Reaction of Mediator on Conducting Polymer

Let us first assume that the mediator reacts directly on the conducting polymer film. The boundary conditions in Eqn. 150 prevail. We also assume that kc + ka)s K ka. In this situation we have saturation, and the rate-determining step either involves a breakdown of the substrate/enzyme complex quantified by the rate constant kc, in which case all the enzyme present is in the ES form, or regeneration of the oxidized enzyme is rate-limiting (quantified by the product ka). In the latter situation all enzyme present is in the 2 form. 

This can readily integrate to obtain the following expression for the flux  

Hence we note that the flux is independent of the substrate concentration, as indeed it should be, since we have saturation. If ka kc, then, Eqn. 155 reduces to 

The decomposition of the ES complex is rate-determining, and the flux is first-order in layer thickness L and total enzyme concentration e. It is also independent of mediator concentration a. Alternatively if kc ka, then regeneration of the oxidized enzyme is rate-determing, and Eqn. 155 reduces to 

Again the flux is first-order in layer thickness L and enzyme concentration e, but it also depends on the mediator concentration a. 

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