Rate equations of some cases of enzyme inhibition and activation—Their application to sodium-activated membrane transport systems

Abstract

The rate equations reported in the present paper refer to the rapid equilibrium kinetics of the following two models: (1) one substrate, two modifiers competing for the same modifier site; (2) one modifier, two substrates competing for the same substrate site. Cases have been considered where the modifier(s) do or do not affect the apparent affinity of the enzyme for the substrate(s); where the modifier(s) do or do not affect the maximal velocity; where compulsory paths in the formation of the enzyme-substrate-modifier compound have to be followed. The equations have been adapted to fit special experimental arrangements, such as constant total concentration of modifiers or, respectively, constant total concentration of substrates. Some equations have been applied to recalculate several data of the literature on sodium-dependent transport system. The good fit of the data with equations derived for the tertiary carrier-substrate-activator model strongly supports Crane's hypothesis on sodium-dependent transport systems.