Table_1_A simulation-free constrained regression approach for flux estimation in isotopically nonstationary metabolic flux analysis with applications in microalgae.xlsx

IntroductionFlux 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.
MethodsFirst, 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.
ResultsWe 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.
DiscussionOur 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 (rs=0.89) to predictions obtained from INCA, a state-of-the-art tool for INST-MFA.

引言
不同生物及生长条件下的通量表型，有助于更深入地理解代谢网络的差异化功能。代谢反应通量是转录、翻译及翻译后修饰的整合结果，直接影响生物的生长与适应性。然而，细胞内代谢反应的通量无法直接测定，需通过代谢通量分析（metabolic flux analysis, MFA）进行估算：该方法将代谢物的同位素标记模式数据与代谢模型相结合。尽管代谢组学技术在光合生物中的应用已从¹³CO₂标记实验中获得了前所未有的数据，但通量估算的瓶颈仍在于同位素非稳态MFA（isotopically nonstationary MFA, INST-MFA）的应用。INST-MFA需要拟合大型耦合常微分方程组，以代谢物池与反应通量作为待优化参数。本研究聚焦光合生物中碳固定的关键途径——卡尔文-本森循环（Calvin-Benson cycle, CBC），旨在探究除经典INST-MFA之外的其他方法，能否为该途径所包含的反应提供可靠的通量估算结果。

方法
首先，本研究证明，利用所有CBC中间产物的标记模式进行通量估算，可被构建为单一约束回归问题，无需重复模拟时间分辨的标记模式。

结果
随后，本研究将无模拟约束回归方法的通量估算结果，与基于经典INST-MFA的结果进行对比：后者所用数据取自不同生长条件下的三种微藻——莱茵衣藻（Chlamydomonas reinhardtii）、索氏小球藻（Chlorella sorokiniana）及奥哈迪小球藻（Chlorella ohadii）的代谢物标记模式。

讨论
研究结果表明，在数据充足的场景下，基于无模拟回归的方法可作为经典INST-MFA的合适替代方案用于通量估算：本研究观察到该方法与当前主流INST-MFA工具INCA的预测结果具有高度的定性一致性，斯皮尔曼秩相关系数rs=0.89。