Mathematical Modelling of the Role of Intra- and Extracellular Activity of Carbonic Anhydrase and Membrane Permeabilities of HCO₃, H₂O and CO₂ in ¹⁸O Exchange

Abstract

Numerical simulation of ¹⁸O exchange between CO₂, H₂O and HCO₃ ⁻ explains the ratio mass 46/mass 44 (=C¹⁸O¹⁶O/C¹⁶O₂) measured by mass spectrometry to approximately 1% relative mean difference. In the presence of intact red blood cells the reaction takes place extra- and intracellularly at different reaction rates. Because CO₂ hydration/dehydration is accelerated intracellularly by carbonic anhydrase, a difference in intra- and extracellular concentration of labelled reactants occurs. The ensuing transfer of reactants across the cell membrane depends on their membrane permeabilities which are approximately P_{CO 2} ≅ 2 cm/s, P_{H 2 O} ≅ 0.002 cm/s and P_{HCO 3} ≅ 0.00015 cm/s (values from the literature). We found that the numerical simulation is affected most by P_{HCO 3} . The influence of the other permeabilities is at least ten times less. Therefore within the range of normal literature values, P_{HCO 3} is the only permeability that has a rate limiting effect on ¹⁸O exchange. This is why, in turn, P_{HCO 3} can be derived from an experimentally determined time course of mass 46/mass 44 by a fitting procedure. Another crucial parameter that can be estimated from the experimental results is the intraerythrocytic carbonic anhydrase activity A_i .

Key Words:

• Carbonic anhydrase
• differential equations
• Erythrozytes
• isotopes exchange
• mathematical modelling
• oxygen 18