Oddsdóttir Hildur Æsa, Hagrot Erika, Chotteau Véronique, Forsgren Anders
Department of Mathematics, Optimization and Systems Theory, KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden,
J Math Biol. 2015 Oct;71(4):903-20. doi: 10.1007/s00285-014-0844-1. Epub 2014 Oct 17.
Elementary flux modes (EFMs) are pathways through a metabolic reaction network that connect external substrates to products. Using EFMs, a metabolic network can be transformed into its macroscopic counterpart, in which the internal metabolites have been eliminated and only external metabolites remain. In EFMs-based metabolic flux analysis (MFA) experimentally determined external fluxes are used to estimate the flux of each EFM. It is in general prohibitive to enumerate all EFMs for complex networks, since the number of EFMs increases rapidly with network complexity. In this work we present an optimization-based method that dynamically generates a subset of EFMs and solves the EFMs-based MFA problem simultaneously. The obtained subset contains EFMs that contribute to the optimal solution of the EFMs-based MFA problem. The usefulness of our method was examined in a case-study using data from a Chinese hamster ovary cell culture and two networks of varied complexity. It was demonstrated that the EFMs-based MFA problem could be solved at a low computational cost, even for the more complex network. Additionally, only a fraction of the total number of EFMs was needed to compute the optimal solution.
基本通量模式（EFMs）是代谢反应网络中连接外部底物与产物的途径。利用基本通量模式，代谢网络可以转化为其宏观对应物，其中内部代谢物已被消除，仅保留外部代谢物。在基于基本通量模式的代谢通量分析（MFA）中，通过实验测定的外部通量用于估计每个基本通量模式的通量。对于复杂网络而言，枚举所有基本通量模式通常是难以实现的，因为基本通量模式的数量会随着网络复杂性的增加而迅速增长。在这项工作中，我们提出了一种基于优化的方法，该方法动态生成基本通量模式的一个子集，并同时解决基于基本通量模式的代谢通量分析问题。所获得的子集包含对基于基本通量模式的代谢通量分析问题的最优解有贡献的基本通量模式。我们通过一个案例研究检验了该方法的实用性，该案例使用了来自中国仓鼠卵巢细胞培养的数据以及两个不同复杂程度的网络。结果表明，即使对于更复杂的网络，基于基本通量模式的代谢通量分析问题也能够以较低的计算成本得到解决。此外，计算最优解仅需要基本通量模式总数的一小部分。
