Editing Dissociation constant (section)

==Protein–ligand binding==<!-- This section is linked from [[Antibody]] and [[MDMA]] -->
{{Main|Receptor–ligand kinetics}}
The dissociation constant is commonly used to describe the [[Chemical affinity|affinity]] between a [[Ligand (biochemistry)|ligand]] <chem>L</chem> (such as a [[drug]]) and a [[protein]] <chem>P</chem>; i.e., how tightly a ligand binds to a particular protein.  Ligand–protein affinities are influenced by [[non-covalent| non-covalent intermolecular interactions]] between the two molecules such as [[hydrogen bond]]ing, [[electrostatic| electrostatic interactions]], [[hydrophobic]] and [[van der Waals force]]s. Affinities can also be affected by high concentrations of other macromolecules, which causes [[macromolecular crowding]].<ref>{{Cite journal
 | last1 = Zhou   | first1 = H.
 | last2 = Rivas  | first2 = G.
 | last3 = Minton | first3 = A.
 | title = Macromolecular crowding and confinement: biochemical, biophysical, and potential physiological consequences
 | journal = Annual Review of Biophysics
 | volume = 37
 | pages = 375–397
 | year = 2008
 | pmid = 18573087
 | doi = 10.1146/annurev.biophys.37.032807.125817
 | pmc = 2826134 
}}</ref><ref>{{Cite journal
 | last1 = Minton | first1 = A. P.
 | title = The influence of macromolecular crowding and macromolecular confinement on biochemical reactions in physiological media
 | journal = The Journal of Biological Chemistry
 | volume = 276
 | issue = 14
 | pages = 10577–10580
 | year = 2001
 | pmid = 11279227
 | doi = 10.1074/jbc.R100005200   
| url = http://www.jbc.org/content/276/14/10577.full.pdf
 | doi-access = free
 }}</ref>

The formation of a [[Protein–ligand complex|ligand–protein complex]] <chem>LP</chem> can be described by a two-state process

:<chem>
 L + P <=> LP
</chem>

the corresponding dissociation constant is defined

:<math chem="">
 K_\mathrm{D} = \frac{\left[ \ce{L} \right] \left[ \ce{P} \right]}{\left[ \ce{LP} \right]}
</math>

where <chem>[P], [L]</chem>, and <chem>[LP]</chem> represent [[molar concentration]]s of the protein, ligand, and protein–ligand complex, respectively.

The dissociation constant has [[Molar concentration|molar]] units (M) and corresponds to the ligand concentration <chem>[L]</chem> at which half of the proteins are occupied at equilibrium,<ref>{{Cite journal|last1=Björkelund|first1=Hanna|last2=Gedda|first2=Lars|last3=Andersson|first3=Karl|date=2011-01-31|title=Comparing the Epidermal Growth Factor Interaction with Four Different Cell Lines: Intriguing Effects Imply Strong Dependency of Cellular Context|journal=PLOS ONE|volume=6|issue=1|pages=e16536|doi=10.1371/journal.pone.0016536|pmid=21304974|issn=1932-6203|bibcode=2011PLoSO...616536B|pmc=3031572|doi-access=free}}</ref> i.e., the concentration of ligand at which the concentration of protein with ligand bound <chem>[LP]</chem> equals the concentration of protein with no ligand bound <chem>[P]</chem>.  The smaller the dissociation constant, the more tightly bound the ligand is, or the higher the affinity between ligand and protein.  For example, a ligand with a nanomolar (nM) dissociation constant binds more tightly to a particular protein than a ligand with a micromolar (μM) dissociation constant.

Sub-picomolar dissociation constants as a result of non-covalent binding interactions between two molecules are rare.  Nevertheless, there are some important exceptions.  [[Biotin]] and [[avidin]] bind with a dissociation constant of roughly 10<sup>−15</sup> M = 1 fM = 0.000001 nM.<ref>{{Cite journal
 | last1 = Livnah  | first1 = O.
 | last2 = Bayer   | first2 = E.
 | last3 = Wilchek | first3 = M.
 | last4 = Sussman | first4 = J.
 | year = 1993
 | journal = Proceedings of the National Academy of Sciences of the United States of America
 | pages = 5076–5080
 | pmid = 8506353
 | pmc = 46657
 | doi = 10.1073/pnas.90.11.5076
 | volume = 90
 | title = Three-dimensional structures of avidin and the avidin-biotin complex
 | issue = 11
 |bibcode = 1993PNAS...90.5076L
| doi-access = free
 }}</ref>
[[Ribonuclease inhibitor]] proteins may also bind to [[ribonuclease]] with a similar 10<sup>−15</sup> M affinity.<ref>{{Cite journal
 | last1 = Johnson     | first1 = R.
 | last2 = Mccoy       | first2 = J.
 | last3 = Bingman     | first3 = C.
 | last4 = Phillips Gn | first4 = J.
 | last5 = Raines      | first5 = R.
 | title = Inhibition of human pancreatic ribonuclease by the human ribonuclease inhibitor protein
 | journal = Journal of Molecular Biology
 | volume = 368
 | issue = 2
 | pages = 434–449
 | year = 2007
 | pmid = 17350650
 | doi = 10.1016/j.jmb.2007.02.005
 | pmc = 1993901 
}}</ref>  

The dissociation constant for a particular ligand–protein interaction can change with solution conditions (e.g., [[temperature]], [[pH]] and salt concentration). The effect of different solution conditions is to effectively modify the strength of any [[non-covalent|intermolecular interactions]] holding a particular ligand–protein complex together.

Drugs can produce harmful side effects through interactions with proteins for which they were not meant to or designed to interact. Therefore, much pharmaceutical research is aimed at designing drugs that bind to only their target proteins (negative design) with high affinity (typically 0.1–10 nM) or at improving the affinity between a particular drug and its ''[[in-vivo|in vivo]]'' protein target (positive design).

===Antibodies===
In the specific case of antibodies (Ab) binding to antigen (Ag), usually the term '''affinity constant''' refers to the association constant.
:<chem>
 Ab + Ag <=> AbAg 
</chem>

:<math chem="">
 K_\mathrm{A} = \frac{\left[ \ce{AbAg} \right]}{\left[ \ce{Ab} \right] \left[ \ce{Ag} \right]} = \frac{1}{K_\mathrm{D}} 
</math>

This [[chemical equilibrium]] is also the ratio of the on-rate (''k''<sub>forward</sub> or ''k''<sub>a</sub>) and off-rate (''k''<sub>back</sub> or ''k''<sub>d</sub>) constants. Two antibodies can have the same affinity, but one may have both a high on- and off-rate constant, while the other may have both a low on- and off-rate constant.

:<math chem="">
 K_A = \frac{k_\text{forward}}{k_\text{back}}  = \frac{\mbox{on-rate}}{\mbox{off-rate}}
</math>