modelAllosteric_Hemoglobin2_MWC

Monod,Wyman,Changeux (1965) - The same allosteric hemoglobin model as Allosteric_Hemoglobin_MWC implemented by Speciation blocks
Diagram of Allosteric_Hemoglobin2_MWCOpen the diagram
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Information

Before silumation in "Dymola 2014 FD01" please chose "Euler" method!


To understand the model is necessary to study the principles of MWC allosteric transitions first published by

[1] Monod,Wyman,Changeux (1965). "On the nature of allosteric transitions: a plausible model." Journal of molecular biology 12(1): 88-118.


In short it is about binding oxygen to hemoglobin.

Oxgen are driven by its partial pressure using clock source - from very little pressure to pressure of 10kPa.

(Partial pressure of oxygen in air is the air pressure multiplied by the fraction of the oxygen in air.)

Hemoglobin was observed (by Perutz) in two structuraly different forms R and T.

These forms are represented by blocks T0..T4 and R0..R4, where the suffexed index means the number of oxygen bounded to the form.


In equilibrated model can be four chemical reactions removed and the results will be the same, but dynamics will change a lot. ;)

If you remove the quaternaryForm1,quaternaryForm2,quaternaryForm3,quaternaryForm4 then the model in equilibrium will be exactly the same as in MWC article.


Parameters was fitted to data of Severinghaus article from 1979. (For example at pO2=26mmHg is oxygen saturation sO2 = 48.27 %).

Parameters

TypeNameDefaultDescription
Types.MolarEnergydHT10000Enthalpy of heme oxygenation in T hemoglobin form
Types.MolarEnergydHR20000Enthalpy of heme oxygenation in R hemoglobin form
Types.MolarEnergydHL-1000Enthalpy of reaction T->R as hemoglobin tetramer structure change
Types.FractionL7.0529*10^6=[T0]/[R0] .. dissociation constant of relaxed <-> tensed change of deoxyhemoglobin tetramer
Types.Fractionc0.00431555=KR/KT .. ration between oxygen affinities of relaxed vs. tensed subunit
Types.ConcentrationKR0.000671946oxygen dissociation on relaxed(R) hemoglobin subunit
Types.ConcentrationKTKR/coxygen dissociation on tensed(T) hemoglobin subunit
Types.AmountOfSubstancetotalAmountOfHemoglobin1

Components

TypeNameDefaultDescription
Components.ChemicalReactionquaternaryForm
Components.SpeciationR0_in_R
Components.SpeciationT0_in_T
Components.Substance[4]OxyRHmOxygenated subunit in R structure of hemoglobin tetramer
Components.ChemicalReaction[4]oxygenation_R
Components.Substance[4]DeoxyRHmDeoxygenated subunit in R structure of hemoglobin tetramer
Components.Substance[4]OxyTHmOxygenated subunit in T structure of hemoglobin tetramer
Components.ChemicalReaction[4]oxygenation_T
Components.Substance[4]DeoxyTHmDeoxygenated subunit in T structure of hemoglobin tetramer
Components.Substanceoxygen_unbound
Modelica.Blocks.Sources.ContinuousClockclock
Modelica.Blocks.Math.Add[4]add
Modelica.Blocks.Math.Add[4]add1
Sources.UnlimitedGasStorageoxygen_in_air
Components.GasSolubilitypartialPressure1
SteadyStates.Components.MolarConservationLawtotalHb
Modelica.Blocks.Math.Sumsum1
Modelica.Blocks.Math.DivisionsO2_hemoglobin oxygen saturation
Modelica.Blocks.Math.SuminternalHeathemoglobin enthalpy heat
Modelica.Blocks.Math.Add[4]add2
Modelica.Blocks.Math.Add[4]add3

Revisions

2013

Marek Matejak, Charles University, Prague, Czech Republic