# Myoglobin and Hemoglobin as Example Proteins, cont.

### Hemoglobin

Hemoglobin is an alpha-alpha-beta-beta 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..

## 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 [Figure 4.52A]:

So how can we understand these curves? Can describe binding as dissociation equilibrium,then:

MbO2 Mb + O2

The equilibriium expression is then: K = [Mb][O2] / [MbO2]

and in terms of saturation can write: Y = [MbO2] / {[MbO2] + [Mb]}

Substituting for the myoglobin terms can rewrite in terms of oxygen:

Y = [O2] / {[O2] +K}, the equation of a hyperbola.

If expressed as pressures, then

Y =pO2 / {pO2 + P50} where P50 = pO2 @ 50% saturation.

Note that the binding curve for Mb is indeed hyperbolic in shape.

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 oxygen, if one releases oxygen they must all release oxygen) then

Hb(O2)4 Hb+ 4O2

and K = [Hb] [O2]4 / [Hb(O2)4]

and for saturation, substituting as above with Mb:

Y = (pO2)4 / {(pO2)4 + (P50)4}

But this assumption of total cooperativity doesn't work, the curve is too steep.

### FYI

Hill equation: We can rearrange our equation to find the degree of cooperativity. If we generalize:Y = (pO2)n / {(pO2)n + (P50)n}. Rearranging:

Y / (1- Y) = (pO2 / P50)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:

Hb(O2)4 Hb(O2)3 + O2

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:

HbO2 Hb + O2

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.
• Compare R & T binding [Figure 4.52B]
• 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 BPG (BisPhosphoGlycerate = DPG in older literature).[Figure of BPG, p 127] BPG affects the binding of oxygen by all of the oxygen sites, binds in center of Hb [Figure 4.54]
• BPG effects - BPG raisees the P50 value from 12 torr in purified Hb to 26 torr in the rbc. This occurs by a stabilization of the T (low affinity) state, which in turn opposes O2 binding, the [O2] must increase to maintain the same level of binding, or more will be released if the pO2 stays the same. [Figure 4.52B]

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:

• Atomic fluctuations (10-15- 10-11 sec; 0.001 - 0.1 nanometer) Myoglobin example.
• Collective motions of covalently linked atoms, from aa R-groups to domains (10-12 - 10-3 sec; 0.001 - >0.5 nanometer)
• Triggered conformational changes: in response to ligand binding, covalent modification etc.
How do we know about the mobility of protein structures?
• X-ray diffraction studies of proteins with and without ligand bound
• NMR (phe, his ring protons/carbons show up on edges of signal envelope)
• H-exchange
• Antibody binding: make antibodies to normally interior aa residues, over time protein ppt forms as interior groups momentarily exposed.

### Cooperativity/regulation

Look at cooperativity/regulation curves for enzymes/binding proteins. [Fig. 5.20] 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 (less sigmoid curve).
• 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 (more sigmoid curve).

So how to explain the cooperative behavior of allosteric proteins? Need to explain both kinds of effects.

• Homotropic allosterism as occurs with O2 binding in Hb.
• Heterotropic regulation of O2 binding, as occurs with BPG in Hb.
• Lowers affinity for oxygen (curve)
• How - Stabilizes deoxyform
• Use to adapt to high elevation, smoking
• In lungs BPG is released by high oxygen concentration.

### 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 (note better fit in R form [Figure 5.21A]);
• 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 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 step-wise rather than concerted. [Figure 5.21B]

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

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