- Author:
- Weiwei Ai <wai484@aucklanduni.ac.nz>
- Date:
- 2024-04-18 18:08:11+12:00
- Desc:
- Add BG for steady-state simulation (i.e, a longer pulse)
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/b65/rawfile/c8bc4b889b3850d67cea87048416591cdb681ffd/Facilitated transporter/CellMLV2/GLUT1_ss_io.cellml
<?xml version="1.0" encoding="UTF-8"?>
<model xmlns="http://www.cellml.org/cellml/2.0#" name="GLUT1_BG">
<import xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="params_BG.cellml">
<component component_ref="params_BG" name="params_BG"/>
</import>
<import xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="./units.cellml">
<units units_ref="fmol" name="fmol"/>
<units units_ref="J_per_K_mol" name="J_per_K_mol"/>
<units units_ref="fmol_per_s" name="fmol_per_s"/>
<units units_ref="J_per_mol" name="J_per_mol"/>
<units units_ref="per_fmol" name="per_fmol"/>
<units units_ref="mM" name="mM"/>
<units units_ref="mM_per_s" name="mM_per_s"/>
<units units_ref="pL" name="pL"/>
<units units_ref="uM" name="uM"/>
</import>
<units name="amol">
<unit prefix="atto" units="mole"/>
</units>
<component name="GLUT1_BG">
<variable name="t" units="second"/>
<variable name="K_Ai" units="per_fmol" interface="public"/>
<variable name="K_Ao" units="per_fmol" interface="public"/>
<variable name="K_1" units="per_fmol" interface="public"/>
<variable name="K_2" units="per_fmol" interface="public"/>
<variable name="K_3" units="per_fmol" interface="public"/>
<variable name="K_4" units="per_fmol" interface="public"/>
<variable name="kappa_r1" units="fmol_per_s" interface="public"/>
<variable name="kappa_r2" units="fmol_per_s" interface="public"/>
<variable name="kappa_r3" units="fmol_per_s" interface="public"/>
<variable name="kappa_r4" units="fmol_per_s" interface="public"/>
<variable name="q_Ai" units="fmol"/>
<variable name="q_Ao" units="fmol"/>
<variable name="lambda" units="dimensionless"/>
<variable name="q_tot" units="fmol"/>
<variable name="v_max" units="fmol_per_s"/>
<variable name="k_m_1" units="dimensionless"/>
<variable name="k_m_2" units="dimensionless"/>
<variable name="k_m_3" units="dimensionless"/>
<variable name="v" units="fmol_per_s"/>
<variable name="v_max_free" units="fmol_per_s"/>
<variable name="v_free" units="fmol_per_s"/>
<variable name="k_m_1_free" units="dimensionless"/>
<variable name="k_m_2_free" units="dimensionless"/>
<variable name="k_m_3_free" units="dimensionless" initial_value="218.96"/>
<variable name="k_oi_math" units="mM" initial_value="0.1094"/>
<variable name="k_io_math" units="mM" initial_value="1.609"/>
<variable name="v_oi_max" units="mM_per_s" initial_value="0.004839"/>
<variable name="v_io_max" units="mM_per_s" initial_value="0.07117"/>
<variable name="V_E" units="pL" initial_value="1"/>
<variable name="GC" units="uM" initial_value="6.67"/>
<variable name="g_i" units="mM" initial_value="1e-8"/>
<variable name="g_o" units="mM" initial_value="1e-8"/>
<variable name="V_i" units="pL" initial_value="0.09"/>
<variable name="V_o" units="pL" initial_value="0.09"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:cellml="http://www.cellml.org/cellml/2.0#">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>g_i</ci>
</apply>
<cn cellml:units="mM_per_s">1</cn>
</apply>
<apply>
<eq/>
<ci>q_Ao</ci>
<apply>
<times/>
<ci>g_o</ci>
<ci>V_o</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_Ai</ci>
<apply>
<times/>
<ci>g_i</ci>
<ci>V_i</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>q_tot</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>GC</ci>
<ci>V_E</ci>
<cn cellml:units="fmol">1</cn>
</apply>
<cn cellml:units="amol">1000</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>v_max_free</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>v_oi_max</ci>
<ci>V_E</ci>
</apply>
<ci>k_m_1_free</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k_m_1_free</ci>
<apply>
<times/>
<ci>k_oi_math</ci>
<ci>V_i</ci>
<ci>K_Ai</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k_m_2_free</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>v_io_max</ci>
<ci>V_E</ci>
</apply>
<ci>v_max_free</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>lambda</ci>
<apply>
<divide/>
<ci>kappa_r2</ci>
<ci>kappa_r1</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>v_max</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>q_tot</ci>
<ci>kappa_r2</ci>
<ci>K_3</ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<ci>K_3</ci>
<ci>K_1</ci>
</apply>
<apply>
<divide/>
<ci>K_3</ci>
<ci>K_4</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k_m_1</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<divide/>
<ci>K_3</ci>
<ci>K_1</ci>
</apply>
<apply>
<divide/>
<ci>K_3</ci>
<ci>K_4</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<ci>K_3</ci>
<ci>K_2</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>lambda</ci>
<ci>K_3</ci>
</apply>
<ci>K_4</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k_m_2</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<divide/>
<ci>K_3</ci>
<ci>K_1</ci>
</apply>
<apply>
<divide/>
<ci>K_3</ci>
<ci>K_4</ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>lambda</ci>
<ci>K_3</ci>
</apply>
<ci>K_1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k_m_3</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<divide/>
<ci>K_3</ci>
<ci>K_1</ci>
</apply>
<apply>
<divide/>
<ci>K_3</ci>
<ci>K_4</ci>
</apply>
</apply>
<apply>
<times/>
<ci>lambda</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>K_3</ci>
<ci>K_2</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>v_max</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>K_Ao</ci>
<ci>q_Ao</ci>
</apply>
<apply>
<times/>
<ci>K_Ai</ci>
<ci>q_Ai</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Ao</ci>
<ci>q_Ao</ci>
</apply>
<ci>k_m_1</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Ai</ci>
<ci>q_Ai</ci>
</apply>
<ci>k_m_2</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Ao</ci>
<ci>q_Ao</ci>
<ci>K_Ai</ci>
<ci>q_Ai</ci>
</apply>
<ci>k_m_3</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_free</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>v_max_free</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>K_Ao</ci>
<ci>q_Ao</ci>
</apply>
<apply>
<times/>
<ci>K_Ai</ci>
<ci>q_Ai</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Ao</ci>
<ci>q_Ao</ci>
</apply>
<ci>k_m_1_free</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Ai</ci>
<ci>q_Ai</ci>
</apply>
<ci>k_m_2_free</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>K_Ao</ci>
<ci>q_Ao</ci>
<ci>K_Ai</ci>
<ci>q_Ai</ci>
</apply>
<ci>k_m_3_free</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<connection component_1="params_BG" component_2="GLUT1_BG">
<map_variables variable_1="K_Ai" variable_2="K_Ai"/>
<map_variables variable_1="K_Ao" variable_2="K_Ao"/>
<map_variables variable_1="K_1" variable_2="K_1"/>
<map_variables variable_1="K_2" variable_2="K_2"/>
<map_variables variable_1="K_3" variable_2="K_3"/>
<map_variables variable_1="K_4" variable_2="K_4"/>
<map_variables variable_1="kappa_r1" variable_2="kappa_r1"/>
<map_variables variable_1="kappa_r2" variable_2="kappa_r2"/>
<map_variables variable_1="kappa_r3" variable_2="kappa_r3"/>
<map_variables variable_1="kappa_r4" variable_2="kappa_r4"/>
</connection>
</model>
