摘要翻译：
基于约束的建模在代谢网络分析中得到了广泛的应用，如生物合成预测和通量优化等。线性约束，如质量守恒约束、可逆性约束、生物容量约束等，可以强加于线性算法。然而，近年来出现了一种基于热力学第二定律的非线性约束，称为“回路定律”，对现有的算法提出了挑战。证明这种非线性约束对线性解是不可行的，并成功地施加在采样过程中。在质量守恒约束、生物容量约束以及包括可逆性和“回路定律”在内的热力学约束条件下，引入Monte-Carlo抽样和模拟退火方法，优化幽门螺杆菌基因组尺度代谢网络(iIT341 GSM/GPR）的生物量合成。利用采样法优化了生物量合成速率这一非线性目标函数，该目标函数与可还原电子的总收益数统一。为了验证样本是否包含内部循环，基于求解一组不等式，开发了一种自动解决方案。此外，本文还提出了一种新的途径--无用途径，它具有三个特点：（1）质量流量自平衡；（2）具有交换反应；（3）与生物质合成无关。为了消除采样结果中无用途径的通量，提出了一种基于线性规划的方法，结果表明，改进了与生物质合成有关的途径中反应通量之间的相关性。
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英文标题：
《Imposition of Different Optimizing Object with Non-Linear Constraints on
  Flux Sampling and Elimination of Free Futile Pathways》
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作者：
Lu Xie, Yi Zhang
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最新提交年份：
2009
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分类信息：

一级分类：Quantitative Biology        数量生物学
二级分类：Other Quantitative Biology        其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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英文摘要：
  Constraint-based modeling has been widely used on metabolic networks analysis, such as biosynthetic prediction and flux optimization. The linear constraints, like mass conservation constraint, reversibility constraint, biological capacity constraint, can be imposed on linear algorithms. However, recently a non-linear constraint based on the second thermodynamic law, known as "loop law", has emerged and challenged the existing algorithms. Proven to be unfeasible with linear solutions, this non-linear constraint has been successfully imposed on the sampling process. In this place, Monte - Carlo sampling with Metropolis criterion and Simulated Annealing has been introduced to optimize the Biomass synthesis of genome scale metabolic network of Helicobacter pylori (iIT341 GSM / GPR) under mass conservation constraint, biological capacity constraint, and thermodynamic constraints including reversibility and "loop law". The sampling method has also been employed to optimize a non-linear objective function, the Biomass synthetic rate, which is unified by the total income number of reducible electrons. To verify whether a sample contains internal loops, an automatic solution has been developed based on solving a set of inequalities. In addition, a new type of pathway has been proposed here, the Futile Pathway, which has three properties: 1) its mass flow could be self-balanced; 2) it has exchange reactions; 3) it is independent to the biomass synthesis. To eliminate the fluxes of the Futile Pathways in the sampling results, a linear programming based method has been suggested and the results have showed improved correlations among the reaction fluxes in the pathways related to Biomass synthesis.
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PDF链接：
https://arxiv.org/pdf/0711.1193