Step 1: Understanding the Concept:
Amino acids have a common backbone but differ in their side chains (R-groups).
The size, bulk, and steric hindrance of an amino acid depend on the molecular structure, branching, and number of carbon atoms in its side chain.
Step 3: Detailed Explanation:
Let us analyze the side-chain structures of the given amino acids:
1. (B) Glycine:
The side chain of Glycine is a single hydrogen atom ($-\text{H}$).
This is the smallest and simplest side chain among all amino acids, providing minimal steric hindrance.
2. (A) Alanine:
The side chain of Alanine is a single methyl group ($-\text{CH}_3$).
This is slightly larger than Glycine's hydrogen atom.
3. (D) Leucine:
The side chain of Leucine is an isobutyl group ($-\text{CH}_2-\text{CH}(\text{CH}_3)_2$).
It contains four carbon atoms with branching at the gamma-carbon.
4. (C) Isoleucine:
Isoleucine is a structural isomer of Leucine with a sec-butyl side chain ($-\text{CH}(\text{CH}_3)-\text{CH}_2-\text{CH}_3$).
It contains four carbon atoms with branching at the beta-carbon.
Because the methyl branch is closer to the peptide backbone (at the beta-carbon), the side chain of Isoleucine is bulkier and exerts greater steric hindrance than Leucine.
Therefore, the increasing order of side chain size is: (B) Glycine $\rightarrow$ (A) Alanine $\rightarrow$ (D) Leucine $\rightarrow$ (C) Isoleucine.
Step 4: Final Answer:
The correct increasing sequence is (B), (A), (D), (C).
This matches Option (C).