Catalyzes the calcium-dependent formation of isopeptide cross-links between glutamine and lysine residues in various proteins, as well as the conjugation of polyamines to proteins. Involved in the formation of the cornified envelope (CE), a specialized component consisting of covalent cross-links of proteins beneath the plasma membrane of terminally differentiated keratinocytes. Catalyzes small proline-rich proteins (SPRR1 and SPRR2) and LOR cross-linking to form small interchain oligomers, which are further cross-linked by TGM1 onto the growing CE scaffold (By similarity). In hair follicles, involved in cross-linking structural proteins to hardening the inner root sheath. L-glutaminyl-[protein] + L-lysyl-[protein] = [protein]-L-lysyl-N(6)-5-L-glutamyl-[protein] + NH4(+) Binds 3 Ca(2+) cations per subunit. Binds 1 Ca(2+) as a zymogen, and binds 2 more Ca(2+) cations, or other divalent metal cations, after proteolytic processing. Consists of two polypeptide chains, which are synthesized as a precursor form of a single polypeptide. Activated by proteolytic processing. In vitro activation is commonly achieved by cleavage with dispase, a neutral bacterial protease. Dispase cleavage site was proposed to lie between Ser-470 and Ser-471 (PubMed:8099584) or between Pro-465 and Phe-466 (PubMed:16565075). Physiological activation may be catalyzed by CTSL and, to a lesser extent, by CTSS, but not by CTSB, CTSD nor CTSV (PubMed:16565075). The disease is caused by variants affecting the gene represented in this entry. Belongs to the transglutaminase superfamily. Transglutaminase family.