Hybrid optimization for 13C metabolic flux analysis using systems parametrized by compactification

The importance and power of isotope-based metabolic flux analysis and its contribution to understanding the metabolic network is increasingly recognized. Its application is, however, still limited partly due to computational inefficiency. 13C metabolic flux analysis aims to compute in vivo metabolic fluxes in terms of metabolite balancing extended by carbon isotopomer balances and involves a nonlinear least-squares problem. To solve the problem more efficiently, improved numerical optimization techniques are necessary.

For flux computation, we developed a gradient-based hybrid optimization algorithm. Here, independent flux variables were compactified into [0, 1)-ranged variables using a single transformation rule. The compactified parameters could be discriminated between non-identifiable and identifiable variables after model linearization. The developed hybrid algorithm was applied to the central metabolism of Bacillus subtilis with only succinate and glutamate as carbon sources. This creates difficulties caused by symmetry of succinate leading to limited introduction of 13C labeling information into the system. The algorithm was found to be superior to its parent algorithms and to global optimization methods both in accuracy and speed. The hybrid optimization with tolerance adjustment quickly converged to the minimum with close to zero deviation and exactly re-estimated flux variables. In the metabolic network studied, some fluxes were found to be either non-identifiable or nonlinearly correlated. The non-identifiable fluxes could correctly be predicted a priori using the model identification method applied, whereas the nonlinear flux correlation was revealed only by identification runs using different starting values a posteriori.

This fast, robust and accurate optimization method is useful for high-throughput metabolic flux analysis, a posteriori identification of possible parameter correlations, and also for Monte Carlo simulations to obtain statistical qualities for flux estimates. In this way, it contributes to future quantitative studies of central metabolic networks in the framework of systems biology.