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# Binding Affinity

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 Sub Topics Affinity is a measure of the intrinsic binding strength of the ligand binding reaction. Affinity is also known as the tendency of a molecule to associate with another. The affinity of a drug is its ability to bind to its biological target. An alternative approach aimed at obtaining structural information about opioid receptors outlined here focuses on the structural analysis of the ligand binding sites of receptors outlined here focuses on the structural analysis of the ligand binding sites of receptors by affinity labeling. The affinity ligands can specifically capture their corresponding target molecules through specific interactions. Affinity membrane that base their separation functions on size discrimination of the solute. Affinity membrane is developed to permit the purification of molecules based on physical or chemical properties or biological functions rather then molecular weight.

## Binding Affinity Definition

Ligand "binding" by a receptor is typically the result of several non covalent interactions. The strength of this binding is termed as affinity.

Binding of one ligand molecule does not effect binding of another, which includes two major components
• Removal of a ligand molecule from the available pool by binding does not alter the concentration of free ligand; that is the fraction of total ligand that is bound to the receptor is relatively small.
• Binding is not cooperative an assumption that is likely to be violated in instances where multiple ligand molecules bind to a single receptor or where receptor proteins form complexes and will often result in non linear scatchars plots.

## Antibody Binding Affinity

One of the most important performance criteria for antibodies is the strength of binding to the antigen without this property the antibody will not localize. Affinity can be defined by the equilibrium binding constant of the antibody target antigen interaction.

Antibody binding to antigen is non covalent and reversible. The binding of antibody to antigen follows the basic thermodynamic principles of any reversible bi molecular interaction. Thus if [Ab] = molar concentration of the unoccupied antibody binding sites, [Ag] = molar concentration of the unoccupied antigen binding sites, and [Ab-Ag] is the molar concentration of the antibody antigen complex,

the affinity constant

$K_{A} = \frac{[Ab-Ag]}{[AB]\times[Ag]}$

In practical terms affinity describes the amount of antibody antigen complex that will be found at equilibrium.

The time taken to reach equilibrium is dependent on the rate of diffusion and does not vary from one antibody to another. However high affinity antibodies will bind larger amounts of antigen in a shorter period of time than low affinity antibodies. High affinity antibodies perform better in all immunochemical techniques. This is due not only to their higher capacity but also to the stability of the complex.

## Kd Binding Affinity

A measure of the strength of the antibody antigen interaction is essential in comparing MAbs to the same or different antigens. The strength of the antibody antigen interaction is measured through the binding affinity. This can be considered as the sum of all the non covalent interactions between antibody and antigen involved in the binding reaction. The antibody affinity is quantified through the association constant Ka.

For a binding reaction

Ab + Ag $\rightarrow$ AbAg complex

Ka is the equilibrium constant of this reaction and can be determined from the equilibrium concentrations of the reactants and complex using the law of mass action.

$K_{a} = \frac{[AbAg\ complex]}{[Ab][Ag]}$

Frequently the dissociation constant Kd of the reaction is used in preference to the association constant. The dissociation constant is the Binding Affinity Constant of the reverse reaction and therefore given by

$K_{d} = \frac{[Ab][Ag]}{AbAg\ complex}$

Kd is also of course the reciprocal of the association constant: Kd = $\frac{1}{K_{a}}$ and the units of Kd are M.

## Ki Binding Affinity

Usually the affinity is indicated by the Ki value which is the equilibrium dissociation constant the lower the Ki the higher the affinity. For a competitive inhibitor Ki is calculated from the IC50 using the equation of Cheng and Prusoff, which takes into account the dissociation constant of the radio ligand and its concentration.

$K_{i} = \frac{IC_{50}}{1+\frac{[S]}{K_{m}}}$

## Binding Affinity Calculation

Binding between antibodies and antigens is a reversible reaction and takes a few seconds to several hours to achieve its equilibrium. The reaction may be described by the law of mass action with several assumptions. The most important are the antibody must be monvalent recognizing only one epitope on the antigen thus having one affinity; both reagents must be pure and in a solution and the reaction vessel. In practice these assumptions are not completely met. The reaction between the monovalent antibody (Ab) and the monovalent antigen (H) can be written as follows.

Ab + H $\rightleftharpoons$ AbH

Where Ka is the association constant and Kd is the dissociation constant. The equilibrium constant Keq also called the "antibody affinity" according to bound to unbound monovalent antibody.

$K_{eq} = \frac{K_{a}}{K_{d}} = \frac{[AbH]}{[Ab][H]}$

When binding of univalent to multivalent antibody is measured the scatchard plot is useful after rearrangement of the Langmuir adsorption isotherm.

$\frac{d}{n} = \frac{K[H]}{(1+K[H])}$

$\frac{d}{[H]} = nk - dK$

It can be calculated with extrapolation of experimental data that K is equal to 1/[H] when half the antigen binding sites in bivalent antibody are hapten bound.