Mathematical analysis for impedance change with proteolytic digestion of gelatin

Abstract

A mathematical analysis is proposed to demonstrate an inter-relationship between the proteolytic digestion of gelatin on the surface of an interdigitated gold electrode and the resulting rate of impedance change, at different collagenase concentrations, in a biosensor used to detect protease in solution. The impedance change due to digestion of the gelatin layer by collagenase for the overall digestion process was expressed in two different stages: an initial exponential period where the rate of impedance change with enzymic digestion was slow, leading to a critical thickness; after which there was a greater change in impedance associated with subsequent dissolution of the layer and partial or complete uncoating of the digits on the electrode surface. An inter-relationship between the rate of impedance change and collagenase concentration within the range 0.2–0.6 mg ml⁻¹ was predicted for the early stages of the digestion process. A kinetic theory for the rapid rate of impedance change with collagenase concentrations could not be developed owing to the rate remaining almost constant for all concentrations of collagenase, after the critical thickness had been reached. An inter-relationship between the rate of impedance change and stirrer speed was also demonstrated.