Metabolic flux analysis (MFA) aims at quantifying the magnitude of intracellular fluxes in metabolic networks. A key question in this analysis is choosing a set of measurements (external fluxes, concentration and isotopic distribution of metabolites) that is capable of yielding a unique flux distribution (identifiability). Since the system of equations that need to be solved to infer intracellular fluxes is nonlinear, this question is very difficult to answer even under a steady-state assumption.

Recently we introduced an optimization-based framework that uses incidence structure analysis to determine the smallest (or most cost-effective) set of measurements leading to complete flux elucidation using stationary MFA (S-MFA) (Chang et al., 2008). This approach relies on an integer linear programming formulation OptMeas that allows for the measurement of external fluxes and the complete (or partial) enumeration of the isotope forms of metabolites without requiring any of these to be chosen in advance. Since OptMeas approximately satisfies the identifiability, we subsequently query and refine the measurement sets suggested by OptMeas to minimize the measurement cost while ensuring a unique flux distribution. We showed that OptMeas is capable of generating optimal measurement sets for small to medium-sized demostration examples. Moreover, OptMeas suggested a number of additional measurements that lead to maximum flux elucidation in a large-scale amorphadiene producing E. coli strain. OptMeas is particularly useful in identifying essential measurements that are critical for the unique flux elucidation.

Although S-MFA has been extensively used to estimate flux distributions, it could be sometimes impractical 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 (mass isotopomer distributions in general) of internal metabolites at a number of different time points. We extend the OptMeas procedure 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 for identifiability and optimality. 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.