**Core Concept**
Glycogen synthesis is a critical process in glucose metabolism that involves the conversion of glucose molecules into a polysaccharide stored in the liver and muscles. This process is essential for maintaining blood glucose levels during fasting periods. The key enzymes involved in glycogen synthesis are glycogen synthase and glycogen branching enzyme.

**Why the Correct Answer is Right**
Leucine is an essential amino acid that cannot be used for glycogen synthesis due to its unique metabolic pathway. Leucine is primarily metabolized through the ketogenesis pathway, where it is converted to acetyl-CoA and then to ketone bodies. This pathway is not directly involved in glycogen synthesis, unlike other amino acids that can be converted to glucose through gluconeogenesis. The inability of leucine to be used for glycogen synthesis is due to its lack of a suitable precursor molecule that can be fed into the glycogen synthesis pathway.

**Why Each Wrong Option is Incorrect**
**Option A:** Alanine can be used for glycogen synthesis, as it can be converted to pyruvate and then to glucose through gluconeogenesis, which can eventually be used to synthesize glycogen.

**Option B:** Threonine is an essential amino acid that can be converted to glycogen through its metabolites, which can be used as precursors in the glycogen synthesis pathway.

**Option D:** Methionine is an essential amino acid that can be converted to glycogen through its metabolites, which can be used as precursors in the glycogen synthesis pathway.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that glycogen synthesis is a critical process that requires specific amino acids as precursors. Amino acids like leucine, which are primarily metabolized through ketogenesis, cannot be used for glycogen synthesis.

**✓ Correct Answer: C. Leucine**