**Core Concept**
The question tests the understanding of **proteolytic enzymes**, specifically **trypsin**, and their substrate specificity. Trypsin is a **serine protease** that plays a crucial role in **protein digestion**. It has a high degree of specificity for certain amino acid residues.

**Why the Correct Answer is Right**
Trypsin cleaves peptide chains at the carboxyl side of **lysine** and **arginine** residues, except when either is followed by **proline**. This specificity is due to the shape and chemical properties of the **active site** of trypsin, which allows it to bind and hydrolyze bonds adjacent to these positively charged amino acids.

**Why Each Wrong Option is Incorrect**
**Option A:** While arginine is indeed a target for trypsin, the question asks for the answer that is most directly associated with trypsin's action, and between arginine and lysine, both are correct but the question format suggests a single best answer.
**Option B:** Glutamate is not a residue that trypsin specifically targets for cleavage.
**Option D:** Proline is not typically a site for trypsin cleavage and can even prevent cleavage when it follows a lysine or arginine.

**Clinical Pearl / High-Yield Fact**
Remembering that trypsin specifically targets **lysine** and **arginine** is crucial for understanding **pancreatic enzyme function** and **digestive physiology**.

**Correct Answer:** C. Lysine