Final answer:
The variable domain of both the heavy and light chains of an antibody determines its ability to bind to a specific antigen.
Step-by-step explanation:
The specific portion of the antibody that directly binds to an antigen is determined by the variable domain. This variable domain is present in both the heavy chain and light chain of an antibody. The heavy and light chains' variable domains interact to form the binding site, making it possible for the antibody to bind a specific epitope on the antigen. Conversely, the constant domain of an antibody, which is the same across all antibodies of a specific class, determines the immunological mechanism of action of the antibody but does not contribute to antigen binding. Therefore, the correct answer is the variable domain.