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Homework Help: Question about Cells and Cell Channels

  1. Mar 25, 2009 #1
    Imagine that it is possible to design cells of varying size. A cell is to be
    designed with a membrane that has a stable number of open channels. To
    this end, the number of channels must meet the following condition: the
    standard deviation of the number of open channels shall be no more than
    one percent of the expected number of open channels.

    (a) In terms of p and q, give the formula for M, where M is the
    minimum number of channels that the cell must have.

    (b) Assuming a spherical cell, give a formula for a, where a is the
    minimum radius that the cell must have to hold the required number
    of channels, at density D. (answer must be in terms of q, D and p,
    and constants only).

    (c) What is the minimum radius, a, that the cell must have to hold the
    required number of channels if the probability p is fixed at 0.05 and
    D is 200 channels per μm2?

    This is just review so if anyone could help me figure out this problem i would appreciate it. I know the answer to c is 8.69um, but unsure how to reach that result.
  2. jcsd
  3. Mar 25, 2009 #2


    User Avatar
    Science Advisor
    2017 Award

    Read up on the Poisson distribution.
  4. Mar 25, 2009 #3
    thats not mentioned in our chapter at all (or in class) , could it be something else?

    some help with solving the problem would be helpful.
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