Why does deleting just one nucleotide cause a dramatic change in the amino acid sequence produced by translation

The sequence of nucleotides determines the order of amino acids in a protein, the order of amino acids determines the shape and the shape determines the function. A very good example of one misplaced nucleotide having tremendous effects is sickle cell disease, where thymine is replaced with adenine(CAC instead of CTC). It means that glutamic acid is replaced with valine. This alters the shape of the protein(Beta chain of hemoglobin). So the red blood cells are deformed and carry a lot less oxygen leading to a lot of symptoms just because of one misplaced letter.

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the denominator has a very specific role.