/
ca_i_up.cellml
executable file
·223 lines (223 loc) · 8.47 KB
/
ca_i_up.cellml
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<?xml version='1.0'?>
<!-- no Ca_cytonetic model here to keep it clean. Also no concentrations: just mol
try Cm of 200 pF for whole cell (1e-5 F is TOO LARGE)
try convention of Pan: q1 is inside.-->
<model name="ca_up_only" 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_BG.cellml">
<units name="mM" units_ref="mM"/>
<units name="per_mol" units_ref="per_mol"/>
<units name="J_per_mol" units_ref="J_per_mol"/>
<units name="mol_per_s" units_ref="mol_per_s"/>
<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"/>
</import>
<import xlink:href="../Units_kinetic.cellml">
<units name="microA_per_microF" units_ref="microA_per_microF"/>
</import>
<units name="millivolt">
<unit prefix="milli" units="volt"/>
</units>
<component name="environment">
<!-- K mols from Pan. vol_c is 1e-15, vol_ext is 1e-14 m3-->
<variable name="time" public_interface="out" units="second"/>
<variable initial_value="200e-12" name="C_m" public_interface="out" units="farad"/>
<variable initial_value="0" name="qCa_NSR" public_interface="out" units="mole"/>
<variable initial_value="0.00456e-15" name="qCa_cyto" public_interface="out" units="mole"/>
<variable initial_value="1e-15" name="qEnz_up" public_interface="out" units="mole"/>
<variable initial_value="2494.34" name="RT" public_interface="out" units="J_per_mol"/>
<variable initial_value="1" name="z" public_interface="out" units="dimensionless"/>
<variable initial_value="96500" name="F" public_interface="out" units="C_per_mol"/>
<variable name="v_Re1" public_interface="in" units="mol_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>qCa_cyto</ci>
</apply>
<apply>
<minus/>
<ci>v_Re1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>qCa_NSR</ci>
</apply>
<ci>v_Re1</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>qEnz_up</ci>
</apply>
<cn cellml:units="mol_per_s">0</cn>
</apply>
</math>
</component>
<component name="BG_up">
<variable name="t" public_interface="in" units="second"/>
<variable name="RT" public_interface="in" units="J_per_mol"/>
<variable name="z" public_interface="in" units="dimensionless"/>
<variable name="F" public_interface="in" units="C_per_mol"/>
<!-- Parameters-->
<variable name="C_m" public_interface="in" units="farad"/>
<variable initial_value="5e1" name="K_q1" units="per_mol"/>
<variable initial_value="5e1" name="K_q2" units="per_mol"/>
<variable initial_value="3E0" name="K_Re1" units="mol_per_s"/>
<variable initial_value="2" name="G_pore" units="dimensionless"/>
<variable initial_value="1" name="G_ion" units="dimensionless"/>
<!-- 0<Gion<1 (it is the open probability)-->
<!-- State variables-->
<variable name="q1" public_interface="in" units="mole"/>
<variable name="q2" public_interface="in" units="mole"/>
<variable name="q3" public_interface="in" units="mole"/>
<variable name="i_BG_in_to_out" units="microA_per_microF"/>
<variable name="v_Re1" public_interface="out" units="mol_per_s"/>
<variable name="u1" units="J_per_mol"/>
<variable name="u2" units="J_per_mol"/>
<variable name="u3" units="J_per_mol"/>
<variable name="u4" units="J_per_mol"/>
<variable name="u5" units="J_per_mol"/>
<!-- Convention: positive flow from inside to outside-->
<!-- Conservation laws-->
<!-- ode(q1, t) = -v_Re1;
ode(q2, t) = v_Re1;
ode(q3, t) = 0{mol_per_s};-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>u4</ci>
<apply>
<plus/>
<ci>u1</ci>
<ci>u3</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>u5</ci>
<apply>
<plus/>
<ci>u2</ci>
<ci>u3</ci>
</apply>
</apply>
<!-- Constitutive relations-->
<apply>
<eq/>
<ci>u1</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_q1</ci>
<ci>q1</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u2</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>K_q2</ci>
<ci>q2</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u3</ci>
<apply>
<times/>
<ci>RT</ci>
<apply>
<ln/>
<apply>
<times/>
<ci>G_pore</ci>
<ci>G_ion</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>v_Re1</ci>
<apply>
<times/>
<ci>K_Re1</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>u4</ci>
<ci>RT</ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci>u5</ci>
<ci>RT</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<!-- for comparison, calculate the change in concentration AND current as well-->
<apply>
<eq/>
<ci>i_BG_in_to_out</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>v_Re1</ci>
<ci>F</ci>
</apply>
<ci>C_m</ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="BG_up"/>
<map_variables variable_1="time" variable_2="t"/>
<map_variables variable_1="RT" variable_2="RT"/>
<map_variables variable_1="z" variable_2="z"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="qCa_cyto" variable_2="q1"/>
<map_variables variable_1="qCa_NSR" variable_2="q2"/>
<map_variables variable_1="qEnz_up" variable_2="q3"/>
<map_variables variable_1="C_m" variable_2="C_m"/>
<map_variables variable_1="v_Re1" variable_2="v_Re1"/>
</connection>
</model>