Step 1: Understanding the Concept:
Ketone bodies—acetoacetate, $\beta$-hydroxybutyrate (3-hydroxybutyrate), and acetone—are water-soluble organic compounds produced by the liver from acetyl-CoA during periods of prolonged fasting, carbohydrate restriction, or untreated diabetes.
Step 2: Detailed Explanation:
Ketogenesis takes place in the mitochondrial matrix of hepatocytes.
The final step of the pathway produces acetoacetate.
Acetoacetate can undergo slow, spontaneous non-enzymatic decarboxylation to form acetone, which is excreted via the lungs.
Alternatively, acetoacetate can be enzymatically reduced to D-$\beta$-hydroxybutyrate (also named D-3-hydroxybutyrate).
The reversible interconversion between acetoacetate and 3-hydroxybutyrate is catalyzed by the mitochondrial enzyme D(-) 3-hydroxybutyrate dehydrogenase.
This reaction is a redox process coupled to the $\text{NAD}^+/\text{NADH}$ cofactor pool:
\[ \text{Acetoacetate} + \text{NADH} + \text{H}^+ \rightleftharpoons \text{D-3-hydroxybutyrate} + \text{NAD}^+ \]
When ketone bodies are utilized as fuel by extrahepatic tissues (such as the brain, skeletal muscle, or heart) during ketolysis, 3-hydroxybutyrate is oxidized back to acetoacetate by the same enzyme.
The acetoacetate is then converted to acetyl-CoA, which enters the TCA cycle to generate ATP.
Step 3: Final Answer:
The enzyme that interconverts acetoacetate and 3-hydroxybutyrate is D(-) 3-Hydroxybutyrate dehydrogenase.