Described herein are heterodimers containing at least one first polypeptide and at least one second polypeptide, wherein the first polypeptide and the second polypeptide meet at an interface, wherein the interface of the first polypeptide contains an engineered protuberance which is positionable in an engineered cavity in the interface of the second polypeptide； and (i) the first polypeptide contains an MHC class II α1 domain, an MHC class II α2 domain, or a combination thereof； and the second polypeptide comprises an MHC class II β1 domain, an MHC class II β2 domain, or a combination thereof； or (ii) the first polypeptide contains an MHC class II β1 domain, an MHC class II β2 domain, or a combination thereof； and the second polypeptide comprises an MHC class II α1 domain, an MHC class II α2 domain, or a combination thereof.
