Mathematical simulation of membrane processes and metabolic fluxes of the pancreatic beta-cell.

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](c)) 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](c), [Ca(2+)](c), and all other variables, including those of mitochondria, are brought about on the one hand by a [Ca(2+)](m) dependent activation of mitochondrial ATP production, on the other hand by a [Ca(2+)](c)-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.