Final answer:
Activation of one GPCR results in the activation of 1,000,000 pyruvate dehydrogenase molecules, through a signaling cascade that includes heterotrimeric G-proteins, adenylyl cyclase, cAMP, and protein kinase A.
Step-by-step explanation:
When one ligand-activated GPCR is activated, it can activate 50 heterotrimeric G-proteins. Each G-protein can activate one adenylyl cyclase. Each adenylyl cyclase can produce 100 cyclic AMP (cAMP) molecules, which in turn can each activate 20 protein kinase A (PKA) molecules. These 20 PKA molecules can phosphorylate 10 pyruvate dehydrogenase molecules each. To find out how many pyruvate dehydrogenases are activated by the initial activation of one GPCR, we perform the following calculation:
1 GPCR x 50 G-proteins x 1 adenylyl cyclase x 100 cAMP x 20 PKA x 10 pyruvate dehydrogenase = 1,000,000 activated pyruvate dehydrogenases.
Therefore, the activation of a single GPCR can lead to the activation of 1,000,000 pyruvate dehydrogenase molecules, thereby promoting gluconeogenesis.