Protein Function - Hemoglobin

Last time we got into the quantitative description of O₂ binding in Mb, and we saw that it has a hyperbolic binding curve. Depending on the O₂ partial pressure, more or less oxygen will bind and be released from Mb. The Kd (or P₅₀) of Mb is 0.26 kPa, giving us the following binding curve:

This is great for an oxygen storage protein, because it will keep O₂ (bind with high affinity) over a wide range of O₂ partial pressures. This means that O₂ will be released from Mb only when things get really really bad and the tissues are very O₂-defficient.

However, this is not a very good idea for an oxygen transport protein. The normal O₂ pressures in the lungs and tissues are, respectively, 13 kPa and 4 kPa. Under this conditions (look the graph), the affinity of Mb for O₂ is high, and O₂ bound while Mb was in the lungs will not be released in the tissues.

If we do the math using the equations for q, we will see that in the lungs (pO₂ = 13 kPa), q = 0.98, which means that 98% of the binding sites are occupied. In tissue, pO₂ = 4 kPa, so q = 0.94, so 94% of the binding sites will be occupied. This means that Mb will only be able to deliver a 4% of the O₂ it picked up in the lungs when it gets to the tissues. We clearly see that Mb is not a very efficient oxygen carrier...

What if we increase the P₅₀ of Mb so that it releases more O₂ when we get to lower pO₂'s? Say that we set P₅₀ to 8.5 kPa (the mid-point between 13 kPa and 4 kPa, the O₂ partial pressures in the lung and tissues). Doing the math again, we get a 60% occupancy in the lungs, and a 40% in tissues. This is not good for several reasons. First, we get only 60% occupancy in the lungs, and we are wasting 40% of the sites in Mb. Second, only 20% of the O₂ absorbed in the lungs is released in the tissues.

What do we do? Ovbiously, we need something in which the binding affinity for oxygen changes a lot when we go from low pO₂ to high pO₂. We cannot use something with a hyperbolic binding curve, because we shown above this does not work. Somehow we have to change the binding affinity of O₂, so that it is very high when we have a lot of oxygewn around (lungs) and it is low when pO₂ drops below 4 kPa (tissues). Our 'system' has to be able to 'detect' these changes in  pressure, and change its binding affinity as a function of this.

In a protein like Mb, where we have only one binding site, we cannot get anything like this; it will bind  and that's that. What we need is a protein with multiple binding sites, and in which binding to one of the sites afftects the affinity of the other binding sites for the ligand. A protein that can do this pretty effectively is hemoglobin (Hb).

Hemoglobin structure

Good, so we know that in Hb the binding of one ligand will affect the binding of other ligands. So how many binding sites do we have, and how does it work anyway?

Hemoglobing is a tetrameric protein (it has four subunits), with two pairs of different subunits. It has two identical a subunits and two identical b subunits, called Hba and Hbb. The a subunit is composed by 141 residues, and the b by 146 amino acid residues:

Despite that there are only 27 amino acids conserved between the a subunit, the b subunit, and myoglobin, the three polypeptides have a remarkably similar tertiray structure. This can be clearly seen in th CHIME page, where I placed models of each of the Hb subunits and Mb:

The naming of the a-helices in Hb is similar to that of Mb, with the exception of the a subunit of Hb (Hba), which lacks the D helix. The proximal and distal His residues (the ones 'below' and 'on top' of the porphyrine ring) are conserved, and they conserve the relative positions in the a helices. Therefore, His F8 is the histidine residue that coordinates with iron in all three, and His E7 is the one that blocks the free coordination site. The numbering with respect to the primary structure does change: His F8 is His93 in Mb, His87 in Hba, and His92 in Hbb - His E7 is His64 in Mb, His58 in Hba, and His63 in Hbb. As was the case for Mb, the heme binding pocket is formed primarily by the E and F helices in both Hba and Hbb.

The quaternary structure of Hb (the disposition of the four Hb subunits) is stabilized by a large number of non-bonded interactions between the different subunits. There are near 30 'catalogued' interactions in the interface between the a₁b₁ (and a₂b₂), and near 20 in the interface between the a₁b₂ (and a₂b₁) subunits. Most are hydrophobic in nature, but there are also h-bonds and ionic interactions (salt-bridges). These last ones are crucial to the activity of Hb as we will discuss below.

O₂ binding and structural changes in Hb (binding cooperativity)

OK, now we know how it looks like, but how does it work? We will start by spillilng out the beans. The main reason that changes the affinity of Hb for oxygen as a function of the pO₂ is that binding of O₂ to one subunit affects the structure of the other subunits in Hb.

Hb exists in two conformational states, called the T state (tense) and the R state (relaxed). O₂ binds to either conformation of Hb, but it does so with different affinities. Hb in the R state has a higher O₂ affinity than Hb in the T state. When there is no oxygen bound to any of the subunits (deoxyhemoglobin, or deoxyHb), the T state is favoured energetically, and it is therefore predominant. The stabilization of the T state in the absence of oxygen is due to a large number of salt-bridges along the a₁b₂ (and a₂b₁) interface.

When an O₂ molecule binds to T state Hb, the subunit suffers a small conformational change. The free heme ring in deoxyHb is slightly puckered. That means, it is a little bent out of planarity. We can think of it this way - His F8 (the proximal histidine) is pulling from the Fe²⁺ in the heme towards it. This makes the Fe²⁺ to be slightly outside of the plane of the heme ring, and makes the whole heme ring distorted. When O₂ binds to the other heme coordination site, it will pull the Fe²⁺ towards itself, and therefore the Fe²⁺ will go back to the heme plane, flatening the heme ring. These pushing and pulling causes a shift in the position of His F8 and of the position of the F helix. Val E11, which is also in the surroundings of the binding site, also shift its position, draging with it the whole E helix. The changes in the conformation of the heme ring and the positions of amino acid residues around the binding site are small, but they translate to a shifting of amino acids residues involved in the inter-subunit salt bridges. Several of the salt-bridges that stabilized the T state Hb are broken.

For example, an ion pair in the b subunits between the His HC3 (the 3^rd histidine residue in the C-terminal region of the H helix) and Asp FG1 (the 1^st aspartate in the FG loop region) that is present in the T state is broken after binding of O₂ and changing conformation to the R state.

The T z R conformational change has an overall effect of shifting the ab subunit pairs, making then slide past each other. The pocket that exists between the b subunits in the T state (seen clearly as the whole in the color picture) narrows a lot upon transition to the R state. We will see why this is very important next time.

Why is the affinity for O₂ higher in the R state than in the T state, and how much higher is the affinity? We just said that when Hb undergoes the T z R conformational change, several salt-bridges are broken. As we know, salt-bridges will stabilize the structure of a protein, making it less flexible. We saw last time that this flexibility was crucial for the protein to 'breath', and this breathing created transient cavities through which O₂ moved around and reached the heme binding site. The more salt-bridges we have, the more constrained Hb gets, and the less it breathes. Therefore, O₂ will have less access to cavities, and it will be harder for it to get to the binding site. This change in the dynamics of Hb causes the affinity of O₂ for Hb in the R state to be 300 times higher than the affinity of Hb in the T state.

Now, how is that all these conformational changes and changes in O₂ affinity make Hb useful for O₂ transport? Lets say we are a deoxyHb protein in the T state. We have a low(er) affinity for O₂, so while the partial pressure of O₂ is low, we stay that way, and we bind very little oxygen. If we were floating around in the tissues, were pO₂ is low, we would not bind O₂ appreciably. Now, the blood stream takes us to the lungs, were the pO₂ is high. Even if we are in the T state, some of our subunits will start binding some O₂. The binding of O₂ to these subunits triggers the conformational change to the R state on the other subunits, and now we want even more O₂, because the affinity for O₂ is higher on the other subunits. More of our subunits bind O₂, and more T z R conformational changes take place, rising even more the affinity for oxygen. There is plenty O₂ in the lungs, so the end product is that we bind as much O₂ as we can.

Now the blood stream takes us back to the tissues, where pO₂ is low. Although we are in the R state and have high affinity for O₂, we still have to remember that this is an equilibrium, and if we lower the 'reactants' we will push the equilibrium to the left (unbinding). Therefore, we will start loosing O₂. As we loose O₂ in one subunit, which stabilizes the R state, we will start undergoing R z T conformational changes. So if one of our subunits loses O₂, we can go the T state more easily. This will lower the affinity for O₂ in the remaining subunits, and the end product is that we release quite a bit of the oxygen we had stored.

The oxygen binding curve (or occupancy curve) as a function of pO₂ is not hyperbolic anymore, but sigmoidal, which means that we have a region in which we suffer a transition from low-binding affinity (mostly T) to high-binding affinity (mostly R):

If we add numbers using the example we had above for Mb, we see that a change of pO₂ from 13 kPa to 4 kPa, which meant that only 4% of the oxygen bound to Mb was released, means that 40% of the oxygen that was bound at 13 kPa will be released at 4 kPa.

This is called cooperative binding, and all protein that exibits cooperative binding will have asigmoidal binding curve like the one shown above. Cooperative binding is not only seen in Hb, but in all allosteric proteins. An allosteric protein is a protein in which the binding of a ligand is modulated by the binding of another ligand in a different binding site. The modulation, as we saw for Hb, occurs through conformational changes caused by the binding of the modulator, which in turn affect the binding affinity of the the original ligand.

The modulator and the normal ligand can be identical, as they are in Hb. Here the ligand is oxygen, and the binding of oxygen (the modulator) to one binding site changes the conformation of other subunits, and increases the affinity of the binding sites in these subunits for oxygen (the ligand). We say that the interaction is homotropic. In many cases the normal ligand is different to the modulator, and the interaction is said to be heterotropic.

Quantitative description of cooperative O₂ binding in Hb

As we did for Mb, we can add numbers to the binding of O₂ to Hb and do a full quantitative description. Since we have a protein with multiple binding sites (n), the equilibrium we are concerned is:

Again, we redifine q to take into account the n binding sites:

We now do some math, and rearrange the equation quite a bit:

Now, if we take the log on both sides of the expression, we get:

Again, we are talking about binding of O₂ to Hb, so we substitute pO₂ for [L] and we get:

This equation is commonly known as the Hill equation, and the plot that we get from it if we plot log[ q / ( 1 - q ) ] vs log( [L] ) is a Hill plot:

Based on the equation, the plot above shold have a slope of n, but experimentally this is not what is found. In reallity, if we have a protein with cooperative binding, the slope reflects the degree of interaction between the different n binding sites, or the degree of cooperativity of the protein. This number is determined experimentally, and is called the Hill coefficient (n_H). A n_H higher than 1 indicates positive cooperativity, as in Hb. The theoretical value for n_H is 4, and it would imply that all binding sites bind the ligand (O₂) with high affinity. This is not the case, as we have to consider that there are molecules of Hb in that have mixed conformational states (R and T), and so no molecule of Hb will have all high affinity binding sites at any moment. The value of n_H determined experimentally is close to 3 (2.8). The blue line in the curve represents Mb, which shows no cooperativity.

Why do we have the change in the curve from n_H = 1, to n_H = 3, to n_H = 1? We have to think that while all Hb is in the T state, there will be no cooperativity. When the T z R conformational change starts taking place, binding will become cooperative, and so n_H will increase. After we reach saturation of most of the sites in Hb and all sites are in the R state, binding will again be non-cooperative, and n_H goes back to 1 reflecting this.

In some very rare cases (most of them mistakes), a protein will have a n_H < 1, which indicates negative cooperativity. This means that the binding of one molecule of ligand prevents the binding of other molecules of ligand.

Next time we will analyze different two models that exist to describe the T z R conformational change, and we will also see how other species (CO₂ and H⁺) affect the binding of O₂ to Hb.

Prepared by Guillermo Moyna, 1999.