On three genetic repressilator topologies
Novel mathematical models of three different repressilator topologies are introduced. As designable transcription factors have been shown to bind to DNA non-cooperatively, we have chosen models containing non-cooperative elements. The extended topologies involve three additional transcription regulatory elements—which can be easily implemented by synthetic biology—forming positive feedback loops. This increases the number of variables to six, and extends the complexity of the equations in the model. To perform our analysis we had to use combinations of modern symbolic algorithms of computer algebra systems Mathematica and Singular.
Synthetic biology is one of the most rapidly developing fields of biology. Synthetic
genetic circuits are of high interest due to their possible applications in
biosensing, bioremediation, diagnostics, therapeutics, etc. Genetic oscillators
are some of the most studied circuits due to their complexity and the possibility
of many different topologies. Building synthetic genetic oscillators with
controllable periods and amplitudes would be of great interest to the synthetic
biology field as they could for example potentially be used for treatment of
diseases related to the circadian cycle.
Common Design 