Unbound Inhibitor Exposure at Renal Transporters

Why Total Plasma Concentration Is Not Enough

A plasma assay generally reports the total inhibitor concentration: unbound molecules plus molecules reversibly bound to plasma proteins. A transporter, however, interacts with inhibitor available at its binding site. Translating a measured total concentration into that local unbound exposure is therefore an essential step in using an inhibition model. The translation depends on both protein binding and where the transporter’s binding site is located.

For a transporter on the basolateral membrane of a proximal tubule cell, the relevant inhibitor concentration is ordinarily the unbound concentration in the aqueous space on the blood-facing side, subject to the assumption that this concentration is represented by unbound plasma concentration. For a binding site accessible from inside the cell, plasma unbound concentration alone may not describe exposure: the inhibitor must also enter the cell, and intracellular binding may affect its total concentration. The distinction is between unbound concentration at a specified site and total concentration in a sampled compartment.

The unbound fraction does not mean that protein-bound inhibitor is permanently unavailable. Reversible binding can replenish unbound inhibitor as free molecules distribute or interact with a transporter. The unbound concentration is used because it represents the free concentration in the aqueous phase under the model’s binding assumptions. It is not correct to multiply the inhibitor’s total concentration by the fraction of plasma that is not protein-bound in some unrelated sense; \(f_{u,p}\) is specifically a concentration ratio.

From Plasma Measurement to Transporter-Site Exposure

The simplest translation assumes rapid binding equilibrium, linear binding over the relevant range, and a measured unbound fraction that applies to the patient population and conditions being modeled. If the transporter site is on the blood-facing surface and free plasma is taken to represent the local free concentration, then \(C_{u,\mathrm{site}}\approx C_{u,p}\). If the site is intracellular, an additional access factor is needed:

Here \(K_{p,uu,\mathrm{cell}}\) describes unbound distribution, not total drug accumulation. A cell-to-plasma ratio based on total concentrations, \(K_{p,\mathrm{cell}}=C_{\mathrm{cell,total}}/C_{p,\mathrm{total}}\), is not interchangeable with \(K_{p,uu,\mathrm{cell}}\). If the intracellular unbound fraction is \(f_{u,\mathrm{cell}}\), then under compatible equilibrium and measurement definitions, \(C_{u,\mathrm{cell}}=f_{u,\mathrm{cell}}C_{\mathrm{cell,total}}\). A high total cell concentration can coexist with modest unbound intracellular concentration when intracellular binding or sequestration is substantial.

Concentration units must be consistent with the inhibition constant \(K_i\). If the inhibition model uses molar concentrations, convert the calculated site concentration to molar units before forming a ratio such as \(C_{u,\mathrm{site}}/K_i\). In the simple competitive model, exposure enters through the inhibitor concentration at the relevant site; the resulting effect also depends on the substrate concentration and the model’s other parameters. Thus, a site concentration alone is not a complete prediction of the change in transport.

Intracellular Access and Inhibition Calculations

For a transporter whose inhibitor-binding site is accessible from the cytosol, an estimate of unbound plasma exposure must be adjusted for intracellular access. \(K_{p,uu,\mathrm{cell}}=1\) means that the unbound intracellular and plasma concentrations are equal under the conditions represented by the ratio. A value below 1 indicates lower unbound cell concentration than plasma; a value above 1 indicates higher unbound cell concentration. These interpretations apply to unbound concentrations, not total tissue levels.

A common source of error is to assume \(K_{p,uu,\mathrm{cell}}=1\) merely because a total cell-to-plasma ratio is near 1, or because the compound is detectable inside cells. Neither observation establishes equality of unbound concentrations. Evidence for cell access may come from an appropriate unbound distribution measurement, a validated mechanistic model, or a justified equilibrium assumption. The relevant estimate may also depend on time: a steady-state partition ratio should not automatically be applied to a rapidly changing concentration profile.

Deriving an Unbound Concentration Under Saturable Binding

A fixed \(f_{u,p}\) is inappropriate if protein binding is concentration-dependent over the range being modeled. One simple equilibrium model represents bound inhibitor with a finite binding capacity \(B_{\max}\) and dissociation constant \(K_d\). In this model, total concentration equals free concentration plus concentration bound to the protein:

This form assumes one effective class of reversible binding sites, equilibrium, and compatible concentration units for \(B_{\max}\), \(K_d\), and the measured concentrations. Multiplying both sides by \(K_d+C_{u,p}\) gives a quadratic:

The physically meaningful solution is the nonnegative root. The other root is negative when all parameters and total concentration are positive, so it cannot represent a concentration. Once \(C_{u,p}\) is obtained, an intracellular site concentration can still be estimated using a justified \(K_{p,uu,\mathrm{cell}}\); the saturable binding calculation changes the plasma-unbound estimate, not the definition of the cell-access ratio.

Assumptions, Diagnostics, and Alternatives

The translation is only as reliable as the measurements and assumptions behind it. Before using a site concentration in a transporter model, check that total and unbound concentrations refer to the same time point, that concentration units match those of \(K_i\), and that the binding measurement represents the relevant conditions. For example, changes in protein concentrations, assay conditions, or concentration range can make a measured \(f_{u,p}\) unsuitable for another setting. If binding is nonlinear, inspect whether the apparent unbound fraction changes across the observed concentration range rather than imposing a single value.

For an intracellular site, check whether the access ratio is actually an unbound ratio and whether the evidence supports its use at the relevant time and concentration. Large disagreement between a predicted unbound cell concentration and an independent measurement is a warning that the assumed partition ratio, binding model, or equilibration timescale may be wrong. A high total cell concentration does not resolve this discrepancy unless intracellular binding is also characterized. For a blood-facing site, assuming equality with plasma-unbound concentration may fail if local gradients or slow distribution matter.

There are two useful alternatives to the simple calculation. First, direct measurement of unbound plasma concentration can avoid estimating it from total concentration and a binding fraction, although the assay must be validated at the relevant range. Second, direct or mechanistic estimation of unbound intracellular exposure can replace an assumed \(K_{p,uu,\mathrm{cell}}\). These approaches may be more informative but require suitable data. A total-concentration-only model is simpler, yet it cannot represent changes in binding or access unless those effects are built into its parameters.

In a PBPK simulation, the relevant concentration can vary over time. The conversion should therefore be applied to the concentration profile, not just to an unrelated peak or average, if the model requires time-varying transporter inhibition. A single exposure value may be an intentional summary, but it should be defined and justified. Predictions are limited by the accuracy of the binding and access inputs, the assumption that the inhibition constant is appropriate to the transporter system, and the model’s representation of local conditions.

Common Mistake and Key Takeaway

Wrong reasoning: “The total cell-to-plasma concentration ratio is 2, so the inhibitor concentration at an intracellular transporter is twice total plasma concentration.” This substitutes a total concentration ratio for the unbound site concentration and ignores both plasma binding and intracellular binding. Correction: estimate plasma-unbound concentration first, then use a justified unbound cell-to-plasma ratio: \(C_{u,\mathrm{cell}}=K_{p,uu,\mathrm{cell}}f_{u,p}C_{p,\mathrm{total}}\). If either factor is unknown, report the assumption or uncertainty rather than treating total tissue accumulation as proof of intracellular free exposure.