Dissociation constant

Dissociation constant

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In chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

, biochemistry
Biochemistry, sometimes called biological chemistry, is the study of chemical processes in living organisms, including, but not limited to, living matter. Biochemistry governs all living organisms and living processes...

, and pharmacology
Pharmacology is the branch of medicine and biology concerned with the study of drug action. More specifically, it is the study of the interactions that occur between a living organism and chemicals that affect normal or abnormal biochemical function...

, 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
Complex (chemistry)
In chemistry, a coordination complex or metal complex, is an atom or ion , bonded to a surrounding array of molecules or anions, that are in turn known as ligands or complexing agents...

 falls apart into its component molecules, or when a salt splits up into its component ions. The dissociation constant is usually denoted and is the inverse
Multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the...

 of the association constant. In the special case of salts, the dissociation constant can also be called an ionization constant.

For a general reaction

in which a complex breaks down into x A
subunits and y B subunits, the dissociation constant is defined

where [A], [B], and [AxBy] are the concentrations of A, B, and the
complex AxBy, 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, Kd has a simple physical interpretation: when [A]=Kd, [B]=[AB] or equivalently [AB]/([B]+[AB])=1/2. That is, Kd, 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.

Protein-ligand binding

The dissociation constant is commonly used to describe the affinity
Chemical affinity
In chemical physics and physical chemistry, chemical affinity is the electronic property by which dissimilar chemical species are capable of forming chemical compounds...

 between a ligand
Ligand (biochemistry)
In biochemistry and pharmacology, a ligand is a substance that forms a complex with a biomolecule to serve a biological purpose. In a narrower sense, it is a signal triggering molecule, binding to a site on a target protein.The binding occurs by intermolecular forces, such as ionic bonds, hydrogen...

 () (such as a drug
A drug, broadly speaking, is any substance that, when absorbed into the body of a living organism, alters normal bodily function. There is no single, precise definition, as there are different meanings in drug control law, government regulations, medicine, and colloquial usage.In pharmacology, a...

) and a protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...

 () i.e. how tightly a ligand binds to a particular protein. Ligand-protein affinities are influenced by non-covalent intermolecular interactions between the two molecules such as hydrogen bond
Hydrogen bond
A hydrogen bond is the attractive interaction of a hydrogen atom with an electronegative atom, such as nitrogen, oxygen or fluorine, that comes from another molecule or chemical group. The hydrogen must be covalently bonded to another electronegative atom to create the bond...

ing, electrostatic interactions, hydrophobic and Van der Waals force
Van der Waals force
In physical chemistry, the van der Waals force , named after Dutch scientist Johannes Diderik van der Waals, is the sum of the attractive or repulsive forces between molecules other than those due to covalent bonds or to the electrostatic interaction of ions with one another or with neutral...

s. They can also be affected by high concentrations of other macromolecules, which causes macromolecular crowding
Macromolecular crowding
The phenomenon of macromolecular crowding alters the properties of molecules in a solution when high concentrations of macromolecules such as proteins are present. Such conditions occur routinely in living cells; for instance, the cytosol of Escherichia coli contains about 300–400 milligrammes per...


The formation of a ligand-protein complex () can be described by a two-state process

the corresponding dissociation constant is defined

where [], [] and [] represent molar concentrations of the protein, ligand and complex, respectively.

The dissociation constant has molar units (M), which correspond to the concentration of ligand [] 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 [], equals the concentration of protein with no ligand bound []. 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 (M) 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
Biotin, also known as Vitamin H or Coenzyme R, is a water-soluble B-complex vitamin discovered by Bateman in 1916. It is composed of a ureido ring fused with a tetrahydrothiophene ring. A valeric acid substituent is attached to one of the carbon atoms of the tetrahydrothiophene ring...

 and avidin
Avidin is a tetrameric biotin-binding protein produced in the oviducts of birds, reptiles and amphibians deposited in the whites of their eggs. In chicken egg white, avidin makes up approximately 0.05% of total protein...

 bind with a dissociation constant of roughly M = 1 fM = 0.000001 nM.
Ribonuclease inhibitor
Ribonuclease inhibitor
Ribonuclease inhibitor is a large , acidic , leucine-rich repeat protein that forms extremely tight complexes with certain ribonucleases. It is a major cellular protein, comprising ~0.1% of all cellular protein by weight, and appears to play an important role in regulating the lifetime of RNA.RI...

 proteins may also bind to ribonuclease
Ribonuclease is a type of nuclease that catalyzes the degradation of RNA into smaller components. Ribonucleases can be divided into endoribonucleases and exoribonucleases, and comprise several sub-classes within the EC 2.7 and 3.1 classes of enzymes.-Function:All organisms studied contain...

 with a similar M affinity.
The dissociation constant for a particular ligand-protein interaction can change significantly with solution conditions (e.g. temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

, pH
In chemistry, pH is a measure of the acidity or basicity of an aqueous solution. Pure water is said to be neutral, with a pH close to 7.0 at . Solutions with a pH less than 7 are said to be acidic and solutions with a pH greater than 7 are basic or alkaline...

 and salt concentration). The effect of different solution conditions is to effectively modify the strength of any 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 protein target (Positive Design).


In the specific case of antibodies (Ab) binding to antigen (Ag), usually the affinity constant is used. It is the inverted dissociation constant.

This chemical equilibrium
Chemical equilibrium
In a chemical reaction, chemical equilibrium is the state in which the concentrations of the reactants and products have not yet changed with time. It occurs only in reversible reactions, and not in irreversible reactions. Usually, this state results when the forward reaction proceeds at the same...

 is also the ratio of the on-rate (kforward) and off-rate (kback) 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.

Acid base reactions

For the deprotonation
Deprotonation is the removal of a proton from a molecule, forming the conjugate base.The relative ability of a molecule to give up a proton is measured by its pKa value. A low pKa value indicates that the compound is acidic and will easily give up its proton to a base...

 of acid
An acid is a substance which reacts with a base. Commonly, acids can be identified as tasting sour, reacting with metals such as calcium, and bases like sodium carbonate. Aqueous acids have a pH of less than 7, where an acid of lower pH is typically stronger, and turn blue litmus paper red...

s, K is known as Ka, the acid dissociation constant
Acid dissociation constant
An acid dissociation constant, Ka, is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction known as dissociation in the context of acid-base reactions...

. Stronger acids, for example sulfuric
Sulfuric acid
Sulfuric acid is a strong mineral acid with the molecular formula . Its historical name is oil of vitriol. Pure sulfuric acid is a highly corrosive, colorless, viscous liquid. The salts of sulfuric acid are called sulfates...

 or phosphoric acid
Phosphoric acid
Phosphoric acid, also known as orthophosphoric acid or phosphoric acid, is a mineral acid having the chemical formula H3PO4. Orthophosphoric acid molecules can combine with themselves to form a variety of compounds which are also referred to as phosphoric acids, but in a more general way...

, have larger dissociation constants; weaker acids, like acetic acid
Acetic acid
Acetic acid is an organic compound with the chemical formula CH3CO2H . It is a colourless liquid that when undiluted is also called glacial acetic acid. Acetic acid is the main component of vinegar , and has a distinctive sour taste and pungent smell...

, have smaller dissociation constants.

(The symbol , 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, which is defined as:

This p 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
The ammonium cation is a positively charged polyatomic cation with the chemical formula NH. It is formed by the protonation of ammonia...

) have only one dissociable group, the second (carbonic acid
Carbonic acid
Carbonic acid is the inorganic compound with the formula H2CO3 . It is also a name sometimes given to solutions of carbon dioxide in water, because such solutions contain small amounts of H2CO3. Carbonic acid forms two kinds of salts, the carbonates and the bicarbonates...

, bicarbonate
In inorganic chemistry, bicarbonate is an intermediate form in the deprotonation of carbonic acid...

, glycine
Glycine is an organic compound with the formula NH2CH2COOH. Having a hydrogen substituent as its 'side chain', glycine is the smallest of the 20 amino acids commonly found in proteins. Its codons are GGU, GGC, GGA, GGG cf. the genetic code.Glycine is a colourless, sweet-tasting crystalline solid...

) 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: pK1, pK2, pK3 and so on. For amino acids, the pK1 constant refers to its carboxyl (-COOH) group, pK2 refers to its amino (-NH3) group and the pK3 is the pK value of its side chain
Side chain
In organic chemistry and biochemistry, a side chain is a chemical group that is attached to a core part of the molecule called "main chain" or backbone. The placeholder R is often used as a generic placeholder for alkyl group side chains in chemical structure diagrams. To indicate other non-carbon...


Dissociation constant of water

As a frequently used special case, the dissociation constant of water
Self-ionization of water
The self-ionization of water is the chemical reaction in which a proton is transferred from one water molecule to another, in pure water or an aqueous solution, to create the two ions, hydronium, H3O+ and hydroxide, OH−...

 is often expressed as Kw:

The concentration of water is not included in the definition
of Kw, for reasons described in the article equilibrium constant.

The value of Kw 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 Kw / 10−14 pKw
0°C 0.1 14.92
10°C 0.3 14.52
18°C 0.7 14.16
25°C 1.2 13.92
30°C 1.8 13.75
50°C 8.0 13.10
60°C 12.6 12.90
70°C 21.2 12.67
80°C 35 12.46
90°C 53 12.28
100°C 73 12.14