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Biophysics Fall 2011 
Homework 4
You are encouraged to work together, but each of you needs to hand in your own solution. The solution
needs to be typed, not handwritten. You should email the solution as a pdf file by Wednesday, Dec 7. This
homework is optional. If you hand the homework in, it will be evaluated and counted.
Problem 1
Consider a spherical protein with a radius of 3 nm, for which the diffusion coefficient is about
100
μ
m
2
/s. How long will it take to diffuse 40 nm? Suppose there is a constant force of 1 pN.
How long will it take to diffuse 40 nm in the direction of the force? How long will it take to
diffuse 40 nm against the force?
Problem 2
There is strong evidence that chemoreceptors in E. coli tend to cluster near one pole. One
hypothesis about the role of such clustering is that it might increase the ability of a bacterium to
better detect molecules in its environment. Determine if this is indeed a better strategy for
absorbing (i.e. counting) molecules of chemoattractant. Approximate E. coli as a sphere a = 1
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This note was uploaded on 12/12/2011 for the course PHYS 146a taught by Professor Staff during the Fall '11 term at UC Irvine.
 Fall '11
 staff
 Physics, Work

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