| The extreme genetic engineering of simple organisms can result in a variety of useful biotechnological, medical, and industrial applications ranging from whole-cell biosensors to gene therapy. By designing the DNA sequences of novel synthetic gene networks, one can "program" an organism to sense new signals and respond to them according to a desired dynamical or logical behavior. With the decreasing time cost of constructing synthetic gene networks, there is a stronger need for computational tools that determine the necessary DNA sequence for a desired behavior. Consequently, we have developed a computer-aided methodology that models the molecular interactions in a synthetic gene network, efficiently predicts its stochastic dynamical behavior, and whose predicts result in the intelligent selection of DNA sequences that exhibit a desired behavior.; This dissertation (273 pages, 81 figures, and 36 tables) expands results from five (out of six total) published papers and two unpublished works. It also contains a thorough introduction to probability theory, stochastic processes, numerical methods for stochastic differential equations, stochastic chemical kinetics, the regulation of gene expression in bacteria, and the modeling of synthetic gene networks in bacteria.; The novel results in this dissertation include: (1, 2) A full description of two novel stochastic numerical methods that greatly speed up the stochastic simulation of an arbitrary, non-linear system of bio/chemical reactions with many reactions and chemical species while retaining accuracy. They are called Hybrid jump/continuous Markov stochastic simulator (HyJCMSS) and an Equation-Free Probabilistic Steady-State Approximation (EF-PSSA). (3) The description of Hy3S: Hybrid stochastic simulation for supercomputers (http://hysss.sourceforge.net). It is an open-source software package that includes our advanced stochastic numerical methods and an easy-to-use graphical user interface. (4, 5) The design criteria for a three-gene genetic oscillator and a new type of synthetic gene network called an AND protein device. (6) The construction, FACS characterization, and mathematical analysis of a synthetic promoter that only expresses the reporter gfp gene when the aTC and IPTG inducers are both present in sufficient concentration. (7) The development of two novel stochastic numerical methods that compute the full stochastic bifurcation diagram of a stochastic chemical system. |
