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

K. Pappaert, G.V. Baron and G. Desmet
Free University of Brussels, BE

microarray hybridization modeling, diffusion-reaction model

Molecular diffusion limits the hybridization rate in microarrays, 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. This is done by generating a convective flow increasing the transport rate of the sample molecules beyond their normal diffusion rate. Considering the existence of different kinetic regimes in diffusion-driven 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 3-D diffusion equation and looking at the influence 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 a convective-driven systems. It clearly demonstrates that convective-driven systems are able to enhance the hybridization rate, leading to higher signal intensities and faster hybridization times. This finding enables us to accurately design convective-driven hybridization systems.

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