Algebraic Methods for the Analysis of Redundancy and Identifiability in Metabolic 13C-Labelling Systems

Abstract

Stationary !?C tracer experiments supply a large amount of information related to metabolic fluxes in microorganisms. The unknownintracellular fluxes can be determined from some directly measured metabolic fluxes and the fractional labelling of intracellular carbon atom pools. Metabolic ?C-Labelling Systems are modelled by large algebraic equation systems with respect to fluxes and fractional labels. Identifiability of the unknownintracellular fluxes and redundancy of measured quantities are of great importance for the design and evaluation of experiments. This contribution presents algebraic methods to treat these problemsa priori and a posteriori. The Gröbnerbasis algorithm from polynomialideal theory is shownto be capable of solving all relevant problems. Ideas from algebraic geometry prove to be helpful in designing corresponding computer algebraic solution strategies. As an application example some global results on the identifiability of bidirectional reaction steps are derived.