- Author:
- Alan Garny <a.garny@auckland.ac.nz>
- Date:
- 2020-05-25 18:24:55+12:00
- Desc:
- Initial implementation of the MRG2001 model.
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/5f5/rawfile/b52b20d66fed3ffb821f9acf272f6eebd76c6765/mcintyre_richardson_grill_model_2001.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="mcintyre_richardson_grill_model_2001" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<units name="ms">
<unit prefix="milli" units="second"/>
</units>
<units name="mV">
<unit prefix="milli" units="volt"/>
</units>
<units name="per_ms">
<unit exponent="-1" units="ms"/>
</units>
<units name="per_mV_ms">
<unit exponent="-1" units="mV"/>
<unit units="per_ms"/>
</units>
<units name="mA_per_cm2">
<unit prefix="milli" units="ampere"/>
<unit exponent="-2" prefix="centi" units="metre"/>
</units>
<units name="mF_per_cm2">
<unit prefix="milli" units="farad"/>
<unit exponent="-2" prefix="centi" units="metre"/>
</units>
<units name="S_per_cm2">
<unit units="siemens"/>
<unit exponent="-2" prefix="centi" units="metre"/>
</units>
<component name="environment">
<variable name="t" public_interface="out" units="ms"/>
</component>
<component name="membrane">
<!-- This computes the nodal membrane potential, hence we use C_n as the
capacitance and i_Naf, i_Nap, i_Ks and i_Lk as the currents involved
in the membrane dynamics.
Note #1: we also use i_Kf, but by default its conductance is set to
0 S/cm2. The authors mention that, based on experimental
data, the value for g_Kf should be ~0.02 S/cm2, which is the
reason they tested their model with a range of values
between 0.01 and 0.04 S/cm2.
Note #2: no initial values for the membrane potential (i.e. V_m) and
the different gating variables (i.e. m, h, p, s and n) are
provided. So, we set V_m to -80 mV (i.e. the resting
potential used in the internodal segments) and 0 for the
different gating variables. From there, the model was run
without a stimulus and for several days worth of simulation
to reach steady state.
Note #3: there is no information about the kind of stimulus that
should be applied to generate a "default" action potential.
However, various stimulus durations are mentioned, varying
between 100 µs and 3 ms. So, we arbitrarily went for 0.5 ms.
As for the stimulus amplitude, we went for one that gives an
action potential (actually, a series of action potentials!).-->
<variable name="t" public_interface="in" units="ms"/>
<variable initial_value="-88.5901439103062" name="V_m" public_interface="out" units="mV"/>
<variable name="i_Stim" units="mA_per_cm2"/>
<variable name="i_Naf" public_interface="in" units="mA_per_cm2"/>
<variable name="i_Nap" public_interface="in" units="mA_per_cm2"/>
<variable name="i_Ks" public_interface="in" units="mA_per_cm2"/>
<variable name="i_Kf" public_interface="in" units="mA_per_cm2"/>
<variable name="i_Lk" public_interface="in" units="mA_per_cm2"/>
<variable initial_value="0.002" name="C_n" units="mF_per_cm2"/>
<variable initial_value="50" name="E_Na" public_interface="out" units="mV"/>
<variable initial_value="-90" name="E_K" public_interface="out" units="mV"/>
<variable initial_value="-90" name="E_Lk" public_interface="out" units="mV"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Stim</ci>
<piecewise>
<piece>
<cn cellml:units="mA_per_cm2">0.2</cn>
<apply>
<and/>
<apply>
<geq/>
<ci>t</ci>
<cn cellml:units="ms">10</cn>
</apply>
<apply>
<leq/>
<ci>t</ci>
<cn cellml:units="ms">10.1</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="mA_per_cm2">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>V_m</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<ci>i_Stim</ci>
</apply>
<ci>i_Naf</ci>
<ci>i_Nap</ci>
<ci>i_Ks</ci>
<ci>i_Kf</ci>
<ci>i_Lk</ci>
</apply>
</apply>
<ci>C_n</ci>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_channel">
<variable name="t" private_interface="out" public_interface="in" units="ms"/>
<variable name="i_Naf" public_interface="out" units="mA_per_cm2"/>
<variable initial_value="3" name="g_Naf" units="S_per_cm2"/>
<variable name="m" private_interface="in" units="dimensionless"/>
<variable name="h" private_interface="in" units="dimensionless"/>
<variable name="V_m" private_interface="out" public_interface="in" units="mV"/>
<variable name="E_Na" public_interface="in" units="mV"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Naf</ci>
<apply>
<times/>
<ci>g_Naf</ci>
<apply>
<power/>
<ci>m</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>h</ci>
<apply>
<minus/>
<ci>V_m</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_channel_m_gate">
<variable name="t" public_interface="in" units="ms"/>
<variable initial_value="0.0302964457761589" name="m" public_interface="out" units="dimensionless"/>
<variable name="alpha_m" units="per_ms"/>
<variable name="beta_m" units="per_ms"/>
<variable name="V_m" public_interface="in" units="mV"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>m</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_m</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>m</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_m</ci>
<ci>m</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_m</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_mV_ms">6.57</cn>
<apply>
<plus/>
<ci>V_m</ci>
<cn cellml:units="mV">20.4</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V_m</ci>
<cn cellml:units="mV">20.4</cn>
</apply>
</apply>
<cn cellml:units="mV">10.3</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_m</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_mV_ms">0.304</cn>
</apply>
<apply>
<plus/>
<ci>V_m</ci>
<cn cellml:units="mV">25.7</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V_m</ci>
<cn cellml:units="mV">25.7</cn>
</apply>
<cn cellml:units="mV">9.16</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_channel_h_gate">
<variable name="t" public_interface="in" units="ms"/>
<variable initial_value="0.841520865130776" name="h" public_interface="out" units="dimensionless"/>
<variable name="alpha_h" units="per_ms"/>
<variable name="beta_h" units="per_ms"/>
<variable name="V_m" public_interface="in" units="mV"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>h</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_h</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>h</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_h</ci>
<ci>h</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_h</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_mV_ms">0.34</cn>
</apply>
<apply>
<plus/>
<ci>V_m</ci>
<cn cellml:units="mV">114</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V_m</ci>
<cn cellml:units="mV">114</cn>
</apply>
<cn cellml:units="mV">11</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_h</ci>
<apply>
<divide/>
<cn cellml:units="per_ms">12.6</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V_m</ci>
<cn cellml:units="mV">31.8</cn>
</apply>
</apply>
<cn cellml:units="mV">13.4</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="persistent_sodium_channel">
<variable name="t" private_interface="out" public_interface="in" units="ms"/>
<variable name="i_Nap" public_interface="out" units="mA_per_cm2"/>
<variable initial_value="0.01" name="g_Nap" units="S_per_cm2"/>
<variable name="p" private_interface="in" units="dimensionless"/>
<variable name="V_m" private_interface="out" public_interface="in" units="mV"/>
<variable name="E_Na" public_interface="in" units="mV"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Nap</ci>
<apply>
<times/>
<ci>g_Nap</ci>
<apply>
<power/>
<ci>p</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<minus/>
<ci>V_m</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="persistent_sodium_channel_p_gate">
<variable name="t" public_interface="in" units="ms"/>
<variable initial_value="0.0969864645712442" name="p" public_interface="out" units="dimensionless"/>
<variable name="alpha_p" units="per_ms"/>
<variable name="beta_p" units="per_ms"/>
<variable name="V_m" public_interface="in" units="mV"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>p</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_p</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>p</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_p</ci>
<ci>p</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_p</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_mV_ms">0.0353</cn>
<apply>
<plus/>
<ci>V_m</ci>
<cn cellml:units="mV">27</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V_m</ci>
<cn cellml:units="mV">27</cn>
</apply>
</apply>
<cn cellml:units="mV">10.2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_p</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_mV_ms">0.000883</cn>
</apply>
<apply>
<plus/>
<ci>V_m</ci>
<cn cellml:units="mV">34</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V_m</ci>
<cn cellml:units="mV">34</cn>
</apply>
<cn cellml:units="mV">10</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_potassium_channel">
<variable name="t" private_interface="out" public_interface="in" units="ms"/>
<variable name="i_Ks" public_interface="out" units="mA_per_cm2"/>
<variable initial_value="0.08" name="g_Ks" units="S_per_cm2"/>
<variable name="s" private_interface="in" units="dimensionless"/>
<variable name="V_m" private_interface="out" public_interface="in" units="mV"/>
<variable name="E_K" public_interface="in" units="mV"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Ks</ci>
<apply>
<times/>
<ci>g_Ks</ci>
<ci>s</ci>
<apply>
<minus/>
<ci>V_m</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="slow_potassium_channel_s_gate">
<variable name="t" public_interface="in" units="ms"/>
<variable initial_value="0.00997371545602793" name="s" public_interface="out" units="dimensionless"/>
<variable name="alpha_s" units="per_ms"/>
<variable name="beta_s" units="per_ms"/>
<variable name="V_m" public_interface="in" units="mV"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>s</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_s</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>s</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_s</ci>
<ci>s</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_s</ci>
<apply>
<divide/>
<cn cellml:units="per_ms">0.3</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V_m</ci>
<cn cellml:units="mV">53</cn>
</apply>
</apply>
<cn cellml:units="mV">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_s</ci>
<apply>
<divide/>
<cn cellml:units="per_ms">0.03</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V_m</ci>
<cn cellml:units="mV">90</cn>
</apply>
</apply>
<cn cellml:units="mV">1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="juxtaparanodal_fast_potassium_channel">
<variable name="t" private_interface="out" public_interface="in" units="ms"/>
<variable name="i_Kf" public_interface="out" units="mA_per_cm2"/>
<variable initial_value="0" name="g_Kf" units="S_per_cm2"/>
<variable name="n" private_interface="in" units="dimensionless"/>
<variable name="V_m" private_interface="out" public_interface="in" units="mV"/>
<variable name="E_K" public_interface="in" units="mV"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Kf</ci>
<apply>
<times/>
<ci>g_Kf</ci>
<apply>
<power/>
<ci>n</ci>
<cn cellml:units="dimensionless">4</cn>
</apply>
<apply>
<minus/>
<ci>V_m</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="juxtaparanodal_fast_potassium_channel_n_gate">
<variable name="t" public_interface="in" units="ms"/>
<variable initial_value="0.000886041197111556" name="n" public_interface="out" units="dimensionless"/>
<variable name="alpha_n" units="per_ms"/>
<variable name="beta_n" units="per_ms"/>
<variable name="V_m" public_interface="in" units="mV"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>n</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_n</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>n</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_n</ci>
<ci>n</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_n</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_mV_ms">0.0462</cn>
<apply>
<plus/>
<ci>V_m</ci>
<cn cellml:units="mV">83.2</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V_m</ci>
<cn cellml:units="mV">83.2</cn>
</apply>
</apply>
<cn cellml:units="mV">1.1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_n</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_mV_ms">0.0824</cn>
</apply>
<apply>
<plus/>
<ci>V_m</ci>
<cn cellml:units="mV">66</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V_m</ci>
<cn cellml:units="mV">66</cn>
</apply>
<cn cellml:units="mV">10.5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="leakage_channel">
<variable name="i_Lk" public_interface="out" units="mA_per_cm2"/>
<variable initial_value="0.007" name="g_Lk" units="S_per_cm2"/>
<variable name="V_m" private_interface="out" public_interface="in" units="mV"/>
<variable name="E_Lk" public_interface="in" units="mV"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Lk</ci>
<apply>
<times/>
<ci>g_Lk</ci>
<apply>
<minus/>
<ci>V_m</ci>
<ci>E_Lk</ci>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="fast_sodium_channel">
<component_ref component="fast_sodium_channel_m_gate"/>
<component_ref component="fast_sodium_channel_h_gate"/>
</component_ref>
<component_ref component="persistent_sodium_channel">
<component_ref component="persistent_sodium_channel_p_gate"/>
</component_ref>
<component_ref component="slow_potassium_channel">
<component_ref component="slow_potassium_channel_s_gate"/>
</component_ref>
<component_ref component="juxtaparanodal_fast_potassium_channel">
<component_ref component="juxtaparanodal_fast_potassium_channel_n_gate"/>
</component_ref>
</group>
<connection>
<map_components component_1="environment" component_2="membrane"/>
<map_variables variable_1="t" variable_2="t"/>
</connection>
<connection>
<map_components component_1="environment" component_2="fast_sodium_channel"/>
<map_variables variable_1="t" variable_2="t"/>
</connection>
<connection>
<map_components component_1="environment" component_2="persistent_sodium_channel"/>
<map_variables variable_1="t" variable_2="t"/>
</connection>
<connection>
<map_components component_1="environment" component_2="slow_potassium_channel"/>
<map_variables variable_1="t" variable_2="t"/>
</connection>
<connection>
<map_components component_1="environment" component_2="juxtaparanodal_fast_potassium_channel"/>
<map_variables variable_1="t" variable_2="t"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="fast_sodium_channel"/>
<map_variables variable_1="V_m" variable_2="V_m"/>
<map_variables variable_1="i_Naf" variable_2="i_Naf"/>
<map_variables variable_1="E_Na" variable_2="E_Na"/>
</connection>
<connection>
<map_components component_1="fast_sodium_channel" component_2="fast_sodium_channel_m_gate"/>
<map_variables variable_1="t" variable_2="t"/>
<map_variables variable_1="V_m" variable_2="V_m"/>
<map_variables variable_1="m" variable_2="m"/>
</connection>
<connection>
<map_components component_1="fast_sodium_channel" component_2="fast_sodium_channel_h_gate"/>
<map_variables variable_1="t" variable_2="t"/>
<map_variables variable_1="V_m" variable_2="V_m"/>
<map_variables variable_1="h" variable_2="h"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="persistent_sodium_channel"/>
<map_variables variable_1="V_m" variable_2="V_m"/>
<map_variables variable_1="i_Nap" variable_2="i_Nap"/>
<map_variables variable_1="E_Na" variable_2="E_Na"/>
</connection>
<connection>
<map_components component_1="persistent_sodium_channel" component_2="persistent_sodium_channel_p_gate"/>
<map_variables variable_1="t" variable_2="t"/>
<map_variables variable_1="V_m" variable_2="V_m"/>
<map_variables variable_1="p" variable_2="p"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="slow_potassium_channel"/>
<map_variables variable_1="V_m" variable_2="V_m"/>
<map_variables variable_1="i_Ks" variable_2="i_Ks"/>
<map_variables variable_1="E_K" variable_2="E_K"/>
</connection>
<connection>
<map_components component_1="slow_potassium_channel" component_2="slow_potassium_channel_s_gate"/>
<map_variables variable_1="t" variable_2="t"/>
<map_variables variable_1="V_m" variable_2="V_m"/>
<map_variables variable_1="s" variable_2="s"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="juxtaparanodal_fast_potassium_channel"/>
<map_variables variable_1="V_m" variable_2="V_m"/>
<map_variables variable_1="i_Kf" variable_2="i_Kf"/>
<map_variables variable_1="E_K" variable_2="E_K"/>
</connection>
<connection>
<map_components component_1="juxtaparanodal_fast_potassium_channel" component_2="juxtaparanodal_fast_potassium_channel_n_gate"/>
<map_variables variable_1="t" variable_2="t"/>
<map_variables variable_1="V_m" variable_2="V_m"/>
<map_variables variable_1="n" variable_2="n"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="leakage_channel"/>
<map_variables variable_1="V_m" variable_2="V_m"/>
<map_variables variable_1="i_Lk" variable_2="i_Lk"/>
<map_variables variable_1="E_Lk" variable_2="E_Lk"/>
</connection>
</model>
