Regulation and Homeostasis in Metabolic Control Theory: Interplay between Fluctuations of Variables and Parameter Changes

Abstract

The question of regulation is invariably a question of sensitivity of a system either to changes in its parameters or to fluctuations of its internal state. To investigate quantitative aspects of the regulation of metabolic systems, here we calculate the time-dependent relaxation of a system challenged with a perturbation of an enzyme activity (a parameter). Second we derive the time-dependent relaxation of the system challenged with the fluctuation of the concentration of an internal metabolite (a variable). We show that the response of a system to a transient fluctuation of a metabolite concentration, can be exactly mimicked by an appropriate perturbation of enzyme rates. This allows us to interpret the different terms of the system’s response to a fluctuation of a metabolite concentration, in terms of additive effects exercised by this metabolite on enzyme rates. The magnitude of each of these effects on a systemic property, is measured by its regulatory strength, which is the product of an elasticity and a control coefficient.