exam3_pra_probs - 20.320 Spring 2006 Exam 3 Review Practice...

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20.320 Spring 2006 Exam 3 Review Practice Problems 1) Provided that a large number of individuals are involved, the kinetics of mutation can be usefully described by conventional mass-action kinetics. a. In a bacterial population of 1000 L of 3x10 7 cells/ml, the mutation of one gene g 1 to a second type g 2 occurs with a frequency of 10 -8 per cell division, and the mutation from g 2 to g 1 occurs at a frequency 10 -6 per cell division. Calculation the “equilibrium” concentrations of each species. b. In cells able to repair damaged DNA enzymatically, it is reasonable to suppose that, since the enzyme exists, there is an equilibrium between normal and damaged DNA: k 1 ZZZX Normal YZZZ damaged k -1 E repair Suppose ultraviolet light opens a second forward path parallel to the first with rate constant k 1 . Show that the equilibrium population fraction of damaged DND rises from k k + k 1 1 to 1 . k + k k + k 1 + k 1 1 1 1 2) Repressor protein for the phage λ P R promoter can bind to three different operator sites designated O R 1, O R 2, and O R 3. As indicated in the figure, binding of repressor to any site except O R 3 blocks the P R promoter. Assume that repressor-operator binding is at equilibrium and that the equilibrium constants for repressor binding to the three sites are K 1 , K 2 , and K 3 , respectively. P R O R 3 O R 2 O R 1 a. Develop a general equation for the fraction of P R promoters accessible for RNA polymerase binding in terms of the equilibrium constants and the total amount of repressor protein and P R O R sequences in the cell b. Evaluate the fraction of accessible promoters for a cell containing 25 P
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exam3_pra_probs - 20.320 Spring 2006 Exam 3 Review Practice...

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