Combinatorial Genetic Regulatory Network Analysis Tools for High Throughput Transcriptomic Data

A series of genome-scale algorithms and high-performance implementations is described and shown to be useful in the genetic analysis of gene transcription. With them it is possible to address common questions such as: "are the sets of genes co-expressed under one type of conditions the same as those sets co-expressed under another?" A new noise-adaptive graph algorithm, dubbed "paraclique," is introduced and analyzed for use in biological hypotheses testing. A notion of vertex coverage is also devised, based on vertex-disjoint paths within correlation graphs, and used to determine the identity, proportion and number of transcripts connected to individual phenotypes and quantitative trait loci (QTL) regulatory models. A major goal is to identify which, among a set of candidate genes, are the most likely regulators of trait variation. These methods are applied in an effort to identify multiple-QTL regulatory models for large groups of genetically co-expressed genes, and to extrapolate the consequences of this genetic variation on phenotypes observed across levels of biological scale through the evaluation of vertex coverage. This approach is furthermore applied to definitions of homology-based gene sets, and the incorporation of categorical data such as known gene pathways. In all these tasks discrete mathematics and combinatorial algorithms form organizing principles upon which methods and implementations are based.