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Haemoglobin shows positive cooperativity with oxygen. When an oxygen atom binds to one of hemoglobin's four binding sites, the affinity to oxygen of the three remaining available binding sites increases; i.e. oxygen is more likely to bind to a hemoglobin bound to one oxygen than to an unbound hemoglobin. This is referred to as cooperative binding.

Now the following is an oxygen dissociation curve

Haemoglobin reaches 50% saturation when the partial pressure of oxygen reaches about 28 mm Hg. Now partial pressure had to be increased by about 70 mm Hg for haemoglobin to reach maximum saturation. If haemoglobin is a cooperative molecule, once haemoglobin reaches 50% saturation it should be easier to attain ~100% saturation. But it is taking a difference of 70 mm Hg. Whereas 50% saturation requires only 28 mm Hg. Hope this makes sense. Please answer this and correct my understanding. Thank you

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As you may notice from the graph you provided, there actually is no such thing as true 100% saturation: there is always an asymptotic approach to 100%, regardless of cooperativity.

Let's think, though, of what is actually plotted in that graph: $p_{O_2}$ effectively oxygen concentration, versus number of total percentage of binding sites that have an $O_2$ bound.

However, this also means that as you go up on the y-axis, the number of sites available to bind also goes down. So even if those sites have a high affinity for oxygen, there aren't as many of them open!

That's one big problem with the type of plot you show: it doesn't highlight the cooperativity very well. Therefore, people sometimes plot this information in a "Hill plot", with an algebraic shuffling and log scaling like this:

enter image description here

See Wikipedia

...where $\theta$ represents the fraction of receptors bound to ligand, and $L$ is the (unbound) ligand concentration. $n$ is the Hill Coefficient, i.e., the cooperativity.

When plotted this way, you can easily see the effect of the cooperativity of hemoglobin versus myoglobin (which has cooperativity of 1, because it has a single binding site):

enter image description here

http://cbc.arizona.edu/classes/bioc462/462a/NOTES/hemoglobin/hemoglobin_function.htm via Fig. 7-13, Nelson & Cox Principles of Biochemistry, 3rd ed., 2000

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I agree with everything in the answer from Bryan Krause but, in case it helps, here is the explanation that I came up with.

One way to think about this is in terms of the familiar MWC two-state model, which is essentially what you have used to frame your question.

If the concentration of oxygen is high enough for 50% saturation then, to a first approximation, most of the haemoglobin molecules have bound some oxygen and in terms of the whole population of molecules they are mostly in the relaxed, high affinity state in which any unoccupied binding sites will have the dissociation constant that is characteristic of that state. So all you are seeing in the right half of the curve is the usual hyperbolic binding curve for the relaxed form. For any saturation curve this is the behaviour that falls out of the mathematical description of the binding.

In other words, in terms of your word 'easy' it is always less easy to bind the next increment of ligand as you approach saturation because the concentration of occupied binding sites has increased so the rate of dissociation has also increased.

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    $\begingroup$ Yes. The basic fallacy is to think that co-operativity implies a sort of exponential increase in rate. One really has to understand that however efficient the protein-ligand interaction is, complete interaction only occurs at infinite ligand concentration. This is the basic idea of the hyperbolic curve being explained by the Michaelis-Menten model of specific enzyme active sites, and the mathematical treatment that corroborated it. And describing the behaviour of haemoglobin in terms of oxygen binding detracts the student from its importance in the release of oxygen. $\endgroup$ – David Jul 16 '17 at 21:46
  • $\begingroup$ @David Agreed, it can be quite a challenge to persuade students that the key innovation in the design of haemoglobin is the reduction in affinity for oxygen that cooperativity achieves. $\endgroup$ – Alan Boyd Jul 17 '17 at 11:02

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