A Mathematical Model for the Influence of Anionic Effectors on the Phosphofructokinase from Rat Erythrocytes

Abstract

The influence of the positive effectors AMP, sulphate, glucose 1,6-bisphosphate and the negative effector 2,3-bisphosphoglycerate on rat erythrocyte phosphofructokinase has been investigated. The kinetic data have been fitted to the Monod-Wyman-Changeux model as well as to a model based on a closed association-dissociation equilibrium. The application of the fitting procedure yields for both models a good correspondence between theoretical and experimental data and equal results with respect to the action of the effectors on the enzyme. The corresponding dissociation constants for the binding of the positive effectors to the active state are: AMP 35 pM, sulphate 0.43 mM and glucose 1,6-bisphosphate 15 pM. 2,3-Bisphosphoglycerate as an inhibitor stabilizes the inactive state (dissociation constant: 1.4 mM).A preliminary discrimination between the Monod-Wyman-Changeux model and the associationdissociation model has been attempted.Phosphofructokinase activity is regulated by a large number of positive arid negative effectors. Under intracellular conditions only some of them are of regulatory importance [l, 21. An application of the results obtained from kinetic studies on phosphofructokinase to intracellular conditions requires a mathematical description of the kinetic data. In a previous paper a mathematical model for the influence of the substrates and cationic effectors on rat erythrocyte phosphofructokinase was described [3]. It is the aim of this work to present a kinetic model for the action of anionic effectors such as AMP, glucose 1,6-bisphosphate, sulphate and 2,3-bisphosphoglycerate on this enzyme. Only those effectors were chosen whose concentration in the red blood cell would lead to a significant kinetic effect. Sulphate was used instead of phosphate in order to avoid complex formation of the latter with divalent cations. In their kinetic behaviour both ions closely resemble each other [4].

The Regulation of Cellular Systems

“…This can be seen, for example, when calculating the relaxation time of the hexokinase-phosphofructokinase system in glycolysis (about 1.5 h in human erythrocytes), which exceeds the values for the particular enzymes given above, due to the glucose-6-phosphate inhibition of hexokinase (Heinrich et al, 1977).…”

“…The corresponding nonlinearities in the rate equations make the stability analysis rather cumbersome despite the fact that other nonlinearities resulting from allosteric interactions have not been included (cf. also Heinrich et at., 1977).…”

“…Schuster et aI., 1992). Furthermore, in many biochemical models, even the net rates of some reactions are practically restricted to be non-negative, notably when they are quasi-irreversible, that is, when the forward reaction is much faster than the backward reaction (Heinrich et al, 1977;Leiser and Blum, 1987;Joshi and Palsson, 1989a) or when this is implied by the biological function of the pathway (e.g., ATP production by glycolysis).…”

“…For bisphosphoglycerate mutase, Heinrich et al (1977) calculated the relaxation time of 3.9 s. The difference to the value given above results from consideration of the inhibition by 2,3P 2 G. For pyruvate kinase (EC 2.7.1.40), hexokinase (EC 2.7.1.1), and phosphofructokinase (EC 2.7.1.11), relaxation times of 28 s, 36 min, and 74 s, respectively, were calculated. Accordingly, the relaxation time constants of the glycolytic enzymes in human erythrocytes cover at least a range of four orders of magnitude, let alone the enzymes so fast as to be near equilibrium, for which the time constants are very low and difficult to measure or calculate.…”

“…The wide separation of time constants is often called time hierarchy (Park, 1974;Reich and Selkov, 1975;Heinrich et al, 1977). Hierarchic organization is a striking feature of living matter in general.…”