Diederichs Frank
Marschweg 10, D-29690 Schwarmstedt, Germany.
Bull Math Biol. 2006 Oct;68(7):1779-818. doi: 10.1007/s11538-005-9053-9. Epub 2006 Jul 11.
A new type of equation to describe enzyme-catalyzed reactions was developed, which allows the description of processes both at or near equilibrium and far from equilibrium, as they are both known to occur in the living cell. These equations combine kinetic as well as energetic characteristics within one single equation, and they describe the steady state as well as oscillations, as is shown for the glucose metabolism of the pancreatic beta-cell. A simulation of oxidative glucose metabolism could be elaborated, which allows to analyse in detail, how membrane and metabolic oscillations of the pancreatic beta-cell are generated, and how they are kinetically coupled. Glucose metabolism shows steady-state behaviour at a resting glucose concentration ([Glu]) of 4 mM. The steady state is switched to the oscillatory state by a first increase of the conductance of the glucokinase-catalyzed reaction at an elevated [Glu] of 10 mM. This is in fact sufficient to decrease the cytosolic adenosine diphosphate concentration (ADP) at constant intracellular [Ca(2+)]. The associated changes of the ATP and ADP species can reduce the conductance of ATP-sensitive K(+) channels (K(ATP)), thereby initiating bursts of the cell membrane potential (Delta(c)phi) with a concomitant influx of Ca(2+) ions from the extracellular space into the cell. The production of oscillations of ADP, Ca(2+), and all other variables, including those of mitochondria, are brought about on the one hand by a Ca(2+) dependent activation of mitochondrial ATP production, on the other hand by a Ca(2+)-dependent activation of ATP utilisation in the cytosol. Both processes must be coordinated in such a way that ATP production slightly precedes its utilisation. Oscillatory frequencies (fast/slow) are determined by the conductance (high/low, respectively) of flux through pyruvate dehydrogenase and/or citric acid cycle. The simulation shows that the so-called pyruvate paradox possibly results from a relatively low membrane conductance of beta-cells for pyruvate.
人们开发出了一种新型方程来描述酶催化反应，该方程能够描述处于或接近平衡态以及远离平衡态的过程，因为已知这两种情况都会在活细胞中发生。这些方程在一个单一方程中结合了动力学和能量学特征，并且它们描述了稳态以及振荡情况，正如胰腺β细胞的葡萄糖代谢所显示的那样。可以详细阐述氧化葡萄糖代谢的模拟过程，这使得能够详细分析胰腺β细胞的膜振荡和代谢振荡是如何产生的，以及它们在动力学上是如何耦合的。在静息葡萄糖浓度（[Glu]）为4 mM时，葡萄糖代谢呈现稳态行为。当葡萄糖浓度升高至10 mM时，通过首次增加葡萄糖激酶催化反应的电导，稳态转变为振荡状态。事实上，这足以在细胞内[Ca(2+)]恒定的情况下降低胞质二磷酸腺苷浓度（ADP）。ATP和ADP种类的相关变化会降低ATP敏感性钾通道（K(ATP)）的电导，从而引发细胞膜电位（Delta(c)phi）的爆发，并伴随着Ca(2+)离子从细胞外空间流入细胞。ADP、Ca(2+)以及所有其他变量（包括线粒体的变量）的振荡产生，一方面是由线粒体ATP生成的Ca(2+)依赖性激活引起的，另一方面是由胞质溶胶中ATP利用的Ca(2+)依赖性激活引起的。这两个过程必须以这样一种方式进行协调，即ATP生成略先于其利用。振荡频率（快/慢）由通过丙酮酸脱氢酶和/或柠檬酸循环的通量电导（分别为高/低）决定。模拟结果表明，所谓的丙酮酸悖论可能是由于β细胞对丙酮酸的膜电导相对较低所致。
