HW02

Due Monday, February 10 at 11:59 PM.

Submission Instructions

Please email your homework to csm2020-instructors@googlegroups.com. Format the subject line as follows:

HW02_<lastname>_<firstname>

For example,

HW02_Faeder_James

Please attach your file as a pdf. Remember to include any code you used as a supplement at the end of the file.

1. (5 points) PBOC2, problem 5.3 (b-c). (We did (a) in class.)

2. (5 points) PBOC2, problem 5.4 (c).

3. (10 points) PBOC2, problem 5.7 (a-c).

4. (10 points) PBOC2, Problem 6.2.

5. (10 points) PBOC2, Problem 6.10.

6. (10 points) Polymerase binding to a promoter (based on PBOC2, Problem 6.3)

Write an expression for the probability of finding RNA polymerase bound to the promoter as a function of the dissociation constants for specific and nonspecific binding, K_S and K_NS. (Hint: Assume that [DNA_NS]>>K_NS.)
Assuming that the dissociation constants for nonspecific and specific binding are 10 uM and 550 nM respectively, estimate the in vivo binding energy for binding of the RNA polymerase to the promoter.
What is the value of the specific binding energy when the dissociation constant is decreased to 3 nM?

7. (10 points) Free versus bound ligand (based on PBOC2, Problem 6.4).

Derive an expression for the probability of binding as a function of the total ligand and receptor concentrations, L_tot and R_tot.
Determine the fractional error in determining the binding probability from using the approximate formula assuming the ligand is in excess versus using the exact formula you derived in part 1. Assume L_tot=R_tot=K_d=50 nM. Make a plot of the fractional error as a function of L_tot and interpret your result.
Fit the binding curves measured by Maeda et al. (2000) for binding of sigma^70 to RNA polymerase assuming the sigma^70 concentration is 0.4 nM using the expression you derived in part 1. Compare this result to the result of fitting assuming that L is in excess (i.e. L_tot >> R_tot).