Catalyzes the ATP or GTP-dependent addition of one L-glutamate molecule to tetrahydromethanopterin, producing tetrahydrosarcinapterin. 5,6,7,8-tetrahydromethanopterin + ATP + L-glutamate = 5,6,7,8-tetrahydrosarcinapterin + ADP + H(+) + phosphate Binds 2 magnesium or manganese ions per subunit. Cofactor biosynthesis; 5,6,7,8-tetrahydrosarcinapterin biosynthesis. Homodimer. Belongs to the RimK family. MptN subfamily.