# Structural Biochemistry/Protein function/Binding Sites/Cooperativity

Cooperativity can be seen in both enzymes and receptors, and describes the trends that occur when these structures contain multiple binding sites. Cooperativity describes the changes that occur when a binding site of one of these structures is activated or deactivated affecting the other binding sites in the same molecule. It can also be described as the increasing or decreasing affinity for binding of the other sites affected by the original binding site.

An example of a sigmoid curve.

Cooperativity can also be noted in large chain molecules that are made of many identical, or near identical, subunits (DNA, proteins, phospholipids), when these molecules go through phase transitions such as melting, unfolding, or unwinding, known as subunit cooperativity. When a substrate binds to the active site of one enzymatic subunit, the other subunits are stimulated and become active.

The activity of an enzyme can be graphed against the concentration of the substrate. For an enzyme that shows a cooperative behavior, the relation between the two shows a sigmoidal curve instead of Michaelis and Menten behavior. The graph shows a rapid increase in speed. This reflects how the binding on one subunit increases the chance that the other subunits will bind to a substrate.

## Types of Cooperative Binding

Cooperative binding can produce negative cooperativity, positive cooperativity, heterotropic cooperativity, and homotropic cooperativity.

### Negative Cooperativity

An example of negative cooperativity is the decrease in binding affinity once one of the sites is bound. As ligands bind to the protein, the protein's affinity for the ligand decreases. For example, the relationship between glyceraldehyde-3-phosphate and the enzyme glyceraldehyde-3-phosphate dehydrogenase is a clear example of this process.

### Positive Cooperativity

Hemoglobin is made up of four subunits. If one subunit binds to oxygen it increases the chance the other three will do the same.

An example of positive cooperativity can be seen when a substrate binds to an enzyme with multiple binding sites and the other binding sites are affected by this change.

This behavior is seen on the binding of oxygen to hemoglobin to form oxyhemoglobin. Hemoglobin is made out of four subunits, two alpha and two beta. They come together to form a tetramer, each subunit having its own active site to bind oxygen to. This active site contains a porphyrin ring structure with an iron atom in the center. When the subunit is not bound to an oxygen the iron is about 0.4 A below the plane of the ring. When the tetramer is in this state, it is considered to be in the T-state or tense state.

The R-state, or relaxed state occurs when hemoglobin has bound to oxygen. Deoxyhemoglobin, or the T-state, has a low affinity for oxygen. When one molecule binds to a single heme, though, the oxygen affinity increases, which allows the following molecules to bind more easily in succession. This occurs when the iron bound to the oxygen is lifted to lie in the same plane as the ring. This forces the histidine residue it is attached to also move, which in turn forces the alpha helix where the histidine is attached, to move. The carboxyl terminal at the end of the helix is located at the interface of the two alpha-beta dimers therefore favoring the R-state transition. Overall the R-state is more stable than T-state but under certain conditions this can change.

The oxygen affinity of the 3-oxyhemoglobin is about 300 times greater than that of its deoxyhemoglobin counterpart. This behavior leads to the affinity curve of hemoglobin to become sigmoidal, not hyperbolic as with the monomeric myoglobin's affinity curve. In the same way, the ability for hemoglobin to lose oxygen is greater as fewer oxygen molecules are bound. This cooperativity can be seen in Hemoglobin when one of the oxygen binds to one of the tetramer's subunits. This will increase the probability that the other three sites will bind to oxygen.

An example of homotropic cooperativity is the effect that the substrate molecule has on its affinity.

An example of heterotropic cooperativity is when a third substance causes a change in the affinity.

### Concerted Model of Cooperativity

The concerted model (symmetry model or MWC model): enzyme subunits are connected in such a way that a conformational change in one subunit is necessarily conferred to all other subunits. Thus all subunits must exist in the same conformation. Example: In hemoglobin, the tetramer changes conformation together (R state) after four oxygen molecules bind to all four monomers. The transition from the T state to the R state occurs in one step.

The Concerted Model, also known as MWC model or symmetry model, of hemoglobin is used to explain the cooperativity in oxygen binding as well as the transitions of proteins made up of identical subunits. It focuses on the two states of the Hemoglobin; the T and R states. The T state of the hemoglobin is more tense as it is in the deoxyhemoglobin form while the R state of the hemoglobin is more relaxed as it is in the oxyhemglobin form. The T state is constrained due to the subunit-subunit interactions while the R state is more flexible due to the ability of oxygen binding. The binding of oxygen at one site increases the binding affinity in other active sites. Thus in the concerted model of the hemoglobin, it shows that the one oxygen binding to an active site will increase the probability of other oxygen binding to the other active sites. In a concerted model, all oxygen binding sites on Hemoglobin in the T state must be bound before converting to the R state. This is also true in the conversion from the R state to the T state, in which all bounded oxygen must be released before full conversion can take place. At each level of oxygen loading, an equilibrium exists between the T-state and R-state. The equilibrium shifts from strongly favoring the T-state (no oxygen bound) to strongly favoring the R-state (fully loaded with oxygen). Overall, oxygen binding shifts the equilibrium toward the R state. This means that at high oxygen levels, the R form will be prevalent and at lower oxygen levels, the T form will be prevalent. Allosteric effectors of hemoglobin, such as 2,3-BPG, function by shifting the equilibrium towards or away from the T-state, depends on whether it's an inhibitor or a promoter. This model and the sequential model displays the extreme cases of R and T transitions. In a real system, properties from both models are needed to explain the behavior of hemoglobin.

### Sequential model of cooperativity

The sequential model: subunits are not connected in such a way that a conformational change in one induces a similar change in the others. All enzyme subunits do not necessitate the same conformation. The sequential model states that molecules of substrate bind through an induced fit. Example: In hemoglobin, the four monomers change conformation (R state) one at a time as oxygen binds to each monomer. This allows hemoglobin to have R state monomers and T state monomers.

The Sequential Model of the hemoglobin explains the cooperativity involved in the binding of oxygen. This model follows the concept that after binding occurs at one site in the active site, the binding affinity in the other sites around the protein will increase as well. Hence, the plot of substrate concentration versus reaction rate is of a sigmoidal shape. Because of this cooperativity, it does not follow Michaelis-Menten Kinetics. The difference between this model and concerted model is that the T states do not have to convert to R states all at one time. In this model, the ligand will change the conformation of the subunit that it is bound to and induce changes in the neighboring subunits. The sequential model does not require the overall state of the molecule to be in only T state or in only R state. Simply, each binding site influences nearby binding sites until all of the binding sites are in the same state. Neither the sequential model or the concerted model fully explains the nature of hemoglobin. Properties from both models appear in a real system.

## Subunit Cooperativity

Cooperativity not only occurs during ligand binding, but occurs any time energetic interactions simplify or complicate the occurrence of something happening that can involve multiple units as compared with single units. An example is the unwinding of DNA. Sections of DNA must first unwind in order for the DNA to carry out its other functions, such as replication, transcription, and recombination. Positive cooperativity among adjacent DNA nucleotides simplifies the process for unwinding a whole group of adjacent nucleotides compared to unwinding the same number of nucleotides spread along the DNA chain. The cooperative unit size is the number of adjacent bases that will unwind as a single unit because of the effects of positive cooperativity. This process applies to other types of chain molecules, too, such as the folding and unfolding of proteins, as well as the melting of phospholipid chains that comprise the cell membrane.

## Entropy and Cooperativity

Entropy plays an important role in cooperativity. This can be seen in the example of oxygen binding to hemoglobin, where the first oxygen has four different sites that it can bind to. This shows a relatively higher entropy compared with the binding the last oxygen will have, which has only one site left that will bind. In going from an unbound to a bound state, the first oxygen must overcome a larger entropy change versus the final binding oxygen. This entropy difference is the main reason for the positive cooperativity in binding oxygen to hemoglobin.

## Kinetics of cooperativity

When a plot of product formation as a function of substrate concentration produces a sigmoidal curve cooperativity is present. This sigmoidal curve is produced because of the effect of one substrate binding to one active site increasing the activity at the other active sites. The curve increases with a large slope and then levels out to its limit once the substrate saturation is reached. This is sigmoidal behavior.

## Hill Equation

The Hill equation is an equation describing the amount of ligand bound to the macromolecule, or its saturation. The equation is as follows:

${\displaystyle \theta ={[L]^{n} \over (K_{A})^{n}+[L]^{n}}={[L]^{n} \over K_{d}+[L]^{n}}}$

Where: ${\displaystyle \theta }$ represents the fraction of binding sites filled ${\displaystyle [L]}$ represents the concentration of the ligand ${\displaystyle K_{A}}$ represents the concentration of ligand required for half the binding sites to be occupied ${\displaystyle K_{d}}$ represents the dissociation constant ${\displaystyle n}$ represents the Hill coefficient, which describes the cooperativity of the reaction.

When:

• ${\displaystyle n>1}$, the reaction is POSITIVELY cooperative, meaning a ligand binding to a site INCREASES the ligand affinity at other binding sites.
• ${\displaystyle n<1}$, the reaction is NEGATIVELY cooperative, meaning a ligand binding to a site DECREASES the ligand affinity at other binding sites.
• ${\displaystyle n=1}$, the reaction is NOT cooperative, meaning a ligand binding to a site DOES NOT alter the ligand affinity at other binding sites.

The Hill Equation was formulated in 1910 by Archibald Hill (1886–1977), pioneer in biophysics.