ABSTRACT
Section 4.2 focuses on signalling pathways where a linear cascade composed of protein kinases transduces some external signal toward the nucleus. Each kinase can be phosphorylated or dephosphorylated through the action of kinases and phosphatases. More generally, substrate molecules can usually be phosphorylated at multiple sites, with up to 7 sites in prokaryotes, and up to 150 sites in eukaryotes (see, e.g., [172]) leading to a large set of possible phosphoforms. The associated phosphorylation process can be seen as a binding process, and the mathematical tools developed in chapter 5 can be adapted to study signalling switches. We present here some recent mathematical models which aim at explaining the experimentally observed switching-like behaviours of basic signalling modules composed of a kinase, a phosphatase and a substrate, the latter containing N phosphorylation sites where phosphates can bind. Such systems can switch abruptly from an inactive or dephosphorylated state to an active or phosphorylated state when the kinase concentration crosses a critical threshold. More than 30% of the proteins are phosphorylated at possibly multiple sites, and this kind of module is thought to be a fundamental element of cell regulation; see, e.g., [106].
