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# Dissociation Constant

Dissociation constant is an equilibrium constant for the dissociation of a complex into its components. This is a special type of dissociation constant which is used in chemistry, biochemistry, and pharmacology to measure the tendency of an object to reverse dissociate into finer components, or of a complex to separate into its component molecules or of a salt to dissociate into its component ions.

For example, the dissociation of a substrate from an enzyme. The dissociation constant of an acid (Ka) or base (Kb) describes their dissociation into their conjugate base or conjugate acid and a hydroxide ion. This is used to define the binding strength or affinity between the receptors and respective ligands in a complex.

This dissociation constant is inverse of the association constant, and can also be termed as ionization constant. The dissociation constant is written as Kd.

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## Dissociation Constant Equation

Let the interaction between A and B make the product AB and the strength of this interaction will be the balance between AB (product/complex) or A and B (reactant).

The relationship of this interaction can be written as an equation form,

AB $\leftrightharpoons$ A+B

It shows the strength of binding (the complex AB is more stable than its individual parts A and B). If K1 is the rate of dissociation for the dissociation of product AB $\to$ A + B, and K2 is the rate of association or formation of product from reactant A+B $\to$ AB.

At equilibrium, the rate of dissociation of the product AB is equal to the rate of association of reactant A and B. So, at equilibrium, K2 [AB] = K1 [A][B], where [A] and [B] are the concentration of reactant and [AB] is the concentration of the product.
This can be rearranged to:

$\frac{k_2}{k_1}$ = $\frac{[A][B]}{[AB]}$ = Kd

This is an equation for dissociation constant.

The Dissociation constant, Kd shows the strength of binding between A and B. This constant verifies how easy it is to separate the complex AB (dissociation). If a high concentration of A and B reactant is required to form the complex AB, then it also shows that the binding strength is low.

The value of dissociation constant Kd would be higher as more of A and B are required to form complex AB.
If a low concentration of A and B reactants are required to form AB complex, then it results in higher binding strength and lower value of dissociation constant Kd.

## Affinity Constant

An affinity constant is defined as the concentration of the ligand-receptor complex at equilibrium divided y product of the equilibrium concentrations of ligand and receptor. This constant is the reverse of the dissociation constant. This is a kind of mathematical constant that describes the bonding affinity between two molecules at equilibrium. For example, the affinity measure of an enzyme for its substrate.

The reciprocal of the affinity constant determines the location on the ligand concentration scale where half maximal receptor occupancy occurs. The affinity constant is a measure of the complementariness of the structure of the ligand with that of its binding site on the receptor. This is an association constant which is used especially in relation to the binding of macromolecules like in antigen-antibody, hormone-receptor, and enzyme-inhibitor reactions. For example, the measure of the binding strength in hapten-antibody interaction.

## Protein Ligand Binding

Ligands have the ability to bind to the particular site of protein using intermolecular forces such as ionic bonds, hydrogen bonds and van der Walls forces. When a Ligand binds to a receptor protein, it changes the chemical conformation of the receptor. The tendency or strength of binding is called affinity.

The dissociation constant is usually brought into use to describe the accordance between a ligand (L) and a protein (P) or it might also exhibit the extent of binding a ligand to a particular site of protein. This affinity between ligand and protein is affected by intermolecular interactions, non-covalent in nature, between ligand and protein. These are basically hydrogen bonding, hydrophobic, electrostatic interactions, and Van der Walls forces.

These affinities are also affected by the concentration of other macro molecules whose high concentration causes macromolecules crowding and hinders affinity.
The process of formation of a complex of ligand-protein (C) can be explained in the following steps:

### C $\leftrightharpoons$ P + L

So, the dissociation constant for the above equation is:

### Kd = $\frac{[P][L]}{C}$

Where [P], [L] and [C] represent the protein's, ligand's and complex's molar concentration respectively.
Now [C] shows the Ligand concentration at which the Protein and Ligand concentration are bound, while [L] is for the concentration of the ligand at which the concentration of protein with ligand bound and lastly [P] is equivalent to the concentration of protein with no ligand bound.

At equilibrium, [L] and [C] are equal to the [P]. The small value of the dissociation constant shows the good affinity between ligand and protein or that the ligands are tightly bound with protein.
For example- A ligand with nanomolar dissociation constant ((nM) ) exhibits a good affinity to a particular protein than a ligand with micromolar ($\mu$ M) dissociation constant.

Binding interactions of a non-covalent nature between two molecules are rare because of Sub-Pico molar dissociation constants but there are some exceptions.
For example- Biotin and avidin can have a binding with a range of 10-15M = 1fM = 0.000001nM dissociation constant. Similarly, ribonuclease inhibitor proteins may also bind to ribonuclease with a similar 10-15M affinity.

The dissociation constant for a particular ligand-protein interaction is affected by solution conditions like temperature, pH and salt concentration. These different solution conditions can effectively change the strength of intermolecular interactions which holds a particular ligand-protein complex together.

The interaction between drugs and proteins might result in harmful side effects for which they are designed not to interact. Many of pharmaceutical researches are basically aimed at designing drugs that bind to their proteins target only (Negative Design) with high affinity up to 0.1-10 nM.

### Antibodies

The affinity constant is brought into application when antibodies (Ab) bind to antigen (Ag).
This affinity constant is the inversion of dissociation constant.

Ab +Ag $\leftrightharpoons$ Ab Ag
Ka = $\frac{[A_b A_g]}{[A_b][A_g]}$ = $\frac{1}{k_d}$

The chemical equilibrium of the above equation can also be written as the ratio of the on-rate (kforward) and off-rate (kback) constants. A couple of antibodies can have similar affinity but one antibody might have both - (1) high on-rate constant and (2) off-rate constant, while the other might have both (1) low on-rate constant and (2) off-rate constant.

Ka = $\frac{K_forward}{K_back}$ = $\frac{on-rate}{off-rate}$

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