Dynamical Systems and Phase Plane Analysis of Protease−Clay Interactions

Protease, a common extracellular enzyme in soils, was adsorbed onto smectite and bentonite clays exchanged with both Na and Ca cations. Initial concentrations and residual activity of the enzyme were studied together with a new approach to adsorption modeling and an introduction to the technique of phase plane analysis. Protease adsorption reached a maximum level of 0.34 mg mg-1 on the Na-exchanged smectite and a minimum of 0.20 mg mg-1 on the Ca-exchanged bentonite. The inhibition study of protease activity within the clay matrix showed that the enzyme retained a maximum of 9.9% (Na-exchanged smectite) and a minimum of 0% (Ca-exchanged bentonite) of its original activity. As opposed to the classic Langmuir and Freundlich model description, a general form, the Langmuir−Freundlich isotherm in combination with phase plane analysis, was used. The model appeared to agree well with the adsorption data of all four of the enzyme/clay complexes. The use of phase plane analysis was shown to be a powerful tool in equilibrium and kinetic sorption relationships. Kinetic modeling was able to identify problems with our isotherms for higher initial concentrations of protease. For all initial concentrations, film diffusion effects contribute to limiting the overall rate of adsorption.