Estimation of steady-state flux rates in metabolic systems by computer simulations of radioactive tracer experiments

The dynamics of radioactive tracers in metabolic systems can be mathematically modelled by coupled systems of differential equations for both the concentrations and the specific radioactivities of the metabolites involved. Computer simulations, i.e. direct fitting of numerical solutions of these equations to observed time-courses of metabolites and specific radioactivities, enables one to estimate unknown kinetic parameters of the system. The theoretical fundamentals of this approach and the main steps towards the quantitative assessment of flux rates in stationary metabolic systems are outlined. An application of the method to the purine nucleotide metabolism of Ehrlich ascites tumor cells is given based on a simplified model of this pathway. The obtained steady-state flux rates indicate a marked increase in the metabolism of the adenine nucleotides during the proliferating phase in comparison to the resting phase of tumor growth.