Klamt Steffen, Regensburger Georg, Gerstl Matthias P, Jungreuthmayer Christian, Schuster Stefan, Mahadevan Radhakrishnan, Zanghellini Jürgen, Müller Stefan
Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany.
Institute for Algebra, Johannes Kepler University Linz (JKU), Linz, Austria.
PLoS Comput Biol. 2017 Apr 13;13(4):e1005409. doi: 10.1371/journal.pcbi.1005409. eCollection 2017 Apr.
Elementary flux modes (EFMs) emerged as a formal concept to describe metabolic pathways and have become an established tool for constraint-based modeling and metabolic network analysis. EFMs are characteristic (support-minimal) vectors of the flux cone that contains all feasible steady-state flux vectors of a given metabolic network. EFMs account for (homogeneous) linear constraints arising from reaction irreversibilities and the assumption of steady state; however, other (inhomogeneous) linear constraints, such as minimal and maximal reaction rates frequently used by other constraint-based techniques (such as flux balance analysis [FBA]), cannot be directly integrated. These additional constraints further restrict the space of feasible flux vectors and turn the flux cone into a general flux polyhedron in which the concept of EFMs is not directly applicable anymore. For this reason, there has been a conceptual gap between EFM-based (pathway) analysis methods and linear optimization (FBA) techniques, as they operate on different geometric objects. One approach to overcome these limitations was proposed ten years ago and is based on the concept of elementary flux vectors (EFVs). Only recently has the community started to recognize the potential of EFVs for metabolic network analysis. In fact, EFVs exactly represent the conceptual development required to generalize the idea of EFMs from flux cones to flux polyhedra. This work aims to present a concise theoretical and practical introduction to EFVs that is accessible to a broad audience. We highlight the close relationship between EFMs and EFVs and demonstrate that almost all applications of EFMs (in flux cones) are possible for EFVs (in flux polyhedra) as well. In fact, certain properties can only be studied with EFVs. Thus, we conclude that EFVs provide a powerful and unifying framework for constraint-based modeling of metabolic networks.
基本通量模式（EFMs）作为一种描述代谢途径的形式化概念出现，并已成为基于约束的建模和代谢网络分析的既定工具。EFMs是通量锥的特征（支持最小）向量，通量锥包含给定代谢网络的所有可行稳态通量向量。EFMs考虑了由反应不可逆性和稳态假设产生的（齐次）线性约束；然而，其他（非齐次）线性约束，如其他基于约束的技术（如通量平衡分析 [FBA]）经常使用的最小和最大反应速率，不能直接整合。这些额外的约束进一步限制了可行通量向量的空间，并将通量锥转变为一般通量多面体，在其中EFMs的概念不再直接适用。因此，基于EFM的（途径）分析方法和线性优化（FBA）技术之间存在概念上的差距，因为它们作用于不同的几何对象。十年前提出了一种克服这些限制的方法，该方法基于基本通量向量（EFVs）的概念。直到最近，科学界才开始认识到EFVs在代谢网络分析中的潜力。事实上，EFVs恰好代表了将EFMs的概念从通量锥推广到通量多面体所需的概念发展。这项工作旨在为广大读者提供对EFVs的简洁理论和实践介绍。我们强调了EFMs和EFVs之间的密切关系，并证明了EFMs（在通量锥中）的几乎所有应用对于EFVs（在通量多面体中）也是可能的。事实上，某些性质只能用EFVs来研究。因此，我们得出结论，EFVs为基于约束的代谢网络建模提供了一个强大且统一的框架。
