11.24.09. The development of a living embryo, i.e. the positioning and differentiation of thousands of cells, relies on information encoded in the numbers of proteins within these cells. These numbers are small--typically tens or hundreds--and since the proteins themselves are products of probabilistic reactions, these numbers fluctuate. Fluctuations have the most severe effect when the averages they fluctuate around are small, a point well illustrated by bags of M&Ms. On average, one sixth of the M&Ms in a any bag are red, meaning a large bag containing, say, 600 M&Ms, has roughly 100 red ones. Even 10% fluctuations in this number are hardly noticeable (a pile of 110 red M&Ms is not easily distinguished from a pile of 100). A fun-sized bag, on the other hand, contains only 15 or so M&Ms, meaning that 2.5 of them (on average) are red. Fluctuations of only a few M&Ms can mean the difference between five and none, a dramatically noticeable effect, especially if reds are one's favorite (read: are favored by environmental pressures). Cells are fun-sized: their proteins are few in number, and fluctuations in these numbers can produce markedly different phenotypes (the green spots in the picture here, from Golding et al, Cell, 2005, are individual mRNAs--molecules that produce proteins--present in only several copies per bacterial cell). These fluctuations place a physical limit on, e.g., the precision with which a collection of embryonic stem cells can differentiate into specific cell types (see, e.g., Tkacik et al, PNAS, 2008). Using fun-sized M&M packages as models for cells, students explored the concepts of (1) variation, measuring and plotting as histograms the numbers across packages of total and specifically colored M&Ms, and (2) number sense, interpreting data on the numbers of M&Ms per package (nonnegative integers or "whole numbers"), package weights (real numbers), and M&M circumferences (irrational numbers if using pi).
