This thesis develops a novel method, fluorescence grid based aggregation (FGBA), to justify a dynamical model of protein expression using experimental fluorescence histograms. In FGBA method, we first describe the dynamics of the gene-protein system by a chemical master equation (CME), while the protein production rates are unknown. Second, we aggregate the states of the CME into unknown group sizes. Then, we show that these unknown values can be replaced by the data from the experimental fluorescence histograms. Consequently, final probability distributions correspond to the experimental fluorescence histograms.

In particular, we focus our study on Antigen 43 (Ag43), which is an abundant outer membrane protein in Escherichia coli. This protein is not involved in feedback regulation, and instead the encoding gene, agn43, uses a mechanism of generating multiple phases in order to regulate the protein production. In this document, we first employ our FGBA method to the dynamical system of agn43's phase variation introduced by (Lim et al., 2007) and validate our method by comparing the final probability distributions with Lim's experimental fluorescence intensity histograms. Next, we propose a novel toggle switch for the production of Ag43 based on the experimental results on structure, function, and regulation of agn43 presented by (van der Woude et al., 2008).