The so-called mixed feedback loop (MFL) is a small two-gene network where protein $A$ regulates the transcription of protein $B$ and the two proteins form a heterodimer. It has been found to be statistically over-represented in statistical analyses of gene and protein interaction databases and to lie at the core of several computer-generated genetic networks. Here, we propose and mathematically study a model of the MFL and show that, by itself, it can serve both as a bistable switch and as a clock (an oscillator) depending on kinetic parameters. The MFL phase diagram as well as a detailed description of the nonlinear oscillation regime are presented and some biological examples are discussed. The results emphasize the role of protein interactions in the function of genetic modules and the usefulness of modeling RNA dynamics explicitly.

• Received 27 May 2005

DOI:https://doi.org/10.1103/PhysRevE.72.031908