Understanding of the fast mediated bioelectrocatalytic reaction on microelectrodes based on an analytical formula

Abstract

When an enzymatic reaction is extremely fast, the mediated bioelectrocatalytic reaction on the microelectrodes produces a pseudo-steady-state current that is independent of the enzyme activity. To understand this phenomenon, I derive the semi-analytical formula for this system. The semi-analytical formula reproduces the results calculated by the numerical simulations. Based on the analytical formula, the current responses of this system can be fully understood. Furthermore, the analytical formula clearly reveals the conditions necessary to expand the linear range of the current with respect to the substrate concentration; small diffusion coefficient of the substrate, small Michaelis constant for the substrate, large diffusion coefficient of the mediator, large radius of the microelectrode, and high enzyme activity. The results obtained here could be useful for the development of a biosensor using microelectrodes.