Saturday, March 28, 2009
03.20.09. Many bacteria forage for nutrients using a "run and tumble" strategy: they swim straight ("run") until they detect a decrease in nutrient concentration, then they spin around ("tumble") to face a new direction and try again. Students were shown a demo of a running-and-tumbling bacterium whose jagged path was labeled with length measurements, then asked, "How far would the bacterium have had to swim if it went in a straight line instead?" With a bit of guidance ("Do you see the triangles?"), students recognized this as an application of the Pythagorean theorem, and that the answer lay in summing several hypotenuse calculations.
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.
02.25.09. The Food and Drug Administration (FDA) is the governing body charged with, among other things, preventing contamination in the food that we eat. Many times, however, the amounts of contaminants that they allow in foods is surprisingly high (the often stomach-churning data are available freely on the FDA's website here). For example, the FDA allows 30 insect fragments per 100 grams of peanut butter and 75 insect fragments per 50 grams of cocoa powder before recalling these foods. Students used ratios and proportions to calculate from these data the allowed number of insect fragments in a Reese's peanut butter cup. Only after obtaining their result were they permitted to (not without trepidation) enjoy their treat. (For those interested, a peanut butter cup can contain roughly 30 insect fragments before the FDA deems it unfit to eat--not to mention a few rodent hairs...)