1. In lecture we learned about the Lac Repressor. Below is the binding curve for the wild-type Lac repressor binding to lac operator DNA.

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1 LS1a Fall 06 Problem Set #10 Due Friday 12/15 at noon in your TF s drop box on the 2 nd floor of the Science Center all questions including the (*extra*) one should be turned in 1. In lecture we learned about the Lac Repressor. Below is the binding curve for the wild-type Lac repressor binding to lac operator DNA. a) For the binding equation perator-repressor perator + Repressor Write the equation for the equilibrium dissociation constant, K d. b) Using the binding curve, determine the value of K d for repressor binding to operator. c) If k off for Repressor binding to perator is 1 x 10-5 s -1, what is k on? 1

2 d) Calculate the half-life (t 1/2 ) of perator-repressor binding. e) A mutant Lac repressor is found that binds to the operator sequence with a G that is 2.8 kcal/mol lower (more negative) than the G of the wild-type Lac repressor. What is the expected K d for this mutant repressor? [Hint: Alberts p. 98] f) Assuming k on is the same for the mutant and the wild-type repressor, determine k off for the mutant repressor. g) The K d for the Lac repressor binding to random DNA (a sequence different from the lac operator), is 1 x 10-6 M. Using the k on calculated in part (c), determine the t 1/2 for non-specific DNA binding of the Lac repressor. h) The affinity of the Lac repressor mutant described in part (e) for non-specific DNA is affected by the same magnitude ( G =-2.8 kcal/mole). If k on is the same as the value calculated in part (c), how would this mutant affect the ability of the bacteria to respond to lactose. 2

3 2. Toxins released from the bacteria Bacillus anthracis cause anthrax. The generation of toxin depends on the growth environment of the bacteria, and the activation state of various genes. Two key genes are AbrB and Spo0A. To test if the proteins AbrB and Spo0A are phosphorylated, B. anthracis is cultured in media containing radioactive ATP for 5 days. The radioactive ATP can be taken up by the cell and used by kinases in the cell to phosphorylate proteins. The structure of ATP is shown below. NH 2 ATP P # P " P! N N N N H H a) You find that some of the Spo0A is radioactive. Which phosphate group (α, β, or γ) will be transferred to Spo0A by the kinase and therefore has the radioactive isotope of phosphate? b) Why is a kinase necessary for this reaction to occur spontaneously within a reasonable biological time-frame? c) Give three reasons why regulation of protein phosphorylation is important? 3

4 To further investigate, each day a small sample of bacteria is taken from the culture. The bacterial cells are lysed to release all of their proteins. The proteins are loaded on a gel and separated by size. In the following experiments, antibodies are used to reveal the level of protein present at each time point. Tubulin is used as a control to show that the same amount of total protein is present at each time point. The lower graph plots the change in bacterial concentration as a function of time (same timescale as upper graph). The results of this experiment are shown below: If a small sample of the 5-day old culture is used to start a fresh culture and the experiment above is repeated, the results are the same as those above. d) Given the data, explain what appears to be happening to Spo0A in relation to bacterial proliferation. 4

5 If the samples from the experiment in part (d) are then assayed for AbrB levels, the following results are seen: e) What appears to be happening to AbrB in relation to bacterial proliferation? Briefly explain. f) What appears to be happening to AbrB in relation to Spo0A? Briefly explain. If the Spo0A gene is deleted from the bacteria and the experiments are repeated, the proliferation of the bacteria is not affected. The following results are observed: g) Based on the provided data, provide a hypothesis for the relationship between AbrB and Spo0A. 5

6 Next you look at expression of the toxin that causes anthrax. If the samples from the experiment in part (b) are now assayed for toxin levels, the following results are seen: h) What appears to be happening to toxin expression with regards to cell proliferation? Briefly explain. i) What appears to be happening to toxin expression in relation to AbrB? Briefly explain. You decide to see what happens to toxin expression if you change the level of AbrB expression. You either overexpress AbrB or abolish AbrB expression and find that proliferation of the bacteria is not affected. The following levels of toxins are observed: j) Do these results support your answer to part (i)? Briefly explain. 6

7 k) Is deletion of AbrB necessary and sufficient for toxin expression? Explain. l) (*extra*) Based on the data provided, propose a simple model explaining how Spo0A and AbrB are related to toxin expression. 7

8 3. Tumor derived growth factor β (TGFβ) is a secreted protein that has a diverse range of biological functions. TGFβ signaling affects the growth and proliferation of many cell types. Thus, it might not be surprising that mutations in the proteins of the TGFβ signaling pathway can contribute to the development and progression of many tumors. TGFβ signaling is mediated by two receptor protein kinases, TGFβRI and TGFβRII. A co-immunoprecipitation experiment (Alberts p.561 and p.165) is performed using the specified antibody to pull down protein complexes in the presence or absence of TGFβ. The antibodies bind specifically to TGFβRI or TGFβRII. The following results are observed: a) In normal cells is TGFβ binding to a receptor required for heterodimerization of TGFβRI and TGFβRII? Briefly explain why or why not. b) In cell lines where only one of the two receptors is expressed, the kinase domain cannot be activated by TGFβ binding. Based on this fact and the data provided above, what does this tell you about TGFβR homo-dimerization (dimers formed from TGFβRI-TGFβRI or TGFβRII-TGFβRII) and the activation of downstream signaling? Briefly explain. 8

9 c) Can you determine if dimerization is required for TGFβ binding to a receptor? Briefly explain why or why not. SMAD3 is a DNA binding protein that can be phosphorylated by the TGFβ receptor kinases. The phosphorylation state and cellular location of SMAD3 are assayed in cells treated with or without TGFβ and the following results are observed: d) What effect(s) does TGFβ exposure have upon SMAD3? 9