Editing Cooperative binding (section)

=== Christian Bohr and the concept of cooperative binding ===
In 1904, [[Christian Bohr]] studied [[hemoglobin]] binding to [[oxygen]] under different conditions.<ref name=Bohr1904a>{{cite journal | vauthors = Bohr C | date = 1904 | url = https://www.biodiversitylibrary.org/item/50284#page/760/mode/1up | title = Die Sauerstoffaufnahme des genuinen Blutfarbstoffes und des aus dem Blute dargestellten Hämoglobins | language = de | journal = Zentralblatt Physiol. | volume = 23 | pages = 688–690 }}</ref><ref name=Bohr1904b>{{cite journal | vauthors = Bohr C, Hasselbalch K, Krogh A | author-link2 = Karl Albert Hasselbalch | author-link3 = August Krogh | year = 1904 | title = Ueber einen in biologischer Beziehung wichtigen Einfluss, den die Kohlensäurespannung des Blutes auf dessen Sauerstoffbindung übt | journal = Skandinavisches Archiv für Physiologie | volume = 16 | issue = 2| pages = 402–412 | doi = 10.1111/j.1748-1716.1904.tb01382.x | doi-access = free }}</ref> When plotting hemoglobin saturation with oxygen as a function of the [[partial pressure]] of oxygen, he obtained a sigmoidal (or "S-shaped") curve. This indicates that the more oxygen is bound to hemoglobin, the easier it is for more oxygen to bind - until all binding sites are saturated. In addition, Bohr noticed that increasing [[Carbon dioxide|CO<sub>2</sub>]] pressure shifted this curve to the right - i.e. higher concentrations of CO<sub>2</sub> make it more difficult for hemoglobin to bind oxygen.<ref name=Bohr1904b/> This latter phenomenon, together with the observation that hemoglobin's affinity for oxygen increases with increasing pH, is known as the [[Bohr effect]].

[[File:Bohr effect.png|thumb|right|Original figure from [[Christian Bohr]], showing the sigmoidal increase of oxyhemoglobin as a function of the partial pressure of oxygen.]]

A receptor molecule is said to exhibit cooperative binding if its binding to ligand scales non-linearly with ligand concentration. Cooperativity can be positive (if binding of a ligand molecule increases the receptor's apparent affinity, and hence increases the chance of another ligand molecule binding) or negative (if binding of a ligand molecule decreases affinity and hence makes binding of other ligand molecules less likely). The "fractional occupancy" <math>\bar{Y}</math> of a receptor with a given ligand is defined as the quantity of ligand-bound binding sites divided by the total quantity of ligand binding sites:

:<math>
\bar{Y}=\frac{[\text{bound sites}]}{[\text{bound sites}]+[\text{unbound sites}]} = \frac{[\text{bound sites}]}{[\text{total sites}]}
</math>

If <math>\bar{Y}=0</math>, then the protein is completely unbound, and if <math>\bar{Y}=1</math>, it is completely saturated. If the plot of <math>\bar{Y}</math> at equilibrium as a function of ligand concentration is sigmoidal in shape, as observed by Bohr for hemoglobin, this indicates positive cooperativity. If it is not, no statement can be made about cooperativity from looking at this plot alone.

The concept of cooperative binding only applies to molecules or complexes with more than one ligand binding sites. If several ligand binding sites exist, but ligand binding to any one site does not affect the others, the receptor is said to be non-cooperative. Cooperativity can be [[Allosteric regulation#Homotropic|homotropic]], if a ligand influences the binding of ligands of the same kind, or [[Allosteric regulation#Heterotropic|heterotropic]], if it influences binding of other kinds of ligands. In the case of hemoglobin, Bohr observed homotropic positive cooperativity (binding of oxygen facilitates binding of more oxygen) and heterotropic negative cooperativity (binding of CO<sub>2</sub> reduces hemoglobin's facility to bind oxygen.)

Throughout the 20th century, various frameworks have been developed to describe the binding of a ligand to a protein with more than one binding site and the cooperative effects observed in this context.<ref name=Wyman1990>{{cite book | vauthors = Wyman J, Gill SJ | year = 1990 | title = Binding and linkage. Functional chemistry of biological molecules | publisher = University Science Books | location = Mill Valley }}</ref>