BIDIRECTIONAL REACTION STEPS IN METABOLIC NETWORKS .1. MODELING AND SIMULATION OF CARBON-ISOTOPE LABELING EXPERIMENTS

The extension of metabolite balancing with carbon labeling experiments , as described by Marx et al. (Biotechnol. Bioeng. 49: 11-29), results in a much more detailed stationary metabolic flux analysis. As oppose d to basic metabolite flux balancing alone, this method enables both f lux directions of bidirectional reaction steps to be quantitated. Howe ver, the mathematical treatment of carbon labeling systems is much mor e complicated, because it requires the solution of numerous balance eq uations that are bilinear with respect to fluxes and fractional labeli ng. In this study, a universal modeling framework is presented for des cribing the metabolite and carbon atom flux in a metabolic network. Bi directional reaction steps are extensively treated and their impact on the system's labeling state is investigated. Various kinds of modelin g assumptions, as usually made for metabolic fluxes, are expressed by linear constraint equations. A numerical algorithm for the solution of the resulting linear constrained set of nonlinear equations is develo ped. The numerical stability problems caused by large bidirectional fl uxes are solved by a specially developed transformation method. Finall y, the simulation of carbon labeling experiments is facilitated by a f lexible software tool for network synthesis. An illustrative simulatio n study on flux identifiability from available flux and labeling measu rements in the cyclic pentose phosphate pathway of a recombinant strai n of Zymomonas mobilis concludes this contribution. (C) 1997 John Wile y & Sons, Inc.