Control characteristics of regulatory enzyme systems, I: nonlinearities in regulatory enzyme activities

Abstract

The natures and forms of the nonlinearities in regulatory enzyme activities are presented by the control characteristics of a variety of regulatory enzymes that participate in various metabolic reaction systems. Besides the well-established simple feedback inhibition and feedforward activation, the basic reaction patterns of metabolic control considered include: (i) multivalent feedback inhibition; (ii) cooperative end-product inhibition; (iii) cumulative end-product inhibition; and (iv) compensatory feedback control. The characteristic equations describing these controls are derived and evaluated by computer simulation, using continuous system modelling program (CSMP). The results reveal saturation-type nonlinearities, the functional forms of which are mainly specified by two factors: (a) the type of modifier activity (inhibition, activation or both), and (b) the specific values of kinetic parameters, including stoichiometry, affinity constant, and activation constant (denoted by Q). The question of the possibility and type of metabolite oscillations is treated in terms of the sensitivity or degree of the nonlinearity. Using the oscillatory property of metabolites, the asymmetrical nonlinearities of the control characteristics can be approximated by a quasilinearization method in which a piecewise linear approximation is carried out to represent the given nonlinearity, followed by calculation of the describing function series of its approximation.