This is a rather complicated-looking diagram showing the effect of carbon monoxide on the oxygen dissociation curve (ODC) of human hemoglobin (brown), and comparisons to ODCs of normal (red) and anemic (blue) blood. Note that the anemic curve is shifted to the right, while the COHb curve is altered in shape, more closely resembling a hyperbola than a sigmoid (normal & anemic blood). (From: Jain, K.K. 1990, Carbon Monoxide Poisoning, Warren H. Green, Inc., St. Louis, MO)
Thus, carbon monoxide not only decreases the total oxygen carrying capacity of blood by rendering a portion of the hemoglobin sites unusable for oxygen binding, it also shifts the ODC of the remaining hemoglobin such that the hemoglobin binds the oxygen more avidly, thus making it more difficult for oxygen to be released to the tissues and therefore starving the tissues and organs of vital oxygen supplies. It causes asphyxia and is known as an asphyxiant. This constitutes a left-shift of the ODC. Anemia (& high altitude) on the other hand shifts the ODC to the right, enhancing oxygen release to tissues.
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