Adair-based hemoglobin equilibrium with oxygen, carbon dioxide and hydrogen ion activity

Abstract

As has been known for over a century, oxygen binding onto hemoglobin is influenced by the activity of hydrogen ions (H⁺), as well as the concentration of carbon dioxide (CO₂). As is also known, the binding of both CO₂and H⁺ on terminal valine-1 residues is competitive. One-parametric situations of these hemoglobin equilibria at specific levels of H⁺, O₂or CO₂are also well described. However, we think interpolating or extrapolating this knowledge into an 'empirical' function of three independent variables has not yet been completely satisfactory. We present a model that integrates three orthogonal views of hemoglobin oxygenation, titration, and carbamination at different temperatures. The model is based only on chemical principles, Adair's oxygenation steps and Van't Hoff equation of temperature dependences. Our model fits the measurements of the Haldane coefficient and CO₂hemoglobin saturation. It also fits the oxygen dissociation curve influenced by simultaneous changes in H⁺, CO₂and O₂, which makes it a strong candidate for integration into more complex models of blood acid-base with gas transport, where any combination of mentioned substances can appear.

Simple accurate mathematical models of blood HbO2 and HbCO2 dissociation curves at varied physiological conditions: evaluation and comparison with other models

“…3). A new model recently published by Mateják et al (2015), while this article was under preparation, also fits some of these experimental data well under altered physiological conditions. Their approach, a modification of Adair’s four-step algorithm (Adair, 1925), considers the problems in depth, and, like ours, relates the O 2 -Hb and CO 2 -Hb binding effects to the acid-base chemistry of blood based on pH and P CO2 , as proposed by Siggaard-Andersen and others over the years (Rossi-Bernardi & Roughton, 1967; Forster et al , 1968; Siggaard-Andersen, 1971; Siggaard-Andersen & Salling, 1971; Bauer & Schroder, 1972; Siggaard-Andersen et al , 1972a; Siggaard-Andersen et al , 1972b; Siggaard-Andersen & Garby, 1973; Siggaard-Andersen et al , 1984; Siggaard-Andersen & Siggaard-Andersen, 1990).…”

“…The recent model of Mateják et al (2015), based on their version of the Adair equation (1925), is reported to fit well, the data of Severinghaus and colleagues (Roughton et al , 1972; Roughton & Severinghaus, 1973; Severinghaus, 1979), and is also shown to fit the temperature and pH-dependent S HbO2 data of Reeves (1980) and Naeraa (1963), and carbaminohemoglobin data of Bauer and Schröder (1972) and Matthew (1977). Our present S HbO2 and S HbCO2 models fit these diverse data sets as accurately, and also fit the P CO2 , pH, and temperature-dependent data of Joels and Pugh (1958) and Hlastala et al (1977), which were not used by Mateják et al (18).…”

“…Iterative approaches are generally used for this. The Appendix provides fixed-point and quasi-Newton-Raphson iterative methods that would also be applicable to the models of Mateják et al (2015) and others that are not analytically invertible.…”

“…On the other hand, an increase in O 2 partial pressure ( P O2 ) in pulmonary capillaries results in the release of hydrogen ions (H + ) from Hb, which in turn decreases the affinity of Hb for CO 2 , reducing HbCO 2 saturation ( S HbCO2 ) and aiding elimination of CO 2 by the lungs (the Haldane effect). Thus, both the Bohr and Haldane effects are important in defining the Hb-mediated nonlinear biochemical O 2 -CO 2 interactions inside RBCs (Siggaard-Andersen & Garby, 1973; Tyuma, 1984; Matejak et al , 2015). Raising blood temperature ( T ) also lowers the affinity of O 2 for Hb, and increases the delivery of O 2 to tissues.…”

Efficient sampling for polynomial chaos‐based uncertainty quantification and sensitivity analysis using weighted approximate Fekete points

“…These factors influence P 50 either directly or indirectly through each other. Many groups have studied these factors to create models capturing each parameter's influence on P 50 40,41,43‐46 . These groups have assessed the effect of these parameters as well as their synergistic effects using experimental data and computational methods in order to model transport and exchange of oxygen in the lungs and tissue 47 .…”