-hydroxybutyrate dehydrogenase catalyzes the last step in ketogenesis, the reduction of acetoacetate to b-hydroxybutyrate. (a) Write a...

β-hydroxybutyrate dehydrogenase catalyzes the last step in ketogenesis, the reduction of acetoacetate to b-hydroxybutyrate. 

(a) Write a balanced equation for this reaction. 

(b) Calculate the standard free energy (ΔG°′) associated with this reaction, using the data in Table 14.1. Is this reaction favorable in the direction written under standard conditions? If not, what cellular conditions would be required for this reaction to continuously produce β-hydroxybutyrate at a high rate?

Table 14.1.

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TABLE 14.1 Standard reduction potentials of interest in biochemistry Oxidant Acetate + CO₂ + 2H+ + 2e- Succinate + CO₂ + 2H+ + 2e Acetate + 3H+ + 2e¯ Ferredoxin (oxidized) + e 2H+ + 2e™ a-Ketoglutarate + CO₂ + 2H+ + 2e Acetoacetate + 2H+ + 2e Pyruvate + CO₂ + H+ + 2e NAD+ + H+ + 2e™ NADP+ +H+ + 2e™ Lipoate (oxidized) + 2H+ + 2e™ 1,3-Bisphosphoglycerate + 2H+ + 2e Glutathione (oxidized) + 2H+ + 2e FAD (free coenzyme) + 2H+ + 2e- Acetaldehyde + 2H+ + 2e™ Pyruvate + 2H+ + 2e™ Oxaloacetate + 2H+ + 2e O₂ + e a-ketoglutarate + NH + 2H+ + 2e™ FAD (enzyme-bound) + 2H+ + 2e Methylene blue (oxidized) + 2H+ + 2e Fumarate + 2H+ + 2e Q + 2H+ + 2e™ Dehydroascorbate + 2H+ + 2e™ Cytochrome b (+3) + e Cytochrome c₁ (+3) + e Cytochrome c (+3) + e Cytochrome a (+3) + e O₂ + 2H+ + 2e™ Ferricyanide + 2e™ NO (Nitrate) +2H+ + 2e Cytochrome a3(+3) + e¯ Fe (+3) + e O₂ + 2H+ + 2e™ Reductant Pyruvate + H₂O a-Ketoglutarate + H₂O Acetaldehyde + H₂O Ferredoxin (reduced) H₂ Isocitrate B-Hydroxybutyrate Malate NADH NADPH Lipoate (reduced) Glyceraldehyde-3-phosphate + P 2 Glutathione (reduced) FADH₂2 Ethanol Lactate Malate O₂ (superoxide) Glutamate + H₂O FADH₂ (enzyme-bound) Methylene blue (reduced) Succinate QH₂ Ascorbate Cytochrome b (+2) Cytochrome c₁ (+2) Cytochrome c (+2) Cytochrome a (+2) H₂O₂ Ferrocyanide NO₂ (Nitrite) + H₂O Cytochrome a3 (+2) Fe (+2) H₂O n 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 1 1 1 2 2 2 1 1 2 E° (V) -0.70 -0.67 -0.60 -0.43 -0.42 -0.38 -0.35 -0.33 -0.32 -0.32 -0.29 -0.29 -0.23 -0.22 -0.20 -0.19 -0.17 -0.16 -0.14 -0 to -0.30 0.01 0.03 0.04 0.06 0.07 0.23 0.25 0.29 0.30 0.36 0.42 0.55 0.77 0.82