Wednesday, February 10, 2010

outrunning diffusion

01.25.10. Bacteria swim toward higher nutrient concentrations using a "run and tumble" strategy (see 03.20.09 post and this animation from ClearScience, from which a screen shot is shown here). It is important to recognize, however, that regions of high nutrient concentration are constantly changing, since nutrient particles are diffusing throughout the medium (as Kool-Aid mix diffuses throughout a glass of water). A bacterium must reach the nutrients before they diffuse away. As a class, we realized that this criterion can be made quantitative using an inequality: the bacterium's swimming properties (which students quantified as its velocity v and its run length L) must be greater than the nutrient's diffusive properties (which students quantified as the recently discussed diffusion constant D). Examining the units (or 'dimensions') of the three quantities as a class, we realized multiplication of v and L yields the only dimensionally consistent result, giving vL > D. Students isolated L, then substituted D = 1,000 um^2/s and v = 30 um/s (bacteria can swim about 30 times their body length in 1 second!) to compute the minimum run length necessary to "outrun" diffusion: L > D/v ~ 33 um (micrometers), a biologically realistic value.