- Author:
- Soroush <ssaf006@aucklanduni.ac.nz>
- Date:
- 2020-05-10 21:27:00+12:00
- Desc:
- added new sedml
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/297/rawfile/5c6d2c520a9faad399fd954401d658362d25ef03/acid_base.cellml
<?xml version='1.0'?>
<model cmeta:id="acid_base" name="acid_base" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:xlink="http://www.w3.org/1999/xlink">
<import xlink:href="Units/Units.cellml">
<units name="mM" units_ref="mM"/>
<units name="mM_per_s" units_ref="mM_per_s"/>
<units name="mV" units_ref="mV"/>
<units name="mmHg" units_ref="mmHg"/>
<units name="mM_per_mmHg" units_ref="mM_per_mmHg"/>
<units name="mS_per_cm2" units_ref="mS_per_cm2"/>
<units name="mA_per_cm2" units_ref="mA_per_cm2"/>
<units name="C_per_mol" units_ref="C_per_mol"/>
<units name="cm_per_s" units_ref="cm_per_s"/>
<units name="mJ_per_mol_per_kelvin" units_ref="mJ_per_mol_per_kelvin"/>
<units name="umol_per_s_per_cm2" units_ref="umol_per_s_per_cm2"/>
</import>
<import xlink:href="NHE3/Weinstein_1995_NHE3.cellml">
<component component_ref="NHE3" name="NHE3"/>
</import>
<import xlink:href="HATPase/Weinstein_2000_HATPase.cellml">
<component component_ref="H_ATPase" name="H_ATPase"/>
</import>
<import xlink:href="NaK/Strieter_1992_NaK.cellml">
<component component_ref="NaK" name="NaK"/>
</import>
<import xlink:href="NBC/Ostby_2009_NBC.cellml">
<component component_ref="NBC" name="NBC"/>
</import>
<import xlink:href="Diffusion/Diffusion.cellml">
<component component_ref="Diffusion" name="Na_diffusion"/>
</import>
<import xlink:href="Diffusion/Diffusion.cellml">
<component component_ref="Diffusion" name="HCO3_diffusion"/>
</import>
<import xlink:href="Diffusion/Diffusion.cellml">
<component component_ref="Diffusion" name="K_diffusion"/>
</import>
<import xlink:href="Diffusion/Diffusion.cellml">
<component component_ref="Diffusion" name="NH3_diffusion"/>
</import>
<import xlink:href="Diffusion/Diffusion.cellml">
<component component_ref="Diffusion" name="CO2_diffusion_apical"/>
</import>
<import xlink:href="Diffusion/Diffusion.cellml">
<component component_ref="Diffusion" name="CO2_diffusion_basal"/>
</import>
<import xlink:href="Diffusion/Diffusion.cellml">
<component component_ref="Diffusion" name="CO2_diffusion_vessel"/>
</import>
<import xlink:href="CO2/CO2.cellml">
<component component_ref="Hydration" name="CO2_hydration_pt"/>
</import>
<import xlink:href="CO2/CO2.cellml">
<component component_ref="Hydration" name="CO2_hydration_ec"/>
</import>
<import xlink:href="CO2/CO2.cellml">
<component component_ref="Hydration" name="CO2_hydration_if"/>
</import>
<import xlink:href="CO2/CO2.cellml">
<component component_ref="Hydration" name="CO2_hydration_cb"/>
</import>
<import xlink:href="Ammonia/Ammonia.cellml">
<component component_ref="Hydration" name="NH3_hydration_pt"/>
</import>
<import xlink:href="Ammonia/Ammonia.cellml">
<component component_ref="Hydration" name="NH3_hydration_ec"/>
</import>
<import xlink:href="Ammonia/Ammonia.cellml">
<component component_ref="Hydration" name="HPO4_hydration_pt"/>
</import>
<component name="parameters">
<variable initial_value="0" name="theta_NHE3" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="theta_Vtype" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="theta_NaK" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="theta_NBC" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="theta_NH4" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="theta_hyd_pt" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="theta_hyd_ec" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="theta_hyd_if" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="theta_hyd_cb" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="theta_amn_pt" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="theta_amn_ec" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="theta_phs_pt" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="theta_diff_Na" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="theta_diff_HCO3" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="theta_diff_K" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="theta_diff_NH3" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="theta_diff_CO2_apical" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="theta_diff_CO2_basal" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="theta_diff_CO2_vessel" public_interface="out" units="dimensionless"/>
<variable initial_value="96485" name="F" public_interface="out" units="C_per_mol"/>
<variable initial_value="6.1" name="pK_HCO3" public_interface="out" units="dimensionless"/>
<variable initial_value="6.8" name="pK_HPO4" public_interface="out" units="dimensionless"/>
<variable initial_value="9.15" name="pK_NH3" public_interface="out" units="dimensionless"/>
<!-- Krahn, T. A., & Weinstein, A. M. (1996). Acid/base transport in a model of the proximal tubule brush border: impact of carbonic anhydrase. American Journal of Physiology-Renal Physiology, 270(2), F344-F355.
Weinstein, A. M. (1994). Ammonia transport in a mathematical model of rat proximal tubule. American Journal of Physiology-Renal Physiology, 267(2), F237-F248.-->
<variable initial_value="0.58" name="D_Na" public_interface="out" units="cm_per_s"/>
<variable initial_value="0.5e-6" name="D_K" public_interface="out" units="cm_per_s"/>
<variable initial_value="9.1e-5" name="D_Cl" public_interface="out" units="cm_per_s"/>
<variable initial_value="0.2e-7" name="D_HCO3" public_interface="out" units="cm_per_s"/>
<variable initial_value="0.1" name="D_H2CO2" public_interface="out" units="cm_per_s"/>
<variable initial_value="1.28e-3" name="D_H2CO3" public_interface="out" units="cm_per_s"/>
<variable initial_value="0.15" name="D_CO2" public_interface="out" units="cm_per_s"/>
<variable initial_value="6.2e-2" name="D_NH3" public_interface="out" units="cm_per_s"/>
<variable initial_value="0.03" name="s_CO2" public_interface="out" units="mM_per_mmHg"/>
<variable initial_value="50" name="p_CO2" public_interface="out" units="mmHg"/>
<variable initial_value="0.0" name="J_pt_H" public_interface="out" units="umol_per_s_per_cm2"/>
<variable initial_value="0.0" name="J_pt_HCO3" public_interface="out" units="umol_per_s_per_cm2"/>
<variable initial_value="0.0" name="J_pt_Na" public_interface="out" units="umol_per_s_per_cm2"/>
<variable initial_value="0e-6" name="J_ec_NH4" public_interface="out" units="umol_per_s_per_cm2"/>
<variable initial_value="0.0" name="J_cb_K" public_interface="out" units="umol_per_s_per_cm2"/>
<variable initial_value="0.0" name="J_cb_Na" public_interface="out" units="umol_per_s_per_cm2"/>
<variable initial_value="0.0" name="J_cb_H" public_interface="out" units="umol_per_s_per_cm2"/>
<variable initial_value="0.0" name="J_cb_HCO3" public_interface="out" units="umol_per_s_per_cm2"/>
</component>
<component name="renal_proximal_tubule">
<variable initial_value="7.306" name="pH_pt" private_interface="out" units="dimensionless"/>
<variable initial_value="140.0" name="Na_pt" private_interface="out" units="mM"/>
<variable initial_value="4.9" name="K_pt" private_interface="out" units="mM"/>
<variable initial_value="113.2" name="Cl_pt" private_interface="out" units="mM"/>
<variable initial_value="24.0" name="HCO3_pt" private_interface="out" units="mM"/>
<variable initial_value="4.41e-3" name="H2CO3_pt" private_interface="out" units="mM"/>
<variable initial_value="1.5" name="CO2_pt" private_interface="out" units="mM"/>
<variable initial_value="2.97" name="HPO4_pt" private_interface="out" units="mM"/>
<variable initial_value="0.93" name="H2PO4_pt" private_interface="out" units="mM"/>
<variable initial_value="5.0" name="urea_pt" private_interface="out" units="mM"/>
<variable initial_value="2.82e-3" name="NH3_pt" private_interface="out" units="mM"/>
<variable initial_value="0.2" name="NH4_pt" private_interface="out" units="mM"/>
<variable name="H_pt" private_interface="out" units="mM"/>
<variable initial_value="1.0" name="HCO2_pt" private_interface="out" units="mM"/>
<variable initial_value="2.85e-4" name="H2CO2_pt" private_interface="out" units="mM"/>
<variable initial_value="5.0" name="glucose_pt" private_interface="out" units="mM"/>
<variable name="J_NHE3_H" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_NHE3_Na" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_NHE3_NH4" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_Vtype_H" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_diff_CO2_apical" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_diff_NH3" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_hyd_pt" private_interface="in" units="mM_per_s"/>
<variable name="J_amn_pt" private_interface="in" units="mM_per_s"/>
<variable name="J_phs_pt" private_interface="in" units="mM_per_s"/>
<variable name="pK_HCO3" private_interface="out" public_interface="in" units="dimensionless"/>
<variable name="pK_NH3" private_interface="out" public_interface="in" units="dimensionless"/>
<variable name="pK_HPO4" private_interface="out" public_interface="in" units="dimensionless"/>
<variable name="s_CO2" public_interface="in" units="mM_per_mmHg"/>
<variable name="p_CO2" public_interface="in" units="mmHg"/>
<variable name="D_CO2" private_interface="out" public_interface="in" units="cm_per_s"/>
<variable name="D_NH3" private_interface="out" public_interface="in" units="cm_per_s"/>
<variable name="theta_NHE3" public_interface="in" units="dimensionless"/>
<variable name="theta_Vtype" public_interface="in" units="dimensionless"/>
<variable name="theta_diff_NH3" public_interface="in" units="dimensionless"/>
<variable name="theta_hyd_pt" public_interface="in" units="dimensionless"/>
<variable name="theta_amn_pt" public_interface="in" units="dimensionless"/>
<variable name="theta_phs_pt" public_interface="in" units="dimensionless"/>
<variable name="theta_diff_CO2_apical" public_interface="in" units="dimensionless"/>
<variable name="J_pt_H" public_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_pt_HCO3" public_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_pt_Na" public_interface="in" units="umol_per_s_per_cm2"/>
<variable name="beta_CO2" units="mM"/>
<variable name="alpha_NH3" units="dimensionless"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="pt_H_concentration">
<eq/>
<ci>H_pt</ci>
<piecewise>
<piece>
<cn cellml:units="mM" type="e-notation">1<sep/>3</cn>
<apply>
<lt/>
<ci>pH_pt</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
<piece>
<apply>
<times/>
<cn cellml:units="mM" type="e-notation">1<sep/>3</cn>
<apply>
<power/>
<cn cellml:units="dimensionless">10</cn>
<apply>
<minus/>
<ci>pH_pt</ci>
</apply>
</apply>
</apply>
<apply>
<geq/>
<ci>pH_pt</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
</piecewise>
</apply>
<apply id="pt_Na_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Na_pt</ci>
</apply>
<apply>
<plus/>
<ci>J_pt_Na</ci>
<apply>
<times/>
<ci>theta_NHE3</ci>
<ci>J_NHE3_Na</ci>
</apply>
</apply>
</apply>
<apply id="pt_HPO4_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>HPO4_pt</ci>
</apply>
<apply>
<times/>
<ci>theta_phs_pt</ci>
<ci>J_phs_pt</ci>
</apply>
</apply>
<apply id="pt_H2PO4_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>H2PO4_pt</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>theta_phs_pt</ci>
</apply>
<ci>J_phs_pt</ci>
</apply>
</apply>
<apply id="pt_NH4_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>NH4_pt</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>theta_NHE3</ci>
<ci>J_NHE3_NH4</ci>
</apply>
<apply>
<times/>
<ci>theta_amn_pt</ci>
<ci>J_amn_pt</ci>
</apply>
</apply>
</apply>
<apply id="pt_NH3_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>NH3_pt</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>theta_diff_NH3</ci>
</apply>
<ci>J_diff_NH3</ci>
</apply>
<apply>
<times/>
<ci>theta_amn_pt</ci>
<ci>J_amn_pt</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_NH3</ci>
<apply>
<divide/>
<ci>H_pt</ci>
<apply>
<plus/>
<ci>H_pt</ci>
<apply>
<times/>
<cn cellml:units="mM" type="e-notation">1<sep/>3</cn>
<apply>
<power/>
<cn cellml:units="dimensionless">10</cn>
<apply>
<minus/>
<ci>pK_NH3</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="CO2_buffering_power">
<eq/>
<ci>beta_CO2</ci>
<apply>
<times/>
<apply>
<ln/>
<cn cellml:units="dimensionless">10</cn>
</apply>
<ci>HCO3_pt</ci>
</apply>
</apply>
<apply id="pt_CO2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>CO2_pt</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>theta_diff_CO2_apical</ci>
<ci>J_diff_CO2_apical</ci>
</apply>
<apply>
<times/>
<ci>theta_hyd_pt</ci>
<ci>J_hyd_pt</ci>
</apply>
</apply>
</apply>
<apply id="pt_HCO3_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>HCO3_pt</ci>
</apply>
<apply>
<plus/>
<ci>J_pt_HCO3</ci>
<apply>
<times/>
<ci>theta_hyd_pt</ci>
<ci>J_hyd_pt</ci>
</apply>
</apply>
</apply>
<apply id="pt_pH_regulation">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>pH_pt</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>J_pt_H</ci>
<apply>
<times/>
<ci>theta_NHE3</ci>
<ci>J_NHE3_H</ci>
</apply>
<apply>
<times/>
<ci>theta_Vtype</ci>
<ci>J_Vtype_H</ci>
</apply>
<apply>
<times/>
<ci>theta_hyd_pt</ci>
<ci>J_hyd_pt</ci>
</apply>
<apply>
<times/>
<ci>theta_amn_pt</ci>
<ci>J_amn_pt</ci>
</apply>
<apply>
<times/>
<ci>theta_phs_pt</ci>
<ci>J_phs_pt</ci>
</apply>
</apply>
</apply>
<ci>beta_CO2</ci>
</apply>
</apply>
</math>
</component>
<component name="renal_epithelial_cell">
<variable initial_value="7.329" name="pH_ec" private_interface="out" units="dimensionless"/>
<variable initial_value="19.6" name="Na_ec" private_interface="out" units="mM"/>
<variable initial_value="138.1" name="K_ec" private_interface="out" units="mM"/>
<variable initial_value="16.3" name="Cl_ec" private_interface="out" units="mM"/>
<variable initial_value="25.0" name="HCO3_ec" private_interface="out" units="mM"/>
<variable initial_value="4.36e-3" name="H2CO3_ec" private_interface="out" units="mM"/>
<variable initial_value="1.49" name="CO2_ec" private_interface="out" units="mM"/>
<variable initial_value="8.5" name="HPO4_ec" private_interface="out" units="mM"/>
<variable initial_value="2.52" name="H2PO4_ec" private_interface="out" units="mM"/>
<variable initial_value="4.96" name="urea_ec" private_interface="out" units="mM"/>
<variable initial_value="3.48e-3" name="NH3_ec" private_interface="out" units="mM"/>
<variable initial_value="0.23" name="NH4_ec" private_interface="out" units="mM"/>
<variable name="H_ec" private_interface="out" units="mM"/>
<variable initial_value="0.52" name="HCO2_ec" private_interface="out" units="mM"/>
<variable initial_value="0.91e-4" name="H2CO2_ec" private_interface="out" units="mM"/>
<variable initial_value="15.1" name="glucose_ec" private_interface="out" units="mM"/>
<variable initial_value="0.0108" name="J_NaK_max" private_interface="out" units="umol_per_s_per_cm2"/>
<variable name="V_m" private_interface="out" units="mV"/>
<variable name="pK_HCO3" private_interface="out" public_interface="in" units="dimensionless"/>
<variable name="pK_HPO4" private_interface="out" public_interface="in" units="dimensionless"/>
<variable name="pK_NH3" private_interface="out" public_interface="in" units="dimensionless"/>
<variable name="s_CO2" public_interface="in" units="mM_per_mmHg"/>
<variable name="p_CO2" public_interface="in" units="mmHg"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<variable name="J_NHE3_H" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_NHE3_Na" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_NHE3_NH4" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_Vtype_H" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_NaK_Na" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_NaK_K" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="I_NaK" private_interface="in" units="mA_per_cm2"/>
<variable name="J_NBC_Na" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_NBC_HCO3" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_diff_NH3" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_diff_CO2_apical" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_diff_CO2_basal" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_hyd_ec" private_interface="in" units="mM_per_s"/>
<variable name="J_amn_ec" private_interface="in" units="mM_per_s"/>
<variable name="theta_NHE3" public_interface="in" units="dimensionless"/>
<variable name="theta_Vtype" public_interface="in" units="dimensionless"/>
<variable name="theta_NaK" public_interface="in" units="dimensionless"/>
<variable name="theta_NBC" public_interface="in" units="dimensionless"/>
<variable name="theta_NH4" public_interface="in" units="dimensionless"/>
<variable name="theta_hyd_ec" public_interface="in" units="dimensionless"/>
<variable name="theta_amn_ec" public_interface="in" units="dimensionless"/>
<variable name="theta_diff_NH3" public_interface="in" units="dimensionless"/>
<variable name="theta_diff_CO2_apical" public_interface="in" units="dimensionless"/>
<variable name="theta_diff_CO2_basal" public_interface="in" units="dimensionless"/>
<variable name="J_ec_NH4" public_interface="in" units="umol_per_s_per_cm2"/>
<variable name="g_NBC" private_interface="in" units="mS_per_cm2"/>
<variable initial_value="100" name="g_Na" units="mS_per_cm2"/>
<variable initial_value="100" name="g_K" units="mS_per_cm2"/>
<variable name="D_CO2" private_interface="out" public_interface="in" units="cm_per_s"/>
<variable name="D_NH3" private_interface="out" public_interface="in" units="cm_per_s"/>
<variable name="E_NBC" private_interface="in" units="mV"/>
<variable name="beta_CO2" units="mM"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ec_H_concentration">
<eq/>
<ci>H_ec</ci>
<piecewise>
<piece>
<cn cellml:units="mM" type="e-notation">1<sep/>3</cn>
<apply>
<lt/>
<ci>pH_ec</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
<piece>
<apply>
<times/>
<cn cellml:units="mM" type="e-notation">1<sep/>3</cn>
<apply>
<power/>
<cn cellml:units="dimensionless">10</cn>
<apply>
<minus/>
<ci>pH_ec</ci>
</apply>
</apply>
</apply>
<apply>
<geq/>
<ci>pH_ec</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
</piecewise>
</apply>
<apply id="CO2_buffering_power">
<eq/>
<ci>beta_CO2</ci>
<apply>
<times/>
<apply>
<ln/>
<cn cellml:units="dimensionless">10</cn>
</apply>
<ci>HCO3_ec</ci>
</apply>
</apply>
<apply id="ec_potential_eq">
<eq/>
<ci>V_m</ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>theta_NBC</ci>
<ci>g_NBC</ci>
<ci>E_NBC</ci>
</apply>
<apply>
<times/>
<ci>theta_NaK</ci>
<ci>I_NaK</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>g_Na</ci>
<ci>g_K</ci>
<apply>
<times/>
<ci>theta_NBC</ci>
<ci>g_NBC</ci>
</apply>
</apply>
</apply>
</apply>
<apply id="ec_Na_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Na_ec</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<ci>theta_NHE3</ci>
</apply>
<ci>J_NHE3_Na</ci>
</apply>
<apply>
<times/>
<ci>theta_NaK</ci>
<cn cellml:units="dimensionless">3</cn>
<ci>J_NaK_Na</ci>
</apply>
</apply>
<apply>
<times/>
<ci>theta_NBC</ci>
<ci>J_NBC_Na</ci>
</apply>
</apply>
</apply>
<apply id="ec_NH3_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>NH3_ec</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>theta_diff_NH3</ci>
<ci>J_diff_NH3</ci>
</apply>
<apply>
<times/>
<ci>theta_amn_ec</ci>
<ci>J_amn_ec</ci>
</apply>
</apply>
</apply>
<apply id="ec_NH4_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>NH4_ec</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<ci>theta_NHE3</ci>
</apply>
<ci>J_NHE3_NH4</ci>
</apply>
<apply>
<times/>
<ci>theta_amn_ec</ci>
<ci>J_amn_ec</ci>
</apply>
</apply>
<ci>J_ec_NH4</ci>
</apply>
</apply>
<apply id="ec_K_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K_ec</ci>
</apply>
<apply>
<times/>
<ci>theta_NaK</ci>
<cn cellml:units="dimensionless">2</cn>
<ci>J_NaK_K</ci>
</apply>
</apply>
<apply id="ec_CO2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>CO2_ec</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>theta_diff_CO2_apical</ci>
<ci>J_diff_CO2_apical</ci>
</apply>
<apply>
<times/>
<ci>theta_diff_CO2_basal</ci>
<ci>J_diff_CO2_basal</ci>
</apply>
</apply>
</apply>
<apply id="ec_HCO3_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>HCO3_ec</ci>
</apply>
<apply>
<times/>
<ci>theta_hyd_ec</ci>
<ci>J_hyd_ec</ci>
</apply>
</apply>
<apply id="ec_pH_regulation">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>pH_ec</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>theta_NHE3</ci>
<ci>J_NHE3_H</ci>
</apply>
<apply>
<times/>
<ci>theta_Vtype</ci>
<ci>J_Vtype_H</ci>
</apply>
</apply>
<apply>
<times/>
<ci>theta_NBC</ci>
<ci>J_NBC_HCO3</ci>
</apply>
</apply>
<apply>
<times/>
<ci>theta_amn_ec</ci>
<ci>J_amn_ec</ci>
</apply>
</apply>
<ci>beta_CO2</ci>
</apply>
</apply>
</math>
</component>
<component name="renal_interstitial_fluid">
<variable initial_value="7.339" name="pH_if" private_interface="out" units="dimensionless"/>
<variable initial_value="140.3" name="Na_if" private_interface="out" units="mM"/>
<variable initial_value="4.66" name="K_if" private_interface="out" units="mM"/>
<variable initial_value="112.0" name="Cl_if" private_interface="out" units="mM"/>
<variable initial_value="25.6" name="HCO3_if" private_interface="out" units="mM"/>
<variable initial_value="4.36e-3" name="H2CO3_if" private_interface="out" units="mM"/>
<variable initial_value="1.49" name="CO2_if" private_interface="out" units="mM"/>
<variable initial_value="2.98" name="HPO4_if" private_interface="out" units="mM"/>
<variable initial_value="0.86" name="H2PO4_if" private_interface="out" units="mM"/>
<variable initial_value="4.91" name="urea_if" private_interface="out" units="mM"/>
<variable initial_value="2.7e-3" name="NH3_if" private_interface="out" units="mM"/>
<variable initial_value="0.18" name="NH4_if" private_interface="out" units="mM"/>
<variable name="H_if" private_interface="out" units="mM"/>
<variable initial_value="0.77" name="HCO2_if" private_interface="out" units="mM"/>
<variable initial_value="2.04e-4" name="H2CO2_if" private_interface="out" units="mM"/>
<variable initial_value="7.79" name="glucose_if" private_interface="out" units="mM"/>
<variable name="pK_HCO3" public_interface="in" units="dimensionless"/>
<variable name="pK_HPO4" public_interface="in" units="dimensionless"/>
<variable name="pK_NH3" public_interface="in" units="dimensionless"/>
<variable name="s_CO2" public_interface="in" units="mM_per_mmHg"/>
<variable name="p_CO2" public_interface="in" units="mmHg"/>
<variable name="J_NaK_Na" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_NaK_K" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_NBC_Na" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_NBC_HCO3" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_diff_HCO3" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_diff_Na" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_diff_K" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_diff_CO2_basal" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_diff_CO2_vessel" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_hyd_if" private_interface="in" units="mM_per_s"/>
<variable name="theta_NaK" public_interface="in" units="dimensionless"/>
<variable name="theta_NBC" public_interface="in" units="dimensionless"/>
<variable name="theta_hyd_if" public_interface="in" units="dimensionless"/>
<variable name="theta_diff_HCO3" public_interface="in" units="dimensionless"/>
<variable name="theta_diff_Na" public_interface="in" units="dimensionless"/>
<variable name="theta_diff_K" public_interface="in" units="dimensionless"/>
<variable name="theta_diff_CO2_basal" public_interface="in" units="dimensionless"/>
<variable name="theta_diff_CO2_vessel" public_interface="in" units="dimensionless"/>
<variable name="D_HCO3" private_interface="out" public_interface="in" units="cm_per_s"/>
<variable name="D_NH3" private_interface="out" public_interface="in" units="cm_per_s"/>
<variable name="D_CO2" private_interface="out" public_interface="in" units="cm_per_s"/>
<variable name="beta_CO2" units="mM"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="if_H_concentration">
<eq/>
<ci>H_if</ci>
<piecewise>
<piece>
<cn cellml:units="mM" type="e-notation">1<sep/>3</cn>
<apply>
<lt/>
<ci>pH_if</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
<piece>
<apply>
<times/>
<cn cellml:units="mM" type="e-notation">1<sep/>3</cn>
<apply>
<power/>
<cn cellml:units="dimensionless">10</cn>
<apply>
<minus/>
<ci>pH_if</ci>
</apply>
</apply>
</apply>
<apply>
<geq/>
<ci>pH_if</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
</piecewise>
</apply>
<apply id="CO2_buffering_power">
<eq/>
<ci>beta_CO2</ci>
<apply>
<times/>
<apply>
<ln/>
<cn cellml:units="dimensionless">10</cn>
</apply>
<ci>HCO3_if</ci>
</apply>
</apply>
<apply id="if_Na_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Na_if</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>theta_NBC</ci>
<ci>J_NBC_Na</ci>
</apply>
<apply>
<times/>
<ci>theta_NaK</ci>
<cn cellml:units="dimensionless">3</cn>
<ci>J_NaK_Na</ci>
</apply>
<apply>
<times/>
<ci>theta_diff_Na</ci>
<ci>J_diff_Na</ci>
</apply>
</apply>
</apply>
<apply id="if_K_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K_if</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>theta_diff_K</ci>
<ci>J_diff_K</ci>
</apply>
<apply>
<times/>
<ci>theta_NaK</ci>
<cn cellml:units="dimensionless">2</cn>
<ci>J_NaK_K</ci>
</apply>
</apply>
</apply>
<apply id="if_CO2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>CO2_if</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>theta_diff_CO2_basal</ci>
</apply>
<ci>J_diff_CO2_basal</ci>
</apply>
<apply>
<times/>
<ci>theta_diff_CO2_vessel</ci>
<ci>J_diff_CO2_vessel</ci>
</apply>
</apply>
</apply>
<apply id="if_HCO3_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>HCO3_if</ci>
</apply>
<apply>
<times/>
<ci>theta_hyd_if</ci>
<ci>J_hyd_if</ci>
</apply>
</apply>
<apply id="if_pH_regulation">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>pH_if</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>theta_NBC</ci>
<ci>J_NBC_HCO3</ci>
</apply>
<apply>
<times/>
<ci>theta_diff_HCO3</ci>
<ci>J_diff_HCO3</ci>
</apply>
</apply>
<ci>beta_CO2</ci>
</apply>
</apply>
</math>
</component>
<component name="peritubular_capillary_blood">
<variable initial_value="7.306" name="pH_cb" private_interface="out" units="dimensionless"/>
<variable initial_value="140.0" name="Na_cb" private_interface="out" units="mM"/>
<variable initial_value="4.9" name="K_cb" private_interface="out" units="mM"/>
<variable initial_value="113.2" name="Cl_cb" private_interface="out" units="mM"/>
<variable initial_value="24.0" name="HCO3_cb" private_interface="out" units="mM"/>
<variable initial_value="4.41e-3" name="H2CO3_cb" private_interface="out" units="mM"/>
<variable initial_value="1.5" name="CO2_cb" private_interface="out" units="mM"/>
<variable initial_value="2.97" name="HPO4_cb" private_interface="out" units="mM"/>
<variable initial_value="0.93" name="H2PO4_cb" private_interface="out" units="mM"/>
<variable initial_value="5.0" name="urea_cb" private_interface="out" units="mM"/>
<variable initial_value="2.82e-3" name="NH3_cb" private_interface="out" units="mM"/>
<variable initial_value="0.2" name="NH4_cb" private_interface="out" units="mM"/>
<variable name="H_cb" private_interface="out" units="mM"/>
<variable initial_value="1.0" name="HCO2_cb" private_interface="out" units="mM"/>
<variable initial_value="2.85e-4" name="H2CO2_cb" private_interface="out" units="mM"/>
<variable initial_value="5.0" name="glucose_cb" private_interface="out" units="mM"/>
<variable name="pK_HCO3" public_interface="in" units="dimensionless"/>
<variable name="pK_HPO4" public_interface="in" units="dimensionless"/>
<variable name="pK_NH3" public_interface="in" units="dimensionless"/>
<variable name="s_CO2" public_interface="in" units="mM_per_mmHg"/>
<variable name="p_CO2" public_interface="in" units="mmHg"/>
<variable name="J_diff_HCO3" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_diff_Na" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_diff_K" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_diff_CO2_vessel" private_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_hyd_cb" private_interface="in" units="mM_per_s"/>
<variable name="D_HCO3" private_interface="out" public_interface="in" units="cm_per_s"/>
<variable name="D_Na" private_interface="out" public_interface="in" units="cm_per_s"/>
<variable name="D_K" private_interface="out" public_interface="in" units="cm_per_s"/>
<variable name="D_NH3" private_interface="out" public_interface="in" units="cm_per_s"/>
<variable name="D_CO2" private_interface="out" public_interface="in" units="cm_per_s"/>
<variable name="theta_hyd_cb" public_interface="in" units="dimensionless"/>
<variable name="theta_diff_HCO3" public_interface="in" units="dimensionless"/>
<variable name="theta_diff_Na" public_interface="in" units="dimensionless"/>
<variable name="theta_diff_K" public_interface="in" units="dimensionless"/>
<variable name="theta_diff_CO2_vessel" public_interface="in" units="dimensionless"/>
<variable name="J_cb_K" public_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_cb_Na" public_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_cb_H" public_interface="in" units="umol_per_s_per_cm2"/>
<variable name="J_cb_HCO3" public_interface="in" units="umol_per_s_per_cm2"/>
<variable name="beta_CO2" units="mM"/>
<variable name="time" public_interface="in" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="cb_H_concentration">
<eq/>
<ci>H_cb</ci>
<piecewise>
<piece>
<cn cellml:units="mM" type="e-notation">1<sep/>3</cn>
<apply>
<lt/>
<ci>pH_cb</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
<piece>
<apply>
<times/>
<cn cellml:units="mM" type="e-notation">1<sep/>3</cn>
<apply>
<power/>
<cn cellml:units="dimensionless">10</cn>
<apply>
<minus/>
<ci>pH_cb</ci>
</apply>
</apply>
</apply>
<apply>
<geq/>
<ci>pH_cb</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
</piecewise>
</apply>
<apply id="CO2_buffering_power">
<eq/>
<ci>beta_CO2</ci>
<apply>
<times/>
<apply>
<ln/>
<cn cellml:units="dimensionless">10</cn>
</apply>
<ci>HCO3_cb</ci>
</apply>
</apply>
<apply id="cb_Na_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Na_cb</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>J_cb_Na</ci>
</apply>
<apply>
<times/>
<ci>theta_diff_Na</ci>
<ci>J_diff_Na</ci>
</apply>
</apply>
</apply>
<apply id="cb_K_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K_cb</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>J_cb_K</ci>
</apply>
<apply>
<times/>
<ci>theta_diff_K</ci>
<ci>J_diff_K</ci>
</apply>
</apply>
</apply>
<apply id="cb_CO2_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>CO2_cb</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>theta_diff_CO2_vessel</ci>
</apply>
<ci>J_diff_CO2_vessel</ci>
</apply>
</apply>
<apply id="cb_HCO3_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>HCO3_cb</ci>
</apply>
<apply>
<times/>
<ci>theta_hyd_cb</ci>
<ci>J_hyd_cb</ci>
</apply>
</apply>
<apply id="cb_pH_regulation">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>pH_cb</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>J_cb_H</ci>
<ci>J_cb_HCO3</ci>
</apply>
<apply>
<times/>
<ci>theta_diff_HCO3</ci>
<ci>J_diff_HCO3</ci>
</apply>
</apply>
<ci>beta_CO2</ci>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="renal_proximal_tubule">
<component_ref component="NHE3"/>
<component_ref component="H_ATPase"/>
<component_ref component="NH3_diffusion"/>
<component_ref component="CO2_diffusion_apical"/>
<component_ref component="CO2_hydration_pt"/>
<component_ref component="NH3_hydration_pt"/>
<component_ref component="HPO4_hydration_pt"/>
</component_ref>
<component_ref component="renal_epithelial_cell">
<component_ref component="NHE3"/>
<component_ref component="H_ATPase"/>
<component_ref component="NaK"/>
<component_ref component="NBC"/>
<component_ref component="NH3_diffusion"/>
<component_ref component="CO2_diffusion_apical"/>
<component_ref component="CO2_diffusion_basal"/>
<component_ref component="CO2_hydration_ec"/>
<component_ref component="NH3_hydration_ec"/>
</component_ref>
<component_ref component="renal_interstitial_fluid">
<component_ref component="NaK"/>
<component_ref component="NBC"/>
<component_ref component="HCO3_diffusion"/>
<component_ref component="Na_diffusion"/>
<component_ref component="K_diffusion"/>
<component_ref component="CO2_diffusion_basal"/>
<component_ref component="CO2_diffusion_vessel"/>
<component_ref component="CO2_hydration_if"/>
</component_ref>
<component_ref component="peritubular_capillary_blood">
<component_ref component="HCO3_diffusion"/>
<component_ref component="Na_diffusion"/>
<component_ref component="K_diffusion"/>
<component_ref component="CO2_diffusion_vessel"/>
<component_ref component="CO2_hydration_cb"/>
</component_ref>
</group>
<connection>
<map_components component_1="renal_proximal_tubule" component_2="parameters"/>
<map_variables variable_1="theta_NHE3" variable_2="theta_NHE3"/>
<map_variables variable_1="theta_Vtype" variable_2="theta_Vtype"/>
<map_variables variable_1="theta_hyd_pt" variable_2="theta_hyd_pt"/>
<map_variables variable_1="theta_amn_pt" variable_2="theta_amn_pt"/>
<map_variables variable_1="theta_phs_pt" variable_2="theta_phs_pt"/>
<map_variables variable_1="theta_diff_CO2_apical" variable_2="theta_diff_CO2_apical"/>
<map_variables variable_1="theta_diff_NH3" variable_2="theta_diff_NH3"/>
<map_variables variable_1="J_pt_H" variable_2="J_pt_H"/>
<map_variables variable_1="J_pt_HCO3" variable_2="J_pt_HCO3"/>
<map_variables variable_1="J_pt_Na" variable_2="J_pt_Na"/>
<map_variables variable_1="p_CO2" variable_2="p_CO2"/>
<map_variables variable_1="s_CO2" variable_2="s_CO2"/>
<map_variables variable_1="pK_HCO3" variable_2="pK_HCO3"/>
<map_variables variable_1="pK_HPO4" variable_2="pK_HPO4"/>
<map_variables variable_1="pK_NH3" variable_2="pK_NH3"/>
<map_variables variable_1="D_CO2" variable_2="D_CO2"/>
<map_variables variable_1="D_NH3" variable_2="D_NH3"/>
</connection>
<connection>
<map_components component_1="renal_proximal_tubule" component_2="NHE3"/>
<map_variables variable_1="H_pt" variable_2="H_ext"/>
<map_variables variable_1="Na_pt" variable_2="Na_ext"/>
<map_variables variable_1="NH4_pt" variable_2="NH4_ext"/>
<map_variables variable_1="J_NHE3_H" variable_2="J_NHE3_H"/>
<map_variables variable_1="J_NHE3_Na" variable_2="J_NHE3_Na"/>
<map_variables variable_1="J_NHE3_NH4" variable_2="J_NHE3_NH4"/>
</connection>
<connection>
<map_components component_1="renal_proximal_tubule" component_2="H_ATPase"/>
<map_variables variable_1="H_pt" variable_2="H_ext"/>
<map_variables variable_1="J_Vtype_H" variable_2="J_Vtype_H"/>
</connection>
<connection>
<map_components component_1="renal_proximal_tubule" component_2="NH3_diffusion"/>
<map_variables variable_1="NH3_pt" variable_2="C_ext"/>
<map_variables variable_1="J_diff_NH3" variable_2="J_diff"/>
<map_variables variable_1="D_NH3" variable_2="D"/>
</connection>
<connection>
<map_components component_1="renal_proximal_tubule" component_2="CO2_diffusion_apical"/>
<map_variables variable_1="CO2_pt" variable_2="C_ext"/>
<map_variables variable_1="J_diff_CO2_apical" variable_2="J_diff"/>
<map_variables variable_1="D_CO2" variable_2="D"/>
</connection>
<connection>
<map_components component_1="renal_proximal_tubule" component_2="CO2_hydration_pt"/>
<map_variables variable_1="pH_pt" variable_2="pH"/>
<map_variables variable_1="CO2_pt" variable_2="CO2"/>
<map_variables variable_1="HCO3_pt" variable_2="HCO3"/>
<map_variables variable_1="J_hyd_pt" variable_2="J"/>
</connection>
<connection>
<map_components component_1="renal_proximal_tubule" component_2="NH3_hydration_pt"/>
<map_variables variable_1="pH_pt" variable_2="pH"/>
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A kinetically defined Na+/H+ antiporter within a mathematical model of the rat proximal tubule
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