Diffusion-limited reactions in nanoscale electronics
Ryan M. Evans, Arvind K. Balijepalli, Anthony J. Kearsley
To quantify interactions between drug molecules and target receptors, a novel nanoscale electronics instrument is under development. The instrument consists of two regions: a biological region, and an electronics region. The biological region consists of a well containing a buffer fluid, and receptors immobilized on a biochemical gate at the well-surface. The electronics regions consists of a semiconductor channel, through which current is flowing from source to drain. During a typical experiment ligand molecules are injected at the top of the well, and diffuse to the surface to bind with receptors. Ligand binding with receptors modulates current flow through the semiconductor channel, thereby producing a time-dependent current signal which can be used to study the biochemical process of interest. To quantify the coupling between diffusion and reaction, a partial differential equation model for this system is developed. It is shown that one can exploit disparate length scales associated with the device to reduce the coupled PDE model to a single nonlinear integrodifferential equation for the reacting species concentration. A numerical solution to this equation is found with the method of lines, and results reveal the presence of a depletion region on the biochemical gate. The size of the depletion region is directly related to the Damkohler number.