Time Hierarchy in Oscillating Metabolic Systems

Metabolic systems are composed of many biochemical reactions and transport processes with very different rates. Their dynamic interaction produces a temporal organization whose salient feature is the existence of a distinct time hierarchy. Only a subset of the dynamic variables of the system moves with a velocity comparable to the characteristic time scale of the whole metabolic system, while others move very quickly and produce a dynamic “rapid substructure”. The mathematical description of this situation leads to differential equations with small parameters as multipliers of the derivatives of fast components (cf. Reich and Sel’kov 1981).