Correcting Uptake Assays for Binding and Passive Diffusion

Why Uptake Measurements Need Correction

A hepatocyte uptake assay measures substrate associated with the cell preparation, not necessarily substrate transported into the cell by a carrier. The measured signal can include intracellular substrate, substrate bound nonspecifically to cells or surfaces, and substrate remaining in liquid that accompanies the cells during sampling. Even after those contributions are separated, the observed uptake can combine transporter-mediated entry with passive diffusion.

A further distinction is between the nominal substrate concentration added to the well and the unbound concentration available in the assay medium. Substrate binding to medium proteins, plastic, or other assay components can make these concentrations different. Because uptake depends on available substrate, dividing an uptake rate by nominal concentration can misstate the corresponding clearance.

The aim is therefore not simply to subtract a fixed background from one measurement. A defensible estimate requires matched controls, appropriate concentration and time measurements, and explicit accounting for which concentration is used in each calculation.

Definition: Let \(Q_{\mathrm{obs}}(t)\) be the measured substrate amount associated with a hepatocyte sample at time \(t\). A corrected intracellular amount is \(Q_{\mathrm{cell}}(t)=Q_{\mathrm{obs}}(t)-Q_{\mathrm{carry}}(t)-Q_{\mathrm{ns}}(t)\), where \(Q_{\mathrm{carry}}\) is substrate in extracellular liquid carried into the sample and \(Q_{\mathrm{ns}}\) is nonspecific cell-associated substrate not attributed to intracellular uptake. Let \(C_{\mathrm{tot}}\) be the total substrate concentration in the assay medium and \(f_{u,\mathrm{med}}\) its unbound fraction; then \(C_{u,\mathrm{med}}=f_{u,\mathrm{med}}C_{\mathrm{tot}}\).

Correcting the Measured Cell-Associated Amount

Extracellular carryover is the amount of substrate contained in the liquid volume that remains with the cells at sampling. If \(V_{\mathrm{carry}}\) is that volume and the carried liquid has total substrate concentration \(C_{\mathrm{tot}}\), then the carryover amount is \(Q_{\mathrm{carry}}=V_{\mathrm{carry}}C_{\mathrm{tot}}\). The total concentration is used here because the sampled liquid contains both unbound and reversibly bound substrate. The unbound concentration is used for the uptake-rate calculation, not for calculating the amount in a volume of assay medium.

The carryover volume can be estimated with a suitable extracellular marker that does not enter cells during the assay. The marker must remain in the extracellular space and be measured through the same sampling and separation procedure. An estimate from an unrelated procedure or a different separation condition may not represent the liquid actually carried into the sample.

Nonspecific cell association can be estimated with a matched control, such as a condition that suppresses active uptake or a preparation lacking the relevant uptake activity. These controls do not automatically isolate nonspecific binding: they may still include passive entry, residual transporter activity, and extracellular carryover. Carryover must be corrected separately, and the chosen control must be appropriate for the specific binding contribution being estimated. If binding changes with concentration or time, a single background value should not be subtracted from every sample.

Worked Example: Subtracting Extracellular Carryover and Nonspecific Association

In a hypothetical assay, the measured cell-associated amount at a sampling time is \(2.40\) nmol per mg cell protein. An extracellular marker indicates that \(0.012\) mL of assay medium accompanies each mg of protein into the sample. The medium contains \(100\) nmol/mL total substrate. A matched control estimates \(0.30\) nmol/mg of nonspecific cell association after carryover is excluded. Calculate the corrected intracellular amount.

First calculate the substrate in the carried liquid:

Q_{\mathrm{carry}}=V_{\mathrm{carry}}C_{\mathrm{tot}} =(0.012\ \mathrm{mL/mg})(100\ \mathrm{nmol/mL}) =1.20\ \mathrm{nmol/mg}.

Then subtract carryover and nonspecific association from the observed amount:

Q_{\mathrm{cell}} =2.40-1.20-0.30 =0.90\ \mathrm{nmol/mg}.

Under the stated control assumptions, the corrected intracellular amount is \(0.90\) nmol/mg. The subtraction is internally consistent: each term is expressed as an amount per mg of cell protein. A negative corrected amount would be a warning that the estimates or measurements are incompatible, not evidence for negative intracellular substrate.

Using Unbound Medium Concentration

The unbound fraction \(f_{u,\mathrm{med}}\) is the fraction of total substrate in the assay medium that is unbound under the assay conditions. It should be measured or otherwise justified at relevant substrate concentrations and in the same medium composition. When binding is concentration-dependent, one unbound fraction should not be assumed to apply over the entire concentration range.

For example, if \(C_{\mathrm{tot}}=2.00\) µM and \(f_{u,\mathrm{med}}=0.25\), then \(C_{u,\mathrm{med}}=0.500\) µM. Since \(1\) µM equals \(1\) nmol/mL, this is also \(0.500\) nmol/mL. This unit equivalence is useful when dividing a rate in nmol/min by a concentration in nmol/mL.

The assay’s unbound fraction is not a correction to the observed amount of substrate in the well. It is used to express the concentration driving uptake. If the amount carried into the cell sample is being calculated, use the total concentration in the carried liquid; if a clearance is being calculated, use the unbound concentration as the denominator when the intended parameter is clearance relative to unbound substrate.

Separating Transporter-Mediated Uptake From Passive Diffusion

A transporter-inhibited condition can provide an estimate of passive uptake, but only when inhibition is sufficiently complete and the inhibitor does not materially alter passive permeability, cell integrity, substrate binding, or the sampling procedure. A transporter-deficient preparation can offer an alternative, provided it is otherwise comparable to the active preparation. In either design, the amount data must first be corrected for carryover and nonspecific association in each condition.

Use corrected initial slopes rather than assuming that an endpoint amount represents a constant influx rate. Early in an assay, intracellular substrate is often low and the concentration gradient supporting passive entry may be relatively stable. Later, passive net flux can decline or reverse as intracellular concentration rises. The relevant early time interval should therefore be selected based on measurements, not simply chosen by convention.

Model: At matched assay conditions and during a suitable initial-rate interval, write the corrected rate in the active condition as \(J_{\mathrm{active}}=J_{\mathrm{trans}}+J_{\mathrm{passive}}\). If the matched inhibited or transporter-deficient condition has negligible transporter-mediated uptake, then \(J_{\mathrm{control}}\approx J_{\mathrm{passive}}\). Thus \(J_{\mathrm{trans}}\approx J_{\mathrm{active}}-J_{\mathrm{control}}\). The unbound-concentration-based transporter uptake clearance is \(CL_{\mathrm{trans},u}=(J_{\mathrm{active}}-J_{\mathrm{control}})/C_{u,\mathrm{med}}\). This estimate assumes matched unbound concentrations, comparable passive flux and nonspecific corrections, and adequate suppression of transporter activity in the control.

The subtraction has a straightforward justification. Under the stated additive model, the active condition contains both transporter and passive components, while the matched control contains the passive component alone. Subtracting the control rate therefore removes the common passive component:

J_{\mathrm{active}}-J_{\mathrm{control}} \approx (J_{\mathrm{trans}}+J_{\mathrm{passive}})-J_{\mathrm{passive}} =J_{\mathrm{trans}}.

This reasoning fails if the control changes passive permeability or substrate availability, or if appreciable transporter activity remains. In those cases, the difference is not a clean estimate of transporter-mediated uptake. If rates are normalized to cell protein, the resulting clearance has units such as mL/min/mg protein; the normalization must be stated so the quantity is interpretable.

Worked Example: Estimating Unbound Transporter Uptake Clearance

In a hypothetical experiment, corrected initial uptake rates are \(0.84\) nmol/min/mg protein in active hepatocytes and \(0.24\) nmol/min/mg protein in a matched transporter-inhibited condition. The assay medium has \(C_{\mathrm{tot}}=2.00\) µM and \(f_{u,\mathrm{med}}=0.25\). Assume inhibition is complete, passive uptake is unchanged by the inhibitor, and the two conditions have matched unbound concentrations.

The unbound medium concentration is \(C_{u,\mathrm{med}}=(0.25)(2.00)=0.500\) µM, or \(0.500\) nmol/mL. The estimated transporter-mediated rate is

J_{\mathrm{trans}}\approx 0.84-0.24 =0.60\ \mathrm{nmol/min/mg\ protein}.

Divide by the unbound concentration:

CL_{\mathrm{trans},u} =\frac{0.60\ \mathrm{nmol/min/mg}} {0.500\ \mathrm{nmol/mL}} =1.20\ \mathrm{mL/min/mg\ protein}.

The estimate is \(1.20\) mL/min/mg protein under the stated assay conditions. For comparison, dividing the active rate by the same unbound concentration would give \(1.68\) mL/min/mg protein, which includes the control-estimated passive component and is not the transporter-specific clearance.

When Corrections Change the Interpretation

Using total rather than unbound concentration can produce a substantial difference. For a rate held fixed, the apparent clearance relative to total concentration is \(J/C_{\mathrm{tot}}\), whereas clearance relative to unbound concentration is \(J/(f_{u,\mathrm{med}}C_{\mathrm{tot}})\). When \(f_{u,\mathrm{med}}<1\), the latter is larger. Neither value is inherently an arithmetic error; they describe rates relative to different concentration bases. The concentration basis must be explicit, and an unbound-based estimate should not be interpreted as a total-concentration-based estimate.

Worked Example: Effect of the Concentration Basis

A hypothetical corrected transporter-specific rate is \(0.48\) nmol/min/mg protein at \(C_{\mathrm{tot}}=4.00\) µM, with \(f_{u,\mathrm{med}}=0.20\). Calculate both clearances and explain their difference.

The unbound concentration is \(C_{u,\mathrm{med}}=(0.20)(4.00)=0.800\) µM, or \(0.800\) nmol/mL. Relative to total concentration:

CL_{\mathrm{trans,tot}} =\frac{0.48}{4.00\ \mathrm{nmol/mL}} =0.120\ \mathrm{mL/min/mg\ protein}.

Relative to unbound concentration:

CL_{\mathrm{trans},u} =\frac{0.48}{0.800\ \mathrm{nmol/mL}} =0.600\ \mathrm{mL/min/mg\ protein}.

The unbound-based clearance is five times the total-based value because \(f_{u,\mathrm{med}}=0.20\). The uptake rate is the same in both calculations; the difference arises solely from the concentration denominator. Reporting one value without identifying its concentration basis would be ambiguous.

Diagnostics, Alternatives, and Limitations

A correction is credible only if the data and controls support its assumptions. Inspect corrected amounts and time courses by condition and concentration. A nearly constant early slope supports an initial-rate approximation; visible curvature means a single linear slope may depend strongly on the selected interval. Corrected uptake should generally be nonnegative within measurement uncertainty. A negative result, a control rate exceeding the active rate, or a large change in the estimated clearance across nearby sampling windows calls for investigation rather than automatic truncation or averaging.

The main alternatives for estimating passive uptake are matched inhibitor-treated cells and a transporter-deficient or transporter-poor preparation. Inhibitor controls are experimentally convenient, but their interpretation depends on selectivity, completeness of inhibition, and lack of effects on passive entry and binding. A deficient preparation avoids relying on an inhibitor’s pharmacology but can differ from the active preparation in other ways. Agreement between independent approaches can strengthen the interpretation; disagreement signals that the assumptions or preparation differences need attention.

Binding corrections also have limits. An extracellular marker estimates carried liquid but does not by itself quantify substrate bound to the cell surface. Conversely, a binding control does not establish the extracellular volume retained during sampling. These contributions require distinct estimates. The unbound fraction can vary with concentration and medium composition, while nonspecific binding and passive flux can vary with time. A single correction factor may therefore be unsuitable across a concentration or time course.

At higher substrate concentrations, transporter uptake may no longer be proportional to concentration. In that case, the rate difference between active and inhibited conditions remains a transporter-associated rate under the assumptions above, but dividing it by concentration gives an apparent clearance at that concentration rather than a concentration-independent constant. Interpretation should remain tied to the tested conditions.

Common pitfall: “The inhibited-well signal is background, so subtracting its endpoint amount from the active-well endpoint gives transporter uptake.” This reasoning can be wrong because the inhibited signal may include time-varying passive accumulation, residual transport, and unmatched binding or carryover. Correct each condition for carryover and nonspecific association, verify that the control is comparable, and subtract matched initial rates when the additive initial-rate model is justified.

A Practical Analysis Sequence

Establish the measurement basis.
Record how cell-associated signal is converted to amount and how it is normalized, for example per mg cell protein.

Correct each sample.
Estimate extracellular carryover and nonspecific association under matched conditions, then calculate corrected intracellular amounts.

Choose a supported initial interval.
Use time-course data to identify an interval with an approximately linear corrected amount, rather than presuming linearity.

Estimate the passive component.
Use a matched inhibited or transporter-deficient control and assess whether it preserves passive permeability and substrate availability.

Calculate and label clearance.
Subtract the control rate from the active rate, divide by unbound medium concentration, and report units, normalization, and concentration basis.

Check Your Understanding

Answer each question using the stated assumptions. Brief solutions follow the questions.

A sample contains \(1.80\) nmol/mg measured substrate. Carryover volume is \(0.010\) mL/mg, the medium total concentration is \(80\) nmol/mL, and nonspecific association is \(0.20\) nmol/mg. What is the corrected intracellular amount?
Why is total medium concentration used to calculate substrate in carried extracellular liquid, while unbound concentration is used for an unbound-based uptake clearance?
Corrected initial rates are \(0.70\) and \(0.25\) nmol/min/mg protein in active and inhibited conditions. If \(C_{\mathrm{tot}}=1.50\) µM and \(f_{u,\mathrm{med}}=0.40\), what is the estimated transporter uptake clearance, assuming the inhibitor assumptions hold?
Name two reasons that an inhibited-condition endpoint amount may not be a valid estimate of passive uptake in the active condition.

Solutions. 1. Carryover is \((0.010)(80)=0.80\) nmol/mg, so the corrected amount is \(1.80-0.80-0.20=0.80\) nmol/mg. 2. The carried liquid contains total substrate, both bound and unbound, whereas the unbound-based clearance uses the available unbound concentration as its denominator. 3. The transporter rate is \(0.70-0.25=0.45\) nmol/min/mg. The unbound concentration is \((1.50)(0.40)=0.600\) µM, or \(0.600\) nmol/mL. Thus clearance is \(0.45/0.600=0.750\) mL/min/mg protein. 4. The inhibitor may not fully suppress transporter activity, may alter passive permeability or binding, or passive net influx may change over time as intracellular substrate accumulates. Any two of these explain why the endpoint difference need not isolate transporter-mediated uptake.