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Random vs coherent motion (Listeria)

Page history last edited by Joe Redish 9 years, 7 months ago

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?

 

 

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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