580.429 SBE3 2009 Quiz 10 (so-called makeup) Name: Diffusion vs. cell communication in patterning. 1. (2 pts) Let’s model an embryo as a 1D array of cells. Each cell has length L , and there are N total cells, giving a total end-to-end distance R = NL . A small diffusible molecule with diffusion constant D is generated in a single burst at time 0 tightly localized at one end. How long does it take for the mean-square-distance of the density profile to equal R 2 , roughly the time for the signal to diffuse from end to end? Express your answer, T D for pure diffusion, in terms of N , L , and D . T D = R 2 / 2 D = ( NL ) 2 / 2 D 2. (4 pts) An alternative strategy for propagating a signal is cell-to-cell communication. Suppose that the small molecule initiates a signaling cascade resulting in release of more protein. For the signal to propagate through one cell, the following steps must occur: (a) The small molecule diffuses to its target, requiring a mean-square-distance of L 2 . (b) The target is cleaved, which happens so fast we can ignore the time.
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