A receptor is a protein that undergoes a conformation change in response to ligand binding.
Drugs bind to receptors to produce a physiological effect.
The proportion of receptors bound by drug is usually monotonic with drug effect.
Competition of multiple ligands for one receptor explains agonist, antagonist, and partial agonist behavior of drugs.
$$K_{on}[D][R] = K_{off}[DR]$$
$$K_{\text{dissociation}} = \frac{K_{off}}{K_{on}} = \frac{[D][R]}{[DR]}$$
When \([D] = K_d\), then...
$$[D] = \frac{[D][R]}{[DR]}$$
$$[DR] = [R]$$
...half of receptors are in the bound state.
In general,
$$\text{prop. receptors occupied} = \frac{[D]}{[D] + K_d}$$
(don't revise the derivation...)
$$\text{prop. receptors occupied} = \frac{[DR]}{[DR] + [R]}$$
$$= \frac{[D][R]}{K_d([DR] + [R])}$$
$$= \frac{[D][R]}{K_d(\frac{[D][R]}{K_d} + [R])}$$
$$= \frac{[D][R]}{[D][R] + K_d[R])}$$
$$= \frac{[D]}{[D] + K_d}$$
Affinity is the tendency of dissimilar chemical compounds to form compounds.
\(k_{on}\) is the association rate constant. \(k_{off}\) is the dissociation rate constant.
The dissociation constant is \(K_d = frac{k_{off}}{k_{on}}\). When the effect site concentration equals \(K_d\), half of receptors are occupied (so a high \(\K_d\) implies low affinity and vice versa).
The association constant is \(K_a = \K_d^{-1}\). A high \(K_a\) implies high affinity.