**Core Concept**
Paper chromatography separates amino acids based on their hydrophobicity, which is influenced by their molecular structure, particularly the presence of non-polar side chains. In this context, the amino acid with the highest hydrophobicity will migrate fastest on the methylcellulose medium.

**Why the Correct Answer is Right**
Valine (B) has a non-polar side chain, consisting of a branched-chain structure, which makes it more hydrophobic compared to the other options. This increased hydrophobicity allows Valine to interact more strongly with the non-polar methylcellulose, resulting in faster migration. In contrast, Aspartic acid (A) has a negatively charged side chain, making it more hydrophilic and less likely to interact with the methylcellulose. Lysine (C) also has a charged side chain, albeit positively charged, which reduces its hydrophobicity. Glycine (D) has a small, uncharged side chain, but its relatively small size and lack of branching make it less hydrophobic than Valine.

**Why Each Wrong Option is Incorrect**
**Option A:** Aspartic acid is more hydrophilic due to its negatively charged side chain, which reduces its interaction with the non-polar methylcellulose.
**Option C:** Lysine's positively charged side chain makes it less hydrophobic than Valine, resulting in slower migration.
**Option D:** Glycine's small, uncharged side chain does not provide sufficient hydrophobicity to allow it to migrate faster than the other options.

**Clinical Pearl / High-Yield Fact**
When using paper chromatography to separate amino acids, the choice of solvent and stationary phase can significantly affect the results. In this case, the methylcellulose medium is chosen for its ability to separate amino acids based on their hydrophobicity.

✓ Correct Answer: B. Valine