03.13.09. Cells perform their functions by using networks of interacting proteins. For example, the network shown here (from Alon et al, Nature, 1999) describes the protein interactions occuring inside a bacterium that turn the detection of a nutrient into the activation of the bacterium's flagellar motor (the "propeller" it uses to swim toward more nutrients). Mathematically, a network is just a set of dots ("nodes") connected by lines ("edges"). Students drew fully-connected networks with 3, 4, 5,... nodes and counted the number of possible edges. By noticing the pattern, students derived as a class an equation to compute the number of possible edges x from the number of nodes n: x = n(n-1)/2.
