Kd - Dissociation constant

This is a useful measure to describe the strength of binding (or affinity) between receptors and their ligands.

Eg antibody+antigen = 10 -7 to 10 -11 M (remember 10 -7M is equivalent to 0.1mM or 100nM. If you are not confident with units, click here)

TCR+MHC/peptide = 10-6 M

For convenience, call the receptor A and it’s ligand B. The interaction of A and B will involve them being together (product) and apart (reactant), and the strength of this interaction will be the balance of between AB (or ‘on’) or A and B (or ‘off’).

This relationship can be written as an equation:

k1 (rate of dissociation) AB ---> A+B

k2 (rate of association) A+B --->AB

Constants (k1 and k2) are used so that we can convert this linkage ( ---> /<---) to an equals sign.

Therefore, if we know when

AB=A+B

it will tell us the strength of binding (ie is the complex AB more stable than its individual parts, A+B?).

At equilibrium,

k2[AB]=k1[A][B]

…remember, square brackets mean [concentration]

This can be rearranged to: k2 / k1 = [A][B] / [AB] = Kd

This dissociation constant, Kd, indicates the strength of binding between A and B in terms of how easy it is to separate the complex AB (dissociation or ‘off rate’).

If a high concentration of A and B is required to form AB, this indicates that the strength of binding is low. The Kd would therefore be higher (mM rather than nM) as more of A and B are required to form AB.

It follows that the smaller Kd, the stronger the binding. So 10-6M (or 1mM) indicates weak binding compared to 10-9M (or 1nM).

Therefore, we can measure that TCR and MHC/peptide have a relatively low strength of binding compared to lots of other biological receptor ligands (eg antibody and antigen; adhesion molecules).