Dissociation constant

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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_] 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_\mathrm_ \leftrightarrow x\mathrm + y\mathrm]

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

[K_d = \frac]

where [A], [B], and [A_xB_y] are the concentrations of A, B, and the complex A_xB_y, respectively.

Contents

1 Protein-Ligand binding
2 Another notation
3 Dissociation constant of water
4 Acid base reactions
5 See also

Protein-Ligand binding

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 + \mathrm \leftrightarrow \mathrm]

the corresponding dissociation constant is defined

[K_ = \frac right] \left[ mathrm right]} right]}]

where [P], [L] and [C] 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 [L] at which the binding site on the protein is half occupied, i.e., when the concentration of protein with ligand bound [C] equals the concentration of protein with no ligand bound [P]. 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 ([\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^] 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

A dissociation constant [K_] is sometimes expressed by its p[K_], which is defined as:

[\mathrmK_ = -\log_}]

These p[K_]'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, the dissociation constant of water is often expressed as K_w:

[K_w = [H^+][OH^-]]

(The concentration of water [\left[ mathrmO} right]] is not included in the definition of [k_], 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 K_d/10^-14 pK_d
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

Water temperature	K_d/10^-14	pK_d
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

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 \Longleftrightarrow\ H ^ + + H_2 B ^ - \qquad K_1 = \qquad pK_1 = - log K_1 ]

[H_2 B ^ - \Longleftrightarrow\ H ^ + + H B ^ \qquad K_2 = ] \over [H_2 B^ -]} \qquad pK_2 = - log K_2 ]

[H B ^ \Longleftrightarrow\ H ^ + + B ^ \qquad K_3 = ] \over [H B ^ ]} \qquad pK_3 = - log K_3 ]

Dissociation constant

Protein-Ligand binding

Another notation

Dissociation constant of water

Acid base reactions

See also