title: The general modifier ("allosteric") unireactant enzyme mechanism: redundant conditions for reduction of the steady state velocity equation to one that is first degree in substrate and effector.
abstract: The general unireactant modifier mechanism in the absence of product can be described by the following linked reactions: E + S k1 in equilibrium k-1 ES k3----E + P; E + I k5 in equilibrium k-5 EI; EI + S k2 in equilibrium k-2 ESI k4----EI + P; and ES + I k6 in equilibrium k-6 ESI where S is a substrate and I is an effector. A full steady state treatment yields a velocity equation that is second degree in both [S] and [I]. Two different conditions (or assumptions) permit reduction of the velocity equation to one that is first degree in [S] and [I]. These are (a) that k-2k3 = k-1k4 (Frieden, C., J. Biol. Chem. 239, pp. 3522-3531, (1964)) and (b) that the I-binding reactions are at equilibrium (Reinhart, G. D., Arch. Biochem. Biophys. 224, pp. 389-401 (1983)). It is shown that each condition gives rise to the other (i.e., if the I-binding reactions are at equilibrium, then k-2k3 must equal k-1k4 and vice-versa). If one assumes equilibrium for the I-binding steps, the velocity equation derived by the method of Cha (J. Biol. Chem. 243, pp. 820-825 (1968)) is apparently second degree in [I] (Segel, I. H., Enzyme Kinetics, p. 838, Wiley-Interscience (1975)), but reduces to a first degree equation when the relationship derived by Frieden is inserted. If one starts by assuming a single equilibrium condition for I binding, e.g., k-5[EI] = k5[E][I] or k-6[ESI] = k6[ES][I], then a traditional algebraic manipulation of the remaining steady state equations provides first degree expressions for the concentrations of all enzyme species and also discloses the Frieden relationship.
authors.affiliation: Department of Biochemistry and Biophysics, University of California, Davis 95616.
authors.forename: I H
authors.initials: IH
authors.lastname: Segel
authors.forename: R L
authors.initials: RL
authors.lastname: Martin
mesh_terms: D001665:Binding Sites; D004798:Enzymes / Q000378:metabolism*; D007700:Kinetics; D008433:Mathematics; D008956:Models, Chemical
chemical_list: D004798:Enzymes