 Receptor binding occupancy

Receptor binding occupancy is the fraction of binding sites occupied by a ligand. Consider reversible, noncooperative binding at chemical equilibrium, with homogeneous independent sites: every site has the same binding properties, and binding at one site does not change binding at another. Let $L$ denote free ligand, $R$ an unoccupied receptor site and $RL$ the bound complex. In this dilute concentration model,Square brackets denote concentrations; $R_T$ is the total site concentration. Here the dissociation constant $K_d$ has concentration units. Use free ligand in excess so binding negligibly depletes it; only under that approximation may the supplied total ligand concentration substitute for $[L]$. See Analysis of Receptor–Ligand Interactions: equilibrium binding and saturation.

For an illustrative dissociation constant $K_d=10\mathrm{nM}$, where $1\mathrm{nM}=10^{-9}\mathrm{mol}{\mathrm{L}}^{-1}$, free ligand concentrations $1$, $10$ and $100\mathrm{nM}$ give $\theta =1/11\approx 0.091$, $\theta =1/2=0.5$ and $\theta =10/11\approx 0.909$, respectively. At $[L]=K_d$, exactly half the sites are occupied in this model. Raising $[L]$ tenfold from $10$ to $100\mathrm{nM}$ raises occupancy from $50\%$ to about $91\%$, rather than tenfold: the finite pool of sites causes saturation.

A short derivation uses the law of mass action: at chemical equilibrium, association balances dissociation, giving $[RL]=[L][R]/K_d$. Substitute this into $\theta =[RL]/([R]+[RL])$ and cancel $[R]$ to obtain the displayed formula. The limiting values follow directly: zero free ligand gives zero occupancy, and increasing $[L]$ far above $K_d$ drives occupancy toward one.

Receptor binding occupancy is not automatically the fraction of maximal response. Signal amplification, differing effects of bound ligands, and downstream saturation can change the relationship. Consequently, $[L]=K_d$ specifies half occupancy here; it does not universally specify either half-maximal or maximal cellular response. These numbers describe a toy binding model, not measured responses of every receptor. See Higham and Colquhoun, 2024: the affinity–efficacy problem.