"Hook"-calibration of GeneChip-microarrays: Theory and algorithm

Abstract Background: The improvement of microarray calibration methods is an essential prerequisite for quantitative expression analysis. This issue requires the formulation of an appropriate model describing the basic relationship between the probe intensity and the specific transcript concentration in a complex environment of competing interactions, the estimation of the magnitude these effects and their correction using the intensity information of a given chip and, finally the development of practicable algorithms which judge the quality of a particular hybridization and estimate the expression degree from the intensity values. Results: We present the so-called hook-calibration method which co-processes the log-difference (delta) and -sum (sigma) of the perfect match (PM) and mismatch (MM) probe-intensities. The MM probes are utilized as an internal reference which is subjected to the same hybridization law as the PM, however with modified characteristics. After sequence-specific affinity correction the method fits the Langmuir-adsorption model to the smoothed delta-versus-sigma plot. The geometrical dimensions of this so-called hook-curve characterize the particular hybridization in terms of simple geometric parameters which provide information about the mean non-specific background intensity, the saturation value, the mean PM/MM-sensitivity gain and the fraction of absent probes. This graphical summary spans a metrics system for expression estimates in natural units such as the mean binding constants and the occupancy of the probe spots. The method is single-chip based, i.e. it separately uses the intensities for each selected chip. Conclusion: The hook-method corrects the raw intensities for the non-specific background hybridization in a sequence-specific manner, for the potential saturation of the probe-spots with bound transcripts and for the sequence-specific binding of specific transcripts. The obtained chip characteristics in combination with the sensitivity corrected probe-intensity values provide expression estimates scaled in natural units which are given by the binding constants of the particular hybridization.</p

The Effect of Noisy Protein Expression on E. coli/Phage Dynamics

It has long been suspected that population heterogeneity, either at a genetic level or at a protein level, can improve the fitness of an organism under a variety of environmental stresses. However, quantitative measurements to substantiate such a hypothesis turn out to be rather difficult and have rarely been performed. We examine the response of Escherichia coli (E. coli) to infection by viruses known as phage. In order to inject its DNA into a bacterium, the phage must first bind to a specific receptor protein and consequently the number of receptors per bacterium is related to the bacterial susceptibility to infection. Like many proteins in a bacterial population, the number of expressed receptor proteins in an individual cell is not deterministic but stochastic. In this project, experiments and model calculations are used to study how the noisy expression of phage receptors in a bacterial population changes the short-time population dynamics of an isolated and well-mixed E. coli/phage system. We find that when phage are present in the system, the selective killing of bacteria expressing high numbers of phage receptors creates a phenotype selection and the bacterial population can no longer be considered as having a homogeneous susceptibility to the phage pressure. It is shown that a heterogeneous bacterial population is significantly more fit compared to a homogeneous population when confronting a phage attack. We find that a small percentage of cells which are expressing few phage receptors become important because these bacteria persist despite the presence of phage. In view of their important roles in environmental adaptation, in various diseases and potentially in evolution, a fundamental understanding of this minority of cells remains a significant challenge