Humboldt State University ® Department of Chemistry

Richard A. Paselk

Chem 431	Biochemistry	Fall 2001
Lecture Notes:: 26 September	© R. Paselk 2001
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OXYGEN BINDING

Last time we looked at myoglobin oxygen binding. Let's look at hemoglobin now, as seen in the Mb/Hb binding curve below [overhead 33 V&V]:

What about Hb? Obviously more complex. The sigmoid shape (s-shape) 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 and oxygen, if one releases oxygen they must all release oxygen) then ; ; and for saturation:

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 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 O₂ 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:

• Homotropic: this is where the sites are identical, and each sites is allosteric to the others. This is like the cooperative interactions seen in oxygen binding by hemoglobin ­ four (essentially) identical oxygen binding sites interacting with each other allosterically.
• Heterotropic: this is where binding at one kind of site affects the binding at a second kind of site. This occurs in the regulation of oxygen binding in hemoglobin by DPG ­ the DPG affects the binding of oxygen by all of the oxygen sites.

Look at cooperativity/regulation curves for enzymes/binding proteins. (Fig. 7.14, p 173) [overhead: Fig 6-27 P] Get two families of regulators:

• Positive (+) effectors or activators. These shift the binding constant so the binding takes place at lower concentrations, or increases the rate of an enzyme at a given concentration. Notice that (+) effectors decrease cooperativity.
• Negative (-) effectors (sometimes called inhibitors, but we will reserve the term inhibitor for classical enzyme inhibitors which work on non-allosteric proteins): decrease binding, so concentration must be increased to give the same level of activity. Notice that (-) effectors increase cooperativity.

So how to explain the cooperative behavior of allosteric proteins? Need to explain both kinds of effects. We'll use Hb as an example:

• Homotropic allosterism occuring with O₂ binding. Note mechanism involving shift of F-Helix explaining the response of single subunits. (overhead 9-16 V&V; Fig 7-9, p 170)
• Heterotropic regulation of O₂ binding, as occurs with BPG [Bis-PhosphoGlycerate - older lit = DPG] Due to higher binding affinity for BPG in deoxy ["T-State"] in centrral cavity - shifts O₂ binding to higher pO₂ - Hb can't shift to higher binding state of oxy Hb because the BPG won't fit in the smaller hole. (overhead 7-13 V&V of deoxy Hb; see Fig 7-15, p 175 for BPG binding).

Two important models: Symmetry Model of Allosterism and Sequential Model of Allosterism.

Symmetry Model of Allosterism (Monod, Wyman & Changeau)

• Allosteric protein an oligomer of protein subunits that are symmetrically related;
• Protomers can exist in two conformations (designated T[ense]: low affinity for substrate, & R[elaxed]: high affinity for substrate) that are in equilibrium whether or not ligand is bound;
• Ligand can bind to protomers in either conformation, but conformational change alters affinity for the ligand;
• The molecular symmetry of the protein is conserved during conformational change: the protomers must therefore change in a concerted manner.

This may be diagramed in simplified form as in Figure 7.19 of your text (p 179; overhead 9-29 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 step-wise rather than concerted. (Figure 7.20, p 179; overhead 6.29, P; 9-34, V&V)

Note that Hb seems to be a combination of both. Some enzymes appear to fit each model.

Pathway Diagrams

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Last modified 26 September 2001