Final answer:
The variant polypeptide chain in MHC Class I molecules is the α chain.
Step-by-step explanation:
In MHC Class I molecules, the variant polypeptide chain is the α chain. MHC Class I molecules are composed of a longer α protein chain coupled with a smaller β₂ microglobulin protein, and only the α chain spans the cytoplasmic membrane. The α chain folds into three separate domains: α₁, α₂, and α₃. The antigen-binding cleft in MHC Class I molecules is formed by the α₁ and α₂ domains.