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Dissociation constant
In chemistry, biochemistry, and pharmacology, a dissociation constant (<math>K_{d}</math> ) 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 falls apart into its component molecules, or when a salt splits up into its component ions. The dissociation constant is the 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 \cdot [B]^y}{[A_x B_y]} </math>
where [A], [B], and [A_{x}B_{y}] are the concentrations of A, B, and the complex A_{x}B_{y}, respectively.
One reason for the popularity of the dissociation constant in biochemistry and pharmacology is that in the frequently encountered case where x=y=1, K_{d} has a simple physical interpretation: when [A]=K_{d}, [B]=[AB] or equivalently [AB]/([B]+[AB])=1/2. That is, K_{d}, which has the dimensions of concentration, equals the concentration of free A at which half of the total molecules of B are associated with A. This simple interpretation does not apply for higher values of x or y. It also presumes the absence of competing reactions, though the derivation can be extended to explicitly allow for and describe competitive binding. It is useful as a quick description of the binding of a substance, in the same way that EC50 and IC50 describe the biological activities of substances.
Contents
Proteinligand binding
The dissociation constant is commonly used to describe the affinity between a 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. Ligandprotein affinities are influenced by noncovalent intermolecular interactions between the two molecules such as hydrogen bonding, electrostatic interactions, hydrophobic and Van der Waals forces. They can also be affected by high concentrations of other macromolecules, which causes macromolecular crowding.^{[1]}^{[2]}
The formation of a ligandprotein complex (<math>\mathrm{C}</math>) can be described by a twostate 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 concentrations of the protein, ligand and complex, respectively.
The dissociation constant has 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.
Subpicomolar dissociation constants as a result of noncovalent 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.^{[3]} Ribonuclease inhibitor proteins may also bind to ribonuclease with a similar <math>10^{15}</math> M affinity.^{[4]} The dissociation constant for a particular ligandprotein 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 intermolecular interactions holding a particular ligandprotein 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 0.110 nM) or at improving the affinity between a particular drug and its invivo protein target (Positive Design).
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>
\text{Ab} + \text{Ag} \rightleftharpoons \text{AbAg} </math>
 <math>
K_{a} = \frac{\left[ \text{AbAg} \right]}{\left[ \text{Ab} \right] \left[ \text{Ag} \right]} = \frac{1}{K_{d}} </math>
This chemical equilibrium is also the ratio of the onrate (k_{forward}) and offrate (k_{back}) constants. Two antibodies can have the same affinity, but one may have both a high on and offrate constant, while the other may have both a low on and offrate constant.
 <math>
K_{a} = \frac{k_\text{forward}}{k_\text{back}} = \frac{\mbox{onrate}}{\mbox{offrate}} </math>
Acid–base reactions
Acids and bases 


Acid types 
Base types 
For the deprotonation of acids, K is known as K_{a}, the acid dissociation constant. Stronger acids, for example sulfuric or phosphoric acid, have larger dissociation constants; weaker acids, like acetic acid, have smaller dissociation constants.
(The symbol <math>K_{a}</math>, used for the acid dissociation constant, can lead to confusion with the association constant and it may be necessary to see the reaction or the equilibrium expression to know which is meant.)
Acid dissociation constants are sometimes expressed by p<math>K_{a}</math>, which is defined as:
 <math>
\mathrm{p}K_{a} = \log_{10}{K_{a}} </math>
This <math>\mathrm{p}K</math> notation is seen in other contexts as well; it is mainly used for covalent dissociations (i.e., reactions in which chemical bonds are made or broken) since such dissociation constants can vary greatly.
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 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 pK values they are designated by indices: pK_{1}, pK_{2}, pK_{3} and so on. For amino acids, the pK_{1} constant refers to its carboxyl (COOH) group, pK_{2} refers to its amino (NH_{3}) group and the pK_{3} is the pK 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>
Dissociation constant of water
The dissociation constant of water is denoted K_{w}:
<math>K_w = [\mbox{H}^+] [\mbox{OH}^]</math>
The concentration of water <math>\left[ \mbox{H}_2\mbox{O} \right]</math> is omitted by convention, which means that the value of K_{w} differs from the value of K_{eq} that would be computed using that concentration.
The value of K_{w} 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.
Water temperature  K_{w} / 10^{−14}  pK_{w}^{[5]} 

0 °C  0.112  14.95 
25 °C  1.023  13.99 
50 °C  5.495  13.26 
75 °C  19.95  12.70 
100 °C  56.23  12.25 
See also
 Acid
 Equilibrium constant
 K_{i} Database
 Michaelis–Menten kinetics
 Competitive inhibition
 pH
 Scatchard plot
References
 ^ Zhou, H.; Rivas, G.; Minton, A. (2008). "Macromolecular crowding and confinement: biochemical, biophysical, and potential physiological consequences". Annual review of biophysics 37: 375–397. PMC 2826134. PMID 18573087. doi:10.1146/annurev.biophys.37.032807.125817.
 ^ Minton, A. P. (2001). "The influence of macromolecular crowding and macromolecular confinement on biochemical reactions in physiological media". The Journal of Biological Chemistry 276 (14): 10577–10580. PMID 11279227. doi:10.1074/jbc.R100005200.
 ^ Livnah, O.; Bayer, E.; Wilchek, M.; Sussman, J. (1993). "Threedimensional structures of avidin and the avidinbiotin complex". Proceedings of the National Academy of Sciences of the United States of America 90 (11): 5076–5080. Bibcode:1993PNAS...90.5076L. PMC 46657. PMID 8506353. doi:10.1073/pnas.90.11.5076.
 ^ Johnson, R.; Mccoy, J.; Bingman, C.; Phillips Gn, J.; Raines, R. (2007). "Inhibition of human pancreatic ribonuclease by the human ribonuclease inhibitor protein". Journal of Molecular Biology 368 (2): 434–449. PMC 1993901. PMID 17350650. doi:10.1016/j.jmb.2007.02.005.
 ^ Bandura, Andrei V.; Lvov, Serguei N. (2006). "The Ionization Constant of Water over Wide Ranges of Temperature and Density" (PDF). Journal of Physical and Chemical Reference Data 35 (1): 15–30. doi:10.1063/1.1928231.