How does the partial pressure of oxygen affect hemoglobin?
It doesn't affect hemoglobin.
Hemoglobin is an oxygen-transport protein in blood. It does not depend on oxygen. The partial pressure of oxygen WILL affect the amount available for transport through the lung membranes to be picked up by the hemoglobin.
Lower oxygen partial pressure means that less oxygen will be available for "collection" by the hemoglobin, which may have other consequences for bodily function. But, the amount of oxygen available directly for transport by a hemoglobin molecule does not affect the hemoglobin molecule itself.