3-Dimensional Diffusion-Reaction Model for DNA Hybridization on Microarrays

DNA microarrays have, since their introduction around 1995, gained wide use in bio-analytical chemistry. Yet the hybridization is limited by molecular diffusion, leading to overnight waiting times. During the last couple of years a large number of methods were developed to overcome this diffusion-limitation and to enhance the speed and detection limits of the microarray experiments. The generation of a convective flow increases the transport rate of the sample molecules beyond their normal diffusion rate. Considering the existence of different kinetic regimes in diffusiondriven systems, it should be obvious that a sound mathematical framework is needed to interpret the kinetic measurements of microarray experiments. There are however few fundamental reports on the mathematical modeling of the hybridization on microarrays. Here we present an analytical expression for the hybridization on microarrays. This expression was obtained by solving the 3D diffusion equation and looking at the influence of a number of different parameters. We were able to determine the influence of each parameter in the creation of a depletion zone above the spot surface and we were also able to compare the hybridization rate in diffusion- and convection-driven systems. It clearly demonstrates that convective systems are able to enhance the hybridization rate, leading to higher signal intensities and faster hybridization times. This finding enables us to accurately design convection-driven hybridization systems.