A diffusion-reaction model for DNA microarray assays

Chetan Gadgil, Andrew Yeckel, Jeffrey J. Derby, Wei Shou Hu

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)31-45
Number of pages15
JournalJournal of Biotechnology
Issue number1-2
StatePublished - Oct 19 2004

Bibliographical note

Funding Information:
This work was funded in part by grants from the National Science Foundation (BES-97272), National Aeronautics and Space Administration (#NAG8-134), and the Hepatic Genomics project (Academic Health Center, University of Minnesota). We wish to thank the Minnesota Supercomputing Institute for use of computing resources.


  • Diffusion-reaction
  • Hybridization kinetics
  • Mathematical model
  • Microarray design


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