Influence of Oscillatory Enzyme Activity on the Reaction Kinetics: Mathematical Model

In this article, the model of a simple kinetic reaction process with an oscillating change in enzyme activity modulated by cosine-like function is considered. The model includes one substrate and one intermediate product in the reversible and irreversible enzymatic processes. The results obtained by numerical solutions show the small oscillations of enzyme-substrate complex with the phase shift in the steady state with respect to the oscillatory activity of enzyme. This phase shift decreases and tends to zero in dependence on the increasing activity of the enzyme periodic action. The presented model may refer to many enzymatic catalyzed reactions occurring in living organisms.