You may have guessed it but in fact the function of the genes that play a role in rejection of transplants is not in the main to make transplantation difficult. Zinkernagel and Doherty discovered the basis for the function of these genes in 1974. [ZD74] They observed that T cells do not mount a response to viral antigen unless the viral antigen is expressed on the cell surface in association with the protein product of these genes.
There is a huge array of proteins expressed on cell surfaces. Of this huge array a limited number are responsible for transplant rejection. The genes that encode these proteins are the histocompatibility genes. These genes form the major histocompatibility complex (MHC). Rejection of skin grafts between MHC identical mice and the development of severe graft versus host disease in bone marrow transplantation between MHC identical siblings imply the existence of structures other than MHC that can be recognised by T cells to activate the immune response. Many of these genes have been identified and are lumped together as the minor histocompatibility complex (MiHC).