  A partial differential equation (PDE) was developed to describe
time-dependent ligand-receptor interactions for applications in biosensing
using field effect transistors (FET). The model describes biochemical
interactions at the sensor surface (or biochemical gate) located at the bottom
of a solution-well, which result in a time-dependent change in the FET
conductance. It was shown that one can exploit the disparate length scales of
the solution-well and biochemical gate to reduce the coupled PDE model to a
single nonlinear integrodifferential equation (IDE) that describes the
concentration of reacting species. Although this equation has a convolution
integral with a singular kernel, a numerical approximation was constructed by
applying the method of lines. The need for specialized quadrature techniques
was obviated and numerical evidence strongly suggests that this method achieves
first-order accuracy. Results reveal a depletion region on the biochemical
gate, which non-uniformly alters the surface potential of the semiconductor.
