| The application of high-density DNA microarray technology to gene transcription analyses has been responsible for a real paradigm shift in biology. The majority of research groups now have the ability to measure the expression of a significant proportion of the human genome in a single experiment, resulting in an unprecedented volume of data available to the scientific community. Consequently, this has stimulated the development of algorithms to classify and describe the complexity of the transcriptional response of a biological system. However, efforts towards developing the analytical tools necessary to exploit this information for revealing interactions between the components of a cellular system are still in their early stages.; A variety of methods have been proposed to reverse engineer genetic regulatory networks from gene expression profiling data. In this dissertation the applicability of Linear Dynamical Systems (LDS), also known as state-space models (a subclass of Dynamic Bayesian Networks), is examined for this purpose. LDS models have important features that make them attractive for modeling gene expression data. Particularly, LDS models can handle hidden variables that represent the effects of genes that have not been included on the microarray, levels of regulatory proteins or the effects of mRNA degradation. LDS models can also handle continuous variables, such as gene expression measurements. In this dissertation an LDS model with inputs for gene expression time series is developed and applied to a subset of genes involved in the activation of T cells during the generation of an immune response. The structural properties of the model such as observability, controllability, stability, and identifiability are solved for both the general model with inputs and the gene expression model in which the inputs are in fact prior or current observations. Constrained parameter estimation is addressed for both matrix-linear constraints and for a new formulation allowing constraints to be imposed on arbitrary parameter patterns. Bootstrap confidence intervals developed for parameters representing “gene-gene” interactions over time are presented and demonstrated using simulated data. Results from experimental data are presented which suggest testable biological hypotheses concerning influences between gene expression events involved in the activation of human T cells. |
