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(+) Predicted to be exported by the Tat system. The position of the signal peptide cleavage has not been experimentally proven. Belongs to the bacterial TGase family.