Understanding the relationship between network structure and behavior is fundamental to the field of computational and systems biology. A particularly important distinction is the extent to which qualitative aspects of network performance are encoded in network topology as opposed to being determined through quantitative details, such as those of kinetics. Here, we develop a general and rigorous mathematical framework for the analysis of genetic networks and apply it to a family of synthetic gene networks. A key feature of our methodology involves determining network behavior that is insensitive to kinetic parameters such as rate constants and nonlinear functional dependencies of rates on molecular concentrations. Results indicate that behavior observed in some networks cannot be reconciled with standard gene expression and regulation models. We explore relaxing model assumptions to explain the observed behavior, allowing for both dynamic and stochastic phenomena, and propose an alternative model. Our alternative model includes the suggestion of a new mechanism by which the counterintuitive behavior could be achieved; central to the model is the assumption that the Clp protein degradation system, which is responsible for the regulatory proteins used in this study, becomes saturated.