You can't fully understand how hemoglobin molecules interact until you've seen them depicted through a classical pas de deux.
A red blood cell having no hemoglobin is also called a ghost.
hemoglobin he·mo·glo·bin (hē'mə-glō'bĭn)
The red respiratory protein of red blood cells that transports oxygen as oxyhemoglobin from the lungs to the tissues, where the oxygen is readily released and the oxyhemoglobin becomes hemoglobin.
An iron-containing protein present in the blood of many animals that, in vertebrates, carries oxygen from the lungs to the tissues of the body and carries carbon dioxide from the tissues to the lungs. Hemoglobin is contained in the red blood cells of vertebrates and gives these cells their characteristic color. Hemoglobin is also found in many invertebrates, where it circulates freely in the blood. It consists of four peptide units, each attached to a nonprotein compound called heme that binds to oxygen. See Note at red blood cell.
Our Living Language : Ninety percent of the protein in red blood cells is made up of hemoglobin, the main oxygen transport molecule in mammals. A protein with four iron-containing subunits called hemes, hemoglobin is a complex molecule with a complex function. It must bind to oxygen in the lungs, then release that oxygen in the tissues, then bind to carbon dioxide in the tissues and release it in the lungs. Hemoglobin accomplishes oxygen transport by changing its structure, and even its substructures, around the oxygen-binding heme groups, making them more or less accessible to the environment. When oxygen binds to at least one of the heme groups (as happens in the oxygen-rich lungs), all of the heme groups become exposed to the environment and bind oxygen easily. The bond between oxygen and heme is a loose one, however, so that the oxygen can break free in the tissues, where the concentration of oxygen is relatively low, and thereby become available for use in the cells. When the last of the four heme subunits loses its oxygen, the structure of hemoglobin changes again, so that the size of the opening from the environment to the heme groups decreases, making it difficult for an oxygen molecule to rebind to the hemoglobin. In this way, hemoglobin stops itself from competing with the tissues for needed oxygen. When the red blood cell carrying hemoglobin returns to the lungs, where oxygen concentration is high, the cycle of oxygen binding, transport, and release starts again. Normally, iron binds with oxygen to form rust (iron oxide), but the structure of hemoglobin prevents this from happening, since it would inactivate the heme subunits. Carbon dioxide does not bind the heme in hemoglobin, but rather the amino groups at the ends of the hemoglobin's protein subunits. Hemoglobin transport is only one of a number of bodily mechanisms by which carbon dioxide travels from the tissues to the lungs for release to the air.