Synthesis of Biological and Mathematical Methods for Gene Network Control Synthetic biology is an emerging field which melds genetics, molecular biology, network theory, and mathematical systems to understand, build, and predict gene network behavior. As an engineering discipline, developing a mathematical understanding of the genetic circuits being studied is of fundamental importance. In this dissertation, mathematical concepts for understanding, predicting, and controlling gene transcriptional networks are presented and applied to two synthetic gene network contexts. First, this engineering approach is used to improve the function of the guide ribonucleic acid (gRNA)-targeted, dCas9-regulated transcriptional cascades through analysis and targeted modification of the RNA transcript. In so doing, a fluorescent guide RNA (fgRNA) is developed to more clearly observe gRNA dynamics and aid design. It is shown that through careful optimization, RNA Polymerase II (Pol II) driven gRNA transcripts can be strong enough to exhibit measurable cascading behavior, previously only shown in RNA Polymerase III (Pol III) circuits. Second, inherent gene expression noise is used to achieve precise fractional differentiation of a population. Mathematical methods are employed to predict and understand the observed behavior, and metrics for analyzing and quantifying similar differentiation kinetics are presented. Through careful mathematical analysis and simulation, coupled with experimental data, two methods for achieving ratio control are presented, with the optimal schema for any application being dependent on the noisiness of the system under study. Together, these studies push the boundaries of gene network control, with potential applications in stem cell differentiation, therapeutics, and bio-production.autMenn, David JthsWang, XiaodgcKiani, SamiradgcHaynes, KarmelladgcNielsen, DaviddgcMarshall, PamelapblArizona State UniversityengDoctoral Dissertation Biomedical Engineering 2018https://hdl.handle.net/2286/R.I.5046400Doctoral DissertationAcademic theses134 pages115383988661630032421156623systemIn Copyright2018TextBiomedical EngineeringCRISPRgene networknonlinear dynamicsStochasticitySynthetic Biology