Is the heme molecule attached to hemoglobin during the primary level or tertiary level of organization?

Tertiary.

Explanation:

Primary structure of proteins refers to the order of amino acids that make up the protein. The heme is an nonprotein non-amino acid, so it is not involved at this stage.

Tertiary structure of proteins is the overall 3-D folding of the protein (it comes after secondary, which involves folding into a repeated pattern). The heme bonds to its correct position on the hemoglobin during this stage and helps in correct folding.

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