A. How many copies of the mRNA do we need per cell to produce the protein at a rate such that most of it can fold properly?
BioChem Homework 1
1. In the early days of cell-free protein synthesis development, PEP (phosphoenolpyruvate) was used as an energy source (PEP + ADP ATP + Pyruvate). We supplemented with extra amino acids so that we were pretty sure that protein synthesis was energy limited. We also supplemented with 0.33mM NAD+ and with 0.26 mm Coenzyme A so we could activate the pathway from pyruvate to acetyl-CoA to get extra ATP from the reaction sequence: Acetyl-CoA CoA + Acetyl phosphate, and Acetyl phosphate + ADP ATP + acetate. With this scheme, 33mM PEP produced 400 µg/ml of chloramphenicol acetyl transferase (MW=28,000).
A) How efficiently was the ATP being used? (6 pts) (Remember the electrons need to
be balanced – assume that acetate and lactate are the main metabolic byproducts.)
2. As we learned, when we feed glucose too fast to E.coli, they will excrete acetate. We would like to engineer the cells so that they don’t do this, and we are willing to waste some of our glucose by letting the pyruvate “spill out” of the cell in the form of acetolactate. This is formed by the reaction: 2 pyruvate –> acetolactate + CO2, which is catalyzed by the enzyme acetolactate synthase. This is not a native enzyme in E.coli, and I would like to evaluate its effect. I want to be able to divert pyruvate away from the reaction catalyzed by pyruvate dehydrogenase (that produces acetyl CoA) and toward the synthesis of acetolactate only when the glucose flux is too high. As a base case, I will assume that I have about 50g/liter of cells and that this gives me a pyruvate dehydrogenase concentration of about 5 micromolar. I estimate that its turnover number is about 850 min-1 with a km of 0.5 mmolar for pyruvate. I also estimate that I will accumulate about 1 micromolar acetolactate synthase and that it has a turnover number of about 1500 min-1 and a km for pyruvate of about 5 mmolar. For the purposes of this problem, assume that all of the glucose is going through this pathway to produce pyruvate as an intermediate.
A. If we are feeding glucose at a rate of 1.5 mmoles/liter-min and we assume that it is all going through the glycolytic pathway that we studied, what percentage will be going into the TCA cycle and what percent to acetolactate? (4pts)
B. If we accidentally feed glucose at 2.5 mmoles/min-min, what is the percentage? (2pts)
3. We would like to produce properly human growth hormone in the periplasm of E.coli even though two disulfide bonds must be installed in the 200 amino acid long protein for it to fold properly. Based on experimental observations, we suspect that DsbA activity will be rate limiting and that DsbC is not required. We can overexpress DsbA, but as we learned DsbA must be re-oxidized by DsbB and it appears that the diffusion of DsbA to DsbB, its regeneration, and its diffusion to the next target polypeptide is rate limiting. It looks like the maximum rate is only about 1000 disulfide bonds per cell per minute. I expect that the mRNA will have a functional half life of 3 minutes (assume the message degrades initially at the 5’ end), that the translational elongation rate is 16 amino acids per second, that the rate of translational initiation enables a ribosome spacing of about 120 nucleotides, and that the translocon capacity for protein translocation (secretion) is not rate limiting.
A. How many copies of the mRNA do we need per cell to produce the protein at a rate such that most of it can fold properly? (3pts)
B. How fast do we need to produce the message (copies per cell per minute)? (2pts)
C. If the RNA polymerase proceeds at a rate of 48 base pairs per second, and only one RNA polymerase works on each DNA template at a time, how many DNA templates do we need per cell? (2pt)
4. Consider the structure of peptidoglycan that we discussed in lecture 3.
a. List three functional attributes of this structure that make it so ideal for supporting prokaryotic life (1pt).
b. Now consider how such a structure would be assembled by the organism. List five classes of proteins/enzymes that would be required and explain the important attributes of each class of protein/enzyme; that is, what does it need to recognize, what reaction does it need to catalyze, and how would it need to be regulated for proper peptidoglycan to be synthesized (hint: also think about where and how the precursors are produced) (5pts).
5. In lecture 3, I also mentioned the tremendous diversity of sugar polymers that can be produced. Beginning with just glucose and fructose and hooking them together, list at least four ways that we can change the characteristics of the final polymer. (4pts)
6. Think about the competition exercise we did in class and expand it to consider three phases: a) initial glucose utilization (assuming it is already in the water), b) utilization of the grape sugars, and c) utilization of protein and chitin from cricket that falls into the puddle. Assume you can pick up mutations to: 1) double the rate of glucose uptake and store the excess as glycogen 2) express a general sugar transporter that allows you to use all 5-C and 6-C sugars after the grape falls in and breaks open, 3) secrete chitinases and proteases to be able to scavenge useful molecules from dead insects, and 4) produce a potent secreted toxin and intracellular antitoxin (protective molecule).
a. Which mutation would be most advantageous as the first one to acquire in our puddle war? Why? (2pts)
b. I mentioned that higher growth yields (g cell produced/g substrate) could be an important trait for organisms. Explain what environmental condition(s) would select for this advantage. (3pts)
c. Now briefly describe two features of a metabolic system that would allow it to provide higher growth yields. (2pts)
7) M-type pyruvate kinase consists of 2 isoforms, M1 and M2. M2 is expressed mainly during the embryonic stages of life, and M1 takes over thereafter. M2 has recently been found to be expressed in several cancer types. Through an unknown mechanism, M2 allows these cancer cells to convert glucose to lactate even in the presence of plentiful oxygen. This phenomenon is known as the Warburg effect.
a. What advantage does the cancer cell derive from employing the Warburg effect? (3 points)
b. Propose a mechanism by which the chemotherapy agent Drug A (below) can inhibit glycolysis. Please note that Drug A is not a particularly potent inhibitor of any of the glycolytic enzymes, but is nevertheless effective in blocking glycolysis specifically in cells with high levels of glycolytic flux. (4 points)
Drug A
8) On slide 40 of lecture 3, it is stated that the hormone glucagon indirectly stimulates the phosphatase activity of PFK2/FBPase2, leading to increased gluconeogenesis. Explain why an increase in glucose synthesis makes sense even though energy is in demand. Hint: consider the body as a whole, rather than just one particular cell. (2 points)
9) This question involves two studies conducted by a Dutch research group, on the citric acid cycle of the unicellular eukaryote Trypanosoma brucei, an important human pathogen.
a. The citric acid cycle consists of 8 enzymes, all of which are present in brucei. In one of the two studies, the research group used a so-called knock-out mutation to investigate the significance of an intact citric acid cycle in T. brucei. The knock-out mutation resulted in the absence of one of the enzymes employed in the citric acid cycle. Table 1 depicts the intracellular concentrations of citric acid cycle intermediates in wild type (wt) and mutated T. brucei, respectively. Use the data in Table 1 to determine which of the citric acid cycle enzymes was absent in the mutant and explain your reasoning. (2 points)
wild-type knock-out
b. The data below measure the conversion of radiolabeled glucose into carbon dioxide, acetate, and succinate in two ways: product formed by living organisms. Questions: i) what are the predominant fates of carbon from glucose in WT (wild-type) and knock-out (KO) brucei? ii) Are the metabolic fates of glucose significantly different in WT and KO organisms? Please rationalize your observation. iii) How is glucose utilization different in brucei than in humans? (6 points total)
c. The authors of the paper state that their data suggest that the Krebs cycle enzymes are unlikely to form a cyclic path in T. brucei. From the data given above, explain their probable reasoning. (3 points)
d. What other physiological purposes besides energy production do the Krebs cycle enzymes fulfill? Please give at least three examples. (4 points)
10) Control of metabolic flux. Explain how a 100x increase in flux through the glycolytic pathway could be accomplished using much smaller changes in the activities of phosphofructokinase and fructose 1,6- bisphosphatase. Support your argument using example calculations that are not identical to those presented in lecture. (4 points)
11) An enzyme isolated from the extremophile Methanocaldococcus jannaschii catalyzes the following reaction in order to form 6-deoxy-5-ketofructose-1-phosphate (DKFP), a precursor in an unusual metabolic pathway used to synthesize aromatic amino acids in this organism. The starting compounds are fructose 1,6-bisphosphate, and, interestingly, methylglyoxal. 7 points
CH2OPi O
HO H
+
H OH
H OH CH2OPi
O H
O CH3
CH2OPi O
HO H
H OH +
O CH3
O H
H OH CH2OPi
(Molecule A)
DKFP A
a) What is molecule A? (1 point)
b) The enzyme that catalyzes the above reaction uses a Schiff base intermediate, analogous to other enzymes we have studied in the course. With this hint in mind, please draw a detailed mechanism for the reaction above. You needn’t draw the steps leading to the formation or hydrolysis of the Schiff base intermediates. All other steps must be specified with proper arrow pushing for full credit. (6 points)
