Final answer:
The significance of shortening the fatty acid by one carbon through α-oxidation lies in providing an alternative metabolic route for certain branched-chain fatty acids that cannot be processed by β-oxidation.
Step-by-step explanation:
The significance of shortening the fatty acid by one carbon in α-oxidation is that it alters the length of the fatty acid chain, providing a pathway for the metabolism of certain fatty acids that cannot undergo β-oxidation. α-oxidation is particularly important for the catabolism of branched-chain fatty acids, such as phytanic acid, which are found predominantly in the brain and other tissues. During α-oxidation, a hydroxyl group is first introduced to the α-carbon atom, subsequently oxidized to a keto group, and then decarboxylated to remove one carbon atom from the carboxyl end of the molecule, resulting in a fatty acid chain that is shorter by one carbon. This process is essential because it provides an alternative metabolic route for fats that are otherwise resistant to the standard β-oxidation pathway.