A Linear Steady-State Treatment of Enzymatic Chains. General Properties, Control and Effector Strength

TLDR

The authors develop a theoretical framework for linear enzymatic chains, introducing three cardinal terms—control strength, control matrix, and effector strength—to quantitatively describe enzyme systems. Using linear approximation, they derive analytical steady‑state solutions for metabolite concentrations and flux, simplifying the equations with two parameters (thermodynamic equilibrium constant and characteristic time) and obtaining expressions for control strength, control matrix, effector strength, and mass‑action ratios. They compute effector strength for competitive inhibition and Monod‑type allosteric effectors, demonstrating how effectors influence metabolite concentrations.

Abstract

A theoretical analysis of linear enzymatic chains is presented. By linear approximation simple analytical solutions can be obtained for the metabolite concentrations and the flux through the chain for steady-state conditions. The equations are greatly simplified if the common kinetic constants are expressed as functions of two parameters, i.e. the thermodynamic equilibrium constant and the "characteristic time". Three cardinal terms are proposed for the quantitative description of enzyme systems. The first two are the control strength and the control matrix; these indicate the dependence of the flux and the metabolite concentrations, respectively, on the kinetic properties of a given enzyme. The third is the effector strength, which defines the dependence of the velocity of an enzyme on the concentration of an effector; it expresses the importance of an effector. By linear approximation simple analytical expressions were derived for the control strength, the control matrix and the mass-action ratios. The effector strength was calculated for two cases: for a competitive inhibitor and for allosteric effectors according to the Monod (1965) model. The influence of an effector on the concentrations of the metabolites was considered.