Simple biochemical motifs (1, 2, & 3)

This triplet of introductory lectures summarizes a few of the most basic biochemical models with the simple rate equations that they satisfy. I describe production-decay, with Michaelis-Menten and sigmoidal terms, showing how the latter can lead to bistable behaviour and hysteresis. I describe two bistable genetic circuits: the toggle switch by Gardner et al (2000) Nature 403, and the phage-lambda gene by Hasty et al (2000) PNAs 97. The idea of bifurcations is discussed. Finally, I introduce
phosphorylation cycles, and show that sharp responses can arise when the enzymes responsible (kinase and phosphatase) operate near saturation. (This is the so called Goldbeter-Koshland ultrasensitivity).