On the hybridization isotherms of DNA microarrays: the Langmuir model and its extensions

The design of DNA chip experiments utilizes hybridization isotherms relating the equilibrium hybridization at the surface to the composition of the solution. Within this family, the Langmuir isotherm is the simplest and the most frequently used. This tutorial review summarizes the domain of validity of the Langmuir isotherm and discusses the modifications necessary to allow for competitive hybridization in the bulk and at the surface, probe polydispersity and interactions between the probe sites. The equilibrium constant of hybridization at an impenetrable surface is described, as well as the relative merits of the melting temperature and c50 as design parameters. The relevance to various experimental situations, including two-colour experiments, study of point mutations for cancer diagnostics, genotyping of pooled samples and aspects of Latin square experiments, is discussed.