Metabolic flux analysis (MFA) is essential for quantifying intracellular metabolic fluxes. Isotopically non-stationary MFA (INST-MFA) with 13C-labeled CO2 enables the estimation of key parameters–metabolic fluxes and intracellular metabolite pool sizes in autotrophic organisms, where isotopic steady-state labeling patterns are non-informative of intracellular fluxes. However, applications of INST-MFA remains limited by high computational demands and challenges in parameter estimation.
We developed a computational framework for 13C INST-MFA that leverages automatic differentiation to improve optimization efficiency. The approach uses the IPOPT optimizer to integrate automatic differentiation within a system of ordinary differential equations (ODEs), describing the incorporation of 13C label in metabolic pools, and to estimate fluxes and metabolite pool sizes from time-resolved isotopic labeling data. The framework was implemented in Python and evaluated on a metabolic model of central carbon metabolism of Synechocystis sp. PCC 6803 with 60 reactions and 31 metabolites with synthetic and real-world labeling data.
Compared to conventional approaches, our method accurately estimates metabolic fluxes and metabolite pool sizes, together with 90% confidence intervals, while reducing computational time by at least two-fold and improving goodness-of-fit, measured by the reduced X2 statistic. These results demonstrate the potential of automatic differentiation to enhance the scalability and robustness of 13C INST-MFA workflows.

Co-authors: Zoran Nikoloski