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Volume 11,     Number 4,     Winter 2003

 

SPATIAL DEPENDENCE OF HYBRIDIZATION IN THE cDNA MICROARRAY
STEPHEN J. MERRILL, SANGEETA NELSON AND CRAIG A. STRUBLE

Abstract. The cDNA microarray is an experiment in which a large number of molecules (here DNA associated with known genes) are affixed or "printed" to a slide or chip in an array of spots. The hybridization of the "probes" in the printed spots with mRNA-derived fluorescently labeled "targets" allows one to study gene expression in tissue. The experiment has many variations and difficulties, primarily concerning problems of reproducibility and interpretation. A barrier to understanding experiments of this type is the lack of a simplified model of the process to explore aspects of the analysis and variability inherent in the experiment.
In this paper, a mathematical model of one aspect of the experiment is developed, the hybridization of probes with targets. The model consists of several thousand Markov chains, each differing with respect to the transition matrix and the initial vector. The stochastic nature of the process (generally a small number of targets specific for each probe species) is mimicked by the stochastic nature of the chains. This model is applied to describe the dependence of the expected level of hybridization and the variance of that level on the location of a spot on the slide. In consideration of these results, spot position must be considered for any normalization method in addition to adjusting for fluorescence intensity and printing biases. The results also suggest that genes that expected to have a lower level of expression should be spotted near the edges for better detection.

 

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