Receptors & Ligand Binding
Affinity & \(K_d\)

A receptor is a protein (often on a cell surface or inside the cell) that specifically binds a signaling molecule. Think of it as a molecular lock: only the correct key fits.

A ligand is any molecule that binds specifically to a receptor. Ligands can be hormones, neurotransmitters, drugs, or even ions. The binding event transmits information.

Receptor-ligand binding is a reversible chemical reaction that reaches equilibrium. We describe it with two rate constants:

At equilibrium, the ratio of unbound to bound species defines the dissociation constant:

Fractional occupancy \(\theta\) (fraction of receptors bound) follows a hyperbolic relationship with ligand concentration:

\(K_d\) is the ligand concentration at half-maximal occupancy. It gives a single number that captures how tightly a receptor grips its ligand.

These two terms are often confused. They describe different properties of receptor-ligand interactions:

The association constant \(K_a\) is simply the reciprocal of \(K_d\):

Given \(K_d\) and a ligand concentration \([L]\), find fractional occupancy:

A receptor has \(K_d = 10\,\text{nM}\). What fraction is occupied when \([L] = 10\,\text{nM}\)?

Same receptor (\(K_d = 10\,\text{nM}\)). Now \([L] = 90\,\text{nM}\).

At 9 times the \(K_d\), 90% of receptors are occupied. Notice the hyperbolic relationship: you need a 9-fold excess over \(K_d\) to go from 50% to 90%.

Drug A has \(K_d = 2\,\text{nM}\). Drug B has \(K_d = 200\,\text{nM}\). At \([L] = 10\,\text{nM}\), what is \(\theta\) for each?

A receptor has \(K_d = 50\,\text{nM}\). What is the fractional occupancy when \([L] = 50\,\text{nM}\)?

Drug X has \(K_d = 5\,\text{nM}\) and Drug Y has \(K_d = 500\,\text{nM}\). Which statement is correct?

If \(K_d = 20\,\text{nM}\) and \([L] = 180\,\text{nM}\), what is \(\theta\)?

Which equation correctly expresses \(K_d\) in terms of rate constants?

A receptor has \(K_a = 10^8\,\text{M}^{-1}\). What is its \(K_d\)?