Mathematical Analysis of Genetic Circuits

This lecture covers the mathematical analysis of genetic circuits, focusing on the implementation of synthetic plasmids in E. coli. It discusses the use of basic ingredients like lacI, Tet, and lambda repressors to prevent repression of specific promoters. The lecture explores the experimental implementation of these circuits and the effects of switching signals like IPTG, ATC, and temperature pulses. It delves into the concept of limit cycle oscillators and the Poincaré-Bendixon theorem to determine the conditions for the existence of stable limit cycles. The lecture also touches upon the glycolysis cycle and its transformation of glucose into pyruvate, emphasizing the application of mathematical models to understand cellular processes.