Estimating the size of the solution space of metabolic networks
Estimating the size of the solution space of metabolic networks
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DOI：
10.1186/1471-2105-9-240
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发表时间：
2008-05-19
影响因子：
3
通讯作者：
Pagnani, Andrea
中科院分区：
文献类型：
--
作者：
Braunstein, Alfredo;Mulet, Roberto;Pagnani, Andrea
背景：细胞代谢是研究最多的生物相互作用系统之一。虽然网络中个体反应和通路的拓扑性质已经被很好地理解，但对于系统的整体功能行为仍然缺乏理解。在过去的几年里，通量平衡分析(FBA)已经成为在系统水平上研究新陈代谢最成功和最广泛使用的技术。这种方法很大程度上依赖于有机体最大化目标函数的假设。然而，只有在非常特殊的生物条件下(例如，在REACH营养培养基中使大肠杆菌的生物量最大化)，细胞似乎才遵守这样的最优化规律。对于大型代谢系统，由于算法的限制，更精细的分析不假设极值仍然是一个难以捉摸的任务。结果：在这项工作中，我们提出了一种新的算法策略，它提供了与代谢约束相兼容的整个稳定通量集的有效表征。利用统计物理和信息论领域的技术，我们设计了一个消息传递算法来估计包含代谢网络所有可能的稳态流量分布的仿射空间的大小。该算法基于著名的Bethe近似，可以用来近似计算高维非全维凸多面体的体积。我们首先在小型随机代谢网络上将预测的准确性与精确算法进行比较。我们还验证了在红细胞代谢网络的情况下，该算法的预测与基于蒙特卡洛的方法非常接近。然后，我们在大肠杆菌中心代谢的情况下，测试基因敲除对溶液空间大小的影响。最后，我们分析了大肠杆菌代谢网络中反应平均流量的统计特性。结论：我们提出了一种新的高效的分布式算法策略来估计高维非全维凸多面体的仿射空间的大小和形状。结果表明，该方法得到的结果在定量和定性上都与标准算法的结果一致(在这种比较是可能的情况下)在分析大的生物系统时仍然是有效的，其中精确的确定性方法经历了算法时间的爆炸性增长。我们提出的算法可以被认为是蒙特卡罗抽样方法的替代方法。
Background: Cellular metabolism is one of the most investigated system of biological interactions. While the topological nature of individual reactions and pathways in the network is quite well understood there is still a lack of comprehension regarding the global functional behavior of the system. In the last few years flux-balance analysis (FBA) has been the most successful and widely used technique for studying metabolism at system level. This method strongly relies on the hypothesis that the organism maximizes an objective function. However only under very specific biological conditions (e. g. maximization of biomass for E. coli in reach nutrient medium) the cell seems to obey such optimization law. A more refined analysis not assuming extremization remains an elusive task for large metabolic systems due to algorithmic limitations.Results: In this work we propose a novel algorithmic strategy that provides an efficient characterization of the whole set of stable fluxes compatible with the metabolic constraints. Using a technique derived from the fields of statistical physics and information theory we designed a message-passing algorithm to estimate the size of the affine space containing all possible steadystate flux distributions of metabolic networks. The algorithm, based on the well known Bethe approximation, can be used to approximately compute the volume of a non full-dimensional convex polytope in high dimensions. We first compare the accuracy of the predictions with an exact algorithm on small random metabolic networks. We also verify that the predictions of the algorithm match closely those of Monte Carlo based methods in the case of the Red Blood Cell metabolic network. Then we test the effect of gene knock-outs on the size of the solution space in the case of E. coli central metabolism. Finally we analyze the statistical properties of the average fluxes of the reactions in the E. coli metabolic network.Conclusion: We propose a novel efficient distributed algorithmic strategy to estimate the size and shape of the affine space of a non full-dimensional convex polytope in high dimensions. The method is shown to obtain, quantitatively and qualitatively compatible results with the ones of standard algorithms (where this comparison is possible) being still efficient on the analysis of large biological systems, where exact deterministic methods experience an explosion in algorithmic time. The algorithm we propose can be considered as an alternative to Monte Carlo sampling methods.