How do the control mechanisms in glycogen metabolism lead to amplification of response to a stimulus?

This is based on the fact that the response to hormones generates a signaling cascade that eventuates in the activation or inhibition of enzymes involved in glycogen metabolism
The benefit of a multi-step cascade is that it amplifies the signal which means that response can be fast and significant
High level of secondary messenger, cyclic adenosine monophosphate (cAMP) activates a protein called protein kinase A (pKA) which phosphorylates phosphorylase kinase (pK) and activates it
On the other hand at the same time pKA phosphorylates glycogen synthase and inactivate it
pK becomes active that phosphorylates glycogen phosphorylase and makes it active, glycogen phosphorylase catalyse breakdown of glycogen (in liver and muscle cells)
Activated protein kinase A enters in nucleus and phosphorylate a transcriptional activator called cyclic AMP response element binding protein (CREB)
Phosphorylated CREB becomes active and binds to a DNA element called cyclic AMP response element (CRE) and induce transcription of various genes which involved in glucose metabolism