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{{Redirect|Kd|other uses|KD (disambiguation)}}

{{Chemical equilibria}}
In [[chemistry]], [[biochemistry]], and [[pharmacology]], a '''dissociation constant''' is a specific type of [[equilibrium constant]] that measures the propensity of a larger object to separate (dissociate) reversibly into smaller components, as when a [[Complex (chemistry)|complex]] falls apart into its component [[molecules]], or when a [[salt (chemistry)|salt]] splits up into its component [[ions]].  The dissociation constant is usually denoted <math>K_{d}</math> and is the [[Multiplicative inverse|inverse]] of the [[association constant]]. In the special case of salts, the dissociation constant can also be called an [[ionization constant]].

For a general reaction

:<math>
\mathrm{A}_{x}\mathrm{B}_{y} \rightleftharpoons x\mathrm{A} + y\mathrm{B}
</math>

in which a complex <math>\mathrm{A}_{x}\mathrm{B}_{y}</math> breaks down into ''x'' A 
subunits and ''y'' B subunits, the dissociation constant is defined 

:<math>
K_{d} = \frac{[A]^x \times [B]^y}{[A_x B_y]}
</math>

where [A], [B], and [A<sub>x</sub>B<sub>y</sub>] are the concentrations of A, B, and the 
complex A<sub>x</sub>B<sub>y</sub>, respectively.

==Protein-ligand binding==<!-- This section is linked from [[Antibody]] and [[MDMA]] -->
The dissociation constant is commonly used to describe the [[Chemical affinity|affinity]] between a [[Ligand (biochemistry)|ligand]] ('''<math>\mathrm{L}</math>''') (such as a [[drug]]) and a [[protein]] ('''<math>\mathrm{P}</math>''') 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. They can also be affected by high concentrations of other macromolecules, which causes [[macromolecular crowding]].<ref>{{Cite pmid|18573087}}</ref><ref>{{Cite pmid|11279227}}</ref>

The formation of a ligand-protein complex ('''<math>\mathrm{C}</math>''') can be described by a two-state process

:<math>
\mathrm{C} \rightleftharpoons \mathrm{P} + \mathrm{L}
</math>  

the corresponding dissociation constant is defined 

:<math>
K_{d} = \frac{\left[ \mathrm{P} \right] \left[ \mathrm{L} \right]}{\left[ \mathrm{C} \right]}
</math>

where ['''<math>\mathrm{P}</math>'''], ['''<math>\mathrm{L}</math>'''] and ['''<math>\mathrm{C}</math>'''] represent [[molar concentration]]s of the protein, ligand and complex, respectively.  

The dissociation constant has [[Concentration#Molarity|molar]] units (M), which correspond to the concentration of ligand ['''<math>\mathrm{L}</math>'''] at which the binding site on a particular protein is half occupied, i.e. the concentration of ligand, at which the concentration of protein with ligand bound ['''<math>\mathrm{C}</math>'''], equals the concentration of protein with no ligand bound ['''<math>\mathrm{P}</math>'''].  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 (<math>\mu</math>M) dissociation constant.  

Sub-nanomolar 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 <math>10^{-15}</math> M = 1 fM = 0.000001 nM.<ref>{{Cite pmid|8506353}}</ref>
[[Ribonuclease inhibitor]] proteins may also bind to [[ribonuclease]] with a similar <math>10^{-15}</math> M affinity.<ref>{{Cite pmid|17350650}}</ref>  
The dissociation constant for a particular ligand-protein interaction  can change significantly 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 with high affinity (typically 0.1-10 nM) or at improving the affinity between a particular drug and its ''[[in-vivo]]'' protein target.

===Antibodies===
In the specific case of antibodies (Ab) binding to antigen (Ag), usually the affinity constant is used. It is the inverted dissociation constant.
:<math>
\mathrm{Ab} + \mathrm{Ag} \rightleftharpoons \mathrm{AbAg} 
</math>  

:<math>
K_{a} = \frac{\left[ \mathrm{AbAg} \right]}{\left[ \mathrm{Ab} \right] \left[ \mathrm{Ag} \right]} = \frac{1}{K_{d}} 
</math>

This [[chemical equilibrium]] is also the ratio of the on-rate (k<sub>forward</sub>) and off-rate (k<sub>back</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>
K_{a} = \frac{k_{forward}}{k_{back}} = \frac{\mbox{on-rate}}{\mbox{off-rate}}
</math>

== Another notation ==
A dissociation constant <math>K_{a}</math> is sometimes expressed by its p<math>K_{a}</math>, which is defined as:

:<math>
\mathrm{p}K_{a} = -\log_{10}{K_{a}}
</math>

These p<math>K_{a}</math>'s are mainly used for [[covalent]] dissociations (i.e., reactions in which chemical
bonds are made or broken) since such dissociation constants can vary greatly.   

==Dissociation constant of water==
As a frequently used special case, [[Self-ionization of water|the dissociation constant of water]] is often expressed as ''K''<sub>w</sub>:

<math>K_w = [\mbox{H}^+] [\mbox{OH}^-]</math>

The concentration of water <math>\left[ \mbox{H}_2\mbox{O} \right]</math> is not included in the definition
of ''K''<sub>w</sub>, for reasons described in the article [[equilibrium constant]].

The value of ''K''<sub>w</sub> varies with temperature, as shown in the table below.  This variation must be taken into account when making precise measurements of quantities such as pH.

{| class='"wikitable"'
!- valign="bottom" align="left" | '''Water temperature'''
| valign="bottom" align="left" | '''K<sub>w</sub>*10<sup>-14</sup>'''
| valign="bottom" align="left" | '''pK<sub>w</sub>'''
|-----
| valign="bottom" align="left" | 0°C
| valign="bottom" align="left" | 0.1
| valign="bottom" align="left" | 14.92
|-----
| valign="bottom" align="left" | 10°C
| valign="bottom" align="left" | 0.3
| valign="bottom" align="left" | 14.52
|-----
| valign="bottom" align="left" | 18°C
| valign="bottom" align="left" | 0.7
| valign="bottom" align="left" | 14.16
|-----
| valign="bottom" align="left" | 25°C
| valign="bottom" align="left" | 1.2
| valign="bottom" align="left" | 13.92
|-----
| valign="bottom" align="left" | 30°C
| valign="bottom" align="left" | 1.8
| valign="bottom" align="left" | 13.75
|-----
| valign="bottom" align="left" | 50°C
| valign="bottom" align="left" | 8.0
| valign="bottom" align="left" | 13.10
|-----
| valign="bottom" align="left" | 60°C
| valign="bottom" align="left" | 12.6
| valign="bottom" align="left" | 12.90
|-----
| valign="bottom" align="left" | 70°C
| valign="bottom" align="left" | 21.2
| valign="bottom" align="left" | 12.67
|-----
| valign="bottom" align="left" | 80°C
| valign="bottom" align="left" | 35
| valign="bottom" align="left" | 12.46
|-----
| valign="bottom" align="left" | 90°C
| valign="bottom" align="left" | 53
| valign="bottom" align="left" | 12.28
|-----
| valign="bottom" align="left" | 100°C
| valign="bottom" align="left" | 73
| valign="bottom" align="left" | 12.14
|}

== Acid base reactions ==
For the [[deprotonation]] of [[acid]]s, ''K'' is known as ''K''<sub>a</sub>, the  [[acid dissociation constant]].  Stronger acids, for example [[sulfuric acid|sulfuric]] or [[phosphoric acid]], have larger dissociation constants; weaker acids, like [[acetic acid]], have smaller dissociation constants.  A molecule can have several acid dissociation constants. In this regard, that is depending on the number of the protons they can give up, we define ''monoprotic'', ''diprotic'' and ''triprotic'' [[acid#Polyprotic acids|acids]].  The first (e.g. acetic acid or [[ammonium]]) have only one dissociable group, the second ([[carbonic acid]], [[bicarbonate]], [[glycine]]) have two dissociable groups and the third (e.g. phosphoric acid) have three dissociable groups. In the case of multiple p''K'' values they are designated by indices: p''K''<sub>1</sub>, p''K''<sub>2</sub>, p''K''<sub>3</sub> and so on. For amino acids, the p''K''<sub>1</sub> constant refers to its [[carboxyl]] (-COOH) group, p''K''<sub>2</sub> refers to its [[amino]] (-NH<sub>3</sub>) group and the p''K''<sub>3</sub> is the p''K'' value of its [[side chain]].

<math>H_3 B \rightleftharpoons\ H ^ + + H_2 B ^ - \qquad K_1 = {[H ^ +] \cdot [H_2 B ^ -] \over [H_3 B]} \qquad pK_1 = - log  K_1 </math>

<math>H_2 B ^ - \rightleftharpoons\ H ^ + + H B ^ {-2} \qquad K_2 = {[H ^ +] \cdot [H B ^{-2}] \over [H_2 B^ -]} \qquad pK_2 = - log  K_2 </math>

<math>H B  ^{-2} \rightleftharpoons\ H ^ + +  B ^{-3} \qquad K_3 = {[H ^ +] \cdot [ B ^ {-3}] \over [H B ^ {-2}]} \qquad pK_3 = - log  K_3 </math>

==References==
<references/>

== See also ==

* [[Ki Database|''K''<sub>i</sub> Database]]
* [[Acid]]
* [[pH]]
* [[Scatchard plot]]

[[Category:Equilibrium chemistry]]
[[Category:Enzyme kinetics]]

[[ar:ثابت انحلال]]
[[cs:Disociační konstanta]]
[[de:Dissoziationskonstante]]
[[es:Constante de disociación]]
[[fr:Constante de dissociation]]
[[ko:이온화 상수]]
[[it:Costante di dissociazione]]
[[he:קבוע הדיסוציאציה]]
[[lt:Disociacijos konstanta]]
[[pl:Stała dysocjacji]]
[[ru:Константа диссоциации]]
[[sv:Dissociationskonstant]]
[[uk:Константа дисоціації]]
[[Category:2Fix]]