USE OF MATHEMATICAL-MODELS FOR PREDICTING THE METABOLIC EFFECT OF LARGE-SCALE ENZYME-ACTIVITY ALTERATIONS - APPLICATION TO ENZYME DEFICIENCIES OF RED-BLOOD-CELLS

There are numerous examples showing that the metabolism of cells can b e severely impaired if the activity of only one of the participating e nzymes undergoes large-scale alterations, resulting, for example, from spontaneous mutations (inherited or aquired enzymopathies), the admin istration of toxic drugs or self-inactivation of enzymes during cell a ging. However, a quantitative relationship between the degree of enzym e 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 comprehe nsive mathematical model of the energy and redox metabolism for human erythrocytes. We calculate stationary states of the cell metabolism, v arying the activity of each of the participating enzymes by several or ders of magnitude. The metabolic states are then evaluated in terms of a performance function which relates the metabolic variables to the o verall functional fitness of the cell. The performance function for th e erythrocyte takes into account the homeostasis of three essential me tabolic 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 th ose ranges of enzyme activities, in which the metabolic alterations sh ould be either tolerable, associated with non-chronic or chronic disea ses, or letal. For most enzymopathies, the experimental and clinical o bservations can be satisfactorily rationalized by the computational re sults. Moreover, a surprisingly high correlation is found between the range of the activity range where disease is predicted by the model an d the observed number of diseased probands. Another objective of our s tudy was to contribute to the theory of metabolic control. The well-el aborated concept of the metabolic control theory is restricted to (inf initely) small activity alterations. In order to quantify the metaboli c effect of finite (large-scale) changes in the activity of an enzyme, we propose, as a control measure, the effective activity E(alpha), de fined as the relative activity of an enzyme (with respect to the activ ity in a reference state) required to bring about a change in the stat ionary value of a metabolic variable by the (finite) factor alpha. We demonstrate that none of the existing extrapolation methods using the conventional control coefficient is capable to provide reliable predic tions of the effective activities for all enzymes of erythrocyte metab olism. Keywords. Mathematical modelling; metabolic system; enzyme defi ciency; control theory; erythrocyte.