Rapoport T A, Heinrich R, Rapoport S M
Biochem J. 1976 Feb 15;154(2):449-69. doi: 10.1042/bj1540449.
A simple mathematical model for glycolysis in erythrocytes is presented which takes into account ATP synthesis and consumption. The system is described by four ordinary differential equations. Conditions in vivo are described by a stable steady state. The model predicts correctly the metabolite concentrations found in vivo. The parameters involved are in agreement with data on the separate steps. The metabolite changes found in pyruvate kinase-deficient erythrocytes and the species variations among erythrocytes from different animals are described satisfactorily. The roles of the enzymes in the control of metabolites and glycolytic flux are expressed in the form of a control matrix and control strengths [R. Heinrich & T.A. Rapoport (1974) Eur. J. Biochem. 42, 89-95] respectively. Erythrocytes from various species are shown to be adapted to a maximal ATP-consumption rate. The calculated eigenvalues reveal the pronounced time-hierarchy of the glycolytic reactions. Owing to the slowness of the 2,3-bisphospho-glycerate phosphatase reaction, quasi-steady states occur during the time-interval of about 0.5-2h incubation, which are defined by perturbed 2,3-bisphosphoglycerate concentrations. The theoretical predictions agree with experimental data. In the quasi-steady state the flux control is exerted almost entirely by the hexokinase-phosphofructokinase system. The model describes satisfactorily the time-dependent changes after addition of glucose to starved erythrocytes. The theoretical consequences are discussed of the conditions in vitro with lactate accumulation and the existence of a time-independent conservation quantity for the oxidized metabolites. Even in this closed system quasi-steady states occur which are characterized by approximately constant concentrations of all glycolytic metabolites except for the accumulation of lactate, fructose 1,6-bisphosphate and triose phosphate.
本文提出了一个考虑了ATP合成与消耗的红细胞糖酵解简单数学模型。该系统由四个常微分方程描述。体内情况由一个稳定的稳态描述。该模型正确预测了体内发现的代谢物浓度。所涉及的参数与各个步骤的数据一致。丙酮酸激酶缺陷型红细胞中发现的代谢物变化以及不同动物红细胞之间的物种差异得到了满意的描述。酶在代谢物控制和糖酵解通量控制中的作用分别以控制矩阵和控制强度的形式表示[R. Heinrich & T.A. Rapoport (1974) Eur. J. Biochem. 42, 89 - 95]。研究表明，来自不同物种的红细胞适应了最大ATP消耗率。计算得到的特征值揭示了糖酵解反应明显的时间层次结构。由于2,3 - 二磷酸甘油酸磷酸酶反应缓慢，在大约0.5 - 2小时的孵育时间间隔内会出现准稳态，这些准稳态由受扰动的2,3 - 二磷酸甘油酸浓度定义。理论预测与实验数据一致。在准稳态下，通量控制几乎完全由己糖激酶 - 磷酸果糖激酶系统施加。该模型令人满意地描述了向饥饿红细胞添加葡萄糖后随时间的变化。讨论了体外乳酸积累条件以及氧化代谢物存在与时间无关的守恒量的理论后果。即使在这个封闭系统中也会出现准稳态，其特征除了乳酸、果糖1,6 - 二磷酸和磷酸丙糖的积累外，所有糖酵解代谢物的浓度大致恒定。
