Compartmental analysis: theoretical aspects and application

The basic equations governing the kinetics of metabolic compartmental systems are presented. The most difficult problem in compartmental analysis is the so-called inverse problem which is the estimation of model parameters from experimental data. Two examples are considered how to tackle this problem. The first example concerns the distribution of isotopic carbon atoms in the citric acid cycle. Starting from a matrix formulation of the problem the major steps are outlined towards an analytical solution for this rather complex system. An application of the theoretical approach to the citric acid cycle of rabbit reticulocytes is given. The second problem deals with the kinetic characterization of biochemical reactions proceeding at the same time in different physiological spaces with different rates. Such a situation is, for example, the infection of red blood cells by malaria parasites. Both the host cell and the parasite possess the complete glycolytic pathway. A theoretical approach is proposed to estimate the flux rates through this pathway separately for each of the two spaces when only the total rates and metabolite concentrations are available as experimental data.