In this video, we're going to talk about the second region of Hemoglobin's Hill plot, which is this region right here highlighted in yellow that corresponds with hemoglobin's cooperative state. What we need to realize is that after the very first oxygen gas molecule binds to hemoglobin, at that point, hemoglobin subunits are going to begin to display positive cooperativity, where the slope of the line and the hill constant \( NH \) are going to equal a value of 3.

Recall from our previous lesson videos that hemoglobin's oxygen binding behavior in terms of its positive cooperativity is best explained via a combination of both the concerted and sequential models. Of course, what this means is that the Hill constant \( n_H \), which is equal to a value of 3, is not going to equal the variable \( n \), which recall is the number of ligand binding sites on the protein, which we know hemoglobin has, \( n \) equal to 4. These are not equal to each other, and that's totally okay.

If we take a look down below at our image of the Hill plot over here, recall that in this first region of hemoglobin's Hill plot, that corresponds where hemoglobin goes from having 0 oxygens bound up until having its very first oxygen bound. As soon as the first oxygen molecule binds to hemoglobin, again at that point is when the hemoglobin subunits begin to display positive cooperativity. You can see that right here at this region, which again corresponds with hemoglobin binding its first oxygen, is when hemoglobin transitions into its cooperative state here in this region.

Notice that the slope of the line and the hill constant that corresponds with this line here is going to be a value of 3. We can visually see that positive cooperativity is taking place in this cooperative region here because notice that the subunits begin to take on this confirmation that we see here, which represents a subunit with an increased oxygen affinity, which of course is going to correlate with positive cooperativity. You can see that the conformation is shown right here in these two subunits when the first oxygen molecule binds, and it's also shown right here when the second oxygen molecule binds. There's positive cooperativity occurring in this region up until the third oxygen gas molecule binds. At that point, notice that this conformation is not present anywhere in this molecule.

What we're saying here is that hemoglobin is going to continue to display positive cooperativity from the moment it binds its very first oxygen up until the third oxygen gas molecule binds. As soon as the third oxygen gas molecule binds here, then it transitions again into a non-cooperative state, which is this final region which we'll talk about in our next lesson video. But what we can also see is that, in this region right here, in these two hemoglobin subunits, the hemoglobin subunits are not equally competing for oxygen binding. You can clearly see that here with this hemoglobin molecule because you have one subunit in the full R state, you have two subunits in this altered conformational state, and you have one subunit in the full T state. These subunits are going to have different affinities for oxygen and therefore are not going to equally compete for oxygen. Because there is unequal competition for oxygen binding, that is more evidence to show that positive cooperativity is taking place here. This concludes our lesson on hemoglobin's second region, which is again its cooperative state. We'll be able to talk about the final region of hemoglobin's hill plot, up here in green, in our next lesson video. So I'll see you guys there.