Modeling Nonstationary State of Biosensors

Abstract

The biosensors response at a transition state can be modeled solving partial differential equations (PDE) of the substrates diffusion and the biocatalytical conversion with the initial and the boundary conditions. The analytical solutions, however, exist at very limited cases. The Laplace transformation that is typically used for solving the diffusion equations is no longer applicable for the solution of such problems. Therefore, for the modeling of the diffusion and enzymatic reactions the other methods of PDE solving are used.

Carr [61] used the Fourier method to solve (Chapter 1, eq. 7) at S ≪ K _M and S ≫ K _M with the initial and the boundary conditions: S = P = 0 at 0 < x < d and t = 0; ∂S ∕ ∂x = ∂P ∕ ∂x = 0 at x = 0; S = S ₀, P = 0 at x = d.