BACKGROUND: In many approaches to the inference and modeling of regulatory interactions using microarray data, the expression of the gene coding for the transcription factor is considered to be an accurate surrogate for the true activity of the protein it produces. There are many instances where this is inaccurate due to post-translational modifications of the transcription factor protein. Inference of the activity of the transcription factor from the expression of its targets has predominantly involved linear models that do not reflect the nonlinear nature of transcription. We extend a recent approach to inferring the transcription factor activity based on nonlinear Michaelis-Menten kinetics of transcription from maximum likelihood to fully Bayesian inference and give an example of how the model can be further developed. RESULTS: We present results on synthetic and real microarray data. Additionally, we illustrate how gene and replicate specific delays can be incorporated into the model. CONCLUSION: We demonstrate that full Bayesian inference is appropriate in this application and has several benefits over the maximum likelihood approach, especially when the volume of data is limited. We also show the benefits of using a non-linear model over a linear model, particularly in the case of repression.

MOTIVATION: Despite theoretical arguments that so-called 'loop designs' for two-channel DNA microarray experiments are more efficient, biologists continue to use 'reference designs'. We describe two sets of microarray experiments with RNA from two different biological systems (TPA-stimulated mammalian cells and Streptomyces coelicolor). In each case, both a loop and a reference design were used with the same RNA preparations with the aim of studying their relative efficiency. RESULTS: The results of these experiments show that (1) the loop design attains a much higher precision than the reference design, (2) multiplicative spot effects are a large source of variability, and if they are not accounted for in the mathematical model, for example, by taking log-ratios or including spot effects, then the model will perform poorly. The first result is reinforced by a simulation study. Practical recommendations are given on how simple loop designs can be extended to more realistic experimental designs and how standard statistical methods allow the experimentalist to use and interpret the results from loop designs in practice. AVAILABILITY: The data and R code are available at http://exgen.ma.umist.ac.uk CONTACT: [email protected].

The goal of this paper is to demonstrate the introduction of dimensional variables as well as the applications of dimensional analysis in Computer Algebra system (Mathematica). The package Dimensional Analysis developed by author uses nondimensionalization based on II-theorem to simplify equations and to reduce the number of parameters when the governing equations are not known. The package contains symbols, dimensional formulae and units for principal physical quantities, as well as a number of named dimensionless parameters. Another important feature of the package is its ability to check the dimensional homogeneity of the expressions. This package is aimed at helping researchers with the preliminary analysis of models and simplification of large-scale problems by using dimensionless parameters. The package can also be used in teaching.