Transcription is a fundamental biological process of copying genetic information from DNA to messenger RNA and is the first step in the gene expression process. Transcription is governed by a complex system of biochemical and biophysical processes and, despite decades of research, open questions about the molecular mechanisms behind transcription remain. For example, our understanding of the molecular mechanisms behind the transcriptional bursting phenomenon, an observation that messenger RNA molecules are produced in a discontinuous manner, and our understanding of gene expression pattern formation during embryonic development is still incomplete.

The chapters of this thesis are dedicated to developing various mechanistic and phenomenological models of transcription. Since transcription typically involves small numbers of products and random interactions between the reactants, we adopt a stochastic, chemical kinetic approach for our investigations. First, following an observation that transcription involves a spectrum of activity states, we develop a phenomenological, multi-state model of transcription. Using this model, we draw a connection between the number of independent biochemical states of transcription and the number of maxima in the distribution of transcripts produced. We also develop a method of evaluating the number of transcriptional states from experimental data. Second, we develop a mechanistic model that shows that transcriptional bursting can result from the interplay between DNA supercoiling buildup and supercoiling release due to the enzymatic action of gyrase. Using the mean first-passage time analysis and experimental measurements of transcription elongation rate, we calculate the energy needed to produce an additional transcript under the supercoiling conditions. Third, following a set of observations that suggest that collective dynamics of messenger RNA-producing RNA polymerases (RNAPs) play an important role in ensuring transcriptional integrity, we develop two different mechanistic models of transcription which take into account the long-range cooperative interactions between RNAPs and show that such cooperativity can result in a simultaneous increase in transcriptional productivity and decrease in transcriptional noise at an optimal value of mechanochemical coupling. Lastly, in response to recent observations that spatial modulation in chemical kinetic rates of transcript production and promoter activation is associated with gene expression pattern formation in embryos, we developed a phenomenological model that demonstrates that transcriptional two-state ON/OFF model with exponentially varying chemical kinetic rates of either transcript production and promoter turn ON or transcript production and promoter turn OFF rates can produce a spatial gene expression stripe pattern.