# Homework Help: Question about Cells and Cell Channels

1. Mar 25, 2009

### atlbraves49

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. Mar 25, 2009

### Ygggdrasil

Read up on the Poisson distribution.

3. Mar 25, 2009

### atlbraves49

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.