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In chemistry, biochemistry, and pharmacology, 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 (chemistry)|complex falls apart into its component molecules, or when a salt (chemistry)|salt splits up into its component ions. The dissociation constant is usually denoted Kd and 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 AxBy breaks down into x A subunits and y B subunits, the dissociation constant is defined
![K_{d} = \frac{[A]^x \times [B]^y}{[A_x B_y]}](/w/wix/images/math/f/a/7/fa734f7c67752b156fc481a917e07f30.png)
where [A], [B], and [AxBy] are the concentrations of A, B, and the complex AxBy, respectively.
Protein-Ligand binding
The dissociation constant is commonly used to describe the Chemical affinity|affinity between a Ligand (biochemistry)|ligand (L) (such as a drug) and a protein (P) i.e. how tightly a ligand binds to a particular protein. Ligand-protein affinities are influenced by non-covalent| non-covalent intermolecular interactions between the two molecules such as hydrogen bonding, electrostatic| 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 ligand-protein complex (C) can be described by a two-state process
the corresponding dissociation constant is defined
![K_{d} = \frac{\left[ \mathrm{P} \right] \left[ \mathrm{L} \right]}{\left[ \mathrm{C} \right]}](/w/wix/images/math/0/2/d/02d9662e84613b8f2ab83ae3d30de36c.png)
where [P], [L] and [C] represent the concentrations of the protein, ligand and complex, respectively.
The dissociation constant has Concentration#Molarity|molar units (M), which correspond to the concentration of ligand [L] 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 [C], equals the concentration of protein with no ligand bound [P]. 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 (μM) dissociation constant.
Sub-nanomolar dissociation constants as a result of non-covalent binding interactions between two molecules are 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.[3] Ribonuclease inhibitor proteins may also bind to ribonuclease with a similar 10 − 15 M affinity.[4] The dissociation constant for a particular ligand-protein 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 non-covalent|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 with high affinity (typically 0.1-10 nM) or at improving the affinity between a particular drug and its in-vivo protein target.