Model of the pH-dependence of the concentrations of complexes involving metabolites, haemoglobin and magnesium ions in the human erythrocyte

Abstract

The rate of glucose consumption and the concentrations of glycolytic intermediates in human erythrocytes have long been known to be pH sensitive. Despite the extensive literature on modelling erythrocyte metabolism, no model developed so far can adequately describe all of these pH-dependent changes. None of these models have included all the significant association reactions between metabolites, Hb and Mg2+ that will influence metabolism. As part of a larger enterprise to develop a detailed model of erythrocyte glycolysis, we present a sub-model which predicts, as a function of pH and oxygenation state, the concentrations of free and Mg2+-bound metabolites that are substrates, co-factors and effecters of glycolysis. This model shows that pH changes around physiological values can cause large changes in the distribution of metabolites between free, bound and Mg2+-complexed forms, based on binding interactions alone; in oxygenated cells, at pH 7.2-7.6, many glycolytic intermediates undergo changes in concentration of 50-100%. The model also predicts intracellular concentrations of free Mg2+ in erythrocytes to be 0.4 mM and 0.64 mM in oxygenated and deoxygenated cells, respectively, assuming a total magnesium concentration of 3 mM (~88% of the total magnesium usually found in erythrocytes). This is in close agreement with the values found by Flatman [Flatman, P.W. (1980) J. Physiol. 300, 19-30] and the finding by Flatman and Lew [Flatman, P. and Lew, V.L. (1977) Nature 267, 360-362] that the main Mg2+ buffer systems bind ~90% of Mg2+ in the cell. Hexokinase has a high 'flux control coefficient' in human erythrocyte glycolysis, so the dependence of its rate on the pH and oxygenation state of haemoglobin is important. With a low oxygen tension and an intracellular pH of 7.34, the major inhibitor of its activity (2,3-bisphosphoglycerate) is 85% bound to either haemoglobin or Mg2+, and the maximum possible flux of substrata via it would be 2.05 mmol L erythrocytes-1 h-1. However, if the haemoglobin were saturated with oxygen, and the pH were 7.2, it was calculated that the maximum rate would be 1.48 mmol L erythrocytes-1 h-1; this is primarily due to a doubling of the free 2,3-bisphosphoglycerate concentration. However, the full extent of the inhibition is counteracted because the concentration of the Mg2+-2,3-bisphosphoglycerate would be approximately doubled. Many other similar comparisons are possible with this new model, which highlights the complex network of interactions between haemoglobin, Mg2+, H+ and the metabolites as substrates and effecters of the glycolytic reactions.