Location: Modular version of Glucose uptake (including water transport) @ 2ad89252015a / Cell_Concentration.cellml
- Author:
- Nima <nafs080@aucklanduni.ac.nz>
- Date:
- 2019-07-21 09:46:02+12:00
- Desc:
- Modular version of glucose uptake model (contains water transporters and cell volume changes)
- Permanent Source URI:
- https://models.cellml.org/workspace/58c/rawfile/2ad89252015aa87ebc327c2d547bd99bc7629853/Cell_Concentration.cellml
<?xml version='1.0'?>
<model name="Cell_Concentration" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
</component>
<component name="Cell_concentration">
<variable initial_value="0.04" name="Na_i" public_interface="out" units="M"/>
<variable initial_value="0.009" name="glucose_i" public_interface="out" units="M"/>
<variable initial_value="0.105" name="K_i" public_interface="out" units="M"/>
<variable initial_value="6e-5" name="Ca_i" public_interface="out" units="M"/>
<variable initial_value="0.065" name="Cl_i" public_interface="out" units="M"/>
<variable name="HCO3_i" public_interface="out" units="M"/>
<variable name="H_int" public_interface="out" units="M"/>
<variable name="HCO3_m" public_interface="out" units="M"/>
<variable name="HCO3_s" public_interface="out" units="M"/>
<variable initial_value="6.3e-8" name="H_Ext" public_interface="out" units="M"/>
<variable initial_value="6.3e-8" name="H_s" public_interface="out" units="M"/>
<variable initial_value="2e-15" name="v_cell" public_interface="out" units="m3"/>
<variable name="A_Apical" public_interface="in" units="m2"/>
<variable name="J_Na_SGLT" public_interface="in" units="umol_per_s"/>
<variable name="J_Gl_SGLT" public_interface="in" units="umol_per_s"/>
<variable name="J_Na_NaK" public_interface="in" units="umol_per_s"/>
<variable name="J_K_NaK" public_interface="in" units="umol_per_s"/>
<variable name="J_NBC_Na" public_interface="in" units="umol_per_s"/>
<variable name="J_NBC_HCO3" public_interface="in" units="umol_per_s"/>
<variable name="J_KCNQ" public_interface="in" units="umol_per_s"/>
<!--var J_NaCl: umol_per_s {pub: in};-->
<variable name="J_NHE3_Na" public_interface="in" units="umol_per_s"/>
<variable name="J_NHE3_H" public_interface="in" units="umol_per_s"/>
<!-- var J_D_Na: umol_per_s {pub: in};
var J_D_Bl_Na: umol_per_s {pub: in};-->
<variable name="J_GLUT" public_interface="in" units="umol_per_s"/>
<variable name="J_A_GLUT" public_interface="in" units="umol_per_s"/>
<!-- var J_D_K: umol_per_s {pub: in};
var J_D_Bl_K: umol_per_s {pub: in};
var J_D_Cl: umol_per_s {pub: in};
var J_D_Bl_Cl: umol_per_s {pub: in};-->
<variable name="J_AE1_Cl" public_interface="in" units="umol_per_s"/>
<variable name="J_AE1_HCO3" public_interface="in" units="umol_per_s"/>
<variable name="J_CFTR" public_interface="in" units="umol_per_s"/>
<variable name="J_CLC2" public_interface="in" units="umol_per_s"/>
<!--var J_CFTR_HCO3: umol_per_s {pub: in};-->
<variable name="J_ENaC" public_interface="in" units="umol_per_s"/>
<variable name="J_NaKCC" public_interface="in" units="umol_per_s"/>
<!-- var J_IK: umol_per_s {pub: in};-->
<variable name="J_BK" public_interface="in" units="umol_per_s"/>
<!-- var J_D_P_Na: umol_per_s {pub: in};-->
<!-- var J_buf_C: M_per_second {pub: in};
var J_buf_A: M_per_second {pub: in};-->
<variable name="time" public_interface="in" units="second"/>
<variable initial_value="7.2" name="pH_int" public_interface="out" units="per_second"/>
<variable initial_value="7.2" name="pH_Ext" public_interface="out" units="per_second"/>
<variable initial_value="7.2" name="pH_s" public_interface="out" units="per_second"/>
<variable initial_value="1680000" name="rho" public_interface="out" units="per_meter"/>
<variable name="beta" public_interface="out" units="M"/>
<variable initial_value="6.4" name="p_K" public_interface="out" units="dimensionless"/>
<variable initial_value="40" name="P_CO2" public_interface="out" units="dimensionless"/>
<variable initial_value="1.2e-5" name="s" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="theta_1" units="dimensionless"/>
<variable initial_value="1" name="theta_2" units="dimensionless"/>
<variable initial_value="1" name="theta_3" units="dimensionless"/>
<variable initial_value="1" name="theta_4" units="dimensionless"/>
<variable initial_value="1" name="theta_5" units="dimensionless"/>
<variable initial_value="1" name="theta_6" units="dimensionless"/>
<variable initial_value="1" name="theta_7" units="dimensionless"/>
<variable initial_value="1" name="theta_8" units="dimensionless"/>
<variable initial_value="1" name="theta_9" units="dimensionless"/>
<variable initial_value="1" name="theta_10" units="dimensionless"/>
<variable initial_value="1" name="theta_11" units="dimensionless"/>
<variable initial_value="1" name="theta_12" units="dimensionless"/>
<variable initial_value="1" name="theta_13" units="dimensionless"/>
<variable initial_value="1" name="theta_14" units="dimensionless"/>
<variable initial_value="1" name="theta_15" units="dimensionless"/>
<variable initial_value="1" name="theta_16" units="dimensionless"/>
<variable initial_value="1" name="theta_17" units="dimensionless"/>
<variable initial_value="1" name="theta_18" units="dimensionless"/>
<variable initial_value="1" name="theta_19" units="dimensionless"/>
<variable initial_value="1" name="theta_20" units="dimensionless"/>
<variable initial_value="1" name="theta_21" units="dimensionless"/>
<variable initial_value="1" name="theta_22" units="dimensionless"/>
<variable initial_value="1" name="theta_23" units="dimensionless"/>
<variable initial_value="1" name="theta_24" units="dimensionless"/>
<variable initial_value="1" name="theta_25" units="dimensionless"/>
<variable initial_value="1" name="theta_26" units="dimensionless"/>
<variable initial_value="1" name="theta_27" units="dimensionless"/>
<variable initial_value="1.8e-5" name="v_w" public_interface="out" units="m3_per_mole"/>
<variable name="J_w_A" public_interface="out" units="umol_per_s"/>
<variable name="J_w_B" public_interface="out" units="umol_per_s"/>
<variable name="J_w_P" public_interface="out" units="umol_per_s"/>
<variable name="J_D_P_Gl" public_interface="out" units="umol_per_s"/>
<variable initial_value="14e-5" name="L_A" public_interface="out" units="m_per_s"/>
<variable initial_value="6e-5" name="L_B" public_interface="out" units="m_per_s"/>
<variable initial_value="4e-7" name="L_P" public_interface="out" units="m_per_s"/>
<variable initial_value="7e-10" name="L_P_Gl" public_interface="out" units="m_per_s"/>
<variable name="NII" public_interface="out" units="M"/>
<variable name="chi_i" public_interface="out" units="mole"/>
<variable initial_value="0.001" name="psi" public_interface="out" units="M"/>
<variable name="Na_m" public_interface="in" units="M"/>
<variable name="K_m" public_interface="in" units="M"/>
<variable name="glucose_m" public_interface="in" units="M"/>
<variable name="Cl_m" public_interface="in" units="M"/>
<variable name="Na_s" public_interface="in" units="M"/>
<variable name="K_s" public_interface="in" units="M"/>
<variable name="glucose_s" public_interface="in" units="M"/>
<variable name="Cl_s" public_interface="in" units="M"/>
<!--var dif: dimensionless {pub: out};-->
<!-- var alpha: dimensionless {init: 0.1, pub: out};-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>NII</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless" type="e-notation">1<sep/>-3</cn>
<ci>chi_i</ci>
</apply>
<ci>v_cell</ci>
</apply>
</apply>
</math>
<!--chi_i = 1e-3{dimensionless}*(NII * v_cell);-->
<variable initial_value="1" name="alpha_1" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="alpha_2" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="alpha_3" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="alpha_4" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="alpha_5" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="alpha_6" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="alpha_7" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="alpha_8" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="alpha_9" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="alpha_10" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="alpha_11" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="alpha_12" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="alpha_13" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="alpha_14" public_interface="out" units="dimensionless"/>
<variable initial_value="1" name="alpha_15" public_interface="out" units="dimensionless"/>
<!-- var A: M {pub: out};
var B: M {pub: out};
var Gl_net_P: M {init: 0, pub: out};
var Gl_net_A: M {init: 0, pub: out};
var Gl_net_B: M {init: 0, pub: out};
var Net_gl: M {pub: out};-->
<variable initial_value="0" name="Cell_electroneutrality" public_interface="out" units="M"/>
<variable initial_value="0" name="Blood_electroneutrality" public_interface="out" units="M"/>
<variable initial_value="0" name="Lumen_electroneutrality" public_interface="out" units="M"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>chi_i</ci>
<apply>
<times/>
<cn cellml:units="dimensionless" type="e-notation">1<sep/>3</cn>
<ci>v_cell</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>Na_i</ci>
<ci>K_i</ci>
</apply>
<ci>Cell_electroneutrality</ci>
</apply>
<ci>Cl_i</ci>
</apply>
<ci>HCO3_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>HCO3_s</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>Na_s</ci>
<ci>K_s</ci>
</apply>
<ci>Blood_electroneutrality</ci>
</apply>
<ci>Cl_s</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>HCO3_m</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>Na_m</ci>
<ci>K_m</ci>
</apply>
<ci>Lumen_electroneutrality</ci>
</apply>
<ci>Cl_m</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>beta</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2.3</cn>
<ci>HCO3_i</ci>
<ci>A_Apical</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Na_i</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="m3_mole_per_litre_per_umol" type="e-notation">1<sep/>-9</cn>
<ci>v_cell</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>theta_1</ci>
<ci>J_Na_SGLT</ci>
</apply>
<apply>
<times/>
<ci>theta_2</ci>
<ci>J_Na_NaK</ci>
</apply>
</apply>
<apply>
<times/>
<ci>theta_15</ci>
<ci>J_ENaC</ci>
</apply>
<apply>
<times/>
<ci>theta_16</ci>
<ci>J_NaKCC</ci>
</apply>
<apply>
<times/>
<ci>theta_19</ci>
<ci>J_NBC_Na</ci>
</apply>
<apply>
<times/>
<ci>theta_3</ci>
<ci>J_NHE3_Na</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless" type="e-notation">1<sep/>9</cn>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>v_cell</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>glucose_i</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="m3_mole_per_litre_per_umol" type="e-notation">1<sep/>-9</cn>
<ci>v_cell</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>theta_26</ci>
<cn cellml:units="dimensionless">1</cn>
<ci>J_A_GLUT</ci>
</apply>
<apply>
<times/>
<ci>theta_6</ci>
<ci>J_Gl_SGLT</ci>
</apply>
</apply>
<apply>
<times/>
<ci>theta_7</ci>
<cn cellml:units="dimensionless">1</cn>
<ci>J_GLUT</ci>
</apply>
</apply>
<apply>
<times/>
<ci>glucose_i</ci>
<cn cellml:units="dimensionless" type="e-notation">1<sep/>9</cn>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>v_cell</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K_i</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="m3_mole_per_litre_per_umol" type="e-notation">1<sep/>-9</cn>
<ci>v_cell</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>theta_8</ci>
<ci>J_K_NaK</ci>
</apply>
<apply>
<times/>
<ci>theta_17</ci>
<ci>J_NaKCC</ci>
</apply>
<apply>
<times/>
<ci>theta_27</ci>
<ci>J_KCNQ</ci>
</apply>
<ci>J_BK</ci>
</apply>
<apply>
<times/>
<ci>K_i</ci>
<cn cellml:units="dimensionless" type="e-notation">1<sep/>9</cn>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>v_cell</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Cl_i</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="m3_mole_per_litre_per_umol" type="e-notation">1<sep/>-9</cn>
<ci>v_cell</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<ci>theta_11</ci>
</apply>
<ci>J_CFTR</ci>
</apply>
<ci>J_CLC2</ci>
</apply>
<apply>
<times/>
<ci>theta_18</ci>
<cn cellml:units="dimensionless">2</cn>
<ci>J_NaKCC</ci>
</apply>
<apply>
<times/>
<ci>theta_14</ci>
<ci>J_AE1_Cl</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Cl_i</ci>
<cn cellml:units="dimensionless" type="e-notation">1<sep/>9</cn>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>v_cell</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>pH_int</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="m3_mole_per_litre_per_umol" type="e-notation">1<sep/>-9</cn>
<ci>rho</ci>
</apply>
<ci>beta</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>theta_20</ci>
<ci>J_NBC_HCO3</ci>
</apply>
<apply>
<times/>
<ci>theta_22</ci>
<ci>J_NHE3_H</ci>
</apply>
</apply>
<apply>
<times/>
<ci>theta_25</ci>
<ci>J_AE1_HCO3</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>v_cell</ci>
</apply>
<apply>
<times/>
<cn cellml:units="umole_per_mole" type="e-notation">1<sep/>-6</cn>
<ci>v_w</ci>
<apply>
<minus/>
<ci>J_w_B</ci>
<ci>J_w_A</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_w_A</ci>
<apply>
<times/>
<cn cellml:units="dimensionless" type="e-notation">1<sep/>9</cn>
<ci>L_A</ci>
<ci>A_Apical</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha_1</ci>
<ci>Na_m</ci>
</apply>
<apply>
<times/>
<ci>alpha_2</ci>
<ci>Cl_m</ci>
</apply>
<apply>
<times/>
<ci>alpha_3</ci>
<ci>glucose_m</ci>
</apply>
<apply>
<times/>
<ci>alpha_4</ci>
<ci>K_m</ci>
</apply>
<apply>
<times/>
<ci>alpha_5</ci>
<ci>HCO3_m</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha_6</ci>
<ci>Na_i</ci>
</apply>
<apply>
<times/>
<ci>alpha_7</ci>
<ci>Cl_i</ci>
</apply>
<apply>
<times/>
<ci>alpha_8</ci>
<ci>glucose_i</ci>
</apply>
<apply>
<times/>
<ci>alpha_9</ci>
<ci>K_i</ci>
</apply>
<apply>
<times/>
<ci>alpha_10</ci>
<ci>HCO3_i</ci>
</apply>
<ci>NII</ci>
</apply>
</apply>
<ci>psi</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_w_B</ci>
<apply>
<times/>
<cn cellml:units="dimensionless" type="e-notation">1<sep/>9</cn>
<ci>L_B</ci>
<ci>A_Apical</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha_6</ci>
<ci>Na_i</ci>
</apply>
<apply>
<times/>
<ci>alpha_7</ci>
<ci>Cl_i</ci>
</apply>
<apply>
<times/>
<ci>alpha_8</ci>
<ci>glucose_i</ci>
</apply>
<apply>
<times/>
<ci>alpha_9</ci>
<ci>K_i</ci>
</apply>
<apply>
<times/>
<ci>alpha_10</ci>
<ci>HCO3_i</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha_11</ci>
<ci>Na_s</ci>
</apply>
<apply>
<times/>
<ci>alpha_12</ci>
<ci>Cl_s</ci>
</apply>
<apply>
<times/>
<ci>alpha_13</ci>
<ci>glucose_s</ci>
</apply>
<apply>
<times/>
<ci>alpha_14</ci>
<ci>K_s</ci>
</apply>
<apply>
<times/>
<ci>alpha_15</ci>
<ci>HCO3_s</ci>
</apply>
</apply>
</apply>
<ci>NII</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_w_P</ci>
<apply>
<times/>
<cn cellml:units="dimensionless" type="e-notation">1<sep/>9</cn>
<ci>L_P</ci>
<ci>A_Apical</ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha_1</ci>
<ci>Na_m</ci>
</apply>
<apply>
<times/>
<ci>alpha_2</ci>
<ci>Cl_m</ci>
</apply>
<apply>
<times/>
<ci>alpha_3</ci>
<ci>glucose_m</ci>
</apply>
<apply>
<times/>
<ci>alpha_4</ci>
<ci>K_m</ci>
</apply>
<apply>
<times/>
<ci>alpha_5</ci>
<ci>HCO3_m</ci>
</apply>
<ci>psi</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha_11</ci>
<ci>Na_s</ci>
</apply>
<apply>
<times/>
<ci>alpha_12</ci>
<ci>Cl_s</ci>
</apply>
<apply>
<times/>
<ci>alpha_13</ci>
<ci>glucose_s</ci>
</apply>
<apply>
<times/>
<ci>alpha_14</ci>
<ci>K_s</ci>
</apply>
<apply>
<times/>
<ci>alpha_15</ci>
<ci>HCO3_s</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>J_D_P_Gl</ci>
<apply>
<times/>
<cn cellml:units="dimensionless" type="e-notation">1<sep/>9</cn>
<ci>L_P_Gl</ci>
<ci>A_Apical</ci>
<apply>
<minus/>
<ci>glucose_m</ci>
<ci>glucose_s</ci>
</apply>
</apply>
</apply>
<!-- ode(Gl_net_A, time) = 1e-9{m3_mole_per_litre_per_umol}/v_cell*(theta_26*J_A_GLUT+theta_6*J_Gl_SGLT)-glucose_i/(1e3{dimensionless}*v_cell)*1e-6{dimensionless}*v_w*(J_w_B-J_w_A);
ode(Gl_net_B, time) = 1e-9{m3_mole_per_litre_per_umol}/v_cell*-theta_7*J_GLUT-glucose_i/(1e3{dimensionless}*v_cell)*1e-6{dimensionless}*v_w*(J_w_B-J_w_A);
Net_gl = J_A_GLUT+J_Gl_SGLT-J_GLUT;-->
<apply>
<eq/>
<ci>H_int</ci>
<apply>
<power/>
<cn cellml:units="dimensionless">10</cn>
<apply>
<minus/>
<ci>pH_int</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>HCO3_i</ci>
<apply>
<times/>
<ci>s</ci>
<ci>P_CO2</ci>
<apply>
<power/>
<cn cellml:units="dimensionless">10</cn>
<apply>
<minus/>
<ci>pH_int</ci>
<ci>p_K</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
</model>