Step 1: Understanding the Concept:
Acyl-CoA acetyltransferase, commonly known as thiolase, is the enzyme that catalyzes the fourth and final step of the mitochondrial $\beta$-oxidation pathway.
This pathway sequentially breaks down fatty acids to generate acetyl-CoA molecules for the citric acid cycle.
Detailed Explanation:
The $\beta$-oxidation of fatty acids involves a repeating sequence of four enzymatic reactions:
1. Oxidation of acyl-CoA to trans-$\Delta^2$-enoyl-CoA, catalyzed by acyl-CoA dehydrogenase.
2. Hydration of trans-$\Delta^2$-enoyl-CoA to L-$\beta$-hydroxyacyl-CoA, catalyzed by enoyl-CoA hydratase.
3. Oxidation of L-$\beta$-hydroxyacyl-CoA to $\beta$-ketoacyl-CoA, catalyzed by $\beta$-hydroxyacyl-CoA dehydrogenase.
4. Thiolytic cleavage of $\beta$-ketoacyl-CoA by a molecule of free coenzyme A (CoASH), catalyzed by acyl-CoA acetyltransferase (thiolase).
In this final step, the thiolase cleaves the bond between the $\alpha$ and $\beta$ carbons of the $\beta$-ketoacyl-CoA substrate.
This reaction yields one molecule of acetyl-CoA and a shortened acyl-CoA chain (shortened by two carbons), which can re-enter the $\beta$-oxidation cycle.
Step 2: Final Answer:
The substrate for the enzyme acyl-CoA acetyltransferase is $\beta$-ketoacyl-CoA.