Equilibrium states and oscillations for localized two-enzyme kinetics: A model for circadian rhythms

Two models of localized catalysis are presented. In Problem I we study cooperatively coupled enzymes bound to membranes separated from each other. In Problem II the interaction of a membrane bound with a soluble (homogeneously distributed on a finite interval) enzyme is considered, with non-linearity in the bulk solution. One of the models is developed to describe cellular circadian rhythms at the molecular level.