**Core Concept**
Vitamin K plays a crucial role in the post-translational modification of proteins, specifically through the gamma-carboxylation of glutamic acid residues. This process is essential for the activation of various proteins involved in blood coagulation, including clotting factors II, VII, IX, and X.

**Why the Correct Answer is Right**
The gamma-carboxylation reaction involves the transfer of a carboxyl group from vitamin K to glutamic acid residues, converting them into gamma-carboxyglutamic acid (Gla). This modification is necessary for the binding of calcium ions, which is essential for the proper function of these clotting factors. The enzyme responsible for this reaction is gamma-glutamyl carboxylase, which requires vitamin K as a cofactor.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is not relevant to vitamin K's role in post-translational modification.
**Option B:** Vitamin K is not involved in the phosphorylation of proteins; that is the role of protein kinases.
**Option C:** This option is not a known function of vitamin K in post-translational modification.

**Clinical Pearl / High-Yield Fact**
Vitamin K deficiency can lead to bleeding disorders due to impaired clotting factor production. This is why vitamin K is often administered to newborns to prevent hemorrhagic disease of the newborn (HDN).

**Correct Answer:** D.