Dissociation constant

Concepts in Chemical Equilibria
Acid dissociation constant
Binding constant
Chemical equilibrium
Dissociation constant
Distribution coefficient
Distribution ratio
Equilibrium constant
Equilibrium unfolding
Equilibrium stage
Liquid-liquid extraction
Phase diagram
Phase rule
Reaction quotient
Relative volatility
Solubility equilibrium
Stability constant
Thermodynamic equilibrium
Theoretical plate
Vapor-liquid equilibrium
edit

In equilibrium constant that measures the propensity of a larger object to separate (dissociate) reversibly into smaller components, as 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 ionization constant.

For a general reaction

$\mathrm{A}_{x}\mathrm{B}_{y} \rightleftharpoons x\mathrm{A} + y\mathrm{B}$

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

$K_{d} = \frac{[A]^x \times [B]^y}{[A_x B_y]}$

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

Protein-Ligand binding

The dissociation constant is commonly used to describe the affinity between a Van der Waals forces.

The formation of a ligand-protein complex ( $C$ ) can be described by a two-state process

$\mathrm{C} \rightleftharpoons \mathrm{P} + \mathrm{L}$

the corresponding dissociation constant is defined

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

where [ $P$ ], [ $L$ ] and [ $C$ ] represent the concentrations of the protein, ligand and complex, respectively.

The dissociation constant has 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 ( $μ$ M) 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. avidin bind with a dissociation constant of roughly $10 - 15$ M = 1 fM = 0.000001 nM.^[1] While ribonuclease with a similar $10 - 15$ M affinity.^[2] The dissociation constant for a particular ligand-protein interaction can change significantly with solution conditions (e.g. 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.

Another notation

A dissociation constant $K a$ is sometimes expressed by its p $K a$ , which is defined as:

p K a = - log 10 K a

These p $K a$ '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 $\left[ \mbox{H}_2\mbox{O} \right]$ is not included in the definition of $k w$ , for reasons described in the article 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_w10^-14**	pK_w
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 amino (-NH₃) group and the pK₃ is the pK value of its side chain.

$H_3 B \rightleftharpoons\ H ^ + + H_2 B ^ - \qquad K_1 = {[H ^ +] \cdot [H_2 B ^ -] \over [H_3 B]} \qquad pK_1 = - log K_1$

$H_2 B ^ - \rightleftharpoons\ H ^ + + H B ^ {-2} \qquad K_2 = {[H ^ +] \cdot [H B ^{-2}] \over [H_2 B^ -]} \qquad pK_2 = - log K_2$

$H B ^{-2} \rightleftharpoons\ H ^ + + B ^{-3} \qquad K_3 = {[H ^ +] \cdot [ B ^ {-3}] \over [H B ^ {-2}]} \qquad pK_3 = - log K_3$

References

^ Livnah O, Bayer EA. et al (1993). "Three-dimensional structures of avidin and the avidin-biotin complex". Proc Natl Acad Sci USA. 90 (11): 5076-5080. PMID 8506353.
^ Johnson RJ, McCoy JG. et al (2007). "Inhibition of Human Pancreatic Ribonuclease by the Human Ribonuclease Inhibitor Protein". J. Mol. Biol retrieved ahead of print. PMID 17350650.