Saturday, March 28, 2009

networks and patterns

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.