Ebenhöh O, Heinrich R
Humboldt-Universität zu Berlin, Institut für Biologie/Theoretische Biophysik, Invalidenstrasse 42, D-10115 Berlin, Germany.
Bull Math Biol. 2001 Jan;63(1):21-55. doi: 10.1006/bulm.2000.0197.
The structural design of ATP and NADH producing systems, such as glycolysis and the citric acid cycle (TCA), is analysed using optimization principles. It is assumed that these pathways combined with oxidative phosphorylation have reached, during their evolution, a high efficiency with respect to ATP production rates. On the basis of kinetic and thermodynamic principles, conclusions are derived concerning the optimal stoichiometry of such pathways. Extending previous investigations, both the concentrations of adenine nucleotides as well as nicotinamide adenine dinucleotides are considered variable quantities. This implies the consideration of the interaction of an ATP and NADH producing system, an ATP consuming system, a system coupling NADH consumption with ATP production and a system consuming NADH decoupled from ATP production. It is examined in what respect real metabolic pathways can be considered optimal by studying a large number of alternative pathways. The kinetics of the individual reactions are described by linear or bilinear functions of reactant concentrations. In this manner, the steady-state ATP production rate can be calculated for any possible ATP and NADH producing pathway. It is shown that most of the possible pathways result in a very low ATP production rate and that the very efficient pathways share common structural properties. Optimization with respect to the ATP production rate is performed by an evolutionary algorithm. The following results of our analysis are in close correspondence to the real design of glycolysis and the TCA cycle. (1) In all efficient pathways the ATP consuming reactions are located near the beginning. (2) In all efficient pathways NADH producing reactions as well as ATP producing reactions are located near the end. (3) The number of NADH molecules produced by the consumption of one energy-rich molecule (glucose) amounts to four in all efficient pathways. A distance measure and a measure for the internal ordering of reactions are introduced to study differences and similarities in the stoichiometries of metabolic pathways.
运用优化原理分析了三磷酸腺苷（ATP）和烟酰胺腺嘌呤二核苷酸（NADH）生成系统的结构设计，如糖酵解和柠檬酸循环（TCA）。假定这些与氧化磷酸化相结合的途径在其进化过程中就ATP生成速率而言已达到了高效率。基于动力学和热力学原理，得出了关于此类途径最佳化学计量关系的结论。在先前研究的基础上，腺嘌呤核苷酸以及烟酰胺腺嘌呤二核苷酸的浓度均被视为可变参数。这意味着要考虑一个ATP和NADH生成系统、一个ATP消耗系统、一个将NADH消耗与ATP生成相偶联的系统以及一个与ATP生成解偶联的NADH消耗系统之间的相互作用。通过研究大量替代途径，考察了实际代谢途径在哪些方面可被视为最优。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。通过这种方式，可以计算出任何可能的ATP和NADH生成途径的稳态ATP生成速率。结果表明，大多数可能的途径导致的ATP生成速率非常低，而非常高效的途径具有共同的结构特性。通过进化算法对ATP生成速率进行优化。我们的分析结果与糖酵解和TCA循环的实际设计密切相符。（1）在所有高效途径中，ATP消耗反应位于靠近起始端。（2）在所有高效途径中，NADH生成反应以及ATP生成反应位于靠近末端。（3）在所有高效途径中，消耗一个富能分子（葡萄糖）产生的NADH分子数量均为四个。引入了一个距离度量和一个反应内部排序的度量来研究代谢途径化学计量关系中的差异和相似性。
