Limit Theorems for Hybridization Reactions on Oligonucleotide Microarrays

TL;DR

This paper establishes limit theorems for the distributions of hybridization reactions on DNA microarrays, showing that gamma and beta distributions can approximate observed fluorescence data, aiding in target concentration estimation.

Contribution

It introduces new limiting laws for stationary distributions in models of hybridization reactions, connecting them to practical fluorescence data analysis.

Findings

Gamma- and beta-type distributions approximate fluorescence readings.

Limit theorems provide theoretical foundation for data modeling.

Potential for improved target concentration estimation methods.

Abstract

We derive herein the limiting laws for certain stationary distributions of birth-and-death processes related to the classical model of chemical adsorption-desorption reactions due to Langmuir. The model has been recently considered in the context of a hybridization reaction on an oligonucleotide DNA microarray. Our results imply that the truncated gamma- and beta- type distributions can be used as approximations to the observed distributions of the fluorescence readings of the oligo-probes on a microarray. These findings might be useful in developing new model-based, probe-specific methods of extracting target concentrations from array fluorescence readings.