The basic flow equations of electrophysiology in the presence of chemical reactions: II. A practical application concerning the pH and voltage effects accompanying the diffusion of O2 through hemoglobin solution

Previous papers by F. M. Snell (Jour. Theor. Biol.,8, 469–479, 1965) and M. A. Fox and H. D. Landahl (Bull. Math. Biophysics,27, Spec. Issue, 183–190, 1965) have found that the formulation by previous authors for the oxygen flow rates through hemoglobin solution as a function of pressure determined by E. Hemmingsen and P. F. Scholander (Science,132, 1379–1381, 1960) did not give a satisfactory quantitative fit of the curve for constant pressure difference. The suggestion of Fox and Landahl that the Bohr effect involving the shift in acidity accompanying the oxidation of Hb should give rise to voltage and pH differences in oxyhemoglobin transport is examined in more detail. In this paper, the previous expressions for the total oxygen flow rate in terms of the end point concentrations are extended to include the effects of the electrical field. Estimates of the potential difference shows it to be negligible. A derivation of a voltage-pH relation shows that the Nernst relation does not apply and a negligible voltage difference does not preclude a pH shift which is the more probable explanation of the discrepancies observed. Several other predictions suitable for experimental testing are made.