FB Mathematik und Informatik, Freie Universität Berlin, Arnimallee 6, 14195, Berlin, Germany.
Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany.
J Math Biol. 2023 Aug 30;87(3):50. doi: 10.1007/s00285-023-01982-w.
Elementary flux modes (EFMs) play a prominent role in the constraint-based analysis of metabolic networks. They correspond to minimal functional units of the metabolic network at steady-state and as such have been studied for almost 30 years. The set of all EFMs in a metabolic network tends to be very large and may have exponential size in the number of reactions. Hence, there is a need to elucidate the structure of this set. Here we focus on geometric properties of EFMs. We analyze the distribution of EFMs in the face lattice of the steady-state flux cone of the metabolic network and show that EFMs in the relative interior of the cone occur only in very special cases. We introduce the concept of degree of an EFM as a measure how elementary it is and study the decomposition of flux vectors and EFMs depending on their degree. Geometric analysis can help to better understand the structure of the set of EFMs, which is important from both the mathematical and the biological viewpoint.
基本通量模式（Elementary flux modes，EFMs）在代谢网络的约束分析中起着重要作用。它们对应于代谢网络在稳态下的最小功能单元，因此已经研究了近 30 年。代谢网络中所有 EFMs 的集合往往非常大，并且在反应数量上可能具有指数大小。因此，需要阐明该集合的结构。在这里，我们专注于 EFMs 的几何性质。我们分析了代谢网络稳态通量锥的面格中 EFMs 的分布，并表明锥体内的 EFMs 仅在非常特殊的情况下才会出现。我们引入了 EFMs 度数的概念，作为衡量其基本程度的一种度量，并研究了通量向量和 EFMs 根据其度数的分解。几何分析可以帮助更好地理解 EFMs 集合的结构，这从数学和生物学的角度来看都是很重要的。
