Metabolic modeling has gained accuracy in the last decades, but the resulting models are of high dimension and difficult to use for control purpose. Here we propose a mathematical approach to reduce high dimensional linearized metabolic models, which relies on time scale separation and the quasi steady state assumption. Contrary to the flux balance analysis assumption that the whole system reaches an equilibrium, our reduced model depends on a small system of differential equations which represents the slow variables dynamics. Moreover, we prove that the concentration of metabolites in quasi steady state is one order of magnitude lower than the concentration of metabolites with slow dynamics (under some flux conditions). Also, we propose a minimization strategy to estimate the reduced system parameters. The reduction of a toy network with the method presented here is compared with other approaches. Finally, our reduction technique is applied to an autotrophic microalgae metabolic network. © 2018 American Institute of Chemical Engineers AIChE J, 65: 18–31, 2019

中文翻译：

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通过拟稳态逼近动态减少线性化代谢网络

在过去的几十年中，代谢建模已经获得了准确性，但是生成的模型具有较高的维数，并且难以用于控制目的。在这里，我们提出了一种数学方法来减少高维线性化代谢模型，该方法依赖于时间标度分离和准稳态假设。与整个系统达到平衡的磁通平衡分析假设相反，我们的简化模型依赖于代表微分方程动力学的小型微分方程组。此外，我们证明准稳态下的代谢物浓度比动力学较慢（在某些通量条件下）的代谢物浓度低一个数量级。此外，我们提出了一种最小化策略来估计减少的系统参数。用本文介绍的方法对玩具网络的简化与其他方法进行了比较。最后，我们的还原技术被应用于自养微藻代谢网络。©2018美国化学工程师学会AIChE J，65：18-31，2019