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Answers to Problem Set 3 Lecture 18 (PDH and TCA cycle) 1. Catalytic coenzymes (TPP, lipoic acid, and FAD) are modified but regenerated in each reaction cycle. Thus, they can play a role in the processing of many molecules of pyruvate. Stoichiometric coenzymes (coenyme A and NAD+) are used in only one reaction because they are the components of products of the reaction. 2. (a) After one round of the citric acid cycle, the label emerges in C-2 and C-3 of oxaloacetate. (b) The label emerges in CO2 in the formation of acetyl CoA from pyruvate. (c) After one round of the citric acid cycle, the label emerges in C-1 and C-4 of oxaloacetate. (d and e) Same fate as that in part a. 3. (a) The steady-state concentrations of the products are low compared with those of the substrates. (b) The ratio of malate to oxaloacetate must be greater than 1.57 x 104 for oxaloacetate to be formed. GG19-7. citrate isocitrate α-ketoglutarate succinate CH2-COOH HO-C3-COOH C4H2-COOH CH2-COOH HC-C*OOH HO- C*H-COOH CH2-COOH H2C O=C*-C*OOH H2C*-COOH H2C*-COOH C4 oxidized by aconitase, C3 reduced; no net oxidation Starred C’s oxidized by isocitrate DH Starred C’s oxidized by α ketoglutarate DH Starred C’s oxidized by succinate DH GG19-10. [isocitrate]/[citrate] = 0.1. When [isocitrate] = 0.03 mM, [citrate] = 0.3 mM. Lecture 19 (Electron transport system) 1. a. 4; b. 3; c. 1; d. 5; e. 2. 2. Rotenone: NADH and NADH-Q oxidoreductase will be reduced. The remainder will be oxidized. Antimycin A: NADH, NADH-Q oxidoreductase and coenzyme Q will be reduced. The remainder will be oxidized. Cyanide: All will be reduced. GG20-1. [FAD] + 2cyt c(Fe2+) + 2H+ <==> [FADH2] + 2 cyt c(Fe3+) The e- acceptor is FAD; the e- donor is cyt c(Fe2+) ΔEo’ = -0,219 – (0.254) = -0.473 ΔGo’ = -nFΔEo’ = -2(96.5 kJ/V-mol)(-0.473 V) =+91.3 kJ/mol This reaction does not go (forward). Turned around (FADH2 –e- -> cyt c) it would be ΔGo’ = -91.3 kJ/mol and would go. GG20-3. NAD+ + 2H+ + 2e- <==> NADH + H+ E = ΔEo’ + RT/nF ln([ox]/[red]) = -0.32 + (8.31)(298)/(2)(96,500) ln([NAD+][H+]2/[NADH][H+]) Because [NAD+]/[NADH] = 1 and [H+]2/[H+] = [H+], We can rewrite the formula above to: E = = -0.32 + RT/nF ln([H+] = -0.32 – 2.31(0.0128)(ΔpH) ΔpH = 1 At pH 8, ΔpH = 1 and E = - 0.35 V GG20-8. NADH + H+ + 2UQ(ox) <==> NAD+ + 2UQH(red) a. ΔEo’ = Eo’(acceptor: UQ) - Eo’(donor: NADH) = +0.06 – (-0.32) = +0.038 V o ΔG ’ = -nFΔEo’ = -2(96,400)( 0.038) = -73.3 kJ/mol b. Keq = exp10(-ΔGo’/2.3RT) = = exp10((73,300)/(2.3)(8.31)(298)) = 7.4 x 1012 c. Assume that the energy available = (-73.3)(0.75) = -54,975 kJ/mol so the energy needed to form ATP can be as much as +54,975 To form ATP, ADP + Pi --> ATP + H2O, ΔGo’ = +30.5 kJ/mol; also assume [Pi] = 1 mM, ΔG = ΔGo’ + RT ln ([ATP]/[ADP][Pi]) ΔGo’ – RT ln ([Pi]) + RT ln ([ATP]/[ADP]) 54,975 = 30,500 –(8.31)(298) ln (0.001) + (8.31)(298) ln ([ATP]/[ADP]) ln ([ATP]/[ADP]) = 2.976; [ATP]/[ADP] = 19.6 GG20-9. succinate + ½ O2 <==> fumarate + H2O a. ΔEo’ (succinate -> fumarate) = -0.031 V ΔEo’ (1/2 O2 -> H2O) = 0.816 V ΔEo’ (combined) = 0.785 o o ΔG ’ = -nFΔE ’ = -2(96.400)(0.785) = -151 kJ/mol b. Keq = exp10(-ΔGo’/RT) = exp10(151,000/2.3(8.3)(298)) = 3.24 x 1026 Lecture 20 (ATP synthesis) 1. a. 12.5; b. 14; c. 32; d. 13.5; e. 30; f. 16. 2. a. The P:O ratio is equal to the product of (H+/2e-) and (P/H+). Note that the P:O ratio is identical with the P:2e- ratio. (Note also that the P/H+ ratio depends on the number of subunits in the ATP synthase collar, and this may vary among organisms.) b. 2.5 and 1.5 respectively. H+ energy gradient problem As described in lecture, the free energy of a reaction involving electrically charged materials can be described by the following formula: ΔG = RT ln ([product]/[reactant]) + z F ΔEo’ (z = charge) This formula can apply to the movement of H+ (z = 1) across a membrane: ΔG = -2.3 RT ΔpH + z F ΔEo’ ΔpH = pHout – pHin (H+ moving from inside to outside the membrane: thus pHout is the product, pHin is the reactant) a) Show that a difference of 1 pH unit is equivalent to a 59 mV difference. -2.3(8.31)(298)(-1 [low pH out]) ~ (1)(96,485)(ΔEo’) 5695.7 ~ 96,487 ΔEo’ ΔEo’ = 0.059 V [positive voltage outside] b) With a difference across the membrane of 1 pH unit and 59 mV (0.059 V) per proton, how many protons are needed to force synthesis of one ATP: ADP + Pi → ATP + H2O? (Assume standard conditions for ATP, ADP, and Pi concentrations: ΔG’ = ΔGo’) ΔG = -2.3 RT ΔpH + z F ΔEo’ = -2.3(8.31)(298)(-1) + (n)(96,485)(0.059) = 30,500 n = 4.36 c) Alternatively, what voltage difference would be needed if one proton were to force the synthesis of one ATP? (Assume the same pH difference and standard conditions as above.) ΔG = -2.3 RT ΔpH + z F ΔEo’ = -2.3(8.31)(298)(-1) + (1)(96,485)(x) = 30,500 x = 0.257 V 3. The available energy from the translocation of two, three, and four protons is -38.5, 57.7, and -77.4 kJ/mol, respectively. The free energy consumed in synthesizing a mole of ATP under standard conditions is 30.5 kJ. Hence, the residual free energy of -8.1, 27.2, and -46.7 kJ/mol can drive the synthesis of ATP until the [ATP]/[ADP][Pi] ratio is 26.2, 6.5 x 104, and 1.6 x 108, respectively. Suspensions of isolated mitochondria synthesize ATP until this ratio is greater than 104, which shows that the number of protons translocated per ATP synthesized is at least three. 4. 12/3 = 4; 14/3 = 4.7 Lecture 21 (Photosynthesis) 1. CO2 is the acceptor. H2O is the donor. Light energy powers e- flow. GG21-1. Given: by absorption of 1 photon @ 700 nm, photosystem II ΔEo’ = 1 V ΔEo’ = 96,485 J/mol Absorbed energy = hν = (hc/λ) N = 171,139 J/mol h = 6.63 x 10-34 Js c = 3 x 108 m/s λ = 700 x 10-9 m N = 6.023 x 1023 mol-1 Efficiency = 96,485/171,139 = 0.56 2. We need to factor in the NADPH because it is an energy-rich molecule. Recall that NADH is worth 2.5 ATP if oxidized by the electron-transport chain. 12 NADPH = 30 ATP. 18 ATP are used directly, and so the equivalent of 48 molecules of ATP are required for the synthesis of glucose. GG21-5. Given: non-cyclic H+ pumping: 3 H+/e- = 3 H+/2 hν cyclic H+ pumping: 2 H+/e- = 2 H+/1 hν ATP synthesis: 3 ATP/14 H+ Efficiencies: non-cyclic: 3 ATP/14 H+ (3 H+/2 hν) = 0.32 ATP/hν cyclic: 3 ATP/14 H+ (2 H+/1 hν) = 0.43 ATP/hν GG21-8. Assume 12 c-subunits means 12 H+ are needed to drive one turn of the csubunit rotor and the synthesis of 3 ATP by the CF1 part of the ATP synthase. If the R. viridis cytochrome bc1 complex drives the translocation of 2 H+/e-, then 2 hν gives 4 H+, and 6 hν gives 12 H+ and thus 3 ATP (thus 2 hν yield 1 ATP.) GG21-10. RuBP + CO2 + H2O --> 2 3-PGA 2 3-PGA + 2 ATP --> 2 1,3-bisPGA + 2 ADP 2 1,3-bisPGA + 2 NADPH + 2 H+ --> 2 G3P + 2 NADP+ + 2Pi 2 G3P + 2 H2O --> glucose + 2 Pi RuBP + CO2 + 2 ATP + 2 NADPH + 3 H2O + 2 H+ --> glucose + 2 ADP + 4 Pi + 2 NADP+ GG21-14. 12 H2O --> 6 O2 provide 24 H+ to 6 CO2 --> C6H12O6 + 6 H2O Added: 6 CO2 + 12 H2O --> C6H12O6 + 6 O2 + 6 H2O Thus, water is taken up in light reactions and produced in dark reaction. Lecture 22 (Gluconeogenesis) 1. In glycolysis, the formation of pyruvate and ATP by pyruvate kinase is irreversible. This step is bypassed by two reactions in gluconeogenesis: (1) the formation of oxaloacetate from pyruvate and CO2 by pyruvate carboxylase and (2) the formation of phosphoenolpyruvate from oxaloacetate and GTP by phosphoenolpyruvate carboxykinase. The formation of fructose-1,6-bisphosphate by phosphofructokinase is bypassed by fructose-1,6-bisphosphatase in gluconeogenesis, which catalyzes the conversion of fructose-1,6-bisphosphate into fructose 6-phosphate. Finally, the hexokinase-catalyzed formation of glucose-6-phosphate in glycolysis is bypassed by glucose-6-phosphatase, but only in the liver. 2. For synthesis of one molecule of glucose from two molecules of pyruvate: 6 NTP ((4 ATP, 2 GTP); 2 NADH 3. a. c. d. NTP molecules for synthesis of glucose from glucose-6-phosphate: none. b. fructose-1,6-bisphosphate: none. two molecules of oxaloacetate: 4 (2 ATP, 2 GTP). two molecules of dihydroxyacetone phosphate: none. 4. (a) glycolysis: 2, 3, 6, 9; (b) gluconeogenesis: 1, 4, 5, 7, 8. 5. a. What was the rationale for comparing the activities of these two enzymes? If both enzyme operated simultaneously, the two reactions would take place and the net results would be simply, ATP + H2O --> ADP + Pi. The energy of ATP hydrolysis would be released as heat. b. Do these results support the notion that bumblebees use futile cycles to generate heat? Not really. For the cycle to generate heat, both enzymes must be functional at the same time in the same cell. c. In which species might futile cycling take place? The species B. terrestris and B. rufocinctus might show some futile cycling because both enzymes are active to a substantial degree. d. Do these results prove that futile cycling does not (or does) participate in heat generation? No. These results simply suggest that simultaneous activity of phosphofructokinase and fuctose-16-bisphophatase is unlikely to be employed to generate heat in the species shown. Lecture 23 (Fatty acid catabolism) 1. b. fatty acid in the cytoplasm c. activation of fatty acid by joining to CoA a. reaction with carnitine g. acyl-CoA in mitochondrion h. d. e. f. FAD-linked oxidation hydration NAD+-linked oxidation thiolysis 2. Palmitic acid yields 106 molecules of ATP. Palmitoleic acid has a double bond between carbons C-9 and C-10. When palmitoleic acid is processed in ß oxidation, one of the oxidation steps (to introduce a double bond before the addition of water) will not take place, because a double bond already exists. Thus, FADH2 will not be generated, and palmitoleic acid will yield 1.5 fewer molecules of ATP than palmitic acid, for a total of 104.5 molecules of ATP. For heptadecanoic acid, activation fee to form acyl CoA, -2 ATP; 7 acetyl CoA, +70 ATP; 7 NADH, +17.5 ATP; 7 FADH2, +10.5 ATP; propionyl-CoA --> succinyl-CoA, -1 ATP; succinyl-CoA --> succinate, +1 ATP; succinate --> fumarate, +1.5 ATP; malate --> OAA, +2.5 ATP; total 100 ATP 3. Glucose: glycolysis, +2 ATP; 2 NADH @ 1.5 = 3 ATP; 2x4 NADH @ 2.5 = 20 ATP; 2 FADH2 @ 1.5 = 3 ATP; 2 GTP = 2 ATP; total = 30 ATP Caprioic (hexanoic) acid: activation, -2 ATP; 2 NADH @ 2.5 = 5 ATP; 2 FADH2 @ 1.5 = 3 ATP; 3 acetyl-CoA through CAC =30 ATP; total = 36 ATP 4. Hummingbird flight: Weight lost = 4-2.7 = 1.3 g lipid At 37 kJ/g (Table 23.1), energy used = 48.1 kJ (but this conversion number relates to dry weight of adipose tissue) GG23-12. More hummingbird flight: 10 h across the Gulf Assume 4.81 kJ/h (above) and 0.25 l O2/h (given) Energy per O2 = 4.81/0.25 = 19.24 kJ/l O2 Compare to human 8-minute miler: 12.7 kcal/min x 4.18 J/cal = 53 kJ/min Time running on 48.1 kJ (trans-Gulf flight) = 48.1/53 = 0.9 min Miles to lose 1 lb body fat: 1 lb = 454 g => 16,798 kJ (@ 37 kJ/g) At 53 kJ/min, losing 16,798 kJ takes 317 min At 8 min/mile, 317 min is 39.6 miles Lecture 24 (Fatty acid synthesis) 1. e. formation of malonyl ACP b. condensation d. reduction of a carbonyl a. dehydration. c. release of a C16 fatty acid 2. All of the labeled carbon atoms will be retained. Because we need 8 acetyl CoA molecules and only 1 carbon atom is labeled in the acetyl group, we will have 8 labeled carbon atoms. The only acetyl CoA used directly will retain 3 tritium atoms. The 7 acetyl CoA molecules used to make malonyl CoA will lose 1 tritium atom on addition of the CO2 and another one at the dehydration step. Each of the 7 malonyl CoA molecules will retain 1 tritium atom. Therefore, the total retained tritium is 10 atoms. The ratio of tritium to 14C is 1.25. GG24-6. ATP ADP glycerol-3-P glycerol ethanolamine ATP fattyacyl-CoA CoA ADP acylglycerol-3-P CTP fattyacyl-CoA CoA phosphatidic acid, (or 1,3-diacylglycerol-3-P) PPi CDP-ethanolamine Pi CMP phosphatidylethanolamine glycerol + 2 fattyacyl-CoA + 2ATP + CTP + ethanolamine --> phosphatidylethanolamine + 2ADP + CMP + PPi + 2CoA + Pi ΔGo’ = - 4 high-energy bonds + combining 4 components into one GG24-11. ATP equivalents needed to form palmitic acid from acetyl-CoA, using 3.5 ATP/NADPH: 7 acetyl-CoA + 7 ATP + 7 HCO3- --> 7 malonyl-CoA + 7 ADP + 7 Pi + 7H+ acetyl-CoA + 7 malonyl-CoA + (2x7) NADPH + 14H+ ---> palmitoyl-CoA + 7 HCO3- + (2x7) NADP+ + 7 CoSH ATP equivalents: 7 + 2x7x3.5 = 8x7 = 56 Lecture 25 (Nitrogen metabolism) 1. The seven precursors of the carbon skeletons of the 20 amino acids: oxaloacetate, pyruvate, ribose-5-P, phosphoenolpyruvate, erythrose-4-phosphate, α-ketoglutarate, and 3-phosphoglycerate. GG25-1. Oxidation number of N in nitrate, nitrite, NO, N2O, and N2: NO3-: +5 NO2-: +3 NO: +2 N2O: +1 N2: 0 GG25-2. ATP equivalents for formation of NH4+ from NO3- and N2, using 3 ATP per NADH, NADPH, and reduced Fd: a. NO3- --> NO2-: 1 NADH, NO2- --> NH4+: 6 Fd, GOGAT: b. N2: 8 e-, 4 NADPH, 3 ATP 18 ATP 1 ATP 22 ATP 12 ATP 16 ATP 28 ATP GG25-4. ATP equivalents for formation of urea: HCO3- + ATP --> carbamate + ADP carbamate + ATP --> carbamoyl-P + ADP citruline + ATP --> argininosuccinate + AMP 1 ATP 1 ATP 2 ATP 4 ATP