Is a G-Protein considered a second messenger?

No, second messengers are defined as molecules, not proteins. You're correct in that you're looking at the regulatory mechanisms of the system, but you need to understand that the function of second messengers is signal amplification, whereas regulation of GPCRs can occur at many levels (right down to the rates of gene transcription for example).

Adenylate Cyclase (AC) is a good example of an enzyme that relies on a GPCR. AC itself is NOT a second messenger, but it does increase the cystolic cAMP concentration, and cAMP in this case would be considered a second messenger (Note: cAMP is a molecule whereas AC a protein).

G Protein Second Messenger

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RE:

Is a G-Protein considered a second messenger?

So the neurotransmitter binds to the g-protein coupled receptor site, which, long story short, changes the GPCR and activates a G-Protein on the intracellular side, causing a cascade that leads to blah blah blah blah. That would make the neurotransmitter a ligand and the G-Protein a second...