Robust non-linear differential equation models of gene expression evolution across Drosophila development

Robust modeling of differential gene expression data using normal/independent distributions: a Bayesian approach

In this paper, the problem of identifying differentially expressed genes under different conditions using gene expression microarray data, in the presence of outliers, is discussed. For this purpose, the robust modeling of gene expression data using some powerful distributions known as normal/independent distributions is considered. These distributions include the Student’s t and normal distributions which have been used previously, but also include extensions such as the slash, the contaminated normal and the Laplace distributions. The purpose of this paper is to identify differentially expressed genes by considering these distributional assumptions instead of the normal distribution. A Bayesian approach using the Markov Chain Monte Carlo method is adopted for parameter estimation. Two publicly available gene expression data sets are analyzed using the proposed approach. The use of the robust models for detecting differentially expressed genes is investigated. This investigation shows that the choice of model for differentiating gene expression data is very important. This is due to the small number of replicates for each gene and the existence of outlying data. Comparison of the performance of these models is made using different statistical criteria and the ROC curve. The method is illustrated using some simulation studies. We demonstrate the flexibility of these robust models in identifying differentially expressed genes.

Modeling the Drosophila gene cluster regulation network for muscle development

The development of accurate and reliable dynamical modeling procedures that describe the time evolution of gene expression levels is a prerequisite to understanding and controlling the transcription process. We focused on data from DNA microarray time series for 20 Drosophila genes involved in muscle development during the embryonic stage. Genes with similar expression profiles were clustered on the basis of a translation-invariant and scale-invariant distance measure. The time evolution of these clusters was modeled using coupled differential equations. Three model structures involving a transcription term and a degradation term were tested. The parameters were identified in successive steps: network construction, parameter optimization, and parameter reduction. The solutions were evaluated on the basis of the data reproduction and the number of parameters, as well as on two biology-based requirements: the robustness with respect to parameter variations and the values of the expression levels not being unrealistically large upon extrapolation in time. Various solutions were obtained that satisfied all our evaluation criteria. The regulatory networks inferred from these solutions were compared with experimental data. The best solution has half of the experimental connections, which compares favorably with previous approaches. Biasing the network toward the experimental connections led to the identification of a model that is only slightly less good on the basis of the evaluation criteria. The non-uniqueness of the solutions and the variable agreement with experimental connections were discussed in the context of the different hypotheses underlying this type of approach.