基元磁通模式的鲁棒生成
Robust generation of elementary flux modes
摘要：
基本通量模式（EFM）是从代谢反应网络定义的向量，给出底物和产物之间的连接。基于EFM的代谢通量分析（MFA）通过最小二乘数据拟合从外部通量测量估计每个EFM上的通量。在以前的工作中，我们提出了一个最优化方法的列生成类型，有利于基于EFM的MFA时，代谢反应网络是如此之大，枚举所有的EFM是禁止的。在这项工作中，我们扩展了这个模型，包括测量误差在一个强大的优化框架。在鲁棒最优化问题中，最小二乘数据拟合最小化，但在给定区间内，每种代谢物的误差尽可能不利。一般而言，包括鲁棒性可使最优化问题明显更难。然而，我们表明，在我们的情况下，鲁棒性问题可以说是一个凸二次规划问题，即，与原来的非鲁棒问题形式相同。此外，我们证明了列生成技术的非鲁棒性问题也可以扩展到强大的问题。此外，在该色谱柱生成框架中引入了指示未测量的代谢物间隔的选项。在一个案例研究中，包括鲁棒性的模型的效果进行了评估，这表明，我们的非鲁棒性问题的解决方案实际上也接近最优的鲁棒性时被认为是。另一方面，增加未测量代谢物的间隔导致最优解发生变化。这意味着包含未测量代谢物的间隔比直接考虑测量误差更重要，尽管误差高达20%。
英文摘要：
Elementary flux modes (EFMs) are vectors defined from a metabolic reaction network, giving the connections between substrates and products. EFMs-based metabolic flux analysis (MFA) estimates the flux over each EFM from external flux measurements through least-squares data fitting. In previous work we presented an optimization method of column generation type that facilitates EFMs-based MFA when the metabolic reaction network is so large that enumerating all EFMs is prohibitive. In this work we extend this model by including errors on measurements in a robust optimization framework. In the robust optimization problem, the least-squares data fitting is minimized subject to the error on each metabolite being as unfavourable as it can be, within a given interval. In general, inclusion of robustness may make the optimization problem significantly harder. However, we show that in our case the robust problem can be stated as a convex quadratic programming problem, i.e., of the same form as the original non-robust problem. Additionally, we demonstrate that the column-generation technique of the non-robust problem can be extended also to the robust problem. Furthermore, the option to indicate intervals on metabolites that are not measured is introduced in this column generation framework. The effect of including robustness in the model is evaluated in a case-study, which indicated that the solutions of our non-robust problems are in fact near-optimal also when robustness is considered. On the other hand, the addition of intervals on unmeasured metabolites resulted in a change of optimal solution. Implying that the inclusion of intervals on unmeasured metabolites is more important than the direct consideration of measurement errors, this despite up to 20% errors.
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