Dissociation Constant

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_{d}

and is the Inverse
of the Affinity Constant . In the special case of Salt s, the dissociation constant can also be called an Ionization Constant .

For a general reaction

:

\mathrm{A}_{x}\mathrm{B}_{y} \leftrightarrow x\mathrm{A} + y\mathrm{B}

in which a complex

\mathrm{A}_{x}\mathrm{B}_{y}

breaks down into ''x'' A
subunits and ''y'' B subunits, the dissociation constant is defined

:

K_d = rac{[A]^x 	imes [B]^y}{B_y}

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

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{P} + \mathrm{L} \leftrightarrow \mathrm{C}

the corresponding dissociation constant is defined

:

K_{d} = rac{\left \mathrm{P} 
ight \left \mathrm{L} 
ight}{\left \mathrm{C} 
ight}

where [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 {Link without Title} at which the binding site on the protein
is half occupied, i.e., when the concentration of protein with ligand bound {Link without Title} equals
the concentration of protein with no ligand bound {Link without Title} . 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^{-15}

M = 1 fM = 0.000001 nM,
while Ribonuclease Inhibitor binds to Ribonuclease s 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_{d}

is sometimes expressed by its p

K_{d}

, which is defined as:

:

\mathrm{p}K_{d} = -\log_{10}{K_{d}}

These p

K_{d}

'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 =

{Link without Title} {Link without Title}

(The concentration of water

\left \mathrm{H_{2}O} 
ight

is not included in the definition
of

k_{w}

, 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 .

ACID BASE REACTIONS

For the (-COOH) group, p''K''₂ refers to its Amino (-NH₃) group and the p''K''₃ is the p''K'' value of its side chain.

} \qquad pK_1 = - log K_1

} \qquad pK_2 = - log K_2

} \qquad pK_3 = - log K_3

Information About

Dissociation Constant