A concentrated drop of serine is dropped into a bucket containing a single E. coli cell. The cell is at the bottom of the bucket, which is 0.2 meters away from the serine droplet.
a) Estimate how long would it take for molecules of serine to reach the E. coli cell by pure diffusion (assume the E. coli does not move and use the approximation of x2 = 2Dt).
b) Now assume the E. coli can move. Estimate how long would it take for the cell to swim to the center of the serine droplet using chemotaxis. You can assume the cell swims in a straight line towards the serine. Typical swim speeds for an E. coli can be found in several places, including the bionumbers website (
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