代谢网络通量平衡分析的改进多参数规划算法
An improved multi-parametric programming algorithm for flux balance analysis of metabolic networks
摘要：
通量平衡分析已被证明是分析代谢网络的有效工具。在通量平衡分析中，通过求解线性规划来确定反应速率和最佳途径，在线性规划中，生长速率在质量平衡约束下最大化。响应于环境刺激的各种细胞功能可以使用通量平衡分析通过相对于细胞外条件参数化线性程序来量化。然而，对于实际感兴趣的大多数大型基因组规模的代谢网络，所产生的参数问题具有多个和高度退化的最优解，这在计算上是具有挑战性的处理。本文提出了一种基于有效集方法的多参数规划改进算法。退化和多重处理，分别通过引入广义逆和辅助目标函数制定的最优性条件。这些改进对于代谢网络特别有效，因为它们的化学计量矩阵通常是稀疏的;因此，可以利用稀疏线性代数的快速有效算法来计算广义逆和零空间基。我们说明了我们的算法的应用，通过研究减少代谢模型的谷氨酸棒杆菌和大肠杆菌的基因组规模的模型的代谢网络的通量平衡分析。然后，我们展示了如何从这些研究中产生的临界区域可以与最佳代谢模式，并讨论了物理相关性的最佳途径所产生的各种辅助目标函数。与现有的多参数规划工具相比，该算法的计算速度提高了五倍以上，证明该算法在处理基因组尺度的代谢模型方面很有前途。
英文摘要：
Flux balance analysis has proven an effective tool for analyzing metabolic networks. In flux balance analysis, reaction rates and optimal pathways are ascertained by solving a linear program, in which the growth rate is maximized subject to mass-balance constraints. A variety of cell functions in response to environmental stimuli can be quantified using flux balance analysis by parameterizing the linear program with respect to extracellular conditions. However, for most large, genome-scale metabolic networks of practical interest, the resulting parametric problem has multiple and highly degenerate optimal solutions, which are computationally challenging to handle. An improved multi-parametric programming algorithm based on active-set methods is introduced in this paper to overcome these computational difficulties. Degeneracy and multiplicity are handled, respectively, by introducing generalized inverses and auxiliary objective functions into the formulation of the optimality conditions. These improvements are especially effective for metabolic networks because their stoichiometry matrices are generally sparse; thus, fast and efficient algorithms from sparse linear algebra can be leveraged to compute generalized inverses and null-space bases. We illustrate the application of our algorithm to flux balance analysis of metabolic networks by studying a reduced metabolic model of Corynebacterium glutamicum and a genome-scale model of Escherichia coli. We then demonstrate how the critical regions resulting from these studies can be associated with optimal metabolic modes and discuss the physical relevance of optimal pathways arising from various auxiliary objective functions. Achieving more than five-fold improvement in computational speed over existing multi-parametric programming tools, the proposed algorithm proves promising in handling genome-scale metabolic models.
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