Step 1: Understanding the Question:
The question asks about the biochemical conversion of one form of auxin (Indole-3-butyric acid or IBA) into another (Indole-3-acetic acid or IAA) through the $\beta$-oxidation pathway.
IBA is often considered a storage form or a precursor of the more physiologically active auxin, IAA.
Key Formula or Approach:
The approach involves comparing the carbon chain lengths of the side chains attached to the indole ring in both hormones.
$\beta$-oxidation is a metabolic process that shortens fatty acid chains by removing two carbon atoms (as acetyl-CoA) in each cycle.
Step 2: Detailed Explanation:
• Structure of Indole-3-butyric acid (IBA): IBA consists of an indole ring with a butyric acid side chain. Butyric acid is a four-carbon carboxylic acid. Therefore, the side chain of IBA has 4 carbons.
• Structure of Indole-3-acetic acid (IAA): IAA consists of an indole ring with an acetic acid side chain. Acetic acid is a two-carbon carboxylic acid. Therefore, the side chain of IAA has 2 carbons.
• The $\beta$-oxidation Mechanism: In plants, $\beta$-oxidation occurs primarily in the peroxisomes. In each round of this cycle, the carboxylic acid chain is shortened by exactly two carbon atoms. The enzymes involved include acyl-CoA oxidase, multifunctional protein (MFP), and l-3-ketoacyl-CoA thiolase.
• Calculation of Rounds: To reduce a 4-carbon chain (IBA) to a 2-carbon chain (IAA), the chain must lose $4 - 2 = 2$ carbons. Since one round of $\beta$-oxidation removes exactly 2 carbons, only one round is required.
• Physiological Context: Many plant species utilize this conversion to regulate local auxin levels. Mutant plants defective in peroxisomal $\beta$-oxidation enzymes often show resistance to exogenous IBA because they cannot convert it into the active IAA form.
Step 3: Final Answer:
One round of $\beta$-oxidation is sufficient to remove two carbons from the butyric acid side chain of IBA to produce the acetic acid side chain of IAA.