Bier M, Teusink B, Kholodenko B N, Westerhoff H V
University of Chicago, Dept. of Surgery MC 6035, IL 60637, USA.
Biophys Chem. 1996 Nov 29;62(1-3):15-24. doi: 10.1016/s0301-4622(96)02195-3.
The principles involved in the control of the frequency of sustained metabolic oscillations are developed in the context of glycolytic oscillations in Saccharomyces cerevisiae. To this purpose, an existing mathematical model that describes the experimentally obtained oscillations was simplified to a core model. Frequency, relative phase, average concentrations and amplitudes of the oscillations were well approximated by writing the two remaining metabolic variables of the core model (representing [ATP] and [hexose]) as harmonic functions of time and by requiring them to fulfill the differential equations. The extent to which an enzyme (-conglomerate) controls the frequency in a sustained oscillation is defined as the log-log derivative of that frequency with respect to enzyme activity. In both the full model and the core model this control of frequency and the control over the average concentrations proved to be distributed over the enzymes. We identified a summation theorem, stating that the sum of such control coefficients over all processes equals unity for frequency and zero for the average concentrations.
在酿酒酵母糖酵解振荡的背景下，研究了控制持续代谢振荡频率所涉及的原理。为此，将描述实验获得的振荡的现有数学模型简化为一个核心模型。通过将核心模型的两个剩余代谢变量（代表[ATP]和[己糖]）写为时间的谐波函数，并要求它们满足微分方程，振荡的频率、相对相位、平均浓度和振幅得到了很好的近似。一种酶（聚集体）在持续振荡中控制频率的程度定义为该频率相对于酶活性的对数-对数导数。在完整模型和核心模型中，这种频率控制和对平均浓度的控制都被证明分布在各种酶上。我们确定了一个求和定理，即所有过程中此类控制系数的总和对于频率等于1，对于平均浓度等于0。
