Over the last 25 years, several mathematical models of erythrocyte metabolism have been developed. Although these models have identified the key features in the regulation and control of erythrocyte metabolism, many important aspects remain unexplained. In particular, none of these models have satisfactorily accounted for 2,3-bisphosphoglycerate (2,3-BPG) metabolism. 2,3-BPG is an important modulator of haemoglobin oxygen affinity, and hence an understanding of the regulation of 2,3-BPG concentration is important for understanding blood oxygen transport. A detailed, comprehensive, and hence realistic mathematical model of erythrocyte metabolism is presented that can explain the regulation and control of 2,3-BPG concentration and turnover. The model is restricted to the core metabolic pathways, namely glycolysis, the 2,3-BPG shunt and the pentose phosphate pathway (PPP), and includes membrane transport of metabolites, the binding of metabolites to haemoglobin and Mg(2+), as well as pH effects on key enzymic reactions and binding processes. The model is necessarily complex, since it is intended to describe the regulation and control of 2,3-BPG metabolism under a wide variety of physiological and experimental conditions. In addition, since H(+) and blood oxygen tension are important external effectors of 2,3-BPG concentration, it was important that the model take into account the large array of kinetic and binding phenomena that result from changes in these effectors. Through an iterative loop of experimental and simulation analysis many values of enzyme-kinetic parameters of the model were refined to yield close conformity between model simulations and 'real' experimental data. This iterative process enabled a single set of parameters to be found which described well the metabolic behaviour of the erythrocyte under a wide variety of conditions.

This is the first in a series of three papers [see also Mulquiney and Kuchel (1999) Biochem. J. 342, 579-594; Mulquiney and Kuchel (1999) Biochem. J. 342, 595-602] that present a detailed mathematical model of erythrocyte metabolism which explains the regulation and control of 2,3-bisphosphoglycerate (2,3-BPG) metabolism. 2,3-BPG is a modulator of haemoglobin oxygen affinity and hence plays an important role in blood oxygen transport and delivery. This paper presents an in vivo kinetic characterization of 2,3-BPG synthase/phosphatase (BPGS/P), the enzyme that catalyses both the synthesis and degradation of 2,3-BPG. Much previous work had indicated that the behaviour of this enzyme in vitro is markedly different from that in vivo. (13)C and (31)P NMR were used to monitor the time courses of selected metabolites when erythrocytes were incubated with or without [U-(13)C]glucose. Simulations of the experimental time courses were then made. By iteratively changing the parameters of the BPGS/P part of the model until a good match between the NMR-derived data and simulations were achieved, it was possible to characterize BPGS/P kinetically in vivo. This work revealed that: (1) the pH-dependence of the synthase activity results largely from a strong co-operative inhibition of the synthase activity by protons; (2) 3-phosphoglycerate and 2-phosphoglycerate are much weaker inhibitors of 2,3-BPG phosphatase in vivo than in vitro; (3) the K(m) of BPGS/P for 2,3-BPG is significantly higher than that measured in vitro; (4) the maximal activity of the phosphatase in vivo is approximately twice that in vitro, when P(i) is the sole activator (second substrate); and (5) 2-phosphoglycollate appears to play no role in the activation of the phosphatase in vivo. Using the newly determined kinetic parameters, the percentage of glycolytic carbon flux that passes through the 2, 3-BPG shunt in the normal in vivo steady state was estimated to be 19%.

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This is the third of three papers [see also Mulquiney, Bubb and Kuchel (1999) Biochem. J. 342, 565-578; Mulquiney and Kuchel (1999) Biochem. J. 342, 579-594] for which the general goal was to explain the regulation and control of 2,3-bisphosphoglycerate (2,3-BPG) metabolism in human erythrocytes. 2,3-BPG is a major modulator of haemoglobin oxygen affinity and hence is vital in blood oxygen transport. A detailed mathematical model of erythrocyte metabolism was presented in the first two papers. The model was refined through an iterative loop of experiment and simulation and it was used to predict outcomes that are consistent with the metabolic behaviour of the erythrocyte under a wide variety of experimental and physiological conditions. For the present paper, the model was examined using computer simulation and Metabolic Control Analysis. The analysis yielded several new insights into the regulation and control of 2,3-BPG metabolism. Specifically it was found that: (1) the feedback inhibition of hexokinase and phosphofructokinase by 2, 3-BPG are equally as important as the product inhibition of 2,3-BPG synthase in controlling the normal in vivo steady-state concentration of 2,3-BPG; (2) H(+) and oxygen are effective regulators of 2,3-BPG concentration and that increases in 2,3-BPG concentrations are achieved with only small changes in glycolytic rate; (3) these two effectors exert most of their influence through hexokinase and phosphofructokinase; (4) flux through the 2,3-BPG shunt changes in absolute terms in response to different energy demands placed on the cell. This response of the 2,3-BPG shunt contributes an [ATP]-stabilizing effect. A 'cost' of this is that 2, 3-BPG concentrations are very sensitive to the energy demand of the cell and; (5) the flux through the 2,3-BPG shunt does not change in response to different non-glycolytic demands for NADH.

Over the last 25 years, several mathematical models of erythrocyte metabolism have been developed. Although these models have identified the key features in the regulation and control of erythrocyte metabolism, many important aspects remain unexplained. In particular, none of these models have satisfactorily accounted for 2,3-bisphosphoglycerate (2,3-BPG) metabolism. 2,3-BPG is an important modulator of haemoglobin oxygen affinity, and hence an understanding of the regulation of 2,3-BPG concentration is important for understanding blood oxygen transport. A detailed, comprehensive, and hence realistic mathematical model of erythrocyte metabolism is presented that can explain the regulation and control of 2,3-BPG concentration and turnover. The model is restricted to the core metabolic pathways, namely glycolysis, the 2,3-BPG shunt and the pentose phosphate pathway (PPP), and includes membrane transport of metabolites, the binding of metabolites to haemoglobin and Mg# + , as well as pH effects on key enzymic reactions and binding processes. The