Final answer:
TCR subunits do indeed have a transmembrane portion, anchoring the receptor in the T cell membrane and allowing the variable region to extend into the extracellular space to bind antigens.
Step-by-step explanation:
Yes, TCR subunits do have a transmembrane portion. T cell receptors (TCRs) are composed of two chains, each having a constant and a variable region, which are anchored in the T cell membrane by a transmembrane region. The variable region extends into the extracellular space and is responsible for binding processed antigens associated with MHC I or MHC II molecules on antigen-presenting cells (APCs). The diversity of TCRs, which allows the recognition of a multitude of different antigens, arises from the millions of unique binding sites generated through a process of genetic recombination known as V(D)J recombination.