Journal of Biotechnology 114 (2004) 31–45 A diffusion–reaction model for DNA microarray assays Chetan Gadgil, Andrew Yeckel, Jeffrey J. Derby, Wei-Shou Hu ∗ Department of Chemical Engineering and Materials Science, 421 Washington Avenue SE, University of Minnesota, Minneapolis, MN 55455, USA Received 27 January 2004; received in revised form 11 May 2004; accepted 24 May 2004 Abstract DNA microarrays are extensively used for the quantification of the degree of differential mRNA expression. The assay involves hybridization of mobile DNA strands with immobilized complementary DNA strands to form duplexes. The overall duplex formation rate depends on the rate of transport of strands in solution to the corresponding spot on the surface, and the rate of the hybridization reaction. We present a theoretical model that incorporates both kinetics of the reversible hybridization reaction and diffusional transport of the labeled strands, and analyze DNA microarray hybridization using this model. Simulations are carried out in a geometrically realistic domain for labeled DNA concentrations corresponding to rare and abundant transcripts for typical assay conditions. The rate of strand diffusion in solution is shown to strongly affect the overall hybridization rate. We compute the minimum inter-spot spacing for replicate spots to enhance sensitivity. We also determine the hybridization time for which reliable estimates of the relative mRNA abundance of two species can be obtained using total fluorescence intensities. An analytical solution for the concentration distribution of mobile strands at intermediate hybridization times provides a convenient tool to calculate the mobile strand concentration profiles. This model provides a framework for the process analysis of all microarray assays currently used for genomic transcriptional analysis. © 2004 Elsevier B.V. All rights reserved. Keywords: Diffusion–reaction; Hybridization kinetics; Microarray design; Mathematical model 1. Introduction The recent completion of several genome sequenc- ing projects have enabled the cataloguing of genes present in the genome. Genes encode proteins that per- form diverse regulatory, catalytic and structural func- tions in a cell. The production of messenger RNA (mRNA) strands from the corresponding gene is the first step in protein production. Changes in the cellular environment due to disease, altered extracellular envi- ∗ Corresponding author. Tel.: +1-612-625-0546; fax: +1-612-626-0587. E-mail address: acre@cems.umn.edu (W.-S. Hu). ronment or developmental state lead to changes in the concentrations of specific mRNA sequences. DNA mi- croarrays enable the simultaneous assay of the relative concentration of thousands of mRNA sequences. They have been used for a diverse set of important applica- tions including classification and prediction of cancer (Khan et al., 2001) studies of metabolic activity in re- sponse to protein overproduction in E. coli (Oh and Liao, 2000), analysis of point mutations (Gerry et al., 1999), and transcriptional profiling of pathogen–host interactions (Kato-Maeda et al., 2001). DNA microarrays utilize the fundamental prop- erty of nucleic acid sequences specifically binding (hybridizing) to their complementary sequences. An 0168-1656/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jbiotec.2004.05.008