Catalyzes the cross-linking of proteins and the conjugation of polyamines to proteins. L-glutaminyl-[protein] + L-lysyl-[protein] = [protein]-L-lysyl-N(6)-5-L-glutamyl-[protein] + NH4(+) Binds 1 Ca(2+) ion per subunit. Widely expressed. Belongs to the transglutaminase superfamily. Transglutaminase family.