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. GRADING RULES 1. Incorrect calculus takes 25% away 2. Correct variables, and written formulas that should be 50 % 3. Significant digits –if not done right 10% away
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