The study of gene regulation has been an important topic in biology for decades. Activation and silencing of genes affect everything from everyday breathing to deadly diseases, and thus concern not only academic biologists, but also healthcare professionals and thus the general population. Researchers now have mapped out many species' entire genomic sequences, but annotation is incomplete concerning stretches of DNA that regulate genes, as well as protein coding regions. Accompanying the expansion in sequence data, new technologies have provided copious amounts of expression data suitable for modeling studies. Experimental and computational biology now combine to answer many of the complicated questions behind gene regulation and gene function, although we lack a complete picture of the physical and chemical reactions of the complex gene regulatory machinery. To better understand the processes of gene regulation we need to develop mathematical models that describe how DNA sequences direct differentiated gene expression, predict the expression of unknown genes or variants of genes, and reveal the driving forces behind gene regulation. With new high throughput techniques leading to large data sets of increased quality, mathematicians need no longer make speculative hypotheses; they now can connect their models directly with varying levels of biological inputs and verify the model predictions with quantitative data sets. My studies develop new approaches for quantitative assessment and application of mathematical tools important for gene regulatory studies.
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