Background: Epigenetic modification of DNA via methylation is one of the key inventions in eukaryotic evolution. It provides a source for the switching of gene activities, the maintenance of stable phenotypes and the integration of environmental and genomic signals. Although this process is widespread among eukaryotes, both the patterns of methylation and their relevant biological roles not only vary noticeably in different lineages, but often are poorly understood. In addition, the evolutionary origins of DNA methylation in multicellular organisms remain enigmatic. Here we used a new 'epigenetic' model, the social honey bee Apis mellifera, to gain insights into the significance of methylated genes.

Abstract. Analysis of data from an Affymetrix Latin Square spike-in experiment indicates that measured fluorescence intensities of features on an oligonucleotide microarray are related to spike-in RNA target concentrations via a hyperbolic response function, generally identified as a Langmuir adsorption isotherm. Furthermore the asymptotic signal at high spike-in concentrations is almost invariably lower for a mismatch feature than for its partner perfect match feature. We survey a number of theoretical adsorption models of hybridization at the microarray surface and find that in general they are unable to explain the differing saturation responses of perfect and mismatch features. On the other hand, we find that a simple and consistent explanation can be found in a model in which equilibrium hybridization followed by partial dissociation of duplexes during the post-hybridization washing phase.

Recent analyses have shown that the relationship between intensity measurements from high density oligonucleotide microarrays and known concentration is non linear. Thus many measurements of so-called gene expression are neither measures of transcript nor mRNA concentration as might be expected. Intensity as measured in such microarrays is a measurement of fluorescent dye attached to probe-target duplexes formed during hybridization of a sample to the probes on the microarray. We develop several dynamic adsorption models relating fluorescent dye intensity to target RNA concentration, the simplest of which is the equilibrium Langmuir isotherm, or hyperbolic response function. Using data from the Affymerix HG-U95A Latin Square experiment, we evaluate various physical models, including equilibrium and non-equilibrium models, by applying maximum likelihood methods. We show that for these data, equilibrium Langmuir isotherms with probe dependent parameters are appropriate. We describe how probe sequence information may then be used to estimate the parameters of the Langmuir isotherm in order to provide an improved measure of absolute target concentration.

We suggest a technique, related to the concept of 'detection boundary' that was developed by Ingster and by Donoho and Jin, for comparing the theoretical performance of classifiers constructed from small training samples of very large vectors. The resulting 'classification boundaries' are obtained for a variety of distance-based methods, including the support vector machine, distance-weighted discrimination and "k"th-nearest-neighbour classifiers, for thresholded forms of those methods, and for techniques based on Donoho and Jin's higher criticism approach to signal detection. Assessed in these terms, standard distance-based methods are shown to be capable only of detecting differences between populations when those differences can be estimated consistently. However, the thresholded forms of distance-based classifiers can do better, and in particular can correctly classify data even when differences between distributions are only detectable, not estimable. Other methods, including higher criticism classifiers, can on occasion perform better still, but they tend to be more limited in scope, requiring substantially more information about the marginal distributions. Moreover, as tail weight becomes heavier the classification boundaries of methods designed for particular distribution types can converge to, and achieve, the boundary for thresholded nearest neighbour approaches. For example, although higher criticism has a lower classification boundary, and in this sense performs better, in the case of normal data, the boundaries are identical for exponentially distributed data when both sample sizes equal 1. Copyright 2008 Royal Statistical Society.