The current rapid expansion of biological knowledge offers a great opportunity to rationally engineer biological systems that respond to signals such as light and chemical inducers by producing specific proteins. Turning on and off the production of proteins on demand holds great promise for creating significant biotechnological and biomedical applications. With successful stories already registered, the challenge still lies with rationally engineering gene regulatory networks which, like electronic circuits, sense inputs and generate desired outputs. From the literature, we have found kinetic and thermodynamic information describing the molecular components and interactions of the transcriptionally repressing lac, tet, and ara operons. Connecting these components in a model gene network, we determine how to change the kinetic parameters to make this normally nonperiodic system one which has well-defined oscillations. Simulating the designed lac-tet-ara gene network using a hybrid stochastic-discrete and stochastic-continuous algorithm, we seek to elucidate the relationship between the strength and type of specific connections in the gene network and the oscillatory nature of the protein product. Modeling the molecular components of the gene network allows the simulation to capture the dynamics of the real biological system. Analyzing the effect of modifications at this level provides the ability to predict how changes to experimental systems will alter the network behavior, while saving the time and expense of trial and error experimental modifications.