| The analysis of gene expression microarrays plays an important role in elucidating the function of genes, including the discovery of genetic interactions that regulate gene expression. Several methods for modelling such gene regulatory networks exist, including a variety of continuous and discrete models. An interesting alternative to these methods is fuzzy logic. Fuzzy logic is a method for analyzing data that categorizes the data into multiple states with partial membership, thus violating the law of excluded middle. However, the guidelines for modelling gene expression data with fuzzy logic are fairly open. For example, the number of states used to classify the data and the shape of the membership functions used for classification may be altered to produce different implementations of the fuzzy logic method.; In this work, an existing fuzzy logic model is modified to involve an arbitrary number of states. The affect of altering the number of states on the results is investigated, as is the limiting behavior of the algorithm as the number of states tends to infinity. In addition, a probabilistic model is proposed as an alternative to the fuzzy logic model. It is proven that as the number of states used to classify the data goes to infinity, both of these models converge to a limiting regression surface. Thus, a third alternative for modelling gene regulatory networks is developed using regression techniques.; All three models are tested and compared using simulated microarray data and actual yeast cell cycle microarray data. The models effectively recover networks from the simulation study, while returning biologically plausible results using the yeast cell cycle data. In addition, a unique application of the network models is developed which combines results from quantitative trait loci (QTL) and microarray experiments. All three models serve as useful tools for searching microarray data sets for genetic interactions. |
