Bioinformatics and Systems Biology Program, University of California, San Diego, California.
Bioengineering Department, University of California, San Diego, California.
Biophys J. 2011 Feb 2;100(3):544-553. doi: 10.1016/j.bpj.2010.12.3707.
The constraint-based reconstruction and analysis (COBRA) framework has been widely used to study steady-state flux solutions in genome-scale metabolic networks. One shortcoming of current COBRA methods is the possible violation of the loop law in the computed steady-state flux solutions. The loop law is analogous to Kirchhoff's second law for electric circuits, and states that at steady state there can be no net flux around a closed network cycle. Although the consequences of the loop law have been known for years, it has been computationally difficult to work with. Therefore, the resulting loop-law constraints have been overlooked. Here, we present a general mixed integer programming approach called loopless COBRA (ll-COBRA), which can be used to eliminate all steady-state flux solutions that are incompatible with the loop law. We apply this approach to improve flux predictions on three common COBRA methods: flux balance analysis, flux variability analysis, and Monte Carlo sampling of the flux space. Moreover, we demonstrate that the imposition of loop-law constraints with ll-COBRA improves the consistency of simulation results with experimental data. This method provides an additional constraint for many COBRA methods, enabling the acquisition of more realistic simulation results.
约束重建和分析（COBRA）框架已被广泛用于研究基因组尺度代谢网络中的稳态通量解。当前 COBRA 方法的一个缺点是，在计算得到的稳态通量解中可能违反回路定律。回路定律类似于电路中的基尔霍夫第二定律，它指出在稳态下，闭合网络循环周围不能有净通量。尽管回路定律的后果已经为人所知多年，但在计算上很难处理。因此，产生的回路定律约束被忽略了。在这里，我们提出了一种称为无环 COBRA（ll-COBRA）的通用混合整数规划方法，可用于消除与回路定律不兼容的所有稳态通量解。我们将此方法应用于改进三种常见 COBRA 方法的通量预测：通量平衡分析、通量可变性分析和通量空间的蒙特卡罗采样。此外，我们证明了使用 ll-COBRA 施加回路定律约束可以提高模拟结果与实验数据的一致性。该方法为许多 COBRA 方法提供了一个额外的约束，使获得更现实的模拟结果成为可能。
