What Tissue Fraction Unbound Describes
A drug in tissue can be present in an unbound form or associated with tissue components such as proteins, lipids, and other binding sites. Tissue fraction unbound summarizes the proportion of the measured drug concentration in a tissue preparation that is unbound under specified assay conditions. It is a binding measure, not a tissue concentration and not, by itself, a measure of how much drug is present in an organ.
The subscript “hom” matters. In a typical assay, tissue is disrupted and mixed with buffer to make a homogenate. The resulting preparation does not preserve the intact organ’s structure, local environment, or undisturbed tissue concentration. The measured \(f_{u,\mathrm{tiss,hom}}\) is therefore an assay result for a homogenate, not a direct measurement of the unbound fraction or drug concentration in intact tissue. Any adjustment of a homogenate result for the preparation’s dilution is a separate calculation.
How Equilibrium Dialysis Estimates the Ratio
In equilibrium dialysis, tissue homogenate is placed on one side of a membrane and buffer on the other. The membrane permits unbound drug to cross but retains tissue macromolecules. As the system approaches equilibrium, unbound drug redistributes across the membrane. Under the assay’s ideal conditions, the unbound concentration in the buffer receiver compartment represents the unbound concentration in the homogenate donor compartment.
The donor compartment also contains drug bound to tissue components. A validated measurement of total drug in the donor homogenate therefore supplies the denominator, while the receiver concentration supplies an estimate of the unbound concentration for the numerator. The concentrations must refer to the same equilibrium state and be expressed in compatible units and on compatible bases. For example, a receiver concentration in micromoles per litre can be used with a donor total concentration in micromoles per litre when the assay’s sampling and volume conventions support that comparison.
Place a known tissue homogenate preparation in the donor compartment and buffer in the receiver compartment. Record volumes, tissue source, and assay conditions.
Incubate under conditions intended to reach equilibrium while limiting degradation, leakage, and other changes in the system.
Measure receiver drug concentration as the unbound estimate and total drug in the donor homogenate for the denominator. Use validated analytical methods.
Divide the unbound estimate by the donor total concentration, then review recovery and other assay controls before interpreting the ratio.
This interpretation rests on several assumptions. The system must have reached equilibrium; the membrane must allow unbound drug to pass while retaining the relevant tissue binding components; and the receiver concentration must represent the donor’s unbound concentration. Drug should not be appreciably degraded, lost through leakage, or adsorbed to the apparatus. Analytical measurements must be sufficiently accurate, and the total and unbound concentrations must be comparable. If these conditions are not met, the calculated ratio may reflect assay behavior rather than tissue binding.
With valid, nonnegative measurements and \(C_{\mathrm{total,hom}}>0\), the ratio is between 0 and 1, inclusive, provided the numerator represents the unbound portion of the denominator on a compatible basis. If the total concentration is zero, the ratio is undefined; in particular, a zero numerator and zero denominator do not yield a fraction. A calculated value above 1 usually signals incompatible concentration bases, measurement error, or failure of an assay assumption, rather than a physically meaningful unbound fraction.
Worked Example: Calculating a Homogenate Fraction Unbound
In a hypothetical equilibrium-dialysis assay, the measured receiver concentration is \(0.0960\ \mu\mathrm{mol/L}\). Total drug concentration in the donor tissue homogenate at the same equilibrium time is \(2.40\ \mu\mathrm{mol/L}\). Assume equilibrium was reached, the membrane behaved as intended, the concentrations are on compatible bases, and analytical and recovery checks were acceptable.
The estimate is the receiver concentration divided by the donor total concentration: $$ f_{u,\mathrm{tiss,hom}} = \frac{C_{u,\mathrm{hom}}}{C_{\mathrm{total,hom}}} = \frac{0.0960\ \mu\mathrm{mol/L}}{2.40\ \mu\mathrm{mol/L}} = 0.0400. $$
The units cancel, so the estimated homogenate fraction unbound is \(0.0400\), or 4.00%. Under the stated assumptions, this means that 4.00% of the measured drug concentration in this homogenate was unbound under these assay conditions. It does not mean that the intact tissue concentration was \(2.40\ \mu\mathrm{mol/L}\), or that 4.00% of a particular in vivo organ amount was unbound.
Why Homogenate and Intact-Tissue Quantities Differ
Homogenization disrupts tissue structure and mixes tissue material with buffer. That preparation changes the context in which drug and binding components interact. The assay’s donor total concentration is a concentration in the homogenate as prepared and measured; it is not automatically the total concentration per volume of intact tissue. Likewise, the receiver reports an unbound concentration under the assay conditions, not a direct sample of free drug in an intact organ.
This distinction is important when a measured binding result is used as a parameter in a PBPK model. The result can inform binding in a tissue-related preparation, but its interpretation must match the model quantity being parameterized. One must not silently substitute a homogenate concentration for an intact-tissue concentration. Tissue homogenate preparation, measurement basis, and any later adjustment must be documented so the input has a clear meaning.
Worked Example: Keeping the Measurement Basis Clear
Suppose a hypothetical assay reports a receiver concentration of \(0.150\ \mu\mathrm{mol/L}\) and a donor homogenate total concentration of \(3.00\ \mu\mathrm{mol/L}\). Both concentrations refer to the same equilibrium condition and compatible volume basis, and the assay checks support their use.
The measured homogenate ratio is: $$ f_{u,\mathrm{tiss,hom}} = \frac{0.150\ \mu\mathrm{mol/L}}{3.00\ \mu\mathrm{mol/L}} = 0.0500. $$
Thus, the assay estimates 5.00% unbound in the homogenate. If a report describes this as “5.00% unbound in intact tissue,” it has gone beyond what these measurements establish. The data identify the homogenate result; relating that result to intact tissue requires accounting for how the homogenate was prepared. The ratio alone does not perform that conversion.
Assay Checks and Failure Modes
A precise-looking ratio is not necessarily a reliable one. Equilibrium dialysis requires enough time for redistribution, but a receiver concentration that is still changing indicates that equilibrium may not have been reached. Membrane adsorption can lower the drug available to cross. Drug degradation, precipitation, leakage, or nonspecific binding to assay materials can also distort concentrations. Matrix effects in the analytical method may make donor and receiver measurements incomparable even when both are reported in the same units.
Mass recovery is a useful diagnostic. In a simple closed system, the amount of drug accounted for across the compartments should be consistent with the amount introduced, within the assay’s validated expectations. Recovery that is unexpectedly low can indicate loss, degradation, adsorption, or analytical undermeasurement. Recovery that is unexpectedly high can indicate analytical bias, contamination, or a calculation error. Acceptable recovery does not prove that every assumption holds, but poor recovery is a reason to investigate before treating the fraction as a tissue-binding estimate.
Worked Example: Using Recovery as an Assay Diagnostic
In a hypothetical dialysis setup, \(1.00\ \mathrm{nmol}\) of drug is introduced. At the endpoint, the donor compartment has a measured total concentration of \(1.60\ \mu\mathrm{mol/L}\) in a \(0.500\ \mathrm{mL}\) volume, and the receiver has \(0.300\ \mu\mathrm{mol/L}\) in a \(0.500\ \mathrm{mL}\) volume. Assume the reported donor concentration includes all drug measured in the donor homogenate and that the compartment volumes and concentration bases are appropriate for amount calculations.
The amount in the donor is: $$ 1.60\ \mu\mathrm{mol/L} \times 0.000500\ \mathrm{L} = 0.000800\ \mu\mathrm{mol} = 0.800\ \mathrm{nmol}. $$ The receiver amount is: $$ 0.300\ \mu\mathrm{mol/L} \times 0.000500\ \mathrm{L} = 0.000150\ \mu\mathrm{mol} = 0.150\ \mathrm{nmol}. $$
The total measured amount is \(0.800+0.150=0.950\ \mathrm{nmol}\), so recovery is \(0.950/1.00=0.950\), or 95.0%. Whether this meets an assay’s acceptance criterion depends on the validated protocol; the calculation alone cannot establish that. If the recovery is acceptable and the other assumptions hold, the fraction estimate is \(0.300/1.60=0.1875\), or 18.75%. If recovery falls outside the protocol’s acceptable range, that estimate should be treated as questionable and the cause investigated.
Interpreting the Result Responsibly
Equilibrium dialysis is useful because it separates a measurement of unbound drug from the donor’s total drug concentration through a physical equilibration process. It does not eliminate the need for sound assay design. A result depends on the tissue source, homogenate preparation, assay conditions, concentration range, and analytical method. Different conditions can produce different estimates, so the reported value should be accompanied by the information needed to interpret it.
A common mistake is to say, “The receiver concentration is the concentration in intact tissue, so dividing it by the donor concentration gives the intact-tissue fraction unbound.” The receiver is an estimate of the unbound concentration in the homogenate at equilibrium, not a direct measurement in undisturbed tissue. The correction is to name the quantity precisely as \(f_{u,\mathrm{tiss,hom}}\), state the preparation and measurement basis, and avoid interpreting it as an intact-tissue quantity without the appropriate additional reasoning.
The main alternative is to measure drug concentrations in tissue samples directly, but a total tissue measurement alone does not separate unbound from bound drug. Equilibrium dialysis addresses that separation operationally in a homogenate. Neither approach should be treated as interchangeable with the other: the former may quantify total drug in a tissue sample, while the dialysis ratio estimates the unbound fraction in the prepared homogenate. The assay’s limitations and the distinction between these quantities remain essential to interpretation.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- A receiver concentration is \(0.060\ \mu\mathrm{mol/L}\), and donor homogenate total concentration is \(1.50\ \mu\mathrm{mol/L}\). What is the estimated fraction unbound?
- Why is a receiver concentration not automatically an intact-tissue concentration?
- What does a measured total concentration of zero imply for the fraction-unbound ratio, even if the receiver concentration is also zero?
- Name two assay conditions or diagnostics that should be checked before interpreting a calculated ratio.
- A calculated ratio is 1.20. Give two possible explanations and state why it should not be accepted as a valid tissue fraction unbound without review.
Solutions. (1) \(0.060/1.50=0.0400\), or 4.00%, assuming compatible bases and valid assay conditions. (2) The receiver estimates unbound concentration in the homogenate at equilibrium; homogenization disrupts intact tissue structure, so the receiver does not directly sample undisturbed tissue. (3) The ratio is undefined because its denominator is zero, including when the result would otherwise be \(0/0\). (4) Examples include verifying equilibrium, checking mass recovery, assessing membrane adsorption or leakage, and confirming analytical validity. (5) Possible causes include incompatible concentration bases, measurement or calculation error, or failure of membrane or equilibrium assumptions. Since a valid unbound portion cannot exceed the compatible total concentration, the result requires investigation rather than direct interpretation.