Mathematics

Flow control is a fundamental feature for the correct performance of large scale networks, of which familiar examples are the Internet, power grids or even pipe networks. In the biological world, complex cellular pathways rely as heavily on a regulated flow of nucleic acids, transcription factors and other metabolites. It is therefore important to explore and understand all the possibilities for production and degradation rate control in biochemical components. Two designs to regulate and match the RNA production of two in vitro synthetic genetic circuits (J. Kim ) will be considered. In particular, these architectures are based on self inhibition and cross activation mechanisms that can dynamically change the fraction of actively transcribing DNA strands and correctly respond to changes in the chemical environment. The two regulatory architectures are numerically analyzed trough a first order model derived from the set of occurring reactions. Most importantly, experimental results show the effectiveness of the proposed feedback loops in regulating the RNA out-flow of the circuits.