In chemistry, biochemistry, and pharmacology, a dissociation constant (
Contents
- Molecules with one binding site
- Macromolecules with identical independent binding sites
- Protein ligand binding
- Antibodies
- Acidbase reactions
- Dissociation constant of water
- References
For a general reaction:
in which a complex
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
Molecules with one binding site
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
Macromolecules with identical independent binding sites
Many biological proteins and enzymes can possess more than one binding site. Usually, when a ligand
In this case,
where the saturation occurs stepwise
For the derivation of the general binding equation a saturation function
Even if all microscopic dissociation constants are identical, they differ from the macroscopic ones and there are differences between each binding step. The general relationship between both types of dissociation constants for n binding sites is
Hence, the ratio of bound ligand to macromolecules becomes
where
Protein-ligand binding
The dissociation constant is commonly used to describe the affinity between a ligand
The formation of a ligand-protein complex
the corresponding dissociation constant is defined
where
The dissociation constant has molar units (M), which correspond to the concentration of ligand
Sub-picomolar 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. Ribonuclease inhibitor proteins may also bind to ribonuclease with a similar 10−15 M affinity. 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 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).
Antibodies
In the specific case of antibodies (Ab) binding to antigen (Ag), usually the term affinity constant refers to the association constant.
This chemical equilibrium 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 of acids, K is known as Ka, 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.
(The symbol
Acid dissociation constants are sometimes expressed by
This
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.
Dissociation constant of water
The dissociation constant of water is denoted Kw:
The concentration of water
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.