Location: BG_to_channel @ ac991e973394 / BG_TO.cellml
- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2022-04-11 14:49:45+12:00
- Desc:
- Changing method of number of channels present. Guess density. Using SA of human iPSC for Kernik. Updating volumes
- Permanent Source URI:
- https://models.fieldml.org/workspace/82e/rawfile/ac991e97339402cc47ba2b196636cad163b0acf6/BG_TO.cellml
<?xml version='1.0' encoding='UTF-8'?>
<!-- transient outward -->
<model name="BG_transient_outward" 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="microm3" units_ref="microm3"/>
<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="1.0e6" name="C_m" public_interface="out" units="fF"/>
<variable initial_value="0.116325" name="q_K_o" public_interface="out" units="fmol"/>
<variable initial_value="3.65002" 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_TO" public_interface="in" units="fmol_per_sec"/>
<variable name="I_mem_TO" 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_TO</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_K_o</ci>
</apply>
<ci>v_TO</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>q_mem</ci>
</apply>
<ci>I_mem_TO</ci>
</apply>
<apply>
<eq/>
<ci>Vmem</ci>
<apply>
<divide/>
<ci>q_mem</ci>
<ci>C_m</ci>
</apply>
</apply>
</math>
</component>
<component name="TO_parameters">
<variable initial_value="1.91513" name="kappa_TO" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="10.0063" name="kappa_gTO_1" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.053573" name="kappa_gTO_2" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.0622138" name="kappa_gTO_3" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.0155957" name="kappa_gTO_4" public_interface="out" units="fmol_per_sec"/>
<variable initial_value="0.0402291" name="K_K_i" public_interface="out" units="per_fmol"/>
<variable initial_value="0.267055" name="K_K_o" public_interface="out" units="per_fmol"/>
<variable initial_value="0.00553253" name="K_r0s0_TO" public_interface="out" units="per_fmol"/>
<variable initial_value="0.0220702" name="K_r1s0_TO" public_interface="out" units="per_fmol"/>
<variable initial_value="1.03336" name="K_r0s1_TO" public_interface="out" units="per_fmol"/>
<variable initial_value="4.12222" name="K_r1s1_TO" public_interface="out" units="per_fmol"/>
<variable initial_value="1" name="zK" public_interface="out" units="dimensionless"/>
<variable initial_value="2.28623234372134" name="z_rTO_f" public_interface="out" units="dimensionless"/>
<variable initial_value="-1.51477720975217" name="z_sTO_f" public_interface="out" units="dimensionless"/>
<variable initial_value="-0.131848324558065" name="z_rTO_r" public_interface="out" units="dimensionless"/>
<variable initial_value="1.75042355789096" name="z_sTO_r" public_interface="out" units="dimensionless"/>
</component>
<component name="TO">
<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="zK" public_interface="in" units="dimensionless"/>
<variable name="F" private_interface="out" public_interface="in" units="C_per_mol"/>
<variable name="C_m" public_interface="in" units="fF"/>
<!-- Parameters-->
<variable name="kappa_TO" public_interface="in" units="fmol_per_sec"/>
<variable name="K_K_i" public_interface="in" units="per_fmol"/>
<variable name="K_K_o" 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_TO" public_interface="out" units="fmol_per_sec"/>
<variable name="I_mem_TO" 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" units="J_per_C"/>
<variable name="Am_TO" units="J_per_mol"/>
<variable name="Af_TO" units="J_per_mol"/>
<variable name="Ar_TO" units="J_per_mol"/>
<!-- Conservation laws-->
<!-- Constitutive relations - Convention: positive flow from inside TO outside-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Am_TO</ci>
<apply>
<times/>
<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_TO</ci>
<apply>
<plus/>
<ci>mu_r1s1_TO</ci>
<ci>u_K_i</ci>
<ci>Am_TO</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_TO</ci>
<apply>
<plus/>
<ci>mu_r1s1_TO</ci>
<ci>u_K_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_TO</ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="dimensionless">1</cn>
<ci>kappa_TO</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_TO</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_TO</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Am_TO</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_TO</ci>
<ci>Am_TO</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Am_TO</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_TO</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_TO</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_TO</ci>
<apply>
<times/>
<ci>F</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>zK</ci>
</apply>
<ci>v_TO</ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>v_gTO_1</ci>
<ci>v_gTO_2</ci>
</apply>
<apply>
<minus/>
<ci>z_rTO_r</ci>
<ci>z_rTO_f</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>v_gTO_3</ci>
<ci>v_gTO_4</ci>
</apply>
<apply>
<minus/>
<ci>z_sTO_r</ci>
<ci>z_sTO_f</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<!-- GATE-->
<variable name="v_r0s0_TO" units="fmol_per_sec"/>
<variable name="v_r1s0_TO" units="fmol_per_sec"/>
<variable name="v_r0s1_TO" units="fmol_per_sec"/>
<variable name="v_r1s1_TO" units="fmol_per_sec"/>
<variable name="v_gTO_1" units="fmol_per_sec"/>
<variable name="v_gTO_3" units="fmol_per_sec"/>
<variable name="v_gTO_2" units="fmol_per_sec"/>
<variable name="v_gTO_4" units="fmol_per_sec"/>
<variable name="mu_r0s0_TO" units="J_per_mol"/>
<variable name="mu_r1s0_TO" units="J_per_mol"/>
<variable name="mu_r0s1_TO" units="J_per_mol"/>
<variable name="mu_r1s1_TO" units="J_per_mol"/>
<variable name="Af_gTO_1" units="J_per_mol"/>
<variable name="Ar_gTO_1" units="J_per_mol"/>
<variable name="Af_gTO_3" units="J_per_mol"/>
<variable name="Ar_gTO_3" units="J_per_mol"/>
<variable name="Af_gTO_2" units="J_per_mol"/>
<variable name="Ar_gTO_2" units="J_per_mol"/>
<variable name="Af_gTO_4" units="J_per_mol"/>
<variable name="Ar_gTO_4" units="J_per_mol"/>
<variable name="kappa_gTO_1" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_gTO_2" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_gTO_3" public_interface="in" units="fmol_per_sec"/>
<variable name="kappa_gTO_4" public_interface="in" units="fmol_per_sec"/>
<variable name="K_r0s0_TO" public_interface="in" units="per_fmol"/>
<variable name="K_r1s0_TO" public_interface="in" units="per_fmol"/>
<variable name="K_r0s1_TO" public_interface="in" units="per_fmol"/>
<variable name="K_r1s1_TO" public_interface="in" units="per_fmol"/>
<variable name="z_rTO_f" public_interface="in" units="dimensionless"/>
<variable name="z_sTO_f" public_interface="in" units="dimensionless"/>
<variable name="z_rTO_r" public_interface="in" units="dimensionless"/>
<variable name="z_sTO_r" public_interface="in" units="dimensionless"/>
<variable initial_value="0.999993" name="q_r0s0_TO" units="fmol"/>
<variable initial_value="1e-6" name="q_r1s0_TO" units="fmol"/>
<variable initial_value="1e-6" name="q_r0s1_TO" units="fmol"/>
<variable initial_value="1e-6" name="q_r1s1_TO" units="fmol"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Af_gTO_1</ci>
<apply>
<plus/>
<ci>mu_r0s0_TO</ci>
<apply>
<times/>
<ci>z_rTO_f</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_gTO_1</ci>
<apply>
<plus/>
<ci>mu_r1s0_TO</ci>
<apply>
<times/>
<ci>z_rTO_r</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_gTO_3</ci>
<apply>
<plus/>
<ci>mu_r0s0_TO</ci>
<apply>
<times/>
<ci>z_sTO_f</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_gTO_3</ci>
<apply>
<plus/>
<ci>mu_r0s1_TO</ci>
<apply>
<times/>
<ci>z_sTO_r</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_gTO_2</ci>
<apply>
<plus/>
<ci>mu_r0s1_TO</ci>
<apply>
<times/>
<ci>z_rTO_f</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_gTO_2</ci>
<apply>
<plus/>
<ci>mu_r1s1_TO</ci>
<apply>
<times/>
<ci>z_rTO_r</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Af_gTO_4</ci>
<apply>
<plus/>
<ci>mu_r1s0_TO</ci>
<apply>
<times/>
<ci>z_sTO_f</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ar_gTO_4</ci>
<apply>
<plus/>
<ci>mu_r1s1_TO</ci>
<apply>
<times/>
<ci>z_sTO_r</ci>
<ci>F</ci>
<ci>V_mem</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_gTO_1</ci>
<apply>
<times/>
<ci>kappa_gTO_1</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_gTO_1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_gTO_1</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_gTO_3</ci>
<apply>
<times/>
<ci>kappa_gTO_3</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_gTO_3</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_gTO_3</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_gTO_2</ci>
<apply>
<times/>
<ci>kappa_gTO_2</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_gTO_2</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_gTO_2</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_gTO_4</ci>
<apply>
<times/>
<ci>kappa_gTO_4</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Af_gTO_4</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>Ar_gTO_4</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_r0s0_TO</ci>
<apply>
<plus/>
<apply>
<minus/>
<ci>v_gTO_1</ci>
</apply>
<ci>v_gTO_3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_r1s0_TO</ci>
<apply>
<minus/>
<ci>v_gTO_1</ci>
<ci>v_gTO_4</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_r0s1_TO</ci>
<apply>
<plus/>
<apply>
<minus/>
<ci>v_gTO_2</ci>
</apply>
<ci>v_gTO_3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_r1s1_TO</ci>
<apply>
<plus/>
<ci>v_gTO_2</ci>
<ci>v_gTO_4</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_r0s0_TO</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_r0s0_TO</ci>
<ci>q_r0s0_TO</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_r1s0_TO</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_r1s0_TO</ci>
<ci>q_r1s0_TO</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_r0s1_TO</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_r0s1_TO</ci>
<ci>q_r0s1_TO</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>mu_r1s1_TO</ci>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_r1s1_TO</ci>
<ci>q_r1s1_TO</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_r0s0_TO</ci>
</apply>
<ci>v_r0s0_TO</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_r1s0_TO</ci>
</apply>
<ci>v_r1s0_TO</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_r0s1_TO</ci>
</apply>
<ci>v_r0s1_TO</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>q_r1s1_TO</ci>
</apply>
<ci>v_r1s1_TO</ci>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="TO"/>
<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_TO" variable_2="v_TO"/>
<map_variables variable_1="I_mem_TO" variable_2="I_mem_TO"/>
</connection>
<connection>
<map_components component_1="TO" component_2="TO_parameters"/>
<map_variables variable_1="kappa_TO" variable_2="kappa_TO"/>
<map_variables variable_1="kappa_gTO_1" variable_2="kappa_gTO_1"/>
<map_variables variable_1="kappa_gTO_2" variable_2="kappa_gTO_2"/>
<map_variables variable_1="kappa_gTO_3" variable_2="kappa_gTO_3"/>
<map_variables variable_1="kappa_gTO_4" variable_2="kappa_gTO_4"/>
<map_variables variable_1="K_K_i" variable_2="K_K_i"/>
<map_variables variable_1="K_K_o" variable_2="K_K_o"/>
<map_variables variable_1="K_r0s0_TO" variable_2="K_r0s0_TO"/>
<map_variables variable_1="K_r1s0_TO" variable_2="K_r1s0_TO"/>
<map_variables variable_1="K_r0s1_TO" variable_2="K_r0s1_TO"/>
<map_variables variable_1="K_r1s1_TO" variable_2="K_r1s1_TO"/>
<map_variables variable_1="z_rTO_f" variable_2="z_rTO_f"/>
<map_variables variable_1="z_sTO_f" variable_2="z_sTO_f"/>
<map_variables variable_1="z_rTO_r" variable_2="z_rTO_r"/>
<map_variables variable_1="z_sTO_r" variable_2="z_sTO_r"/>
<map_variables variable_1="zK" variable_2="zK"/>
</connection>
</model>