The increasing order of pKa of the following amino acids in aqueous solution is: Glycine, Aspartate, Lysine, Arginine.

First, recall the definition of $$pK_a$$. By the relation $$pK_a = -\log_{10}K_a,$$ a lower $$pK_a$$ value corresponds to a larger acid-dissociation constant $$K_a,$$ hence to a stronger acid. Consequently, when we arrange substances in increasing order of $$pK_a,$$ we are really writing them from the strongest acid (smallest $$pK_a$$) to the weakest acid (largest $$pK_a$$).

Every α-amino acid possesses at least two titratable groups: an α-carboxyl group (-COOH) with $$pK_{a1}\,{\approx}\,2$$ and an α-ammonium group (-NH3+) with $$pK_{a2}\,{\approx}\,9$$. Amino acids that contain an additional ionisable group in the side chain (R-group) have a third $$pK_a,$$ usually written $$pK_{aR}$$. For such amino acids, it is the $$pK_{aR}$$ that is characteristic of the nature of the side chain and varies widely from one amino acid to another, while the α-carboxyl and α-ammonium values stay in their usual narrow ranges.

We now list the pertinent numeric values taken from standard aqueous titration tables:

• Glycine (no ionisable R-group):
   $$pK_{a1}(\text{-COOH}) \approx 2.34$$,    $$pK_{a2}(\text{-NH}_3^+) \approx 9.60$$.

• Aspartate (extra -COOH in the side chain):
   $$pK_{a1}(\text{α-COOH}) \approx 2.09,$$    $$pK_{aR}(\text{β-COOH}) \approx 3.86,$$    $$pK_{a2}(\text{-NH}_3^+) \approx 9.82.$$
Among these, the R-group value $$pK_{aR} = 3.86$$ is the one that distinguishes Aspartate from other amino acids.

• Lysine (extra ε-NH3+ group):
   $$pK_{a1}(\text{α-COOH}) \approx 2.18,$$    $$pK_{a2}(\text{-NH}_3^+\text{ on α-C}) \approx 8.95,$$    $$pK_{aR}(\text{ε-NH}_3^+) \approx 10.53.$$
Here the characteristic value is the basic side-chain $$pK_{aR}=10.53.$$

• Arginine (guanidinium side chain):
   $$pK_{a1}(\text{α-COOH}) \approx 2.17,$$    $$pK_{a2}(\text{-NH}_3^+\text{ on α-C}) \approx 9.04,$$    $$pK_{aR}(\text{guanidinium}) \approx 12.48.$$
Again, the distinctive value is the side-chain $$pK_{aR}=12.48.$$

For comparison we focus on the $$pK_a$$ value that varies from one listed amino acid to the next, namely:

$$ \begin{aligned} \text{Aspartate} &: \; pK_{aR} \approx 3.86,\\[2pt] \text{Glycine} &: \; pK_{a2} \approx 9.60,\\[2pt] \text{Lysine} &: \; pK_{aR} \approx 10.53,\\[2pt] \text{Arginine} &: \; pK_{aR} \approx 12.48. \end{aligned} $$

Writing these numerically in ascending order gives

$$3.86 \lt 9.60 \lt 10.53 \lt 12.48,$$

which translates back to the amino-acid names as

Aspartate < Glycine < Lysine < Arginine.

This sequence exactly matches Option D.

Hence, the correct answer is Option D.