A composition comprising at least one isolated heterodimer conjugated to a nanoparticle, wherein the nanoparticle is non-liposomal and/or has a solid core and wherein the isolated heterodimer comprises at least one first polypeptide, at least one second polypeptide and an autoimmune disease-relevant antigen, wherein the first polypeptide and the second polypeptide meet at an interface, wherein the interface of the first polypeptide comprises an engineered protuberance which is positionable in an engineered cavity in the interface of the second polypeptide, wherein the engineered protuberance comprises an amino acid sequence that is at least 90% identical to the amino acid sequence of SEQ ID NO: 53, wherein the engineered cavity comprises an amino acid sequence that is at least 90% identical to the amino acid sequence of SEQ ID NO: 51; wherein (i) the first polypeptide comprises a soluble MHC class II α1 domain, a soluble MHC class II α2 domain, or a combination thereof; and the second polypeptide comprises a soluble MHC class II β1 domain, a soluble MHC class II β2 domain, or a combination thereof; or (ii) the first polypeptide comprises a soluble MHC class II β1 domain, a soluble MHC class II β2 domain, or a combination thereof; and the second polypeptide comprises a soluble MHC class II α1 domain, a soluble MHC class II α2 domain, or a combination thereof; and wherein the autoimmune disease-relevant antigen is a polypeptide which is at least 11 amino acids in length connected to the MHC class II α1 domain or the MHC class II β1 domain by a flexible linker; and wherein neither the first polypeptide nor the second polypeptide comprises a leucine zipper domain, or an extraneous biotinylation site or purification tag. wherein the nanoparticle is non-liposomal and/or has a solid core and wherein the isolated heterodimer comprises at least one first polypeptide, at least one second polypeptide and an autoimmune disease-relevant antigen, wherein the first polypeptide and the second polypeptide meet at an interface, wherein the interface of the first polypeptide comprises an engineered protuberance which is positionable in an engineered cavity in the interface of the second polypeptide, wherein the engineered protuberance comprises an amino acid sequence that is at least 90% identical to the amino acid sequence of SEQ ID NO: 53, wherein the engineered cavity comprises an amino acid sequence that is at least 90% identical to the amino acid sequence of SEQ ID NO: 51; wherein (i) the first polypeptide comprises a soluble MHC class II α1 domain, a soluble MHC class II α2 domain, or a combination thereof; and the second polypeptide comprises a soluble MHC class II β1 domain, a soluble MHC class II β2 domain, or a combination thereof; or (ii) the first polypeptide comprises a soluble MHC class II β1 domain, a soluble MHC class II β2 domain, or a combination thereof; and the second polypeptide comprises a soluble MHC class II α1 domain, a soluble MHC class II α2 domain, or a combination thereof; and (i) the first polypeptide comprises a soluble MHC class II α1 domain, a soluble MHC class II α2 domain, or a combination thereof; and the second polypeptide comprises a soluble MHC class II β1 domain, a soluble MHC class II β2 domain, or a combination thereof; or (ii) the first polypeptide comprises a soluble MHC class II β1 domain, a soluble MHC class II β2 domain, or a combination thereof; and the second polypeptide comprises a soluble MHC class II α1 domain, a soluble MHC class II α2 domain, or a combination thereof; and wherein the autoimmune disease-relevant antigen is a polypeptide which is at least 11 amino acids in length connected to the MHC class II α1 domain or the MHC class II β1 domain by a flexible linker; and wherein neither the first polypeptide nor the second polypeptide comprises a leucine zipper domain, or an extraneous biotinylation site or purification tag.