Feedback loops in biological networks.

We introduce fundamental concepts for the design of dynamics and feedback in molecular networks modeled with ordinary differential equations. We use several examples, focusing in particular on the mitogen-activated protein kinase (MAPK) pathway, to illustrate the concept that feedback loops are fundamental in determining the overall dynamic behavior of a system. Often, these loops have a structural function and unequivocally define the system behavior. We conclude with numerical simulations highlighting the potential for bistability and oscillations of the MAPK pathway re-engineered through synthetic promoters and RNA transducers to include positive and negative feedback loops.