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Thermodynamics II: problems

Thermodynamics II: problems. Dr Una Fairbrother. Q1. The bacterium Pseudomonas saccharophila contains sucrose phosphorylase an enzyme that catalyses the phosphorolytic cleavage of sucrose Sucrose + P i glucose 1-phosphate + fructose .................…(1).

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Thermodynamics II: problems

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  1. Thermodynamics II:problems Dr Una Fairbrother

  2. Q1. • The bacterium Pseudomonas saccharophila contains sucrose phosphorylase an enzyme that catalyses the phosphorolytic cleavage of sucrose • Sucrose + Pi glucose 1-phosphate + fructose .................…(1)

  3. a) From the following data, calculate the biochemical standard free energy change for the phosphorolysis of sucrose • H2O + sucrose glucose + fructose .................…(2) • ΔG BN = -29 kJ mol-1 • H2O + glucose 1-phosphate glucose + Pi .................…(3) • ΔG BN = -21 kJ mol-1 • and b) calculate the equilibrium constant for the phosphorolysis of sucrose

  4. A1: To calculate a)the biochemical standard free energy ( ΔG BN) for the phosphorolysis of sucrose, • add the ΔG BN values of the two reactions which combine to yield reaction (1) • H2O + sucrose glucose + fructose • ΔG BN = -29 kJ mol-1 .............…(2) • glucose + Pi H2O + glucose 1-phosphate • ΔG BN = +21 kJ mol-1 ..…ie (3) reversed Sucrose + Pi glucose 1-phosphate + fructose ……………..(1) ΔG BN = -8 kJ mol-1 or –8000J

  5. b) to calculate the equilibrium constant (Keq) • ΔG BN = -RT lnKeq • -ΔG BN = lnKeq • RT • lnKeq = 8000 J mol-1 = 3.2 • (8.315 J K-1mol-1)(298 K) • Therefore : Keq = 25

  6. Q2. Could any of the following be used as an energy-rich metabolite for replenishment of cellular ATP from ADP? • MetaboliteΔG BN hydrolysis (kJ mol-1 ) • Phosphoenolpyruvate -62 • 1,3 -bisphosphoglycerate -49 • Phosphocreatine -43 • ATP (to ADP +Pi) -30 • Glucose 6-phosphate -14 • Glycerol 3-phosphate -9

  7. A2. • The approach here is to determine whether the net free energy change for a coupled reaction is negative

  8. eg ΔG BN (kJ mol-1 ) ADP + Pi ATP + H2O +30 Phosphocreatine + H2O creatine + Pi -43 ------------------------------------------------------------- Phosphocreatine + ADP º creatine + ATP -13

  9. Therefore:reaction exergonic and spontaneous, so in this case YES! • NOTE: also phosphoenolpyruvate and 1,3 -bisphosphoglycerate when hydrolysed will provide sufficient free energy.

  10. Q3 • The standard reduction potential for ubiquinone (Q) is + 0.04V and the standard reduction potential for FAD is -0.22V. • Show that the oxidation of FADH2 by Q theoretically liberates enough energy to drive the synthesis of ATP from ADP and Pi under standard conditions.

  11. NOTE: This is a two electron process EON (V) Q + 2H+ + 2e- QH2 +0.04 - (FAD + 2H+ + 2e- FADH2) -(-0.22) Q + FADH2 QH2 + FAD ΔEON= (0.04) -(-0.22) V = 0.04 + 0.22 V = 0.26 V

  12. ΔEON ΔEON found from (half reaction with more positive EON) - (half reaction with less positive EON) ΔG BN = -nFΔEON NOTE: F (Faraday’s constant) 96.48kJV-1mol-1 = (-2)(96.48kJV-1mol-1)(0.26V) = -50.17 kJmol-1 • NOTE: ADP + Pi ATP + H2O ΔG BN= +30 kJmol-1 • Therefore sufficient free energy to support synthesis of ATP!

  13. Q4 • In a rat hepatocyte, the concentrations of ATP, ADP + Pi are 3.4mM, 1.3mM and 4.8mM respectively. Calculate the free energy change for the hydrolysis of ATP in this cell (at 25 oC and otherwise standard conditions) • How does this compare to the standard free energy change?

  14. ΔG = ΔG BN + RT ln[C][D] [A][B] For ATP + H2O ADP + Pi then ΔG = ΔG BN + RT ln [ADP][Pi] [ATP][H2O] Thus: ATP + H2O ADP + Pi ΔG BN= -30 kJmol-1

  15. ΔG = -30,000 Jmol-1 + (8.315 JK-1mol1)(298K)ln (1.3 x 10-3)(4.8 x 10-3) (3.4 x 10-3) = -30,000 Jmol-1 + 2480 Jmol-1ln(1.8 x 10-3) • -30,000 Jmol-1 - 16,000 Jmol-1 • = -46,000 Jmol-1 = -46 kJmol-1 • This is about 1½ times the standard free energy change

  16. Summary • Calculated: • Standard free energy • Equilibrium constant • Net free energy change in coupled reactions • Reduction potential • Free energy change • Well done!

  17. Reading Stryer, Biochemistry Segel, Biochemical calculations, Wiley

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