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Dissociation constant

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Dissociation constant

In chemistry, biochemistry, and pharmacology, a dissociation constant (KD) 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:

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

where [A], [B], and [Ax By] are the equilibrium concentrations of A, B, and the complex Ax By, 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, then [B] = [AB] or, equivalently, . 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. It also presumes the absence of competing reactions, though the derivation can be extended to explicitly allow for and describe competitive binding.[citation needed] 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.

Experimentally, the concentration of the molecule complex [AB] is obtained indirectly from the measurement of the concentration of a free molecules, either [A] or [B]. In principle, the total amounts of molecule [A]0 and [B]0 added to the reaction are known. They separate into free and bound components according to the mass conservation principle:

To track the concentration of the complex [AB], one substitutes the concentration of the free molecules ([A] or [B]), of the respective conservation equations, by the definition of the dissociation constant,

This yields the concentration of the complex related to the concentration of either one of the free molecules

Many biological proteins and enzymes can possess more than one binding site. Usually, when a ligand L binds with a macromolecule M, it can influence binding kinetics of other ligands L binding to the macromolecule. A simplified mechanism can be formulated if the affinity of all binding sites can be considered independent of the number of ligands bound to the macromolecule. This is valid for macromolecules composed of more than one, mostly identical, subunits. It can be then assumed that each of these n subunits are identical, symmetric and that they possess only a single binding site. Then the concentration of bound ligands becomes

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