Mathematical Modelling of Red Blood Cell Enzyme Deficiencies as an Example for Large-Scale Parameter Changes in Biochemical Reaction Systems

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), administration of toxic drugs or self-inactivation of enzymes during cell aging. Beside these unavoidably occuring natural changes of enzyme-kinetic properties, there is substantial interest in medicine and biotechnology to modify the kinetic properties of enzymes in order to manipulate the metabolism and functional performance of specific cells. In all these areas one important subject of mathematically oriented theoretical research is to quantify the metabolic changes caused by changing the activity of a given enzyme in a defined manner. The theoretical approach presented in this paper is based on a comprehensive mathematical model of erythrocyte metabolism encompassing the main pathways of cellular energy and redox metabolism. The decision for the erythrocyte was made in the light of the long tradition and advanced level reached in the mathematical modelling of the metabolism of this cell type (e.g. Rapoport et ai., 1976; Joshi and Palsson, 1990; Schuster et ai., 1988). A second reason was the great number of various enzyme deficiencies which have been elucidated during the last three decades (cf.Valentine et ai., 1983; Tanaka and Zerez, 1990) and which represent an excellent basis for comparing computational results with ‘experiments’ done by nature. Hitherto deficiencies of about 20 enzymes of human erythrocytes associated with widely different degrees of severity and complexity have been identified (Valentine et al., 1983; Fujii and Miwa, 1990). We define a ‘homeostasis function’ which takes into account the metabolic entities essential for cell integrity. This function is used for predicting the range of enzyme activities in which the metabolic alterations should be either tolerable, associated with non-chronic or chronic hemolytic diseases, or letal.