I've been learning a lot about these networks from Professor Uri Alon of the Weizmann Institute, who has posted several of his enlightening lectures to YouTube. In one lecture he discusses chemotaxis, the ability of many bacteria and other cells to swim towards nutrients and away from toxins.
In order to perform chemotaxis, organisms like E. coli have to detect tiny gradients of nutrients or toxins, sometimes as small as 1 molecule in 1,000 over the length of their one-micrometer-long bodies. Ultimately, they accomplish this by randomly swimming in different directions, and when they sense an increase in a nutrient (or decrease in a toxin), they are less likely to turn. It's kind of a unicellular version of Hide the Object ("You're getting warmer!").
Before it can detect changes in the levels of a nutrient or toxin, the cell has to "subtract out" whatever level it currently sees in the environment. This is adaptation, and is related to how your eyes adapt when you step outside into the sunlight, or how your sense of smell adapts after first smelling those chocolate chip cookies baking in your oven. If you smelled cookies baking in a strange house, your nose could lead you to the kitchen, largely because your sense of smell adapts to the amount of cookie aroma in each room you visit. You can tell if you're getting closer, because the cookie scent will become stronger.
Based on the model Alon describes, I built a little simulation showing how this works. In the video below, each white dot represents a bacterium, and the green color represents a delicious nutrient such as aspartate. On the left, the bacteria cannot sense the nutrient, while on the right, they can. You'll notice that the bacteria on the right wiggle and jiggle quite a bit, but they generally stick to the green part of the screen, where all the goodies are. They sometimes move away from the green area, but usually realize their mistake and turn back. The bacteria in this simulation have the properties of gradient sensing and adaptation, even though they are using just three virtual enzymes!
The real system in E. coli is based on only six proteins in total, so it's not much more complicated. Their solution to the problem is different than anything we humans would design, but it's a simple and elegant system that, according to Prof. Alon, resembles many other networks throughout the tree of life. Maybe it can even tell us something about the higher-order functions of our own brains?