The second messenger of the G-protein-coupled (metabotropic) receptor is:a.Phospholipase Cb.Sodium ionsc.c-AMPd.Adenylyl cyclase

The second messenger of the G-protein-coupled (metabotropic) receptor can be either c-AMP (cyclic adenosine monophosphate) or Phospholipase C, depending on the specific pathway activated.

Here's a step-by-step explanation:

1. When a ligand binds to a G-protein-coupled receptor (GPCR), it causes a conformational change in the receptor, which allows it to act as a guanine nucleotide exchange factor (GEF).

2. The GPCR activates the G protein by exchanging the GDP bound to the G protein for a GTP.

3. The G protein then dissociates into two subunits: the Gα subunit (bound to GTP) and the Gβγ dimer.

4. These subunits can then go on to activate various intracellular enzymes.

5. If the Gα subunit is of the Gαs type, it will activate the enzyme Adenylyl cyclase, which converts ATP into c-AMP, making c-AMP the second messenger in this pathway.

6. If the Gα subunit is of the Gαq type, it will activate the enzyme Phospholipase C, which cleaves phosphatidylinositol 4,5-bisphosphate (PIP2) into inositol trisphosphate (IP3) and diacylglycerol (DAG). In this case, IP3 and DAG act as second messengers.

So, the correct answer could be either c-AMP or Phospholipase C, depending on the specific G protein and pathway involved. Sodium ions and Adenylyl cyclase are not considered second messengers.