# HbO2_HbCO2_diss

Blood HbO2 and HbCO2 Dissociation Curves at Varied O2, CO2, pH, 2,3-DPG and Temperature Levels.

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 of 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:

Dash and Bassingthwaighte 2010 pdf

## 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.

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## References

Dash RK and Bassingthwaighte JB. Erratum to: Blood HbO2 and HbCO2 dissociation curves at varied O2, CO2, pH, 2,3-DPG and Temperature Levels. Ann Biomed Eng 38(4): 1683-1701, 2010. Dash, R.K. and Bassingwaighte, J.B., Simultaneous Blood-Tissue Exchange of Oxygen, Carbon Dioxide, Bicarbonate, and Hydrogen Ion, Ann Biomed Eng, Vol 34:7 (Jul 2006) pp.1129-1148.

## Related Models

- Arterial flow with O2, CO2, HCO3- and H+ exchange (Model #0074)
- Fahraeus effect (#0138)
- HbO2 and HbCO2 dissociation (This model)
- Blood-tissue exchange of O2, CO2, HCO3- and H+ (#0134)

## Key Terms

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## Model History

Get Model history in CVS.## Acknowledgements

Please cite **www.physiome.org** in any publication for which this software is used and send one reprint to the address given below:

The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

[This page was last modified 02Nov16, 2:33 pm.]

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