Derivation of Theoretical Equations of the CO₂ Dissociation Curve and the Carbamate Fraction in the Haldane Effect

Abstract

The simultaneous Henderson-Hasselbalch equations in plasma and red cell were solved in order to obtain the CO₂ dissociation curve of oxygenated blood. In order to solve the above two equations the following equation was added, in which the relationship between the intracellular (ΔpHC) and the extracellular pH change (ΔpHP) was defined as follows: pHC=(1+σ)ΔpHP, where 1+σ is a factor to be determined from experimental data on Donnan's ratio for H⁺. From the solution, the ratio of bicarbonate shift to the CO₂ quantity released out of or combined with hemoglobin was calculated. The solution was validated by comparing the above ratio between the theoretical and experimental data. The CO₂ contents calculated at 12Torr in whole blood, red cell, and plasma compartments show good agreement with the respective analyzed values. When the buffer values of hemoglobin and plasma buffer protein were 70.0 and 7.5mmol/ (liter plasma•pH), respectively, σ=-0.21+0.05•ΔpHP, and the Donnan's ratio for HCO3- was assumed to be 0.7 at pH=7.33, the theoretical CO₂ dissociation curve fitted well with the experimental curve. The CO₂ dissociation curve of deoxygenated blood was expressed by adding the measured Haldane effect to the CO₂ content of oxygenated blood. This additive characteristic in turn made it possible to estimate carbamate contribution in the Haldane effect.