Chem 438 

Spring 2007 
Lecture Notes: 14 February 


PREVIOUS 
OXYGEN BINDING
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 [overhead 33 V&V]:
Reviewing the curve in terms of saturation, Y, if Y = 1 then 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").
Can describe binding as dissociation equilibrium,then:
MbO_{2} Mb + O_{2} ; &
for saturation. Substituting, , the equation of a hyperbola. If expressed as pressures, then 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
;
and for saturation, substituting as above with Mb:
But this assumption of total cooperativity doesn't work, the curve is too steep.
Hill equation: We can rearrange our equation to find the degree of cooperativity. If we generalize:. Rearranging:
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.
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:
Look at cooperativity/regulation curves for enzymes/binding proteins. (Fig. 5.21) [overhead: Fig 627 P] Get two families of regulators:
So how to explain the cooperative behavior of allosteric proteins? Need to explain both kinds of effects.
Two important models: 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 Figure 5.22a of your text (p 153; overhead 929 V&V), 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 5.22b, p 153; overhead 6.29, P; 934, V&V)
Note that Hb seems to be a combination of both. Some enzymes appear to fit each model.
Pathway Diagrams 

Last modified 14 February 2007