Location: SLC transporters @ 54428a600e2c / Facilitated transporter / GLUT2_ss_io.cellml
- Author:
- Weiwei Ai <wai484@aucklanduni.ac.nz>
- Date:
- 2024-05-27 16:40:34+12:00
- Desc:
- Fixed typos
- Permanent Source URI:
- http://models.cellml.org/workspace/b65/rawfile/54428a600e2c560005a2d9d0a5608082f90a7c0c/Facilitated transporter/GLUT2_ss_io.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="GLUT2_BG" 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.cellml">
<units name="fmol" units_ref="fmol"/>
<units name="J_per_K_mol" units_ref="J_per_K_mol"/>
<units name="fmol_per_s" units_ref="fmol_per_s"/>
<units name="J_per_mol" units_ref="J_per_mol"/>
<units name="per_fmol" units_ref="per_fmol"/>
<units name="mM" units_ref="mM"/>
<units name="mM_per_s" units_ref="mM_per_s"/>
<units name="pL" units_ref="pL"/>
<units name="uM" units_ref="uM"/>
</import>
<units name="amol">
<unit prefix="atto" units="mole"/>
</units>
<import xlink:href="params_BG.cellml">
<component component_ref="params_BG" name="params_BG"/>
</import>
<component name="GLUT2_BG">
<variable name="t" units="second"/>
<variable name="K_Ai" public_interface="in" units="per_fmol"/>
<variable name="K_Ao" public_interface="in" units="per_fmol"/>
<variable name="K_1" public_interface="in" units="per_fmol"/>
<variable name="K_2" public_interface="in" units="per_fmol"/>
<variable name="K_3" public_interface="in" units="per_fmol"/>
<variable name="K_4" public_interface="in" units="per_fmol"/>
<variable name="kappa_r1" public_interface="in" units="fmol_per_s"/>
<variable name="kappa_r2" public_interface="in" units="fmol_per_s"/>
<variable name="kappa_r3" public_interface="in" units="fmol_per_s"/>
<variable name="kappa_r4" public_interface="in" units="fmol_per_s"/>
<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 initial_value="218.96" name="k_m_3_free" units="dimensionless"/>
<variable initial_value="0.1094" name="k_oi_math" units="mM"/>
<variable initial_value="1.609" name="k_io_math" units="mM"/>
<variable initial_value="0.004839" name="v_oi_max" units="mM_per_s"/>
<variable initial_value="0.07117" name="v_io_max" units="mM_per_s"/>
<variable initial_value="1" name="V_E" units="pL"/>
<variable initial_value="6.67" name="GC" units="uM"/>
<variable initial_value="1e-8" name="g_i" units="mM"/>
<variable initial_value="1e-8" name="g_o" units="mM"/>
<variable initial_value="0.09" name="V_i" units="pL"/>
<variable initial_value="0.09" name="V_o" units="pL"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<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>
<map_components component_1="params_BG" component_2="GLUT2_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>