¹³C-based stationary metabolic flux analysis (S-MFA) has been extensively used to estimate flux distributions from external flux and isotopic measurements. However, S-MFA is impractical for some cases because 1) isotopic steady state is very difficult to attain (e.g., miniaturized experiments), or 2) steady-state measurements are not enough to infer all intracellular fluxes. Isotopically nonstationary MFA (IN-MFA) can overcome some of these limitations by measuring isotopic distributions of internal metabolites at a number of different time points. In current IN-MFA methods, mass isotopomer distributions (MDVs) of internal metabolites are measured by GC-MS or LC-MS/MS at a set of fixed sampling times.

In this work, we extend our recent OptMeas procedure (Chang et al., 2008) developed for the identifiability analysis of S-MFA in order to account for the added concentration variables and differential isotopic balance equations. The extended OptMeas is used to identify the essential metabolites that need to be measured to ensure unique flux elucidation under isotopically nonstationary conditions. The identified essential measurements are then queried and refined to minimize the measurement cost while ensuring a unique flux distribution. It is important to note that this procedure calls for the repetitive solution of the inverse problem of IN-MFA, which is a dynamic optimization (DO) problem. The DO problem is converted to a nonlinear programming (NLP) problem by discretizing the time domain. In order to efficiently solve the resulting large-scale NLP problem, we combine a suitable network decomposition scheme with a Lagrangean decomposition based global optimization algorithm. The proposed approach was tested with a small network example involving eight metabolites and ten fluxes, and then applied to medium-scale demonstration examples including 1,3-propanediol producing E. coli strain. We found that the proposed approach is both scalable and reliable in predicting flux distribution and suggesting essential measurements.

Reference

(1) Chang, Y., Suthers, P. F., Maranas, C. D., Identification of optimal measurement sets for complete flux elucidation in MFA experiments, Biotech Bioeng, accepted, 2008.