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Hemoglobins are tetramers composed of pairs of two different polypeptide subunits. The subunit composition of the principal hemoglobins are α2β2 (HbA; normal adult hemoglobin), α2γ2 (HbF; fetal hemoglobin) and α2δ2 (HbA2; a minor adult hemoglobin)

The total number of amino acids in beta chain and gamma chain is the same-146. The higher affinity of HbF to oxygen is due to presence of serine(in gamma chain) in place of histidine(in beta chain), which inhibits its binding with 2,3-bisphosphoglyceric acid.

Is this the only difference, or are there more such differences in the amino acid sequence?

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Here's a pairwise sequence alignment of the human hemoglobin beta (HBB) and gamma (HBG1) chains:

HBB_HUMAN          1 VHLTPEEKSAVTALWGKVNVDEVGGEALGRLLVVYPWTQRFFESFGDLST     50
                     .|.|.|:|:.:|:|||||||::.|||.|||||||||||||||:|||:||:
HBG1_HUMAN         1 GHFTEEDKATITSLWGKVNVEDAGGETLGRLLVVYPWTQRFFDSFGNLSS     50

HBB_HUMAN         51 PDAVMGNPKVKAHGKKVLGAFSDGLAHLDNLKGTFATLSELHCDKLHVDP    100
                     ..|:||||||||||||||.:..|.:.|||:||||||.|||||||||||||
HBG1_HUMAN        51 ASAIMGNPKVKAHGKKVLTSLGDAIKHLDDLKGTFAQLSELHCDKLHVDP    100

HBB_HUMAN        101 ENFRLLGNVLVCVLAHHFGKEFTPPVQAAYQKVVAGVANALAHKYH    146
                     |||:|||||||.|||.||||||||.|||::||:|..||:||:.:||
HBG1_HUMAN       101 ENFKLLGNVLVTVLAIHFGKEFTPEVQASWQKMVTAVASALSSRYH    146

You can see the H143S (or S143H?) substitution, as well as many more.

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