### Kleene's theorem and the solution of metabolic carbon labeling systems

*Nicole Isermann*

*, Michael Weitzel*

*and Wolfgang Wiechert*

#### Abstract

Carbon Labeling Systems (CLS) are large equation systems that describe the dynamics of labeled carbon atoms in a metabolic network. The rapid solution of these systems is the algorithmic backbone of 13C Metabolic Flux Analysis (MFA) which has become one of the most widely used tools in Metabolic Engineering. A new algorithm is presented for the solution of CLS which is not based on iteration schemes or numerical linear algebra methods but on path tracing of labeled particles. It is shown that the set of all paths from the system input to the internal network nodes directly gives the clue to an explicit solution of CLS. The promising potential of this new solution algorithm are outlined.

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