A $12-$year$-$old boy is brought to the pediatric clinic by his parents with complaints of recurrent episodes of severe pain, particularly in his joints and abdomen. The parents mention these episodes occur more frequently during stressful or extreme weather conditions. The child has a history of delayed growth and has experienced bouts of jaundice in the past.

The child appears fatigued on examination, and there is evidence of jaundice. Laboratory investigations, including a complete blood count, reveal a low hemoglobin level, elevated reticulocyte count, and a high level of unconjugated bilirubin. The peripheral blood smear shows the presence of sickle$-$shaped red blood cells. Suspecting a potential hemoglobin variant or abnormality, the hematologist decides to perform which of the following specialized laboratory tests?

Group of answer choices

western blot

mass spectroscopy

ELISA

sodium dodecyl sulfate polyacrylamide gel electrophoresis