In chemistry and biochemistry, 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 falls apart into its component molecules, or when a salt splits up into its component ions. The dissociation constant is usually denoted $K\_\{d\}$ and is the inverse of the affinity constant. In the special case of salts, the dissociation constant can also be called an ionization constant.

For a general reaction

$$

\mathrm{A}_{x}\mathrm{B}_{y} \leftrightarrow x\mathrm{A} + y\mathrm{B}

in which a complex $\backslash mathrm\{A\}\_\{x\}\backslash mathrm\{B\}\_\{y\}$ breaks down into x A subunits and y B subunits, the dissociation constant is defined

$$

K_d = \frac{\times [B^y}{B_y}

where ^* are the concentrations of A, B, and the complex A_xB_y, respectively.

Protein-Ligand binding

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Dissociation constants are commonly used to describe how tightly a ligand (such as a drug) binds to a protein. Such binding is usually non-covalent, i.e., no chemical bonds are made or broken. Since the binding is usually described by a two-state process

$$

\mathrm{P} + \mathrm{L} \leftrightarrow \mathrm{C}

the corresponding dissociation constant is defined

$$

K_{d} = \frac{\left\mathrm{P} \right \left\mathrm{L} \right}{\left\mathrm{C} \right}

where ^* represent the concentrations of the protein, ligand and bound complex, respectively. The dissociation constant has the units of molar (M), and corresponds to the concentration of ligand ^* at which the binding site on the protein is half occupied, i.e., when 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; for example, a ligand with a nanomolar (nM) dissociation constant binds more tightly than a ligand with a micromolar ($\backslash mu$M) dissociation constant.

Drugs can have harmful side effects, so it's important to design drugs that bind to their target protein even at low concentrations in the bloodstream, i.e., have small dissociation constants (typically, 0.1-10 nM). Much of pharmaceutical research is aimed at identifying molecules that bind tightly to a target protein (e.g., HIV protease) and improving their binding (i.e., lowering their dissociation constant) by small chemical modifications.

Sub-nanomolar dissociation constants for non-covalent binding of two molecules is rare. Nevertheless, there are some important exceptions. Biotin and avidin bind with a dissociation constant of roughly $10^\{-15\}$ M = 1 fM = 0.000001 nM, while ribonuclease inhibitor binds to ribonucleases with roughly 10 fM affinity under physiological conditions. Non-covalent dissociation constants can change significantly with solution conditions (such as temperature, pH or salt concentration) that modify the effective strength of the molecular interactions holding the complex together.

Another notation

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A dissociation constant $K\_\{d\}$ is sometimes expressed by its p$K\_\{d\}$, which is defined as:

$$

\mathrm{p}K_{d} = -\log_{10}{K_{d}}

These p$K\_\{d\}$'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

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As a frequently used special case, the dissociation constant of water is often expressed as K_w:

$K\_w\; =**$

(The concentration of water $\backslash left\backslash mathrm\{H\_\{2\}O\}\; \backslash right$ is not included in the definition of $k\_\{w\}$, for reasons described in equilibrium constant.)

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	Kd/10-14	pKd	-	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

Acid base reactions

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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. 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: 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.

$H\_3\; B\; \backslash Longleftrightarrow\backslash \; H\; ^\; +\; +\; H\_2\; B\; ^\; -\; \backslash qquad\; K\_1\; =\; \{^\; +\backslash cdotB\; ^\; -\backslash overB\}\; \backslash qquad\; pK\_1\; =\; -\; log\; K\_1$

$H\_2\; B\; ^\; -\; \backslash Longleftrightarrow\backslash \; H\; ^\; +\; +\; H\; B\; ^\; \{-2\}\; \backslash qquad\; K\_2\; =\; \{^\; +\backslash cdotB\; ^\{-2\}\backslash overB^\; -\}\; \backslash qquad\; pK\_2\; =\; -\; log\; K\_2$

$H\; B\; ^\{-2\}\; \backslash Longleftrightarrow\backslash \; H\; ^\; +\; +\; B\; ^\{-3\}\; \backslash qquad\; K\_3\; =\; \{^\; +\backslash cdotB\; ^\; \{-3\}\backslash overB\; ^\; \{-2\}\}\; \backslash qquad\; pK\_3\; =\; -\; log\; K\_3$

See also

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• Acid

Enzyme kinetics

ثابت انحلال | Dissoziationskonstante | Dissotsiatsiooniaste | 이온화 상수 | Costante di dissociazione | Stała dysocjacji | Константа диссоциации