Location: BG_Ks @ ef4b8640984c / BG_Ks.cellml
- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2022-04-08 14:02:01+12:00
- Desc:
- Fitting to kinetic hybrid model of LRd + Kernik
- Permanent Source URI:
- https://models.cellml.org/workspace/82d/rawfile/ef4b8640984c620ac0534355377346919cffdeb6/BG_Ks.cellml
<?xml version='1.0' encoding='UTF-8'?>
<!-- slow delayed rectifier (potassium) 1
gate variables
S_Ks00: xs_10 xs_20
S_Ks01: xs_11 xs_20
S_Ks10: xs_10 xs_21
S_Ks11: xs_11 xs_21
gate variable transitions
xs1: a to b
xs2: c to d
xs3: a to c
xs4: b to d-->
<model name="BG_Ks_model" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:xlink="http://www.w3.org/1999/xlink">
<import xlink:href="units_and_constants/units_BG.cellml">
<units name="mM" units_ref="mM"/>
<units name="fmol" units_ref="fmol"/>
<units name="per_fmol" units_ref="per_fmol"/>
<units name="J_per_mol" units_ref="J_per_mol"/>
<units name="J_per_K_per_mol" units_ref="J_per_K_per_mol"/>
<units name="fmol_per_sec" units_ref="fmol_per_sec"/>
<units name="C_per_mol" units_ref="C_per_mol"/>
<units name="J_per_C" units_ref="J_per_C"/>
<units name="fF" units_ref="fF"/>
<units name="fC" units_ref="fC"/>
<units name="fA" units_ref="fA"/>
</import>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
<variable initial_value="153400" name="C_m" public_interface="out" units="fF"/>
<variable initial_value="27.9828" name="q_K_o" public_interface="out" units="fmol"/>
<variable initial_value="5510" name="q_K_i" public_interface="out" units="fmol"/>
<variable initial_value="-8.5e4" name="q_mem" public_interface="out" units="fC"/>
<variable name="Vmem" units="volt"/>
<variable initial_value="8.31" name="R" public_interface="out" units="J_per_K_per_mol"/>
<variable initial_value="310" name="T" public_interface="out" units="kelvin"/>
<variable initial_value="96500" name="F" public_interface="out" units="C_per_mol"/>
<variable name="v_Ks" public_interface="in" units="fmol_per_sec"/>
<variable name="I_mem_Ks" public_interface="in" units="fA"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_K_i</ci>
</apply>
<apply>
<minus/>
<ci>v_Ks</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_K_o</ci>
</apply>
<ci>v_Ks</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_mem</ci>
</apply>
<ci>I_mem_Ks</ci>
</apply>
<apply>
<eq/>
<ci>Vmem</ci>
<apply>
<divide/>
<ci>q_mem</ci>
<ci>C_m</ci>
</apply>
</apply>
</math>
</component>
<component name="Ks_parameters">
<variable initial_value="562.081" name="kappa_Ks" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.0131575" name="kappa_xs1" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.0469146" name="kappa_xs2" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.0131575" name="kappa_xs3" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.0469146" name="kappa_xs4" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.689193" name="K_K_i" public_interface="out" units="per_fmol"/>
<variable initial_value="4.57511" name="K_K_o" public_interface="out" units="per_fmol"/>
<variable initial_value="0.0885882" name="K_S_Ks00" public_interface="out" units="per_fmol"/>
<variable initial_value="0.0248451" name="K_S_Ks01" public_interface="out" units="per_fmol"/>
<variable initial_value="0.0248451" name="K_S_Ks10" public_interface="out" units="per_fmol"/>
<variable initial_value="0.00696797" name="K_S_Ks11" public_interface="out" units="per_fmol"/>
<variable initial_value="1" name="zK" public_interface="out" units="dimensionless"/>
<variable initial_value="0.000400323747581994" name="z_xs_f" public_interface="out" units="dimensionless"/>
<variable initial_value="-1.41544821457997" name="z_xs_r" public_interface="out" units="dimensionless"/>
</component>
<component name="Ks">
<variable name="t" private_interface="out" public_interface="in" units="second"/>
<variable name="R" public_interface="in" units="J_per_K_per_mol"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="F" private_interface="out" public_interface="in" units="C_per_mol"/>
<variable name="C_m" public_interface="in" units="fF"/>
<!-- Parameters-->
<!-- overall ion permeability (GHK) is kappa_{ion}-->
<variable name="kappa_Ks" public_interface="in" units="fmol_per_sec"/>
<variable name="K_K_o" public_interface="in" units="per_fmol"/>
<variable name="K_K_i" public_interface="in" units="per_fmol"/>
<!-- state variables-->
<variable name="q_K_i" public_interface="in" units="fmol"/>
<variable name="q_K_o" public_interface="in" units="fmol"/>
<variable name="q_mem" public_interface="in" units="fC"/>
<variable name="v_Ks" public_interface="out" units="fmol_per_sec"/>
<variable name="I_mem_Ks" public_interface="out" units="fA"/>
<variable name="u_K_i" units="J_per_mol"/>
<variable name="u_K_o" units="J_per_mol"/>
<variable name="V_mem" private_interface="out" units="J_per_C"/>
<variable name="Am_Ks" units="J_per_mol"/>
<variable name="Af_Ks" units="J_per_mol"/>
<variable name="Ar_Ks" units="J_per_mol"/>
<variable name="zK" public_interface="in" units="dimensionless"/>
<!-- Conservation laws-->
<!-- Constitutive relations - Convention: positive flow from inside to outside-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Am_Ks</ci>
<apply>
<times/>
<ci>zK</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u_K_i</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_K_i</ci>
<ci>q_K_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_K_o</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_K_o</ci>
<ci>q_K_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_Ks</ci>
<apply>
<plus/>
<ci>mu_S_Ks11</ci>
<ci>u_K_i</ci>
<ci>Am_Ks</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_Ks</ci>
<apply>
<plus/>
<ci>mu_S_Ks11</ci>
<ci>u_K_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_Ks</ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="dimensionless">1</cn>
<ci>kappa_Ks</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_Ks</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_Ks</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Am_Ks</ci>
<cn cellml:units="J_per_mol">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">1</cn>
<ci>kappa_Ks</ci>
<ci>Am_Ks</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Am_Ks</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_Ks</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_Ks</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>V_mem</ci>
<apply>
<divide/>
<ci>q_mem</ci>
<ci>C_m</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>I_mem_Ks</ci>
<apply>
<times/>
<ci>F</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>zK</ci>
</apply>
<ci>v_Ks</ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>v_xs1</ci>
<ci>v_xs2</ci>
<ci>v_xs3</ci>
<ci>v_xs4</ci>
</apply>
<apply>
<minus/>
<ci>z_xs_r</ci>
<ci>z_xs_f</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- GATE
channel states variables
xs00
xs01
xs10
xs11-->
<variable name="v_S_Ks00" units="fmol_per_sec"/>
<variable name="v_S_Ks01" units="fmol_per_sec"/>
<variable name="v_S_Ks10" units="fmol_per_sec"/>
<variable name="v_S_Ks11" units="fmol_per_sec"/>
<!-- gate variable transitions
R1: 00 to 01
R2: 10 to 11
R3: 00 to 10
R4: 01 to 11-->
<variable name="v_xs1" units="fmol_per_sec"/>
<variable name="v_xs2" units="fmol_per_sec"/>
<variable name="v_xs3" units="fmol_per_sec"/>
<variable name="v_xs4" units="fmol_per_sec"/>
<variable name="mu_S_Ks00" units="J_per_mol"/>
<variable name="mu_S_Ks01" units="J_per_mol"/>
<variable name="mu_S_Ks10" units="J_per_mol"/>
<variable name="mu_S_Ks11" units="J_per_mol"/>
<!-- forward/reverse affinities at each reaction-->
<variable name="Af_xs1" units="J_per_mol"/>
<variable name="Ar_xs1" units="J_per_mol"/>
<variable name="Af_xs2" units="J_per_mol"/>
<variable name="Ar_xs2" units="J_per_mol"/>
<variable name="Af_xs3" units="J_per_mol"/>
<variable name="Ar_xs3" units="J_per_mol"/>
<variable name="Af_xs4" units="J_per_mol"/>
<variable name="Ar_xs4" units="J_per_mol"/>
<!-- gating variables-->
<variable name="kappa_xs1" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_xs2" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_xs3" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_xs4" public_interface="in" units="fmol_per_sec"/>
<variable name="K_S_Ks00" public_interface="in" units="per_fmol"/>
<variable name="K_S_Ks01" public_interface="in" units="per_fmol"/>
<variable name="K_S_Ks10" public_interface="in" units="per_fmol"/>
<variable name="K_S_Ks11" public_interface="in" units="per_fmol"/>
<variable name="z_xs_f" public_interface="in" units="dimensionless"/>
<variable name="z_xs_r" public_interface="in" units="dimensionless"/>
<variable initial_value="0.999997" name="q_S_Ks00" units="fmol"/>
<variable initial_value="1e-6" name="q_S_Ks01" units="fmol"/>
<variable initial_value="1e-6" name="q_S_Ks10" units="fmol"/>
<variable initial_value="1e-6" name="q_S_Ks11" units="fmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Af_xs1</ci>
<apply>
<plus/>
<ci>mu_S_Ks00</ci>
<apply>
<times/>
<ci>z_xs_f</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_xs1</ci>
<apply>
<plus/>
<ci>mu_S_Ks01</ci>
<apply>
<times/>
<ci>z_xs_r</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_xs2</ci>
<apply>
<plus/>
<ci>mu_S_Ks10</ci>
<apply>
<times/>
<ci>z_xs_f</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_xs2</ci>
<apply>
<plus/>
<ci>mu_S_Ks11</ci>
<apply>
<times/>
<ci>z_xs_r</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_xs3</ci>
<apply>
<plus/>
<ci>mu_S_Ks00</ci>
<apply>
<times/>
<ci>z_xs_f</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_xs3</ci>
<apply>
<plus/>
<ci>mu_S_Ks10</ci>
<apply>
<times/>
<ci>z_xs_r</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_xs4</ci>
<apply>
<plus/>
<ci>mu_S_Ks01</ci>
<apply>
<times/>
<ci>z_xs_f</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_xs4</ci>
<apply>
<plus/>
<ci>mu_S_Ks11</ci>
<apply>
<times/>
<ci>z_xs_r</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_xs1</ci>
<apply>
<times/>
<ci>kappa_xs1</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_xs1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_xs1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_xs2</ci>
<apply>
<times/>
<ci>kappa_xs2</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_xs2</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_xs2</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_xs3</ci>
<apply>
<times/>
<ci>kappa_xs3</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_xs3</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_xs3</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_xs4</ci>
<apply>
<times/>
<ci>kappa_xs4</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_xs4</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_xs4</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_S_Ks00</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>v_xs1</ci>
</apply>
<ci>v_xs3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_S_Ks01</ci>
<apply>
<minus/>
<ci>v_xs1</ci>
<ci>v_xs4</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_S_Ks10</ci>
<apply>
<minus/>
<ci>v_xs3</ci>
<ci>v_xs2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_S_Ks11</ci>
<apply>
<plus/>
<ci>v_xs2</ci>
<ci>v_xs4</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_S_Ks00</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S_Ks00</ci>
<ci>q_S_Ks00</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_S_Ks01</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S_Ks01</ci>
<ci>q_S_Ks01</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_S_Ks10</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S_Ks10</ci>
<ci>q_S_Ks10</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_S_Ks11</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_S_Ks11</ci>
<ci>q_S_Ks11</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_S_Ks00</ci>
</apply>
<ci>v_S_Ks00</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_S_Ks01</ci>
</apply>
<ci>v_S_Ks01</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_S_Ks10</ci>
</apply>
<ci>v_S_Ks10</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_S_Ks11</ci>
</apply>
<ci>v_S_Ks11</ci>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="Ks"/>
<map_variables variable_1="time" variable_2="t"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="q_K_i" variable_2="q_K_i"/>
<map_variables variable_1="q_K_o" variable_2="q_K_o"/>
<map_variables variable_1="q_mem" variable_2="q_mem"/>
<map_variables variable_1="C_m" variable_2="C_m"/>
<map_variables variable_1="v_Ks" variable_2="v_Ks"/>
<map_variables variable_1="I_mem_Ks" variable_2="I_mem_Ks"/>
</connection>
<connection>
<map_components component_1="Ks" component_2="Ks_parameters"/>
<map_variables variable_1="kappa_Ks" variable_2="kappa_Ks"/>
<map_variables variable_1="K_K_o" variable_2="K_K_o"/>
<map_variables variable_1="K_K_i" variable_2="K_K_i"/>
<map_variables variable_1="kappa_xs1" variable_2="kappa_xs1"/>
<map_variables variable_1="kappa_xs2" variable_2="kappa_xs2"/>
<map_variables variable_1="kappa_xs3" variable_2="kappa_xs3"/>
<map_variables variable_1="kappa_xs4" variable_2="kappa_xs4"/>
<map_variables variable_1="K_S_Ks00" variable_2="K_S_Ks00"/>
<map_variables variable_1="K_S_Ks01" variable_2="K_S_Ks01"/>
<map_variables variable_1="K_S_Ks10" variable_2="K_S_Ks10"/>
<map_variables variable_1="K_S_Ks11" variable_2="K_S_Ks11"/>
<map_variables variable_1="z_xs_f" variable_2="z_xs_f"/>
<map_variables variable_1="z_xs_r" variable_2="z_xs_r"/>
<map_variables variable_1="zK" variable_2="zK"/>
</connection>
</model>