The study of artificial genetic networks with oscillatory expression patterns may offer unique insights into understanding the underlying biological mechanisms leading to oscillations in nature. Moreover, such networks can be used to achieve various meaningful biotechnological objectives. Thus, it is important to discover a variety of rules that lead to oscillatory expression dynamics at the single-cell level. In this work, we propose a modification of a bistable gene-switching circuit, known as the genetic toggle, to construct a novel oscillatory network. The genetic toggle is an artificial network composed of two promoter-repressor pairs. The particular structure of the network leads to two possible stable patterns, each characterized by high (low) expression levels of one gene (lacI) and low (high) expression levels of the other (cIts). The switch between the two patterns of expression is accomplished by increasing the concentration of an extracellular inducer, which up-regulates the transcriptional activity of the promoter that controls cIts expression. The modification we propose consists of placing a gene that encodes a protease enzyme under the control of the promoter that regulates cIts expression. This in turn offers the ability for transient switching between two states, thus leading to oscillatory expression level dynamics.

The rationale behind the proposed modification was guided by a mathematical model that we developed to describe the dynamics of the modified toggle network. The model was employed as predictive tool to quantify the effect of meaningful system parameters on the oscillatory patterns of gene expression. Simulation studies have revealed that the oscillation onset can be triggered through appropriate design of the promoter strengths and the protein half-lives. Moreover, modulation of the concentration of an extracellular inducer allows fine-tuning of key network parameters such as the oscillation amplitude and period. Thus, our model can serve as a tool for rationally modifying the genetic network and choosing the extracellular conditions to obtain desirable oscillatory patterns of gene expression.