**Core Concept**
The glyconeogenic capability of a cell refers to its ability to synthesize glucose from non-carbohydrate sources such as lactate, glycerol, and glucogenic amino acids. This process is crucial for maintaining blood glucose levels and is regulated by a series of enzyme-catalyzed reactions.

**Why the Correct Answer is Right**
The presence of key enzymes such as glucose-6-phosphatase (G6Pase) and phosphoenolpyruvate carboxykinase (PEPCK) is essential for glyconeogenesis. G6Pase catalyzes the final step of glyconeogenesis by converting glucose-6-phosphate to glucose, which can then be released into the bloodstream. PEPCK, on the other hand, catalyzes the conversion of oxaloacetate to phosphoenolpyruvate, a crucial step in the gluconeogenic pathway.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it is not directly related to the glyconeogenic capability of cells. The presence of insulin, a hormone involved in glucose metabolism, does not directly determine the ability of cells to synthesize glucose.

**Option B:** This option is incorrect because the presence of glucagon, a hormone involved in glucose mobilization, does not directly determine the glyconeogenic capability of cells. While glucagon does stimulate gluconeogenesis, it is not a direct determinant of the process.

**Option C:** This option is incorrect because the presence of insulin-like growth factor-1 (IGF-1) is not directly related to the glyconeogenic capability of cells. IGF-1 is involved in cell growth and differentiation, but not in glucose synthesis.

**Clinical Pearl / High-Yield Fact**
The liver is the primary site of gluconeogenesis in the body, and its glyconeogenic capability is essential for maintaining blood glucose levels during fasting or starvation.

**Correct Answer: C. PEPCK**