A statistical model for microarrays, optimal estimation algorithms, and limits of performance

Abstract

DNA microarray technology relies on the hybridization process, which is stochastic in nature. Currently, probabilistic cross hybridization of nonspecific targets, as well as the shot noise (Poisson noise) originating from specific targets binding, are among the main obstacles for achieving high accuracy in DNA microarray analysis. In this paper, statistical techniques are used to model the hybridization and cross-hybridization processes and, based on the model, optimal algorithms are employed to detect the targets and to estimate their quantities. To verify the theory, two sets of microarray experiments are conducted: one with oligonucleotide targets and the other with complementary DNA (cDNA) targets in the presence of biological background. Both experiments indicate that, by appropriately modeling the cross-hybridization interference, significant improvement in the accuracy over conventional methods such as direct readout can be obtained. This substantiates the fact that the accuracy of microarrays can become exclusively noise limited, rather than interference (i.e., cross-hybridization) limited. The techniques presented in this paper potentially increase considerably the signal-to-noise ratio (SNR), dynamic range, and resolution of DNA and protein microarrays as well as other affinity-based biosensors. A preliminary study of the Cramer-Rao bound for estimating the target concentrations suggests that, in some regimes, cross hybridization may even be beneficial-a result with potential ramifications for probe design, which is currently focused on minimizing cross hybridization. Finally, in its current form, the proposed method is best suited to low-density arrays arising in diagnostics, single nucleotide polymorphism (SNP) detection, toxicology, etc. How to scale it to high-density arrays (with many thousands of spots) is an interesting challenge.