There are more than 300 variants of human hemoglobin gene. Among these only a few are fatal. Hence, the most important factor to be conserved in a protein for its function is the -

Function in biochemistry revolves around a reversible protein-ligand interaction. A molecule bound reversibly by a protein is called a ligand'. A ligand binds at a site on the protein called the `binding site'. which is complementary to the ligand in size, charge and hydrophobic or hydrophilic character. As long as the ligand-binding residues are preserved to allow interaction between the ligand and the binding sites the function will essentially be preserved.