4.3.3.P5
Listeria, like all bacteria emit small molecules as waste product or for signaling. Here we will consider a “race” between a listeria bacteria (about 1 μm across) that swims along a straight track inside a (much larger ~15 μm) mammalian cell that it has infected. The listeria emits a pulse of signaling molecules. The listeria itself moves in the cell at a speed of about 5 μm/s. The question we want to tackle is whether molecules emitted by the listeria cell could move ahead of the cell as they diffuse.
A. Assume that a Listeria cell, when at one end of the mammalian cell, emits a pulse of molecules with diffusion constant of D=200 μm2/s. The Listeria cell then moves to the other side of the mammalian cell, reaching the other side of the cell in 3 seconds. How much time does it take the diffusing molecules to reach the other end of the cell?
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B. Can diffusion be faster than directed motion? Explain your reasoning.
C. If the mammalian cell were three times larger, by how much does the time to diffuse across a whole cell change? Explain your reasoning.
D. A different signaling molecule emitted by the Listeria has had a chemical attached to it that glows when illuminated by a particular light source. A pulse is seen to be emitted at t = 0 and 5 seconds later is observed to have expanded to a blob that has a radius of 2 μm. If you can describe this as diffusion in two dimensions how big would you expect the blob to be if you took another picture at t = 20 s? Can you find the diffusion constant? If you can, do so. If you can’t explain why not.
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