Why Transporter-Site Exposure Is Not One Concentration
An inhibitor can reach transporters from different directions. After an oral dose, the intestinal lumen may be exposed to a high concentration of dissolved drug, while the unbound concentration in plasma is much lower. The liver receives drug both from the systemic circulation and, during absorption, from portal blood. In the kidney, an inhibitor may encounter transporters from unbound plasma on the basolateral side or from tubular fluid on the apical side. These concentrations are not interchangeable.
Exposure estimates are inputs for assessing whether inhibition could be relevant; they are not measurements of concentration at a transporter, and by themselves they do not establish the magnitude of a drug-drug interaction. The appropriate estimate depends on the transporter’s location, the route by which inhibitor reaches it, and the concentration basis used for the in vitro inhibition parameter.
Choose the Site and Concentration Basis First
Before calculating, identify which side of which membrane is relevant. An intestinal transporter exposed from the lumen cannot automatically be assigned the plasma concentration. A hepatic sinusoidal uptake transporter is approached from blood, whereas a transporter on the canalicular membrane is exposed from within hepatocytes. Renal basolateral transporters are approached from plasma; apical transporters are approached from tubular fluid. Estimating hepatocyte or enterocyte intracellular concentration generally requires information about membrane transport, binding, and intracellular partitioning beyond a simple plasma or lumen calculation.
For systemic exposure, distinguish total plasma concentration from unbound plasma concentration. If \(C_{\mathrm{plasma}}\) is total plasma concentration and \(f_{u,p}\) is the fraction unbound in plasma, then the unbound concentration is estimated as \(f_{u,p}C_{\mathrm{plasma}}\). This conversion assumes the unbound fraction is applicable at the concentration and time being considered. It does not convert a plasma concentration into a tissue concentration.
Use a consistent concentration basis when comparing exposure with inhibition data. If an in vitro parameter represents unbound inhibitor concentration, compare it with an unbound exposure estimate when that estimate is justified. If blood flow is used in a hepatic calculation but measured concentrations are on a plasma basis, differences between blood and plasma concentrations may matter; convert consistently when blood-to-plasma partitioning is material.
Intestinal Lumen: A Dose-Based Screening Estimate
A common first-pass estimate for intestinal lumen exposure after oral dosing is the administered dose divided by an assumed intestinal fluid volume, often 250 mL. This is a deliberately simple nominal concentration. It assumes the dose is available in that volume and does not account for incomplete dissolution, precipitation, transit, absorption during dissolution, or spatial variation along the gut.
The result is a nominal total concentration, not necessarily the dissolved concentration or the unbound concentration at an intestinal transporter. If solubility is lower than the nominal concentration, the dissolved concentration cannot be assumed to reach the nominal value. Even the dissolved lumen concentration does not directly specify concentration inside enterocytes, where some transporters may also be encountered.
Worked Example: Nominal and Solubility-Limited Gut Concentrations
Suppose a hypothetical oral inhibitor dose is 600 mg, and its aqueous solubility under relevant conditions is 1.2 mg/mL. Calculate the conventional nominal concentration using 250 mL, then calculate the concentration implied if dissolved drug is capped at the stated solubility. Assume, only for this illustration, that the dose is uniformly distributed in 250 mL and that solubility is the only limit on dissolved concentration.
The nominal estimate is \(600\ \mathrm{mg}/250\ \mathrm{mL}=2.4\ \mathrm{mg/mL}\). The solubility is only 1.2 mg/mL, so a solution at the nominal concentration is not supported by the supplied solubility assumption. A simple solubility-capped estimate is therefore 1.2 mg/mL, not 2.4 mg/mL.
If the hypothetical molecular weight is 400 g/mol, then 1.2 mg/mL equals 1.2 g/L. Thus, \(1.2\ \mathrm{g/L}/400\ \mathrm{g/mol}=0.0030\ \mathrm{mol/L}=3.0\ \mathrm{mmol/L}\). This is a dissolved-lumen estimate under the stated simplifications. It is not an estimate of unbound enterocyte concentration, and it could still be inaccurate if intestinal fluids, formulation, or dissolution kinetics differ from the assumptions.
Hepatic Inlet: Add the Portal Contribution Carefully
For a simplified hepatic inlet estimate after oral dosing, the systemic concentration is augmented by an estimated portal contribution during absorption. Let \(I_{\max}\) denote the maximum total plasma concentration, \(F_a\) the fraction of the oral dose absorbed, \(F_g\) the fraction escaping intestinal metabolism, \(k_a\) the absorption-rate constant, and \(Q_h\) hepatic blood flow. In a simplified plasma-based screening form, the inlet concentration is
The second term is an approximate portal increment: \(F_aF_g\) is the fraction entering portal blood after absorption and gut metabolism, \(k_a\,\mathrm{Dose}\) gives an approximate absorbed mass rate, and division by \(Q_h\) converts that rate to a concentration increment. This approximation treats the portal input as a rate evaluated at a representative point and assumes adequate mixing. It is not a full portal-venous concentration-time profile.
For a hepatic transporter approached from blood, a corresponding unbound estimate can be formed as \(f_{u,p}I_{\mathrm{in,max}}\), if the plasma unbound fraction is appropriate for the concentration range and the calculation is expressed on a consistent plasma basis. The estimate is not the unbound concentration inside hepatocytes. It also does not represent every time point: the maximum may be conservative, while transporter activity and inhibitor exposure may vary over time.
Worked Example: Hepatic Inlet and Unbound Concentrations
Consider a hypothetical oral inhibitor with \(I_{\max}=5.0\ \mathrm{mg/L}\), dose \(=400\ \mathrm{mg}\), \(F_a=0.80\), \(F_g=0.70\), \(k_a=1.0\ \mathrm{h^{-1}}\), \(Q_h=90\ \mathrm{L/h}\), and \(f_{u,p}=0.10\). Assume the simplified inlet equation is suitable, the inputs refer to the same dosing conditions, and plasma and flow bases are being used consistently.
The portal increment is \((0.80)(0.70)(1.0\ \mathrm{h^{-1}})(400\ \mathrm{mg})/(90\ \mathrm{L/h})=2.49\ \mathrm{mg/L}\). Therefore, \(I_{\mathrm{in,max}}=5.0+2.49=7.49\ \mathrm{mg/L}\).
The estimated unbound inlet concentration is \(0.10(7.49\ \mathrm{mg/L})=0.749\ \mathrm{mg/L}\). For comparison, the unbound systemic maximum alone is \(0.10(5.0\ \mathrm{mg/L})=0.500\ \mathrm{mg/L}\). Thus the modelled portal increment raises this particular unbound inlet estimate by 0.249 mg/L. This arithmetic does not show that the concentration at a hepatic transporter is exactly 0.749 mg/L; it shows what follows from the stated inlet and binding assumptions.
Renal Sites: Plasma and Tubular Fluid Are Different
For a renal transporter on the basolateral membrane, unbound plasma concentration is a reasonable first estimate of inhibitor available from blood. A plasma maximum may be used for a conservative screening calculation, or a concentration-time profile may be used when time course matters. This estimate does not establish the concentration at an apical transporter in tubular fluid.
A simple filtered-only calculation can illustrate why tubular-fluid exposure may differ from plasma exposure. Under the restrictive assumptions of filtration of unbound inhibitor, no tubular secretion, no reabsorption, and a constant plasma concentration, the filtered mass rate is \(f_{u,p}C_{\mathrm{plasma}}\mathrm{GFR}\). Dividing by urine flow gives an average concentration in the resulting urine:
Here \(\mathrm{GFR}\) is glomerular filtration rate and \(\dot V_{\mathrm{urine}}\) is urine flow. This calculation is a mass-balance illustration, not a general prediction of concentration at a proximal-tubule transporter. Secretion, reabsorption, changing flow, water removal along the nephron, and local mixing can all change tubular concentrations. In particular, urine concentration should not be substituted uncritically for the concentration at a specific nephron segment.
Worked Example: Filtered-Only Renal Concentration
Suppose a hypothetical inhibitor has total plasma concentration \(4.0\ \mathrm{mg/L}\), \(f_{u,p}=0.25\), GFR \(=7.5\ \mathrm{L/h}\), and urine flow \(=0.060\ \mathrm{L/h}\). Assume a constant concentration, filtration of unbound drug only, and no secretion or reabsorption.
The unbound plasma concentration is \(0.25(4.0)=1.0\ \mathrm{mg/L}\). The filtered mass rate is \((1.0\ \mathrm{mg/L})(7.5\ \mathrm{L/h})=7.5\ \mathrm{mg/h}\). The filtered-only urine concentration estimate is \(7.5\ \mathrm{mg/h}/0.060\ \mathrm{L/h}=125\ \mathrm{mg/L}\).
The result is much higher than the 1.0 mg/L unbound plasma concentration because the assumed filtered mass is contained in a smaller fluid volume. It is not evidence that an apical transporter is exposed to 125 mg/L throughout the nephron: the calculation omits segment-specific fluid handling and transport.
Comparison, Diagnostics, and Limits
| Site or estimate | Typical first estimate | Important qualification |
|---|---|---|
| Intestinal lumen | Oral dose divided by assumed fluid volume | Nominal total concentration; dissolution and local conditions may limit exposure |
| Hepatic blood-facing site | Systemic maximum plus approximate portal increment | Requires consistent flow and concentration bases; not intracellular exposure |
| Renal basolateral site | Unbound plasma concentration | Does not represent tubular-fluid concentration |
| Renal apical site | Site-specific tubular-fluid estimate, if justified | Filtered-only mass balance omits secretion, reabsorption, and segmental changes |
A useful diagnostic is dimensional and conceptual checking. In the hepatic increment, dose multiplied by \(k_a\) has units of mass per time; division by flow gives mass per volume. In the renal calculation, filtered mass per time divided by urine volume per time gives mass per volume. If a result has the wrong units, or if an assumed flow is expressed in incompatible time units, the numerical answer is not interpretable.
Compare approaches only after specifying the same site and concentration basis. A gut-lumen estimate is not a substitute for unbound plasma concentration. The systemic unbound maximum is simpler and can be appropriate for blood-facing sites, but it may omit a portal increment at the liver. A more detailed PBPK simulation can represent changing concentrations, flows, and tissue distribution, but requires reliable input data and model structure. Greater complexity does not guarantee a better estimate when key inputs are poorly known.
Warning signs include a nominal gut concentration far above solubility being reported as dissolved exposure without qualification; a hepatic inlet calculation mixing plasma concentrations with whole-blood flow without considering partitioning; and a renal urine estimate being described as a measured concentration at a transporter. Sensitivity checks on uncertain inputs—such as \(F_a\), \(F_g\), \(k_a\), \(f_{u,p}\), and urine flow—help show whether the estimated exposure is robust or driven by an assumption.
Common mistake: “The dose divided by 250 mL is the intestinal transporter concentration, so it can be compared directly with any inhibition constant.” The correction is that this is only a nominal lumen concentration. Solubility, dissolution, binding, location, and the concentration basis of the in vitro parameter must be considered before interpreting the comparison. Similarly, multiplying total plasma concentration by \(f_{u,p}\) estimates unbound plasma concentration, not unbound concentration in liver or kidney tissue.
Check Your Understanding
Answer each question, then compare with the brief solutions below.
- A 300 mg dose is divided by 250 mL. What is the nominal gut concentration, and what does it fail to establish?
- If total plasma concentration is 8.0 mg/L and \(f_{u,p}=0.05\), calculate unbound plasma concentration.
- In the hepatic inlet equation, what are the units of \(k_a\mathrm{Dose}/Q_h\), and why?
- Why is unbound plasma concentration generally more relevant than total plasma concentration for a basolateral renal transporter?
- A filtered-only renal calculation gives 80 mg/L. Can this automatically be assigned as the concentration at an apical transporter? State one reason.
Solutions. (1) \(300\ \mathrm{mg}/250\ \mathrm{mL}=1.2\ \mathrm{mg/mL}\). It does not establish the dissolved or unbound concentration at a transporter. (2) \(0.05(8.0\ \mathrm{mg/L})=0.400\ \mathrm{mg/L}\). (3) Dose times \(k_a\) has units \(\mathrm{mg/h}\); dividing by \(Q_h\) in \(\mathrm{L/h}\) gives \(\mathrm{mg/L}\). (4) Unbound plasma is the portion not bound to plasma proteins and is the relevant starting estimate for availability from blood, subject to site-specific limitations. (5) No. For example, secretion, reabsorption, water handling, and segmental changes can make local tubular-fluid exposure differ from the filtered-only estimate.