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Chemical.mo
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within Physiolibrary;
package Chemical "Domain with Molar Concentration and Molar Flow"
extends Modelica.Icons.Package;
package Examples
"Examples that demonstrate usage of the Pressure flow components"
extends Modelica.Icons.ExamplesPackage;
model SimpleReaction
extends Modelica.Icons.Example;
import Physiolibrary.Chemical.Components.*;
Substance A(solute_start=0.9)
annotation (Placement(transformation(extent={{-56,-8},{-36,12}})));
ChemicalReaction reaction(K=1)
annotation (Placement(transformation(extent={{-10,-8},{10,12}})));
Substance B(solute_start=0.1)
annotation (Placement(transformation(extent={{42,-8},{62,12}})));
equation
connect(B.q_out, reaction.products[1]) annotation (Line(
points={{52,2},{10,2}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(A.q_out, reaction.substrates[1]) annotation (Line(
points={{-46,2},{-10,2}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
annotation ( Documentation(revisions="<html>
<p><i>2013</i></p>
<p>Marek Matejak, Charles University, Prague, Czech Republic </p>
</html>"),
experiment(StopTime=1e-007));
end SimpleReaction;
model SimpleReaction2
extends Modelica.Icons.Example;
import Physiolibrary.Chemical.Components.*;
Substance A(solute_start=0.9)
annotation (Placement(transformation(extent={{-40,-8},{-20,12}})));
ChemicalReaction reaction(K=1, nP=2)
annotation (Placement(transformation(extent={{-6,-8},{14,12}})));
Substance B(solute_start=0.1)
annotation (Placement(transformation(extent={{36,-8},{56,12}})));
Substance C(solute_start=0.1)
annotation (Placement(transformation(extent={{36,16},{56,36}})));
equation
connect(A.q_out, reaction.substrates[1]) annotation (Line(
points={{-30,2},{-6,2}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(reaction.products[1], B.q_out) annotation (Line(
points={{14,1.5},{24,1.5},{24,2},{46,2}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(reaction.products[2], C.q_out) annotation (Line(
points={{14,2.5},{24,2.5},{24,26},{46,26}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
annotation ( Documentation(revisions="<html>
<p><i>2013</i></p>
<p>Marek Matejak, Charles University, Prague, Czech Republic </p>
</html>"),
experiment(StopTime=1e-009));
end SimpleReaction2;
model ExothermicReaction
extends Modelica.Icons.Example;
import Physiolibrary.Chemical;
Components.Substance A(solute_start=0.9)
annotation (Placement(transformation(extent={{-56,-8},{-36,12}})));
Components.ChemicalReaction
reaction(K=1,
useHeatPort=true,
dH=-1000,
kf=1)
annotation (Placement(transformation(extent={{-10,-8},{10,12}})));
Components.Substance B(solute_start=0.1)
annotation (Placement(transformation(extent={{44,-8},{64,12}})));
Modelica.Thermal.HeatTransfer.Sensors.HeatFlowSensor heatFlowSensor
annotation (Placement(transformation(extent={{12,-58},{32,-38}})));
Physiolibrary.Thermal.Sources.UnlimitedHeat unlimitedHeat(T=310.15)
annotation (Placement(transformation(extent={{74,-58},{54,-38}})));
equation
connect(B.q_out, reaction.products[1]) annotation (Line(
points={{54,2},{10,2}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(A.q_out, reaction.substrates[1]) annotation (Line(
points={{-46,2},{-10,2}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(reaction.heatPort, heatFlowSensor.port_a) annotation (Line(
points={{0,2},{0,-48},{12,-48}},
color={191,0,0},
thickness=1,
smooth=Smooth.None));
connect(unlimitedHeat.port, heatFlowSensor.port_b) annotation (Line(
points={{54,-48},{32,-48}},
color={191,0,0},
thickness=1,
smooth=Smooth.None));
annotation ( Documentation(revisions="<html>
<p><i>2013</i></p>
<p>Marek Matejak, Charles University, Prague, Czech Republic </p>
</html>"),
experiment(StopTime=5));
end ExothermicReaction;
model MichaelisMenten "Basic enzyme kinetics"
import Physiolibrary;
extends Modelica.Icons.Example;
extends Physiolibrary.SteadyStates.Interfaces.SteadyStateSystem(
Simulation=Types.SimulationType.SteadyState);
import Physiolibrary.Types.*;
Physiolibrary.Chemical.Sources.UnlimitedSolutionStorage
P(Conc=0)
annotation (Placement(transformation(extent={{92,-12},{72,8}})));
Physiolibrary.Chemical.Sources.UnlimitedSolutionStorage
S(Conc=0.1)
annotation (Placement(transformation(extent={{-94,-12},{-74,8}})));
parameter AmountOfSubstance tE=0.01 "total amount of enzyme";
parameter Real k_cat(unit="1/s", displayUnit="1/min")= 1
"forward rate of second reaction";
parameter Physiolibrary.Types.Concentration Km = 0.1
"Michaelis constant = substrate concentration at rate of half Vmax";
Physiolibrary.Chemical.Components.Substance
ES( solute_start=0,
Simulation=SimulationType.SteadyState)
annotation (Placement(transformation(extent={{-10,-10},{10,10}})));
Physiolibrary.Chemical.Components.Substance
E( solute_start=tE,
isDependent=true,
Simulation=SimulationType.SteadyState)
annotation (Placement(transformation(extent={{-10,38},{10,58}})));
Components.ChemicalReaction
chemicalReaction(nS=2,
K=2/Km,
kf=2*k_cat/Km)
annotation (Placement(transformation(extent={{-42,-10},{-22,10}})));
Components.ChemicalReaction
chemicalReaction1(nP=2,
K=Modelica.Constants.inf,
kf=k_cat)
annotation (Placement(transformation(extent={{24,-10},{44,10}})));
// Real v(unit="mol/s", displayUnit="mmol/min") "test of MM equation";
equation
normalizedState[1]*tE = E.solute + ES.solute;
//Michaelis-Menton: v=((E.q_out.conc + ES.q_out.conc)*k_cat)*S.concentration/(Km+S.concentration);
connect(S.q_out, chemicalReaction.substrates[1]) annotation (Line(
points={{-74,-2},{-60,-2},{-60,-0.5},{-42,-0.5}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(chemicalReaction1.products[1], P.q_out) annotation (Line(
points={{44,-0.5},{54,-0.5},{54,-2},{72,-2}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(E.q_out, chemicalReaction.substrates[2]) annotation (Line(
points={{0,48},{-50,48},{-50,0.5},{-42,0.5}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(E.q_out, chemicalReaction1.products[2]) annotation (Line(
points={{0,48},{50,48},{50,0.5},{44,0.5}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(chemicalReaction.products[1], ES.q_out) annotation (Line(
points={{-22,0},{0,0}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(ES.q_out, chemicalReaction1.substrates[1]) annotation (Line(
points={{0,0},{24,0}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
annotation ( Documentation(revisions="<html>
<p><i>2013</i></p>
<p>Marek Matejak, Charles University, Prague, Czech Republic </p>
</html>"),
experiment(StopTime=1));
end MichaelisMenten;
package Hemoglobin "Hemoglobin blood gases binding"
model Allosteric_Hemoglobin_MWC "Monod,Wyman,Changeux (1965)"
extends Modelica.Icons.Example;
import Physiolibrary.Chemical.*;
import Physiolibrary.Types.*;
//extends Physiolibrary.SteadyStates.Interfaces.SteadyStateSystem(
// Simulation=SimulationType.SteadyState);
parameter Temperature T=310.15 "Temperature";
// parameter GasSolubility alpha = Modelica.Constants.R*298.15 * 0.0105 * 1e-3
// "oxygen solubility in plasma";
// by Siggaard Andersen: 0.0105 (mmol/l)/kPa
parameter Fraction L = 7.0529*10^6
"=[T0]/[R0] .. dissociation constant of relaxed <-> tensed change of deoxyhemoglobin tetramer";
parameter Fraction c = 0.00431555
"=KR/KT .. ration between oxygen affinities of relaxed vs. tensed subunit";
parameter Concentration KR = 0.000671946
"oxygen dissociation on relaxed(R) hemoglobin subunit"; //*7.875647668393782383419689119171e-5
//10.500001495896 7.8756465463794e-05
parameter Concentration KT=KR/c
"oxygen dissociation on tensed(T) hemoglobin subunit";
// Fraction sO2 "hemoglobin oxygen saturation";
parameter AmountOfSubstance totalAmountOfHemoglobin=1;
// AmountOfSubstance totalAmountOfRforms;
// AmountOfSubstance totalAmountOfTforms;
Components.Substance T0(stateName="T0",Simulation=SimulationType.SteadyState,
solute_start=1)
annotation (Placement(transformation(extent={{32,78},{52,98}})));
Components.Substance T1(stateName="T1",Simulation=SimulationType.SteadyState,
solute_start=0)
annotation (Placement(transformation(extent={{34,36},{54,56}})));
Components.Substance R1(stateName="R1",Simulation=SimulationType.SteadyState,
solute_start=0,
isDependent=true)
annotation (Placement(transformation(extent={{-20,36},{0,56}})));
Components.Substance T2(stateName="T2",Simulation=SimulationType.SteadyState,
solute_start=0)
annotation (Placement(transformation(extent={{34,-10},{54,10}})));
Components.Substance R2(stateName="R2",Simulation=SimulationType.SteadyState,
solute_start=0)
annotation (Placement(transformation(extent={{-20,-10},{0,10}})));
Components.Substance T3(stateName="T3",Simulation=SimulationType.SteadyState,
solute_start=0)
annotation (Placement(transformation(extent={{34,-54},{54,-34}})));
Components.Substance R3(stateName="R3",Simulation=SimulationType.SteadyState,
solute_start=0)
annotation (Placement(transformation(extent={{-20,-54},{0,-34}})));
Components.Substance T4(stateName="T4",Simulation=SimulationType.SteadyState,
solute_start=0,
isDependent=true)
annotation (Placement(transformation(extent={{34,-92},{54,-72}})));
Components.Substance R4(stateName="R4",Simulation=SimulationType.SteadyState,
solute_start=0)
annotation (Placement(transformation(extent={{-20,-92},{0,-72}})));
Components.Substance R0(stateName="R0",Simulation=SimulationType.SteadyState,
solute_start=0)
annotation (Placement(transformation(extent={{-20,78},{0,98}})));
Components.ChemicalReaction quaternaryForm(K=L)
annotation (Placement(transformation(extent={{4,78},{24,98}})));
Components.ChemicalReaction oxyR1(nP=2, K=KR/4)
annotation (Placement(
transformation(
extent={{-10,10},{10,-10}},
rotation=90,
origin={-10,64})));
Components.ChemicalReaction oxyT1(nP=2, K=KT/4)
annotation (Placement(
transformation(
extent={{-10,-10},{10,10}},
rotation=90,
origin={44,64})));
Components.ChemicalReaction oxyR2(nP=2, K=KR/(3/2))
annotation (Placement(
transformation(
extent={{-10,10},{10,-10}},
rotation=90,
origin={-10,22})));
Components.ChemicalReaction oxyR3(nP=2, K=KR/(2/3))
annotation (Placement(
transformation(
extent={{-10,10},{10,-10}},
rotation=90,
origin={-10,-24})));
Components.ChemicalReaction oxyR4(nP=2, K=KR*4)
annotation (Placement(
transformation(
extent={{-10,10},{10,-10}},
rotation=90,
origin={-10,-66})));
Components.ChemicalReaction oxyT2(nP=2, K=KT/(3/2))
annotation (Placement(
transformation(
extent={{-10,-10},{10,10}},
rotation=90,
origin={44,22})));
Components.ChemicalReaction oxyT3(nP=2, K=KT/(2/3))
annotation (Placement(
transformation(
extent={{-10,-10},{10,10}},
rotation=90,
origin={44,-24})));
Components.ChemicalReaction oxyT4(nP=2, K=KT*4)
annotation (Placement(
transformation(
extent={{-10,-10},{10,10}},
rotation=90,
origin={44,-66})));
Components.ChemicalReaction quaternaryForm1(K=c*L)
annotation (Placement(transformation(extent={{8,36},{28,56}})));
Components.ChemicalReaction quaternaryForm2(K=(c^2)*L)
annotation (Placement(transformation(extent={{8,-10},{28,10}})));
Components.ChemicalReaction quaternaryForm3(K=(c^3)*L)
annotation (Placement(transformation(extent={{8,-54},{28,-34}})));
Components.ChemicalReaction quaternaryForm4(K=(c^4)*L)
annotation (Placement(transformation(extent={{10,-92},{30,-72}})));
SteadyStates.Components.MolarConservationLaw hemoglobinConservationLaw(
n=10, Total(displayUnit="mol") = 1,
Simulation=Physiolibrary.Types.SimulationType.SteadyState)
annotation (Placement(transformation(extent={{72,-2},{92,18}})));
Modelica.Blocks.Math.Sum oxygen_bound(k={1,1,2,2,3,3,4,4}, nin=8)
annotation (Placement(transformation(extent={{72,-56},{82,-46}})));
Modelica.Blocks.Math.Division sO2_ "hemoglobin oxygen saturation"
annotation (Placement(transformation(extent={{86,-60},{96,-50}})));
Modelica.Blocks.Math.Sum tHb(nin=10, k=4*ones(10))
annotation (Placement(transformation(extent={{72,-70},{82,-60}})));
Components.Substance oxygen_unbound(solute_start=0.000001*
7.875647668393782383419689119171e-5, Simulation=SimulationType.SteadyState)
annotation (Placement(transformation(extent={{-56,-44},{-36,-24}})));
Modelica.Blocks.Sources.Clock clock(offset=60)
annotation (Placement(transformation(extent={{-94,44},{-74,64}})));
Sources.UnlimitedGasStorage O2_in_air(Simulation=Physiolibrary.Types.SimulationType.SteadyState,
usePartialPressureInput=true,
T=310.15) annotation (Placement(transformation(
extent={{-10,-10},{10,10}},
rotation=270,
origin={-66,24})));
Components.GasSolubility gasSolubility(
useHeatPort=false, kH_T0=
0.026029047188736)
annotation (Placement(transformation(extent={{-76,-14},{-56,6}})));
equation
// sO2 = (R1.solute + 2*R2.solute + 3*R3.solute + 4*R4.solute + T1.solute + 2*T2.solute + 3*T3.solute + 4*T4.solute)/(4*totalAmountOfHemoglobin);
// totalAmountOfRforms = R0.solute + R1.solute + R2.solute + R3.solute + R4.solute;
// totalAmountOfTforms = T0.solute + T1.solute + T2.solute + T3.solute + T4.solute;
// totalAmountOfHemoglobin*normalizedState[1] = totalAmountOfRforms + totalAmountOfTforms;
connect(quaternaryForm.products[1],T0. q_out) annotation (Line(
points={{24,88},{42,88}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxyR1.substrates[1],R1. q_out) annotation (Line(
points={{-10,54},{-10,46}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(R1.q_out,oxyR2. products[1]) annotation (Line(
points={{-10,46},{-10,32},{-10.5,32}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxyR2.substrates[1],R2. q_out) annotation (Line(
points={{-10,12},{-10,0}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxyR3.substrates[1],R3. q_out) annotation (Line(
points={{-10,-34},{-10,-44}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxyR3.products[1],R2. q_out) annotation (Line(
points={{-10.5,-14},{-10.5,-7},{-10,-7},{-10,0}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(R3.q_out,oxyR4. products[1]) annotation (Line(
points={{-10,-44},{-10,-56},{-10.5,-56}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxyR4.substrates[1],R4. q_out) annotation (Line(
points={{-10,-76},{-10,-82}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxyT1.products[1],T0. q_out) annotation (Line(
points={{44.5,74},{44.5,88},{42,88}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxyT1.substrates[1],T1. q_out) annotation (Line(
points={{44,54},{44,46}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(T1.q_out,oxyT2. products[1]) annotation (Line(
points={{44,46},{44,32},{44.5,32}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxyT2.substrates[1],T2. q_out) annotation (Line(
points={{44,12},{44,0}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(T2.q_out,oxyT3. products[1]) annotation (Line(
points={{44,0},{44,-14},{44.5,-14}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxyT3.substrates[1],T3. q_out) annotation (Line(
points={{44,-34},{44,-44}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(T3.q_out,oxyT4. products[1]) annotation (Line(
points={{44,-44},{44,-56},{44.5,-56}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxyT4.substrates[1],T4. q_out) annotation (Line(
points={{44,-76},{44,-82}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(R0.q_out,quaternaryForm. substrates[1]) annotation (Line(
points={{-10,88},{4,88}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(R0.q_out,oxyR1. products[1]) annotation (Line(
points={{-10,88},{-10,74},{-10.5,74}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(R1.q_out,quaternaryForm1. substrates[1]) annotation (Line(
points={{-10,46},{8,46}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(quaternaryForm1.products[1],T1. q_out) annotation (Line(
points={{28,46},{44,46}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(R2.q_out,quaternaryForm2. substrates[1]) annotation (Line(
points={{-10,0},{8,0}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(quaternaryForm2.products[1],T2. q_out) annotation (Line(
points={{28,0},{44,0}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(R3.q_out,quaternaryForm3. substrates[1]) annotation (Line(
points={{-10,-44},{8,-44}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(quaternaryForm3.products[1],T3. q_out) annotation (Line(
points={{28,-44},{44,-44}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(R4.q_out,quaternaryForm4. substrates[1]) annotation (Line(
points={{-10,-82},{10,-82}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(quaternaryForm4.products[1],T4. q_out) annotation (Line(
points={{30,-82},{44,-82}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(R4.solute,hemoglobinConservationLaw. fragment[1]) annotation (
Line(
points={{-10,-92},{-10,-98},{64,-98},{64,2.2},{72,2.2}},
color={0,0,127},
smooth=Smooth.None));
connect(T4.solute,hemoglobinConservationLaw. fragment[2]) annotation (
Line(
points={{44,-92},{44,-98},{64,-98},{64,2.6},{72,2.6}},
color={0,0,127},
smooth=Smooth.None));
connect(R3.solute,hemoglobinConservationLaw. fragment[3]) annotation (
Line(
points={{-10,-54},{64,-54},{64,3},{72,3}},
color={0,0,127},
smooth=Smooth.None));
connect(T3.solute,hemoglobinConservationLaw. fragment[4]) annotation (
Line(
points={{44,-54},{64,-54},{64,3.4},{72,3.4}},
color={0,0,127},
smooth=Smooth.None));
connect(R2.solute,hemoglobinConservationLaw. fragment[5]) annotation (
Line(
points={{-10,-10},{64,-10},{64,3.8},{72,3.8}},
color={0,0,127},
smooth=Smooth.None));
connect(T2.solute,hemoglobinConservationLaw. fragment[6]) annotation (
Line(
points={{44,-10},{64,-10},{64,4.2},{72,4.2}},
color={0,0,127},
smooth=Smooth.None));
connect(R1.solute,hemoglobinConservationLaw. fragment[7]) annotation (
Line(
points={{-10,36},{64,36},{64,4.6},{72,4.6}},
color={0,0,127},
smooth=Smooth.None));
connect(T1.solute,hemoglobinConservationLaw. fragment[8]) annotation (
Line(
points={{44,36},{64,36},{64,5},{72,5}},
color={0,0,127},
smooth=Smooth.None));
connect(R0.solute,hemoglobinConservationLaw. fragment[9]) annotation (
Line(
points={{-10,78},{64,78},{64,5.4},{72,5.4}},
color={0,0,127},
smooth=Smooth.None));
connect(T0.solute,hemoglobinConservationLaw. fragment[10]) annotation (
Line(
points={{42,78},{64,78},{64,5.8},{72,5.8}},
color={0,0,127},
smooth=Smooth.None));
connect(R1.solute,oxygen_bound. u[1]) annotation (Line(
points={{-10,36},{64,36},{64,-51.875},{71,-51.875}},
color={0,0,127},
smooth=Smooth.None));
connect(T1.solute,oxygen_bound. u[2]) annotation (Line(
points={{44,36},{64,36},{64,-51.625},{71,-51.625}},
color={0,0,127},
smooth=Smooth.None));
connect(R2.solute,oxygen_bound. u[3]) annotation (Line(
points={{-10,-10},{64,-10},{64,-51.375},{71,-51.375}},
color={0,0,127},
smooth=Smooth.None));
connect(T2.solute,oxygen_bound. u[4]) annotation (Line(
points={{44,-10},{64,-10},{64,-51.125},{71,-51.125}},
color={0,0,127},
smooth=Smooth.None));
connect(R3.solute,oxygen_bound. u[5]) annotation (Line(
points={{-10,-54},{64,-54},{64,-50.875},{71,-50.875}},
color={0,0,127},
smooth=Smooth.None));
connect(T3.solute,oxygen_bound. u[6]) annotation (Line(
points={{44,-54},{64,-54},{64,-50.625},{71,-50.625}},
color={0,0,127},
smooth=Smooth.None));
connect(R4.solute,oxygen_bound. u[7]) annotation (Line(
points={{-10,-92},{-10,-98},{64,-98},{64,-50.375},{71,-50.375}},
color={0,0,127},
smooth=Smooth.None));
connect(T4.solute,oxygen_bound. u[8]) annotation (Line(
points={{44,-92},{44,-98},{64,-98},{64,-50.125},{71,-50.125}},
color={0,0,127},
smooth=Smooth.None));
connect(oxygen_bound.y,sO2_. u1) annotation (Line(
points={{82.5,-51},{84,-51},{84,-52},{85,-52}},
color={0,0,127},
smooth=Smooth.None));
connect(sO2_.u2,tHb. y) annotation (Line(
points={{85,-58},{84,-58},{84,-65},{82.5,-65}},
color={0,0,127},
smooth=Smooth.None));
connect(R0.solute,tHb. u[1]) annotation (Line(
points={{-10,78},{64,78},{64,-65.9},{71,-65.9}},
color={0,0,127},
smooth=Smooth.None));
connect(T0.solute,tHb. u[2]) annotation (Line(
points={{42,78},{64,78},{64,-65.7},{71,-65.7}},
color={0,0,127},
smooth=Smooth.None));
connect(R1.solute,tHb. u[3]) annotation (Line(
points={{-10,36},{64,36},{64,-65.5},{71,-65.5}},
color={0,0,127},
smooth=Smooth.None));
connect(T1.solute,tHb. u[4]) annotation (Line(
points={{44,36},{64,36},{64,-65.3},{71,-65.3}},
color={0,0,127},
smooth=Smooth.None));
connect(R2.solute,tHb. u[5]) annotation (Line(
points={{-10,-10},{64,-10},{64,-65.1},{71,-65.1}},
color={0,0,127},
smooth=Smooth.None));
connect(T2.solute,tHb. u[6]) annotation (Line(
points={{44,-10},{64,-10},{64,-64.9},{71,-64.9}},
color={0,0,127},
smooth=Smooth.None));
connect(R3.solute,tHb. u[7]) annotation (Line(
points={{-10,-54},{64,-54},{64,-64.7},{71,-64.7}},
color={0,0,127},
smooth=Smooth.None));
connect(T3.solute,tHb. u[8]) annotation (Line(
points={{44,-54},{64,-54},{64,-64.5},{71,-64.5}},
color={0,0,127},
smooth=Smooth.None));
connect(R4.solute,tHb. u[9]) annotation (Line(
points={{-10,-92},{-10,-98},{64,-98},{64,-64.3},{71,-64.3}},
color={0,0,127},
smooth=Smooth.None));
connect(T4.solute,tHb. u[10]) annotation (Line(
points={{44,-92},{44,-98},{64,-98},{64,-64.1},{71,-64.1}},
color={0,0,127},
smooth=Smooth.None));
connect(oxyR1.products[2],oxygen_unbound. q_out)
annotation (Line(
points={{-9.5,74},{-46,74},{-46,-34}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxyR2.products[2],oxygen_unbound. q_out)
annotation (Line(
points={{-9.5,32},{-46,32},{-46,-34}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxyR3.products[2],oxygen_unbound. q_out)
annotation (Line(
points={{-9.5,-14},{-46,-14},{-46,-34}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxyR4.products[2],oxygen_unbound. q_out)
annotation (Line(
points={{-9.5,-56},{-46,-56},{-46,-34}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxygen_unbound.q_out, oxyT1.products[2])
annotation (Line(
points={{-46,-34},{-46,74},{43.5,74}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxygen_unbound.q_out, oxyT2.products[2])
annotation (Line(
points={{-46,-34},{-46,32},{43.5,32}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxygen_unbound.q_out, oxyT3.products[2])
annotation (Line(
points={{-46,-34},{-46,-14},{43.5,-14}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxygen_unbound.q_out, oxyT4.products[2])
annotation (Line(
points={{-46,-34},{-46,-56},{43.5,-56}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxygen_unbound.q_out,gasSolubility. q_in) annotation (Line(
points={{-46,-34},{-66,-34},{-66,-12}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(O2_in_air.q_out,gasSolubility. q_out) annotation (Line(
points={{-66,14},{-66,6}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(clock.y,O2_in_air. partialPressure) annotation (Line(
points={{-73,54},{-66,54},{-66,34}},
color={0,0,127},
smooth=Smooth.None));
annotation ( experiment(StopTime=10000), Documentation(info=
"<html>
<p>To understand the model is necessary to study the principles of MWC allosteric transitions first published by </p>
<p>Monod,Wyman,Changeux (1965). "On the nature of allosteric transitions: a plausible model." Journal of molecular biology 12(1): 88-118.</p>
<p><br/>In short it is about binding oxygen to hemoglobin.</p>
<p>Oxgen are driven by its partial pressure using clock source - from very little pressure to pressure of 10kPa.</p>
<p>(Partial pressure of oxygen in air is the air pressure multiplied by the fraction of the oxygen in air.)</p>
<p>Hemoglobin was observed (by Perutz) in two structuraly different forms R and T.</p>
<p>These forms are represented by blocks T0..T4 and R0..R4, where the suffexed index means the number of oxygen bounded to the form.</p>
<p><br/>In equilibrated model can be four chemical reactions removed and the results will be the same, but dynamics will change a lot. ;)</p>
<p>If you remove the quaternaryForm1,quaternaryForm2,quaternaryForm3,quaternaryForm4 then the model in equilibrium will be exactly the same as in MWC article.</p>
<p><br/>Parameters was fitted to data of Severinghaus article from 1979. (For example at pO2=26mmHg is oxygen saturation sO2 = 48.27 %).</p>
</html>", revisions="<html>
<p><i>2013</i></p>
<p>Marek Matejak, Charles University, Prague, Czech Republic </p>
</html>"));
end Allosteric_Hemoglobin_MWC;
model Allosteric_Hemoglobin2_MWC
"Monod,Wyman,Changeux (1965) - The same allosteric hemoglobin model as Allosteric_Hemoglobin_MWC implemented by Speciation blocks"
import Physiolibrary.Types.*;
extends Modelica.Icons.Example;
// extends Physiolibrary.SteadyStates.Interfaces.SteadyStateSystem(
// Simulation=SimulationType.SteadyState);
// parameter GasSolubility alpha = 0.0105 * 1e-3 "oxygen solubility in plasma"; // by Siggaard Andersen: 0.0105 (mmol/l)/kPa
parameter Fraction L = 7.0529*10^6
"=[T0]/[R0] .. dissociation constant of relaxed <-> tensed change of deoxyhemoglobin tetramer";
parameter Fraction c = 0.00431555
"=KR/KT .. ration between oxygen affinities of relaxed vs. tensed subunit";
parameter Concentration KR = 0.000671946
"oxygen dissociation on relaxed(R) hemoglobin subunit"; //*7.875647668393782383419689119171e-5
//10.500001495896 7.8756465463794e-05
parameter Concentration KT=KR/c
"oxygen dissociation on tensed(T) hemoglobin subunit";
// Fraction sO2 "hemoglobin oxygen saturation";
parameter AmountOfSubstance totalAmountOfHemoglobin=0.001;
Physiolibrary.Chemical.Components.ChemicalReaction
quaternaryForm(K=L)
annotation (Placement(transformation(extent={{-4,-84},{16,-64}})));
Components.Speciation
R0_in_R(NumberOfSubunitTypes=4)
annotation (Placement(transformation(extent={{-32,-76},{-52,-56}})));
Components.Speciation
T0_in_T(NumberOfSubunitTypes=4)
annotation (Placement(transformation(extent={{68,-74},{48,-54}})));
Physiolibrary.Chemical.Components.Substance OxyRHm[4](
each Simulation=SimulationType.SteadyState,
each isDependent=true,
each solute_start=4e-19)
"Oxygenated subunit in R structure of hemoglobin tetramer"
annotation (Placement(transformation(extent={{-98,-36},{-78,-16}})));
Physiolibrary.Chemical.Components.ChemicalReaction oxygenation_R[4](each K=KR, each nP=2)
annotation (Placement(transformation(extent={{-70,-36},{-50,-16}})));
Physiolibrary.Chemical.Components.Substance DeoxyRHm[4](each Simulation=
SimulationType.SteadyState, each solute_start=4e-11)
"Deoxygenated subunit in R structure of hemoglobin tetramer"
annotation (Placement(transformation(extent={{-42,-36},{-22,-16}})));
Physiolibrary.Chemical.Components.Substance OxyTHm[4](
each Simulation=SimulationType.SteadyState,
each isDependent=true,
each solute_start=1e-14)
"Oxygenated subunit in T structure of hemoglobin tetramer"
annotation (Placement(transformation(extent={{14,-36},{34,-16}})));
Physiolibrary.Chemical.Components.ChemicalReaction oxygenation_T[4](each K=KT, each nP=2)
annotation (Placement(transformation(extent={{42,-36},{62,-16}})));
Physiolibrary.Chemical.Components.Substance DeoxyTHm[4](
each Simulation=SimulationType.SteadyState,
each solute_start=0.00025)
"Deoxygenated subunit in T structure of hemoglobin tetramer"
annotation (Placement(transformation(extent={{70,-36},{90,-16}})));
Physiolibrary.Chemical.Components.Substance
oxygen_unbound(Simulation=SimulationType.SteadyState, solute_start=0.000001
*7.875647668393782383419689119171e-5)
annotation (Placement(transformation(extent={{-4,-2},{16,18}})));
Modelica.Blocks.Sources.Clock clock(offset=60)
annotation (Placement(transformation(extent={{-40,74},{-20,94}})));
Modelica.Blocks.Math.Add add[4] annotation (Placement(transformation(
extent={{-4,-4},{4,4}},
rotation=270,
origin={-66,-54})));
Modelica.Blocks.Math.Add add1[4] annotation (Placement(transformation(
extent={{-4,-4},{4,4}},
rotation=270,
origin={44,-54})));
Sources.UnlimitedGasStorage oxygen_in_air(
Simulation=Physiolibrary.Types.SimulationType.SteadyState,
usePartialPressureInput=true,
T=310.15) annotation (
Placement(transformation(
extent={{-10,-10},{10,10}},
rotation=270,
origin={6,60})));
Components.GasSolubility
partialPressure1( kH_T0(displayUnit="(mmol/l)/kPa at 25degC")=
0.026029047188736, T=310.15) annotation (Placement(
transformation(
extent={{-10,-10},{10,10}},
origin={6,32})));
SteadyStates.Components.MolarConservationLaw totalHb(
Simulation=Physiolibrary.Types.SimulationType.SteadyState,
Total(displayUnit="mol") = totalAmountOfHemoglobin,
n=2)
annotation (Placement(transformation(extent={{70,-92},{90,-72}})));
Modelica.Blocks.Math.Sum sum1(nin=8, k=(1/4)*ones(8))
annotation (Placement(transformation(
extent={{-4,-4},{4,4}},
rotation=270,
origin={-74,-82})));
Modelica.Blocks.Math.Division sO2_ "hemoglobin oxygen saturation"
annotation (Placement(transformation(extent={{-64,-96},{-54,-86}})));
equation
// totalAmountOfHemoglobin*normalizedState[1] = sum(OxyRHm.solute) + sum(DeoxyRHm.solute) + sum(OxyTHm.solute) + sum(DeoxyTHm.solute);
// sO2 = (sum(OxyRHm.solute) + sum(OxyTHm.solute))/totalAmountOfHemoglobin;
connect(R0_in_R.species, quaternaryForm.substrates[1])
annotation (Line(
points={{-52,-74},{-4,-74}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(quaternaryForm.products[1], T0_in_T.species)
annotation (Line(
points={{16,-74},{32,-74},{32,-72},{48,-72}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(OxyTHm.q_out, oxygenation_T.substrates[1])
annotation (Line(
points={{24,-26},{42,-26}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxygenation_T.products[1], DeoxyTHm.q_out)
annotation (Line(
points={{62,-26.5},{72,-26.5},{72,-26},{80,-26}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(OxyTHm.solute, add1.u2) annotation (Line(
points={{24,-36},{24,-42},{41.6,-42},{41.6,-49.2}},
color={0,0,127},
smooth=Smooth.Bezier));
connect(add1.u1, DeoxyTHm.solute) annotation (Line(
points={{46.4,-49.2},{46.4,-42},{80,-42},{80,-36}},
color={0,0,127},
smooth=Smooth.Bezier));
connect(partialPressure1.q_out, oxygen_in_air.q_out)
annotation (Line(
points={{6,42},{6,50}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(partialPressure1.q_in, oxygen_unbound.q_out) annotation (Line(
points={{6,24},{6,8}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(clock.y, oxygen_in_air.partialPressure) annotation (Line(
points={{-19,84},{6,84},{6,70}},
color={0,0,127},
smooth=Smooth.None));
connect(add.y, R0_in_R.totalSubunitAmount) annotation (Line(
points={{-66,-58.4},{-66,-66},{-50,-66}},
color={0,0,127},
smooth=Smooth.Bezier));
connect(OxyRHm.solute, add.u2) annotation (Line(
points={{-88,-36},{-88,-44},{-68.4,-44},{-68.4,-49.2}},
color={0,0,127},
smooth=Smooth.Bezier));
connect(DeoxyRHm.solute, add.u1) annotation (Line(
points={{-32,-36},{-32,-36},{-32,-44},{-63.6,-44},{-63.6,-50},{
-63.6,-49.2}},
color={0,0,127},
smooth=Smooth.Bezier));
connect(OxyRHm.q_out, oxygenation_R.substrates[1]) annotation (Line(
points={{-88,-26},{-70,-26}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(DeoxyRHm.q_out, R0_in_R.subunitSpecies) annotation (Line(
points={{-32,-26},{-42,-26},{-42,-56}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxygenation_R.products[1], DeoxyRHm.q_out) annotation (Line(
points={{-50,-26.5},{-42,-26.5},{-42,-26},{-32,-26}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxygenation_R[1].products[2], oxygen_unbound.q_out) annotation (Line(
points={{-50,-25.5},{-36,-25.5},{-36,12},{6,12},{6,8}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxygenation_R[2].products[2], oxygen_unbound.q_out) annotation (Line(
points={{-50,-25.5},{-36,-25.5},{-36,12},{6,12},{6,8}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxygenation_R[3].products[2], oxygen_unbound.q_out) annotation (Line(
points={{-50,-25.5},{-36,-25.5},{-36,12},{6,12},{6,8}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxygenation_R[4].products[2], oxygen_unbound.q_out) annotation (Line(
points={{-50,-25.5},{-36,-25.5},{-36,12},{6,12},{6,8}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxygenation_T[1].products[2], oxygen_unbound.q_out) annotation (Line(
points={{62,-25.5},{78,-25.5},{78,8},{6,8}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxygenation_T[2].products[2], oxygen_unbound.q_out) annotation (Line(
points={{62,-25.5},{78,-25.5},{78,8},{6,8}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxygenation_T[3].products[2], oxygen_unbound.q_out) annotation (Line(
points={{62,-25.5},{78,-25.5},{78,8},{6,8}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(oxygenation_T[4].products[2], oxygen_unbound.q_out) annotation (Line(
points={{62,-25.5},{78,-25.5},{78,8},{6,8}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(T0_in_T.subunitSpecies, DeoxyTHm.q_out)
annotation (Line(
points={{58,-54},{84,-54},{84,-26},{80,-26}},
color={107,45,134},
thickness=1,
smooth=Smooth.None));
connect(add1.y, T0_in_T.totalSubunitAmount)
annotation (Line(
points={{44,-58.4},{44,-64},{50,-64}},
color={0,0,127},
smooth=Smooth.Bezier));
connect(R0_in_R.totalSubsystemAmount, totalHb.fragment[1]) annotation (Line(
points={{-42,-74},{-42,-87},{70,-87}},
color={0,0,127},
smooth=Smooth.Bezier));
connect(T0_in_T.totalSubsystemAmount, totalHb.fragment[2]) annotation (Line(
points={{58,-72},{58,-72},{58,-85},{70,-85}},
color={0,0,127},
smooth=Smooth.Bezier));
connect(OxyRHm.solute, sum1.u[1:4]) annotation (Line(
points={{-88,-36},{-86,-36},{-86,-72},{-74,-72},{-74,-77.2},{-74.1,
-77.2}},
color={0,0,127},
smooth=Smooth.Bezier));
connect(OxyTHm.solute, sum1.u[5:8]) annotation (Line(
points={{24,-36},{24,-70},{-73.3,-70},{-73.3,-77.2}},
color={0,0,127},
smooth=Smooth.Bezier));
connect(sO2_.u1, sum1.y) annotation (Line(
points={{-65,-88},{-74,-88},{-74,-86.4}},
color={0,0,127},
smooth=Smooth.Bezier));
connect(totalHb.totalAmountOfSubstance, sO2_.u2) annotation (Line(
points={{90,-86},{96,-86},{96,-100},{-80,-100},{-80,-94},{-65,-94}},
color={0,0,127},
smooth=Smooth.Bezier));
annotation (Diagram(coordinateSystem(preserveAspectRatio=false, extent={{-100,
-100},{100,100}}), graphics={Ellipse(
extent={{2,-6},{100,-54}},
fillColor={255,181,181},
fillPattern=FillPattern.Solid,
pattern=LinePattern.None), Ellipse(
extent={{-104,-6},{-6,-54}},
fillColor={255,181,181},
fillPattern=FillPattern.Solid,
pattern=LinePattern.None)}),
experiment(StopTime=10000),
Documentation(revisions=
"<html>
<p><i>2013</i></p>
<p>Marek Matejak, Charles University, Prague, Czech Republic </p>
</html>", info="<html>
<p>To understand the model is necessary to study the principles of MWC allosteric transitions first published by </p>
<p>Monod,Wyman,Changeux (1965). "On the nature of allosteric transitions: a plausible model." Journal of molecular biology 12(1): 88-118.</p>
<p><br>In short it is about binding oxygen to hemoglobin.</p>
<p>Oxgen are driven by its partial pressure using clock source - from very little pressure to pressure of 10kPa.</p>
<p>(Partial pressure of oxygen in air is the air pressure multiplied by the fraction of the oxygen in air.)</p>
<p>Hemoglobin was observed (by Perutz) in two structuraly different forms R and T.</p>
<p>These forms are represented by blocks T0..T4 and R0..R4, where the suffexed index means the number of oxygen bounded to the form.</p>
<p><br>In equilibrated model can be four chemical reactions removed and the results will be the same, but dynamics will change a lot. ;)</p>
<p>If you remove the quaternaryForm1,quaternaryForm2,quaternaryForm3,quaternaryForm4 then the model in equilibrium will be exactly the same as in MWC article.</p>
<p><br>Parameters was fitted to data of Severinghaus article from 1979. (For example at pO2=26mmHg is oxygen saturation sO2 = 48.27 %).</p>
</html>"));
end Allosteric_Hemoglobin2_MWC;
end Hemoglobin;