Why Occupancy Claims Need Careful Definitions
A statement such as “the drug achieved 80% target occupancy” sounds precise, but it is incomplete unless the measured quantity, concentration basis, time point, and assay are clear. An occupancy estimate may refer to the fraction of available target bound at a particular time, an indirect change in tracer binding, or a value inferred from a binding model. These are related quantities, but they are not interchangeable.
The central reporting task is to separate what the model defines from what the assay observes. For a simple reversible binding model, occupancy depends on free drug concentration at the target site and binding affinity. In practice, plasma total concentration, tracer signal, target abundance, and functional response can each differ from those quantities. The interpretation must therefore state the assumptions connecting the observation to occupancy.
The Reference Equilibrium Model
For one drug binding reversibly and one-to-one to one target population, let \(D\) be free drug, \(R\) free target, and \(DR\) the drug–target complex. The equilibrium dissociation constant is \(K_D=[D][R]/[DR]\). If total available target is \(R_{\mathrm{tot}}=[R]+[DR]\), then fractional occupancy is \([DR]/R_{\mathrm{tot}}\). Substituting \([DR]=[D][R]/K_D\) gives the standard equilibrium expression.
This expression assumes reversible equilibrium, a single relevant binding site class, one-to-one binding, and that the stated drug concentration is the free concentration at the target. It also treats the target as not materially depleting free drug. It is not automatically appropriate during changing concentrations, for irreversible binding, or when binding kinetics are too slow for equilibrium. Earlier material on irreversible binding and kinetic occupancy addresses those distinctions.
The equation also shows why concentration basis matters. Total drug includes free drug plus drug bound to proteins, cells, or other components, depending on the sample and assay definition. Unless total concentration is a justified proxy for free target-site concentration, inserting it into the equilibrium expression can produce a substantially different estimate.
Worked Example: Total Concentration Is Not Free Concentration
Suppose a hypothetical plasma sample has total drug concentration \(100\) nM and unbound fraction \(f_u=0.020\). Assume, only for this calculation, that unbound plasma concentration equals free concentration at the target site, binding is at equilibrium, and \(K_D=8\) nM.
First calculate free concentration: \(C_{\mathrm{free}}=f_u C_{\mathrm{total}}=0.020(100\ \mathrm{nM})=2.0\) nM. The occupancy estimate is therefore
Under the stated assumptions, the estimate is 20.0% occupancy. If total concentration were incorrectly substituted, the result would be \(100/(8+100)=0.9259\), or 92.6%. That large discrepancy is not a minor rounding issue; it reflects use of a different concentration. In real settings, unbound plasma concentration may also fail to equal free concentration at the target site, so the assumed link itself requires justification.
Affinity Is Not Potency
Affinity describes binding under a specified binding model and experimental condition. In the simple equilibrium model, \(K_D\) is the free drug concentration at which half of the available target is occupied: setting \(O=0.5\) in the equation gives \([D]=K_D\). A lower \(K_D\) indicates stronger affinity in that model and condition.
Potency describes the concentration or dose producing a specified effect in a functional system. An \(EC_{50}\), for example, is the concentration producing half of the observed maximal effect under the assay conditions; it is not generally equal to \(K_D\). Functional amplification, receptor reserve, signaling context, exposure over time, and assay design can separate functional potency from binding affinity. Thus, a statement that a compound is “more potent” does not by itself establish that it has higher affinity or produces greater occupancy at a given free concentration.
Worked Example: Reporting Affinity and Functional Potency Separately
In a hypothetical study, compound A has a binding \(K_D\) of 5 nM and a functional \(EC_{50}\) of 20 nM. Compound B has a binding \(K_D\) of 10 nM and a functional \(EC_{50}\) of 2 nM. The binding assay supports the statement that A has higher affinity under that assay condition, because \(5\) nM is lower than \(10\) nM. The functional assay supports the statement that B has greater potency in that assay, because its \(EC_{50}\) is lower.
These findings are not contradictory: the assays quantify different properties. For illustration, if free concentration at the target were 10 nM and the simple equilibrium assumptions held, the binding-model occupancies would be \(10/(5+10)=0.667\), or 66.7%, for A and \(10/(10+10)=0.500\), or 50.0%, for B. Those occupancy calculations do not predict the functional \(EC_{50}\) without a model linking occupancy to response. Reporting one assay’s potency as the other assay’s affinity would therefore be unjustified.
Tracer Displacement Is an Assay Result, Not Automatically Occupancy
A competitor can reduce binding of a labeled tracer. The observed displacement depends not only on competitor affinity but also on tracer concentration and affinity, as well as whether the experiment satisfies the assumptions of the competitive-binding model. For a simple reversible, mutually exclusive competition assay at equilibrium, the Cheng–Prusoff relation converts an assay \(IC_{50}\) to an estimated inhibition constant \(K_i\):
Here \([L]\) is free tracer concentration and \(K_{D,L}\) is the tracer’s dissociation constant. The conversion assumes a single binding site class, equilibrium, mutually exclusive competition, and appropriate free-concentration conditions. The resulting \(K_i\) is an affinity estimate under that model; the raw \(IC_{50}\) is assay-dependent and is not itself a direct measure of in vivo target occupancy.
Worked Example: Correcting a Tracer-Displacement IC50
A hypothetical competitive assay reports \(IC_{50}=12\) nM. The free tracer concentration is \([L]=3\) nM and its dissociation constant is \(K_{D,L}=2\) nM. Assume the competitive-equilibrium conditions for the Cheng–Prusoff relation are met.
Substitute the reported values:
The model-based affinity estimate is \(K_i=4.8\) nM. It would be incorrect to report “12 nM occupancy” or to claim 12 nM is the drug’s in vivo \(K_D\). If equilibrium, free tracer concentration, or competitive binding assumptions are doubtful, the correction may not be valid; report the \(IC_{50}\) as an assay-specific result and qualify any inferred \(K_i\).
Target Availability and Occupancy Must Be Reported Separately
An assay signal can depend on how much target is available as well as on what fraction is occupied. If \(R_{\mathrm{avail}}\) denotes available target and \(O\) its fractional occupancy, the amount of occupied target is \(O R_{\mathrm{avail}}\). A change in signal therefore need not mean a change in fractional occupancy: availability may have changed, the assay’s sensitivity may have changed, or both may have changed.
Worked Example: Same Occupancy, Different Amount of Bound Target
Suppose a hypothetical tissue initially has 100 pmol of available target and fractional occupancy of 60%. The amount of occupied target is \(0.60(100\ \mathrm{pmol})=60\) pmol. At a later measurement, availability is 50 pmol while fractional occupancy remains 60%. The occupied amount is then \(0.60(50\ \mathrm{pmol})=30\) pmol.
The amount of bound drug has halved, but fractional occupancy has not changed. Conversely, equal amounts of drug-bound target could arise from different combinations of availability and fractional occupancy. A report should specify whether it estimates a fraction, an amount, or an assay signal, rather than treating these as synonymous.
For PET, a commonly used displacement estimate is \(1-BP_{ND,\mathrm{post}}/BP_{ND,\mathrm{baseline}}\), where \(BP_{ND}\) is a binding-potential measure. Interpreting this ratio as occupancy requires, among other conditions, that the relevant target availability and tracer properties are stable and that the change in binding potential is attributable to competition by the drug. A lower post-dose tracer binding signal alone does not establish that every change is due to drug occupancy.
Worked Example: A PET Ratio Can Overstate Occupancy
In a hypothetical PET comparison, baseline \(BP_{ND}=4.0\) and post-dose \(BP_{ND}=1.5\). The usual displacement calculation gives
The estimated displacement is 62.5%. It can be interpreted as occupancy only if the assumptions linking the ratio to drug competition are credible. For example, if target availability also fell to 75% of baseline, a simple proportional model would give a post-to-baseline ratio of \(0.75(1-O)\). Setting this equal to the observed ratio \(0.375\) gives \(1-O=0.375/0.75=0.5\), hence \(O=0.50\), or 50%. Under this illustrative model, availability change accounts for part of the apparent displacement. The calculation demonstrates why a PET ratio is not self-interpreting; the assumed relation and stability conditions must be stated.
Reporting and Diagnostic Checks
A defensible occupancy report identifies the estimand and the evidence supporting it. At minimum, state the target and assay, the time point or sampling window, whether concentration is total or free, the affinity parameter and its source, and the model assumptions used. Give an estimate as a fraction or percentage with an appropriate uncertainty measure when available. If occupancy is inferred indirectly, call it an estimate and name the measurement that supports it.
- Check the concentration basis. Confirm that the concentration entered into a binding equation is free concentration relevant to the target, not an unqualified total concentration.
- Check equilibrium and time. A static equilibrium formula may be inappropriate during changing exposure, slow binding, or irreversible binding. Report the time of measurement and distinguish kinetic from equilibrium estimates.
- Check the measured signal. Determine whether signal can vary with target availability, tracer conditions, nonspecific binding, sample processing, or assay calibration.
- Keep assay quantities distinct. Label \(IC_{50}\), \(K_i\), \(K_D\), \(EC_{50}\), tracer binding, and occupancy according to what was actually estimated.
When a simple equilibrium estimate disagrees with a kinetic or assay-based estimate, do not select whichever value seems more plausible and report it as fact. The disagreement may indicate differing time points, concentration definitions, target availability, or model misspecification. Earlier material on ex vivo artifacts, assay calibration, and binding-model diagnostics provides tools for evaluating particular measurement problems; the reporting principle remains to make the observation-to-occupancy assumptions explicit.
Common Reporting Errors
- Wrong: “Total plasma concentration is above \(K_D\), so occupancy is high.” Correction: The equilibrium formula uses free concentration at the target; justify how the measured concentration relates to it.
- Wrong: “The lower \(EC_{50}\) proves higher binding affinity.” Correction: Functional potency and binding affinity are different quantities and can rank compounds differently.
- Wrong: “The tracer \(IC_{50}\) is the drug’s \(K_D\) and equals in vivo occupancy.” Correction: \(IC_{50}\) is assay-dependent; any conversion to affinity or occupancy requires the relevant model and assumptions.
- Wrong: “A 40% reduction in tracer signal means exactly 40% occupancy.” Correction: Signal can depend on target availability and measurement conditions. A displacement ratio estimates occupancy only under conditions supporting that interpretation.
- Wrong: “Sixty percent occupancy means 60% of the total target pool is bound.” Correction: Occupancy is a fraction of the defined available target pool. State how that pool is defined and measured.
Check Your Understanding
Answer each question, then compare with the worked solutions below.
- With \(K_D=6\) nM and free target-site concentration \(6\) nM at equilibrium, what is the simple-model occupancy? What assumption would make this calculation unsuitable during a dosing interval?
- A competitive assay has \(IC_{50}=18\) nM, free tracer concentration \(4\) nM, and tracer \(K_{D,L}=2\) nM. Calculate \(K_i\) under the Cheng–Prusoff assumptions.
- Explain why a compound with a lower functional \(EC_{50}\) need not have a lower binding \(K_D\).
- Available target falls from 80 pmol to 40 pmol while fractional occupancy remains 25%. Calculate occupied target at both times and state what changed.
Solutions. (1) \(O=6/(6+6)=0.500\), or 50.0%. The calculation is unsuitable if equilibrium is not reached or if concentration changes rapidly enough that a static equilibrium estimate does not represent the time-varying binding state. (2) \(K_i=18/[1+(4/2)]=18/3=6.0\) nM, conditional on the stated competitive-equilibrium assumptions. (3) \(EC_{50}\) describes a functional response, whereas \(K_D\) describes binding affinity in a binding model; signaling amplification, receptor reserve, and assay conditions can separate them. (4) Initially, \(0.25(80)=20\) pmol is occupied; later, \(0.25(40)=10\) pmol is occupied. Fractional occupancy is unchanged at 25%, while available and occupied target amounts have each halved.