Tefagh Mojtaba, Boyd Stephen P
Information Systems Laboratory, Department of Electrical Engineering, Stanford University, Stanford, CA, USA.
J Math Biol. 2019 Apr;78(5):1459-1484. doi: 10.1007/s00285-018-1316-9. Epub 2018 Dec 10.
Flux coupling analysis (FCA) aims to describe the functional dependencies among reactions in a metabolic network. Currently studied coupling relations are qualitative in the sense that they identify pairs of reactions for which the activity of one reaction necessitates the activity of the other one, but without giving any numerical bounds relating the possible activity rates. The potential applications of FCA are heavily investigated, however apart from some trivial cases there is no clue of what bottleneck in the metabolic network causes each dependency. In this article, we introduce a quantitative approach to the same flux coupling problem named quantitative flux coupling analysis (QFCA). It generalizes the current concepts as we show that all the qualitative information provided by FCA is readily available in the quantitative flux coupling equations of QFCA, without the need for any additional analysis. Moreover, we design a simple algorithm to efficiently identify these flux coupling equations which scales up to the genome-scale metabolic networks with thousands of reactions and metabolites in an effective way. Furthermore, this framework enables us to quantify the "strength" of the flux coupling relations. We also provide different biologically meaningful interpretations, including one which gives an intuitive certificate of precisely which metabolites in the network enforce each flux coupling relation. Eventually, we conclude by suggesting the probable application of QFCA to the metabolic gap-filling problem, which we only begin to address here and is left for future research to further investigate.
通量耦合分析（FCA）旨在描述代谢网络中各反应之间的功能依赖性。目前所研究的耦合关系是定性的，即它们确定了这样的反应对：其中一个反应的活性必然要求另一个反应具有活性，但没有给出任何与可能的活性速率相关的数值界限。FCA的潜在应用已得到深入研究，然而，除了一些简单情况外，对于代谢网络中导致每种依赖性的瓶颈是什么尚无头绪。在本文中，我们针对同一通量耦合问题引入了一种定量方法，即定量通量耦合分析（QFCA）。我们证明了FCA提供的所有定性信息在QFCA的定量通量耦合方程中都很容易获得，无需任何额外分析，从而推广了当前的概念。此外，我们设计了一种简单算法来有效地识别这些通量耦合方程，该算法能够有效地扩展到包含数千个反应和代谢物的基因组规模代谢网络。此外，这个框架使我们能够量化通量耦合关系的“强度”。我们还提供了不同的具有生物学意义的解释，包括一种能直观证明网络中哪些代谢物确切地导致了每种通量耦合关系的解释。最后，我们通过提出QFCA在代谢缺口填补问题上可能的应用来得出结论，我们在此仅开始探讨这个问题，留待未来研究进一步深入研究。
