1. Interpretation of the question

We need the increasing order of $pK_a$ for the amino acids:

• Gly = glycine
• Asp = aspartic acid
• Lys = lysine
• Arg = arginine

Here, the relevant comparison is the acidity/basicity of these amino acids in aqueous solution. A lower $pK_a$ means a stronger acid.

2. Recall the nature of side chains

• Aspartic acid (Asp) has an extra carboxylic acid group in the side chain, so it is the most acidic among these.
• Glycine (Gly) has no ionizable side chain; it is neutral.
• Lysine (Lys) has an extra amino group in the side chain, so it is basic.
• Arginine (Arg) has a guanidino group in the side chain, which is even more basic than the amino group of lysine.

Thus, in terms of acidity: $\text{Asp} > \text{Gly} > \text{Lys} > \text{Arg}$

Since stronger acid means lower $pK_a$, the increasing order of $pK_a$ is: $\text{Asp} < \text{Gly} < \text{Lys} < \text{Arg}$

3. Check with known approximate values

Typical values often used are:

• Aspartic acid: $pK_a \approx 2.1$
• Glycine: $pK_a \approx 2.3$
• Lysine: higher than glycine
• Arginine: highest among these basic amino acids

So the order remains: $\boxed{\text{Asp} < \text{Gly} < \text{Lys} < \text{Arg}}$

4. Evaluate options

• A: $\text{Asp} < \text{Gly} < \text{Arg} < \text{Lys}$ ❌
  Wrong, because arginine should have higher $pK_a$ than lysine.

• B: $\text{Gly} < \text{Asp} < \text{Arg} < \text{Lys}$ ❌
  Wrong, because Asp should have lower $pK_a$ than Gly.

• C: $\text{Asp} < \text{Gly} < \text{Lys} < \text{Arg}$ ✅

• D: $\text{Arg} < \text{Lys} < \text{Gly} < \text{Asp}$ ❌
  Completely reversed.

5. Final answer

The correct increasing order is: $\boxed{\text{Asp} < \text{Gly} < \text{Lys} < \text{Arg}}$ So, the correct option is C.