Hemoglobin is an alphaalphabetabeta oligomeric protein: its quaternary structure consists of a tetramer of myoglobin like subunits. [Figure 4.48] The two types of chain are slightly shorter than myoglobin chains (alpha= 141 aa residues, beta= 146 aa residues). [Figure 4.49: Mb = green, globin = blue, globin = purple] There are extensive contacts between an alpha and a beta subunit to give a dimer. The dimers have additional contacts to give the tetramer. Oxygen binding results in a change of conformation in Hb. [Figure 4.53] The change of conformation affects the binding of oxygen..
Let's look at binding in terms of saturation, Y, where if Y = 1 every site of every Myoglobin is occupied by an oxygen molecule (thus if Y = 0.5, then 50% of the myoglobin are binding oxygen and 50% are "empty"). Mb/Hb binding curve [Figure 4.52A]:
So how can we understand these curves? Can describe binding as dissociation equilibrium,then:
MbO_{2 } Mb + O_{2}
The equilibriium expression is then: K = [Mb][O_{2}] / [MbO_{2}]
and in terms of saturation can write: Y = [MbO_{2}] / {[MbO_{2}] + [Mb]}
Substituting for the myoglobin terms can rewrite in terms of oxygen:
Y = [O_{2}] / {[O_{2}] +K}, the equation of a hyperbola.
If expressed as pressures, then
Y =pO_{2} / {pO_{2} + P_{50}} where P_{50} = pO_{2} @ 50% saturation.
Note that the binding curve for Mb is indeed hyperbolic in shape.
What about Hb? Obviously more complex. The sigmoid shape (sshape) of the curve indicates cooperativity. That is, if one site binds, another is more likely to as well (it cooperates with the first site). If the subunits of Hb are fully cooperative (if one subunit binds oxygen they all must bind oxygen, if one releases oxygen they must all release oxygen) then
Hb(O_{2})_{4} Hb+ 4O_{2}
and K = [Hb] [O_{2}]^{4} / [Hb(O_{2})_{4}]
and for saturation, substituting as above with Mb:
Y = (pO_{2})^{4} / {(pO_{2})^{4} + (P_{50})^{4}}
But this assumption of total cooperativity doesn't work, the curve is too steep.
FYIHill equation: We can rearrange our equation to find the degree of cooperativity. If we generalize:Y = (pO_{2})^{n} / {(pO_{2})^{n} + (P_{50})^{n}}. Rearranging: Y / (1 Y) = (pO_{2 }/ P_{50})^{n}
In this equation n is the cooperativity, that is the apparent number of fully cooperative sites. Hill plot: If we take logs of both sides of the Hill equation and plot the results, the exponent, n, shows up as the slope. Thus we can readily find the apparent cooperativity by plotting saturation vs. oxygen pressure (or concentration). For Hb the slope turns out to be n = 2.8. That is, Hb is partially cooperative  its 4 cooperating subunits only partially cooperate to behave like 2.8 completely cooperative subunits.
Note limiting situations at extremes with n = 1. At high concentrations this results because the effective equilibrium is:
In other words it acts like it has a single site (only one site is available at any moment) like myoglobin! At low concentrations of oxygen the opposite effect gives the same result:
Again, only one site is effectively operating (not enough O_{2} to fill more than subunit one site at any given time), so again mimics myoglobin. 
ALLOSTERISM AND REGULATION
Allosteric ("other site") enzyme or binding proteins are proteins with multiple interacting sites. Allosteric proteins can exhibit one or both of two types of allosterism:
Of course for any of these effects to exist, must see some degree of protein flexibility, as we have seen earlierin our discussion of protein folding, and is reviewed in the box below.
PROTEIN DYNAMICS"Breathing" motions:

Look at cooperativity/regulation curves for enzymes/binding proteins. [Fig. 5.20] Get two families of regulators:
So how to explain the cooperative behavior of allosteric proteins? Need to explain both kinds of effects.
Symmetry Model of Allosterism and Sequential Model of Allosterism.
Symmetry Model of Allosterism (Monod, Wyman & Changeau)
This may be diagramed in simplified form as in your text [Figure 5.21A], or in a more "classical picture":
Can also add binding of effectors to this model: positive effectors bind to R (circles) and shift equilibrium to right, negative effectors bind to T (squares) and shift equilibrium to left.
Sequential Model of Allosterism.
In this model the subunits are each influenced by binding to other subs, but change is stepwise rather than concerted. [Figure 5.21B]
Note that Hb seems to be a combination of both. Some enzymes appear to fit each model.
Pathway Diagrams 

© R. A. Paselk 2010;
Last modified 18 February 2013