### Problem Set 2 (pdf)

```PHYSICAL BIOLOGY OF CELL PROBLEM SET 2014 2 Prof. Radenovic Problem sets due by October 2nd
PROBLEM 1.
Assume that the four bases A, C, T, and G occur with equal likelihood in a DNA sequence of
nine monomers.
(a) What is the probability of finding the sequence AAATCGAGT through random
chance?
(b) What is the probability of finding the sequence AAAAAAAAA through random
chance?
(c) What is the probability of finding any sequence that has four A’s, two T’s, two G’s,
and one C, such as that in (a)?
PROBLEM 2.
In the estimate on cell-to-cell variability in the chapter, we learned that the standard deviation
in the number of molecules partitioned to one of the daughter cells upon cell division is given
by
n12  n1
2
 Npq
(a) Derive this result.
(b) Derive the simple and elegant result that the average difference in intensity between the
two daughter cells is given by
 I1  I 2 
2
  I tot
where I1 and I2 are the intensities of daughters 1 and 2, respectively, and Itot is the total
fluorescence intensity of the mother cell and assuming that there is a linear relation between
intensity and number of fluorophores of the form I=N.