The principle of flux minimization and its application to estimate stationary fluxes in metabolic networks
The principle of flux minimization and its application to estimate stationary fluxes in metabolic networks
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DOI：
10.1111/j.1432-1033.2004.04213.x
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发表时间：
2004-07-01
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影响因子：
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通讯作者：
Holzhütter, HG
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作者：
Holzhütter, HG
细胞功能最终与成千上万的化学反应和运输过程所带来的代谢通量有关。基础酶和膜转运蛋白的合成导致细胞对能量和外部资源的某种“努力”。考虑到这些细胞在自然进化过程中应该具有选择优势，使它们能够履行重要功能（如生长、抵御有毒化合物、修复DNA改变等），通过最小的努力，可以假定通量最小化的原理如下：给定可用的外部底物和给定完成特定细胞功能模式所需的一组功能上重要的“目标”通量，固定代谢通量必须变为最小。为了将该原理转换成能够预测稳态代谢通量的数学方法，通过所有单独通量的加权线性组合来测量网络中的总通量，由此将热力学平衡常数用作加权因子，即，热力学平衡越多地位于反应的右手侧，则反向反应的加权因子越大。应用线性规划技术，在目标通量的固定值下，并在所有代谢物的通量平衡（=稳态条件）约束下，使总通量最小化。理论概念适用于两个代谢方案：红细胞的能量和氧化还原代谢，扭脱甲基杆菌AM1的中心代谢。通量最小化方法预测的通量率表现出显着的相关性与通量率通过动力学建模或直接实验测定。较大的偏差发生在由冗余分支组成的网络段，其中通量最小化方法总是将总通量归因于在物理上最有利的分支。然而，与现有的结构建模方法相比，通量最小化的原则似乎是一个很有前途的理论方法来评估稳态通量率在代谢系统中的情况下，详细的动力学模型尚未提供。
Cellular functions are ultimately linked to metabolic fluxes brought about by thousands of chemical reactions and transport processes. The synthesis of the underlying enzymes and membrane transporters causes the cell a certain 'effort' of energy and external resources. Considering that those cells should have had a selection advantage during natural evolution that enabled them to fulfil vital functions (such as growth, defence against toxic compounds, repair of DNA alterations, etc.) with minimal effort, one may postulate the principle of flux minimization, as follows: given the available external substrates and given a set of functionally important 'target' fluxes required to accomplish a specific pattern of cellular functions, the stationary metabolic fluxes have to become a minimum. To convert this principle into a mathematical method enabling the prediction of stationary metabolic fluxes, the total flux in the network is measured by a weighted linear combination of all individual fluxes whereby the thermodynamic equilibrium constants are used as weighting factors, i.e. the more the thermodynamic equilibrium lies on the right-hand side of the reaction, the larger the weighting factor for the backward reaction. A linear programming technique is applied to minimize the total flux at fixed values of the target fluxes and under the constraint of flux balance (= steady-state conditions) with respect to all metabolites. The theoretical concept is applied to two metabolic schemes: the energy and redox metabolism of erythrocytes, and the central metabolism of Methylobacterium extorquens AM1. The flux rates predicted by the flux-minimization method exhibit significant correlations with flux rates obtained by either kinetic modelling or direct experimental determination. Larger deviations occur for segments of the network composed of redundant branches where the flux-minimization method always attributes the total flux to the thermodynamically most favourable branch. Nevertheless, compared with existing methods of structural modelling, the principle of flux minimization appears to be a promising theoretical approach to assess stationary flux rates in metabolic systems in cases where a detailed kinetic model is not yet available.