A simulation-free constrained regression approach for flux estimation in isotopically nonstationary metabolic flux analysis with applications in microalgae

Introduction: Flux phenotypes from different organisms and growth conditions allow better understanding of differential metabolic networks functions. Fluxes of metabolic reactions represent the integrated outcome of transcription, translation, and post-translational modifications, and directly affect growth and fitness. However, fluxes of intracellular metabolic reactions cannot be directly measured, but are estimated via metabolic flux analysis (MFA) that integrates data on isotope labeling patterns of metabolites with metabolic models. While the application of metabolomics technologies in photosynthetic organisms have resulted in unprecedented data from ¹³CO₂-labeling experiments, the bottleneck in flux estimation remains the application of isotopically nonstationary MFA (INST-MFA). INST-MFA entails fitting a (large) system of coupled ordinary differential equations, with metabolite pools and reaction fluxes as parameters. Here, we focus on the Calvin-Benson cycle (CBC) as a key pathway for carbon fixation in photosynthesizing organisms and ask if approaches other than classical INST-MFA can provide reliable estimation of fluxes for reactions comprising this pathway. Methods: First, we show that flux estimation with the labeling patterns of all CBC intermediates can be formulated as a single constrained regression problem, avoiding the need for repeated simulation of time-resolved labeling patterns. Results: We then compare the flux estimates of the simulation-free constrained regression approach with those obtained from the classical INST-MFA based on labeling patterns of metabolites from the microalgae Chlamydomonas reinhardtii, Chlorella sorokiniana and Chlorella ohadii under different growth conditions. Discussion: Our findings indicate that, in data-rich scenarios, simulation-free regression-based approaches provide a suitable alternative for flux estimation from classical INST-MFA since we observe a high qualitative agreement ((Formula presented.)) to predictions obtained from INCA, a state-of-the-art tool for INST-MFA.