Stephani A, Heinrich R
Humboldt-Universität zu Berlin, Institut für Biologie, Germany. amadeus.hu-berlin.de
Bull Math Biol. 1998 May;60(3):505-43. doi: 10.1006/bulm.1997.0028.
It is theoretically analysed whether the structural design of ATP-producing pathways, in particular the design of glycolysis, may be explained by optimization principles. On the basis of kinetic and thermodynamic principles conclusions are derived concerning the stoichiometry of these pathways in states of high ATP production rates. One of the extensions to previous investigations is that the concentrations of the adenine nucleotides are taken into account as variable quantities. This necessitates the consideration of an interaction of the ATP-producing system I with an external ATP-consuming system II. A great variety of pathways is studied which differ in the number and location of ATP-consuming reactions, ATP-producing reactions and reactions involving inorganic phosphate. The corresponding number of possible pathways may be calculated in an explicit manner as a function of the number of those reactions which do not couple to ATP or inorganic phosphate. The kinetics of the individual reactions are described by linear or bilinear functions of reactant concentrations and all rate equations are expressed in terms of equilibrium constants and characteristic times. A thermo-dynamical analysis of the two coupled systems yields upper and lower limits for the concentration of ATP and an explicit expression for the maximal difference between the number of ATP-producing and ATP-consuming reactions of system I. The following results of the optimization are obtained. (i) The ATP production rate always increases if the ATP-producing reactions as well as those reactions characterized by an uptake of inorganic phosphate are shifted as far as possible towards the end of system I. (ii) Explicit conditions for the optimal location of the ATP-consuming reactions are presented. The results are discussed in the context of characteristic times as well as in terms of enzyme kinetic parameters. (iii) For two sets of characteristic times the resulting stoichiometries and their corresponding steady-state fluxes are investigated in detail. One of these stoichiometries shows a close correspondence to contemporary standard glycolysis. (iv) It is shown that most possible pathways result in a very low steady-state flux, that is, the optimal stoichiometry is characterized by a significant selective advantage. (v) The standard free energy profile of a pathway with an optimal stoichiometry is discussed. It differs significantly from the free energy profiles of nonoptimized pathways.
从理论上分析了产生ATP途径的结构设计，特别是糖酵解的设计，是否可以用优化原则来解释。基于动力学和热力学原理，得出了关于这些途径在高ATP产生速率状态下的化学计量关系的结论。与先前研究的一个扩展是，将腺嘌呤核苷酸的浓度作为可变数量来考虑。这就需要考虑产生ATP的系统I与外部消耗ATP的系统II之间的相互作用。研究了各种各样的途径，这些途径在消耗ATP的反应、产生ATP的反应以及涉及无机磷酸盐的反应的数量和位置上有所不同。相应的可能途径的数量可以作为不与ATP或无机磷酸盐偶联的反应数量的函数以显式方式计算。各个反应的动力学由反应物浓度的线性或双线性函数描述，所有速率方程都用平衡常数和特征时间表示。对这两个耦合系统的热力学分析得出了ATP浓度的上限和下限，以及系统I中产生ATP和消耗ATP的反应数量之间最大差异的显式表达式。得到了以下优化结果。(i) 如果产生ATP的反应以及以摄取无机磷酸盐为特征的那些反应尽可能地向系统I末端移动，ATP产生速率总是会增加。(ii) 给出了消耗ATP反应的最佳位置的明确条件。结果在特征时间的背景下以及根据酶动力学参数进行了讨论。(iii) 对于两组特征时间，详细研究了所得的化学计量关系及其相应的稳态通量。其中一种化学计量关系与当代标准糖酵解密切对应。(iv) 结果表明，大多数可能的途径导致非常低的稳态通量，即最佳化学计量关系具有显著的选择优势。(v) 讨论了具有最佳化学计量关系的途径的标准自由能分布曲线。它与未优化途径的自由能分布曲线有显著差异。
