Design of genetic switches with only positive feedback loops

We develop a new methodology to design synthetic genetic switch networks with multiple genes and time delays, by using monotone dynamical theory. We show that the networks with only positive feedback loops have no stable oscillation except equilibria whose stability is also independent of the time delays. Such systems have ideal properties for switch networks and can be designed with out consideration of time delays, because the systems can be reduced from functional spaces to Euclidian spaces due to the independence to time delays. Specifically, we first prove the basic properties of the genetic networks composed of only positive feedback loops, and then propose a procedure to design the switches, which drastically simplifies analysis of the switches and makes theoretical analysis and designing tractable even for large scale systems. Finally, we demonstrate our theoretical results by designing a biologically plausible synthesized genetic switch with experimentally well investigated lacI, tetR, and cI genes.