Use of Mathematical Models for Predicting the Metabolic Effect of Large-Scale Enzyme Activity Alterations. Application to Enzyme Deficiencies of Red Blood Cells

Abstract

There are numerous examples showing that the metabolism of cells can be severely impaired if the activity of only one of the participating enzymes undergoes large-scale alterations, resulting, for example, from spontaneous mutations (inherited or aquired enzymopathies), the administration of toxic drugs or self-inactivation of enzymes during cell aging. However, a quantitative relationship between the degree of enzyme deficiency and the extent of metabolic dysfunction is very difficult to establish by experimental means. An alternative is to tackle this problem by mathematical modelling. Our approach is based on a comprehensive mathematical model of the energy and redox metabolism for human erythrocytes. We calculate stationary states of the cell metabolism, varying the activity of each of the participating enzymes by several orders of magnitude. The metabolic states are then evaluated in terms of a performance function which relates the metabolic variables to the overall functional fitness of the cell. The performance function for the erythrocyte takes into account the homeostasis of three essential metabolic variables: the energetic state (ATP), the reductive capacity (reduced glutathione), and the osmotic state. Based on the behaviour of the performance function at varying enzyme activities, we estimate those ranges of enzyme activities, in which the metabolic alterations should be either tolerable, associated with non-chronic or chronic diseases, or letal. For most enzymopathies, the experimental and clinical observations can be satisfactorily rationalized by the computational results. Moreover, a surprisingly high correlation is found between the range of the activity range where disease is predicted by the model and the observed number of diseased probands. Another objective of our study was to contribute to the theory of metabolic control. The well-elaborated concept of the metabolic control theory is restricted to (infinitely) small activity alterations. In order to quantify the metabolic effect of finite (large-scale) changes in the activity of an enzyme, we propose, as a control measure, the effective activity Ea, defined as the relative activity of an enzyme (with respect to the activity in a reference state) required to bring about a change in the stationary value of a metabolic variable by the (finite) factor α. We demonstrate that none of the existing extrapolation methods using the conventional control coefficient is capable to provide reliable predictions of the effective activities for all enzymes of erythrocyte metabolism.