Step 1: Understanding the Concept:
Vitamin K is an obligate enzymatic cofactor for post-translational $\gamma$-carboxylation of glutamic acid residues in procoagulant clotting factors.
Key Formula or Approach:
\[ \text{Glutamate (Glu)} + \text{CO}_2 + \text{O}_2 \xrightarrow{\text{Vitamin K-dependent } \gamma\text{-Glutamyl Carboxylase}} \gamma\text{-Carboxyglutamate (Gla)} \]
Step 2: Detailed Explanation:
Vitamin K (Phylloquinone Menaquinone):
- Essential fat-soluble vitamin acting as a cofactor for hepatic $\gamma$-glutamyl carboxylase.
- Carboxylates glutamate residues into $\gamma$-carboxyglutamic acid (Gla) domains on Clotting Factors II (Prothrombin), VII, IX, and X, as well as Protein C and Protein S.
- Gla domains are required to chelate $\text{Ca}^{2+}$ and bind negatively charged platelet phospholipid membranes. Vitamin K deficiency causes defective clotting factor activation and severe hemorrhagic diathesis.
Step 3: Final Answer:
Therefore, deficiency of Vitamin K is responsible for blood clotting disorders, matching option (D).