Why Occupancy Is a Translational Quantity
A drug can have different target affinity across species, and the unbound concentration reaching the target can also differ. Those differences jointly determine the fraction of target molecules bound at a given time. Translating receptor occupancy therefore requires more than comparing affinity values: it requires a species-specific estimate of free drug concentration at the target and, when the question concerns the amount of bound target, the abundance of that target.
Occupancy is a binding quantity, not automatically a measure of pharmacological response. A high occupied fraction may support a target-engagement prediction, but the connection from engagement to a biomarker or clinical effect depends on additional biology. The calculations here establish the binding-based comparison and make clear which quantities it uses.
Occupancy When Free Drug Is Known
For the simple binding model, drug \(D\) and unoccupied target \(R\) bind to form the complex \(DR\): \(D+R\rightleftharpoons DR\). The dissociation constant is the ratio of the product of free drug and free target concentrations to bound complex concentration. Since free target is \(R_{\mathrm{tot}}-B\), substitution of \(\theta=B/R_{\mathrm{tot}}\) gives the standard occupancy relationship.
This expression assumes reversible 1:1 binding, a single relevant target-binding population, equilibrium at the time of interest, and a free concentration representative of the target site. It also assumes that binding does not appreciably deplete free drug, or that \(C_{\mathrm{free}}\) has already been determined while accounting for depletion. Concentration units must match: for example, \(K_d\) and free concentration can both be expressed in nM.
When free drug equals \(K_d\), occupancy is 50%. When it is much less than \(K_d\), occupancy is approximately \(C_{\mathrm{free}}/K_d\); when it is much greater, occupancy approaches one. These are statements about the fraction bound, not the number of target molecules bound. If target abundance is known in compatible concentration units, the occupied-target concentration follows from \(B=R_{\mathrm{tot}}\theta\).
Worked Example: Comparing Occupancy and Bound Target Across Species
Suppose a hypothetical preclinical comparison estimates the following target-site quantities: in rat, \(K_d=12\) nM, \(C_{\mathrm{free}}=24\) nM, and \(R_{\mathrm{tot}}=4\) nM; in human, \(K_d=6\) nM, \(C_{\mathrm{free}}=9\) nM, and \(R_{\mathrm{tot}}=10\) nM. Assume equilibrium, 1:1 binding, and negligible ligand depletion. Calculate fractional occupancy and bound-target concentration for each species.
Rat. Using the free concentration in the occupancy equation, \(\theta_{\mathrm{rat}}=24/(12+24)=24/36=0.6667\), or 66.7%. The predicted bound-target concentration is \(B_{\mathrm{rat}}=4(0.6667)=2.667\) nM.
Human. Here, \(\theta_{\mathrm{human}}=9/(6+9)=9/15=0.6000\), or 60.0%. The predicted bound-target concentration is \(B_{\mathrm{human}}=10(0.6000)=6.000\) nM.
The human target has the smaller \(K_d\), indicating higher affinity in this comparison, but the estimated human free concentration is also lower relative to its \(K_d\). Consequently, the predicted human fractional occupancy is lower. The larger human target abundance nevertheless gives a greater predicted concentration of bound target. Thus, “higher occupancy” and “more target bound” are different comparisons.
When Target Abundance Changes Free Concentration
Target abundance does not appear in the simple fractional-occupancy equation when free concentration is given. It does determine the absolute bound-target concentration through \(B=R_{\mathrm{tot}}\theta\). However, if the supplied drug concentration is total rather than free, abundant target can bind enough drug to reduce the free concentration. In that case, inserting total drug concentration into the simple occupancy equation overstates occupancy.
For one target and one drug in a closed compartment, let \(C_{\mathrm{tot}}\) be total drug concentration, including free and bound drug. Conservation of drug gives \(C_{\mathrm{tot}}=C_{\mathrm{free}}+B\). Combining that mass balance with the equilibrium binding equation gives a quadratic for \(B\).
Expanding and rearranging yields \(B^2-(C_{\mathrm{tot}}+R_{\mathrm{tot}}+K_d)B+C_{\mathrm{tot}}R_{\mathrm{tot}}=0\). The physically meaningful solution is the smaller root: the larger root would exceed at least one of the available totals and cannot represent a bound concentration. Defining \(A=C_{\mathrm{tot}}+R_{\mathrm{tot}}+K_d\), the solution and implied free concentration are:
Worked Example: Correcting for Ligand Depletion
In a hypothetical compartment, total drug concentration is \(C_{\mathrm{tot}}=10\) nM, target concentration is \(R_{\mathrm{tot}}=20\) nM, and \(K_d=5\) nM. Assume the system is at equilibrium and the compartment is closed to drug exchange during the calculation. Find occupancy using the mass balance, then compare it with the calculation that incorrectly treats total drug as free.
First, \(A=10+20+5=35\) nM. The discriminant is \(A^2-4C_{\mathrm{tot}}R_{\mathrm{tot}}=35^2-4(10)(20)=1225-800=425\) nM\(^2\), and \(\sqrt{425}=20.62\) nM. Therefore, \(B=(35-20.62)/2=7.192\) nM. The free concentration is \(10-7.192=2.808\) nM, and occupancy is \(7.192/20=0.3596\), or 36.0%.
The mass balance is consistent: \(C_{\mathrm{free}}+B=2.808+7.192=10.000\) nM. Using total concentration as if it were free would instead give \(10/(5+10)=0.6667\), or 66.7% occupancy. That calculation is inappropriate here because binding consumes a substantial share of the available drug.
From Occupancy to a Target-Engagement Prediction
A target-engagement prediction should state what “engagement” means operationally. If it means that a specified fraction of target is occupied, the prediction is based on \(\theta\). If it means the concentration or amount of occupied target, the prediction is based on \(B\), and target abundance matters directly. If an experimental readout is a biomarker, neither quantity alone establishes the expected biomarker change; an additional relationship between binding and that readout is needed.
The occupancy equation can be rearranged to find the free concentration required for a chosen occupancy threshold. For a threshold \(\theta^*\) between zero and one, the required concentration is \(C_{\mathrm{free}}^*=K_d\theta^*/(1-\theta^*)\). This provides a transparent comparison across species: each species has its own \(K_d\), and its predicted free concentration can be compared with its own threshold.
Worked Example: Checking a Cross-Species Occupancy Threshold
Suppose the hypothetical target-engagement criterion is at least 75% occupancy. In mouse, \(K_d=8\) nM and predicted target-site free concentration is 32 nM; target abundance is 2 nM. In human, \(K_d=16\) nM, free concentration is 40 nM, and target abundance is 7 nM. Assume the same equilibrium 1:1 model and negligible depletion in both species. Determine which species meets the fractional-occupancy criterion, and calculate bound-target concentrations.
For a 75% threshold, \(\theta^*/(1-\theta^*)=0.75/0.25=3\), so the required free concentration is \(3K_d\). The mouse threshold is \(3(8)=24\) nM. Since 32 nM exceeds 24 nM, mouse occupancy is \(32/(8+32)=32/40=0.8000\), or 80.0%. Its bound-target concentration is \(2(0.8000)=1.600\) nM.
The human threshold is \(3(16)=48\) nM. Since 40 nM is below 48 nM, human does not meet the criterion: occupancy is \(40/(16+40)=40/56=0.7143\), or 71.4%. Its bound-target concentration is \(7(0.7143)=5.000\) nM. Human has more bound target in concentration units because its target abundance is higher, even though it falls short of the specified fractional-occupancy criterion. Which result is decision-relevant depends on how the target-engagement criterion was defined.
Assumptions, Diagnostics, and Alternatives
The calculations are useful only to the extent that their inputs and binding assumptions are credible. Cross-species free concentrations should refer to the same relevant site and time basis; plasma unbound concentration is not automatically the free concentration at a tissue target. Affinity estimates should refer to comparable target forms and conditions. The earlier material on Species Differences in Target Affinity and Potency provides context for interpreting species-specific affinity; occupancy translation additionally requires exposure and, for bound-target amounts, target abundance.
Potential warning signs include an observed occupancy that does not approach saturation as free concentration rises, estimates that imply \(B>R_{\mathrm{tot}}\) or \(B>C_{\mathrm{tot}}\), and occupancy predictions that change markedly depending on whether total or free concentration was used. A mismatch may indicate concentration or unit errors, an incorrect target-site exposure estimate, non-equilibrium sampling, or failure of the single-site binding model. If observed binding is measured directly, compare predicted and observed occupancy across concentrations rather than relying on one point.
| Approach | What it estimates | Main condition or limitation |
|---|---|---|
| Free-concentration occupancy equation | Fraction occupied, then bound concentration if target abundance is known | Requires representative free concentration and negligible depletion or a separately determined free concentration |
| Mass-balance binding equation | Free concentration and occupancy from total drug and target concentrations | Requires a closed, well-mixed compartment and the stated equilibrium binding model |
| Direct target-occupancy measurement | Observed occupancy under the assay or sampling conditions | Measurement method, sampling time, and species comparability must be considered |
The equilibrium model is not appropriate without modification if binding is not near equilibrium, multiple binding sites or target populations matter, or target abundance changes during the relevant period. Receptor internalization, turnover, and tissue heterogeneity can also make a single static occupancy calculation an incomplete description. Finally, occupancy is not proof of a downstream effect: targets can have spare capacity, and binding may not translate proportionally into a measured response. The calculation is best treated as a mechanistic engagement estimate with explicit inputs and assumptions, not as a response prediction by itself.
Check Your Understanding
Answer each question, then compare with the solutions below.
- A target has \(K_d=15\) nM and free drug concentration is 45 nM. What is fractional occupancy?
- At fixed free drug concentration and \(K_d\), what happens to fractional occupancy if target abundance doubles? What happens to bound-target concentration?
- For \(K_d=10\) nM, what free concentration is required for 80% occupancy?
- Why can total drug concentration overstate occupancy when target abundance is high?
- Two species have equal fractional occupancy, but one has three times the target abundance. Which has the larger bound-target concentration, and by what factor under the same binding assumptions?
Solutions. 1. \(\theta=45/(15+45)=45/60=0.7500\), or 75.0%. 2. Fractional occupancy is unchanged if free concentration remains fixed, because target abundance is absent from the occupancy equation; bound-target concentration doubles because \(B=R_{\mathrm{tot}}\theta\). 3. \(C_{\mathrm{free}}^*=10[0.80/(1-0.80)]=10(4)=40\) nM. 4. Some total drug is bound, so free concentration is lower than total concentration; substituting total concentration into the free-concentration formula can therefore overestimate occupancy. 5. The species with three times the target abundance has three times the bound-target concentration, since \(B=R_{\mathrm{tot}}\theta\) and the fractional occupancy is equal.