Substrate aggregation and cooperative enzyme kinetics: consideration of enzyme access with large aggregates

Consideration was given to a system in which an enzyme substrate indefinitely self-associates according to a general model with f sites of aggregation and a single intrinsic binding constant k. Where enzyme attack occurs at random points on the substrate surface, surface regions will be obscured from enzyme access by aggregate formation. The significance of reduced surface access for the infinite array of different size aggregates which co-exist was explored through use of a reacted site probability function, PA: the proportion of total substrate surface which is accessible to the enzyme was estimated as the fraction of total sites for aggregation which are unoccupied. The effective substrate concentration was thereby specified in terms of total substrate concentration (mA) by the simple expression mA = (1 - PA)mA. Plots of simulated v versus mA data were examined for a Michaelis-Menten enzyme of maximal velocity Vm and Michaelis constant Km to reveal deviations from expected enzyme behaviour; corresponding Hofstee (v/mA versus v) plots were found to be convex to the v axis as is characteristic of a negatively cooperative enzyme. As self-association is known to occur widely with large or small molecules in solution, the experimenter should be aware of the potential for these phenomena in kinetic studies to produce pseudo-allosteric effects, or to mask true allosteric behaviour.