785d4acdd3">
<rdf:value>
The kinetics of the f2 gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#i_Ca_b_calculation_eq">
<cmeta:comment rdf:resource="rdf:#f92a4bb2-6906-4da6-8a8f-d5068f4b3f30"/>
</rdf:Description>
<rdf:Description rdf:about="#i_to_calculation_eq">
<cmeta:comment rdf:resource="rdf:#1d227c42-fee0-475d-a00a-4dab8a384e27"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ec94d11e-ac79-453b-a7e7-a247bb1379ca">
<dcterms:W3CDTF>2003-10-28</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#80fa37d8-7539-423c-9317-8369aad86440">
<dcterms:modified rdf:resource="rdf:#09d3d8db-0618-4332-ad27-13c1baed848c"/>
<rdf:value>
Updated metadata to conform to the 16/1/02 CellML Metadata 1.0
Specification.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#54fcdd85-f255-4742-859f-4bcc330159f6"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4da1457e-a3c8-42a0-af88-342d24366697">
<rdf:value>
The kinetics of the f gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#V_up_calculation_eq">
<cmeta:comment rdf:resource="rdf:#61055f63-82da-465c-a4a7-2a8cc52e2d08"/>
</rdf:Description>
<rdf:Description rdf:about="#E_mh_calculation_eq">
<cmeta:comment rdf:resource="rdf:#d9162a6e-4335-4946-90c0-3b78350eee8a"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2c86e1c5-ccd8-4241-b882-f7fb8fbce4a2">
<rdf:value>
The closing rate of the d gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a3bacf6a-bc7a-42cb-afec-30d1f5010e91">
<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="rdf:#be7b71bc-26c7-4e5a-9b78-1eb567c80dba">
<rdf:value>
The opening rate of the h gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#beta_m_calculation_eq">
<cmeta:comment rdf:resource="rdf:#91e531ff-4996-485f-a2dd-1481e9363b70"/>
</rdf:Description>
<rdf:Description rdf:about="#transient_outward_current_r_gate">
<cmeta:comment rdf:resource="rdf:#a126323b-1fc6-4115-88f4-dfae86930a39"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#976943ff-ab2d-4e67-b1c6-fc880123e22f">
<dcterms:modified rdf:resource="rdf:#936165a6-9ff9-4882-a1ec-21044c42cfb5"/>
<rdf:value>
Corrected several equations.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#cdbde3df-6de7-48fe-b3d1-7a231568db06"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8a8170bd-67b5-4625-8059-8a5a148592d4">
<rdf:value>
The kinetics of the m gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#intracellular_sodium_concentration">
<cmeta:comment rdf:resource="rdf:#15a82e9d-9e38-4b49-8d7c-06fa4e5769e8"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#494dc7e9-d0ba-43d0-9d1d-431f789a9fbb">
<rdf:value>
The rate of change in the cleft potassium concentration is the
combination of potassium ions crossing the cellular membrane and
ions diffusing into the volume from the bulk extracellular stores.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a8eeaa9e-e1c6-46c5-a76a-16d999ef60d9">
<rdf:value>
The total current is simply the sum of the two component currents.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#19dbb93d-30d8-423f-93e0-c5d474b257dd">
<rdf:value>
The DFN model also includes a description of Ca-dependent
inactivation. When calcium ions bind to a regulatory site on the
channel protein, they induce a conformational change such that the
channel no longer conducts, and the secondary current slows or
ceases.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9a7c622e-0124-4904-838c-08268b4fe75a">
<rdf:value>
The opening rate of the r gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6da50c07-5933-477f-89dd-122b76ba3ea7">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cf90baae-6f97-4b7d-a6dc-aa7ea7a8bad2">
<rdf:value>
The closing rate of the p gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8ea810f6-cfd6-46e5-bbc5-ff5dd893dd0b">
<dcterms:W3CDTF>2001-09-28</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#beta_p_calculation_eq">
<cmeta:comment rdf:resource="rdf:#cf90baae-6f97-4b7d-a6dc-aa7ea7a8bad2"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#39331805-814f-46d2-81d1-e77cd6ad63fc">
<vCard:N rdf:resource="rdf:#9e2932d2-2413-4c21-8ab7-202673d186f7"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5eafa933-52f5-4157-a01e-e3f7f457b70d">
<rdf:value>
The change in intracellular potassium ion concentration.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5d305ec1-520c-42ed-8997-7abc88a13dbc">
<dcterms:modified rdf:resource="rdf:#f746dff6-0f33-4111-83ee-27005b906ff1"/>
<rdf:value>
Changed equations after using mathml validator.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#e5f27d75-19f6-44b6-b523-41da86f7934c"/>
</rdf:Description>
<rdf:Description rdf:about="#secondary_inward_current_d_gate">
<cmeta:comment rdf:resource="rdf:#29965a0f-15b5-43c4-823f-0cb394e3d411"/>
</rdf:Description>
<rdf:Description rdf:about="#i_NaK_calculation_eq">
<cmeta:comment rdf:resource="rdf:#34007ede-4a37-40ce-963c-6a4e2d4075dc"/>
</rdf:Description>
<rdf:Description rdf:about="#alpha_y_calculation_eq">
<cmeta:comment rdf:resource="rdf:#af307d10-b452-4d7c-a993-72ef23d28de1"/>
</rdf:Description>
<rdf:Description rdf:about="#dp_dt_eq">
<cmeta:comment rdf:resource="rdf:#bdb535cb-a6b0-43d4-9189-54fe4bb4762e"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0aa739ce-1712-45de-b219-487a363096cb">
<rdf:value>
The closing rate of the h gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#bb377858-2621-4109-92d5-e7a1f13b20df">
<dcterms:modified rdf:resource="rdf:#98f188f7-4e21-4077-8abe-a4f2b5c83b0b"/>
<rdf:value>
Removed document type definition as this is declared as optional
according to the W3C recommendation.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#4e66b4dc-4453-4f44-9219-3c2415455410"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#936165a6-9ff9-4882-a1ec-21044c42cfb5">
<rdf:type rdf:resource="http://purl.org/dc/terms/W3CDTF"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7a089597-5855-4cb2-8d0f-8f3f06346219">
<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="#i_rel_calculation_eq">
<cmeta:comment rdf:resource="rdf:#55a0dac7-f3a3-4bdd-bb61-f12f09b2e6a8"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ac6a7a29-5016-4710-8d08-ef329ab96c18">
<rdf:value>
The rate of change of calcium concentration in the release store.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#66bdb6e5-5e44-4d7b-bb42-0d305044cad0">
<rdf:value>
The transient outward current (i_to) replaces the i_qr
chloride-based current of the MNT model. This current is a
calcium-activated, outward rectifier. It has an inactivation gate,
r.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8ca0a76b-a8e1-479f-8fc9-33f9f3854303">
<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b3c13ef2-b42a-4349-9146-6e3633273aac">
<rdf:value>
Calculation of the time-dependent potassium current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#transient_outward_current">
<cmeta:comment rdf:resource="rdf:#66bdb6e5-5e44-4d7b-bb42-0d305044cad0"/>
</rdf:Description>
<rdf:Description rdf:about="#time_dependent_potassium_current_x_gate">
<cmeta:comment rdf:resource="rdf:#1598a8d2-1546-4076-a9af-869908e011e1"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3fc26de4-2666-4b21-bce4-e7e99b524bcb">
<rdf:value>
The kinetics of the x gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cd959611-433b-4c24-af48-e12b619f0eb6">
<rdf:value>
The closing rate of the f gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1a501ecc-efe1-449d-80e3-4e221c012e4a">
<dcterms:modified rdf:resource="rdf:#ec94d11e-ac79-453b-a7e7-a247bb1379ca"/>
<rdf:value>
Getting the model solving and correcting a bunch of errors and fixing
up the units and moving everything to "per-unit-area" type equations.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#c5ad1e7c-63a8-44fd-b42e-5a72ffd7dc2e"/>
</rdf:Description>
<rdf:Description rdf:about="#sodium_background_current">
<cmeta:comment rdf:resource="rdf:#143ecafb-b951-4ac5-abac-6a0473e75365"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#af307d10-b452-4d7c-a993-72ef23d28de1">
<rdf:value>
The opening rate for the y gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#Na_Ca_exchanger_calculation2_eq">
<cmeta:comment rdf:resource="rdf:#35ba26a0-1ea4-4feb-8441-5a6b9a7ef594"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8d82840c-ca38-4ff0-8356-aa376a213cf2">
<rdf:value>
A representation of extracellular potassium ion concentration based
on a homogeneous three-compartment model.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5cf516ce-4dd9-4d50-acdb-4bb8a562bcf6">
<rdf:value>
Calculation of the background sodium current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6930d4d1-4910-415e-9f82-980c33ed5535">
<dcterms:modified rdf:resource="rdf:#1c538d2f-fb63-4e83-9766-e2065a9eeb5d"/>
<rdf:value>
Changed the model name so the model loads in the database easier.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#c0b5323a-5f49-4844-9b6c-b1169e9e5ca2"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8ba60639-acf7-4e2b-ba00-6f853a100f36">
<rdf:value>
The opening rate of the f gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#16beed7b-b3e4-40fa-9d83-89ee1d1ff4bc">
<rdf:value>
The reversal potentials for the two ions.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#70e02131-778a-4ea4-b5c2-fdc53409304b">
<rdf:value>
The total transmembrane potassium current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#da651906-d6f0-4a03-91da-dfe23e0533e2">
<rdf:value>
Calculation of the time-independent postassium current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#hyperpolarising_activated_current_y_gate">
<cmeta:comment rdf:resource="rdf:#940d94d3-69b2-47b6-8b9f-536ee8ff2f5e"/>
</rdf:Description>
<rdf:Description rdf:about="#intracellular_calcium_concentration">
<cmeta:comment rdf:resource="rdf:#4c1e8181-9d16-4ef9-8155-4568c1f6ead7"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#940d94d3-69b2-47b6-8b9f-536ee8ff2f5e">
<rdf:value>
The activation variable for the "funny" current - the y gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#calcium_background_current">
<cmeta:comment rdf:resource="rdf:#4550554a-7a55-4e2c-a867-373fc995891f"/>
</rdf:Description>
<rdf:Description rdf:about="#i_Na_b_calculation_eq">
<cmeta:comment rdf:resource="rdf:#5cf516ce-4dd9-4d50-acdb-4bb8a562bcf6"/>
</rdf:Description>
<rdf:Description rdf:about="#E_f_calculation_eq">
<cmeta:comment rdf:resource="rdf:#16beed7b-b3e4-40fa-9d83-89ee1d1ff4bc"/>
</rdf:Description>
<rdf:Description rdf:about="#secondary_inward_current">
<cmeta:comment rdf:resource="rdf:#900feb3d-fbd0-45dd-a658-c7472eeca3b3"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6a56d7ba-71dd-47d1-873d-ff1ee250e731">
<rdf:value>
The maximal sodium current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#V_rel_calculation_eq">
<cmeta:comment rdf:resource="rdf:#dc2ef87f-e792-47fa-b7af-5f4b014f5cce"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author1VcardN">
<vCard:Given>D</vCard:Given>
<vCard:Family>DiFrancesco</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4c65dfed-6de7-4222-b1e4-1373772e4cee">
<dcterms:W3CDTF>2002-07-19</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#72b44fc0-e154-4f7b-9e0b-3f1351e1f9b7">
<rdf:value>
The kinetics of the h gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#35ba26a0-1ea4-4feb-8441-5a6b9a7ef594">
<rdf:value>
Calculation of the exchanger current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#extracellular_potassium_concentration">
<cmeta:comment rdf:resource="rdf:#8d82840c-ca38-4ff0-8356-aa376a213cf2"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#83092907-c0ec-42ac-aa48-5024a504acc8">
<rdf:value>
The DFN paper gives two alternative equations for the
i_NaCa current. The simplest makes the current a sine function of
the total energy gradient. The more realistic model uses an
equation which is likely to reproduce better dependence of i_NaCa
on intracellular calcium ions. We utilise the more complex version
here.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4e66b4dc-4453-4f44-9219-3c2415455410">
<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="rdf:#900feb3d-fbd0-45dd-a658-c7472eeca3b3">
<rdf:value>
Like the MNT model, the kinetics of the secondary inward current are
still described in terms of two gate variables d and f, but the time
constants for activation and inactivation processes are much
shorter. The fast component, i_si of this current has been divided
into the individual ion movements of Ca, K and Na. This current
would later be called the L-type calcium current.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#beta_f_calculation_eq">
<cmeta:comment rdf:resource="rdf:#cd959611-433b-4c24-af48-e12b619f0eb6"/>
</rdf:Description>
<rdf:Description rdf:about="#alpha_d_calculation_eq">
<cmeta:comment rdf:resource="rdf:#96475617-de2f-45a5-a419-b12c4417d962"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4a59262d-5f0f-4e23-aac4-7b4312a5972a">
<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:#91e531ff-4996-485f-a2dd-1481e9363b70">
<rdf:value>
The closing rate of the m gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8159b033-0e45-423d-956c-730a5ae34d11">
<rdf:value>
The opening rate of the x gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#alpha_p_calculation_eq">
<cmeta:comment rdf:resource="rdf:#794f2524-5754-43de-a925-f159c8de0e16"/>
</rdf:Description>
<rdf:Description rdf:about="#i_f_calculation_eq">
<cmeta:comment rdf:resource="rdf:#a8eeaa9e-e1c6-46c5-a76a-16d999ef60d9"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#29965a0f-15b5-43c4-823f-0cb394e3d411">
<rdf:value>
The voltage-dependent activation gate for the second inward current
- the d gate.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#I_fK_calculation_eq">
<cmeta:comment rdf:resource="rdf:#34a14fcc-5e10-4f4e-a887-49b7a816d434"/>
</rdf:Description>
</rdf:RDF>
</model>
