Compositions comprising a cell in which a molecular complex with high affinity for its cognate ligand is bound to the surface of the cell are provided. To form the molecular complexes, extracellular domains of transmembrane heterodimeric proteins, particularly T cell receptor and major histocompatibility complex proteins, can be covalently linked to the heavy and light chains of immunoglobulin molecules. The molecular complexes can be used, inter alia, to detect and regulate antigen-specific T cells and as therapeutic agents for treating disorders involving immune system regulation, such as allergies, autoimmune diseases, tumors, infections, and transplant rejection. Optionally, identical antigenic peptides can be bound to each ligand binding site of a molecular complex.