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# HbO2_HbCO2_diss

Blood HbO2 and HbCO2 Dissociation Curves at Varied O2, CO2, pH, 2,3-DPG and Temperature Levels. Based directly on Dash et al. 2010 errata reprint.

Model number: 0149

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## Description

``` ABSTRACT: New mathematical model equations for O2 and CO2 saturations of hemoglobin (SHbO2 and SHbCO2)
are developed here from the equilibrium binding of O2 and CO2 with hemoglobin inside RBCs.
They are in the form of an invertible Hill-type equation with the apparent Hill coefficients
KHbO2 and KHbCO2 in the expressions for SHbO2 and SHbCO2 dependent on the levels of O2 and CO2
partial pressures (PO2 and PCO2), pH, 2,3-DPG concentration, and temperature in blood.
The invertibility ofmol2ml these new equations allows PO2 and PCO2 to be computed efficiently from
SHbO2 and SHbCO2 and vice-versa. The oxyhemoglobin (HbO2) and carbamino-hemoglobin (HbCO2)
dissociation curves computed from these equations are in good agreement with the published
experimental and theoretical curves in the literature. The model solutions describe that,
at standard physiological conditions, the hemoglobin is about 97.2% saturated by O2 and the
amino group of hemoglobin is about 13.1% saturated by CO2. The O2 and CO2 content in whole blood
are also calculated here from the gas solubilities, hematocrits, and the new formulas for SHbO2
and SHbCO2. Because of the mathematical simplicity and invertibility, these new formulas can be
conveniently used in the modeling of simultaneous transport and exchange of O2 and CO2 in the
alveoli-blood and blood-tissue exchange systems.

The equations for O2 and CO2 saturations of hemoglobin (SHbO2 and SHbCO2)
are derived by considering the various kinetic reactions involving the
binding of O2 and CO2 with hemoglobin in RBCs:

kf1p       K1dp
1. CO2+H2O <--> H2CO3 <--> HCO3- + H+;  K1=(kf1p/kb1p)*K1dp
kb1p		K1 = 7.43e-7 M, K1dp = 5.5e-4 M

kf2p          K2dp
2. CO2+HbNH2 <--> HbNHCOOH <--> HbNHCOO- + H+;  K2=(kf2p/kb2p)*K2dp
kb2p		K2 = 2.95e-5, K2dp = 1.0e-6 M

kf3p            K3dp
3. CO2+O2HbNH2 <--> O2HbNHCOOH <--> O2HbNHCOO- + H+; K3=(kf3p/kb3p)*K3dp
kb3p		K3 = 2.51e-5, K3dp = 1.0e-6 M

kf4p
4. O2+HbNH2 <--> O2HbNH2;  K4p=K4dp*func([O2],[H+],[CO2],[DPG],T)
kb4p		K4dp and K4p are to be determined

func = ([O2]/[O2]s)^n0*([H+]s/[H+])^n1*([CO2]s/[CO2])^n2*
([DPG]s/[DPG])^n3*(Temps/Temp)^n4

K5dp
5. HbNH3+ <--> HbNH2 + H+;  K5 = 2.63e-8 M

K6dp
6. O2HbNH3+ <--> O2HbNH2 + H+;  K6 = 1.91e-9 M

The association and dissociation rate constants of O2 with hemoglobin is
assumed to be dependent on [O2], [H+], [CO2], [DPG] and temperature (Temp)
such that the equilibrium constant K4p is proportional to ([O2]/[O2]s)^n0,
([H+]s/[H+])^n1, ([CO2]s/[CO2])^n2, ([DPG]s/[DPG])^n3, and (Temps/Temp)^n4.
The problem is to estimate the values of the proportionality constant K4dp
and the indices n0, n1, n2, n3 and n4 such that SHbO2 is 50% at pO2 = 26.8
mmHg, pH = 7.24, pCO2 = 40 mmHg, [DPG] = 4.65 mM and Temp = 37 C in RBCs
and the HbO2 dissociation curve shifts appropriately w.r.t. pH and pCO2.

```
Oxygen dissociation curves at varying pH: ## Equations

The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.