Glycogen synthase is an enzyme important for making glycogen. in response to glucagon, glycogen synthase is glycogen synthase is an enzyme important for making glycogen. in response to glucagon, glycogen synthase is 1.inactivated by removing a phosphate group (dephosphorylation). 2.activated by phosphorylation. 3.inactivated by phosphorylation. 4.activated by removing a phosphate group (dephosphorylation).