Unbound Drug Concentration at the Intracellular Target

Why Total Plasma Concentration May Not Represent Target Exposure

A plasma assay often reports total drug concentration: drug dissolved in plasma plus drug bound to plasma proteins. An intracellular target, however, is reached by drug that crosses cell membranes, and the unbound concentration is generally the relevant concentration for passive exchange and target access. Tissue binding and membrane transport can further separate intracellular unbound concentration from the value suggested by total plasma concentration.

The calculation is therefore not simply “plasma concentration equals target concentration.” It requires a sequence of assumptions and quantities: plasma protein binding, distribution into the relevant tissue, binding within that tissue, and whether membrane transport permits the assumed distribution. The estimate is most useful when its inputs refer to the same drug, tissue, species, and exposure condition.

Definition: Let \(C_{\mathrm{tot,p}}\) be total plasma drug concentration and \(f_{u,p}\) the unbound fraction in plasma. The unbound plasma concentration is \(C_{u,p}=f_{u,p}C_{\mathrm{tot,p}}\). Let \(C_{\mathrm{tot,t}}\) be total concentration in the relevant tissue and \(f_{u,t}\) its unbound fraction. The tissue unbound concentration is \(C_{u,t}=f_{u,t}C_{\mathrm{tot,t}}\). For an intracellular target, \(C_{u,i}\) denotes unbound drug concentration in the intracellular space containing that target.

From Plasma Binding and Tissue Partitioning to Unbound Tissue Concentration

A tissue-to-plasma partition coefficient \(K_p\) is the ratio of total tissue concentration to total plasma concentration under the specified conditions:

K_p=\frac{C_{\mathrm{tot,t}}}{C_{\mathrm{tot,p}}}

Because total tissue concentration includes tissue-bound drug, \(K_p\) alone does not say how much unbound drug is present. Combining the definitions gives the unbound tissue-to-plasma ratio, often written \(K_{p,uu}\):

K_{p,uu} =\frac{C_{u,t}}{C_{u,p}} =\frac{f_{u,t}C_{\mathrm{tot,t}}}{f_{u,p}C_{\mathrm{tot,p}}} =K_p\frac{f_{u,t}}{f_{u,p}}

If the relevant tissue estimate represents the intracellular space of interest, and distribution has reached the condition represented by the measured ratio, then \(C_{u,i}\) can be approximated by \(K_{p,uu}C_{u,p}\). This calculation explicitly separates three quantities that are easy to conflate: plasma total concentration, plasma unbound fraction, and the unbound tissue-to-plasma ratio.

Assumptions for this conversion: Concentrations and unbound fractions refer to compatible conditions; binding is sufficiently characterized at the concentration of interest; the tissue partition and tissue unbound fraction represent the target-bearing cells; and the measured ratio is applicable to the exposure condition being estimated. A whole-tissue homogenate may not represent intracellular fluid, and a single \(K_{p,uu}\) may not apply if transport or binding is concentration-dependent.

Worked Example: Correcting for Plasma and Tissue Binding

Suppose a hypothetical drug has a total plasma concentration of \(8.0\ \mu\mathrm{mol/L}\), a plasma unbound fraction of \(0.025\), a tissue-to-plasma total partition coefficient of \(K_p=3.0\), and a tissue unbound fraction of \(0.010\). Assume these values describe the relevant target-bearing tissue at the condition of interest.

First calculate unbound plasma concentration:

C_{u,p}=f_{u,p}C_{\mathrm{tot,p}} =0.025(8.0\ \mu\mathrm{mol/L}) =0.200\ \mu\mathrm{mol/L}

Then calculate the unbound tissue-to-plasma ratio:

K_{p,uu}=K_p\frac{f_{u,t}}{f_{u,p}} =3.0\frac{0.010}{0.025} =1.20

Thus the estimated tissue unbound concentration is:

C_{u,t}=K_{p,uu}C_{u,p} =1.20(0.200\ \mu\mathrm{mol/L}) =0.240\ \mu\mathrm{mol/L}

The tissue total concentration would be \(K_pC_{\mathrm{tot,p}}=24.0\ \mu\mathrm{mol/L}\), but only \(1.0\%\) of that is unbound under the stated assumption, giving the same \(0.240\ \mu\mathrm{mol/L}\) estimate. Reporting the tissue total concentration as target exposure would overstate the calculated unbound concentration by a factor of 100.

What Membrane Permeability Adds

A partition ratio describes the concentration relationship under the conditions represented by the ratio; permeability describes how readily drug crosses a membrane. These are related but not interchangeable. In a simple passive system for a neutral molecule, with no active transport, no relevant concentration gradients, and equilibrium established, unbound concentrations on the two sides tend toward equality. A low-permeability membrane can slow access without necessarily changing that final passive equilibrium.

For an intracellular compartment, an effective steady-state transport balance can be written as entry proportional to plasma unbound concentration and exit proportional to intracellular unbound concentration:

\frac{dC_{u,i}}{dt} =k_{\mathrm{in}}C_{u,p}-k_{\mathrm{out}}C_{u,i}

Here \(k_{\mathrm{in}}\) and \(k_{\mathrm{out}}\) are effective first-order transport coefficients, with units of inverse time. They can summarize membrane access and, when the model is used for that purpose, the net influence of transport processes such as active efflux. At steady state under constant \(C_{u,p}\), entry and exit balance. Setting the derivative to zero gives:

0=k_{\mathrm{in}}C_{u,p}-k_{\mathrm{out}}C_{u,i} \qquad\Longrightarrow\qquad \frac{C_{u,i}}{C_{u,p}}=\frac{k_{\mathrm{in}}}{k_{\mathrm{out}}}

This ratio is an effective intracellular unbound partition ratio for the stated model and conditions. A lower effective entry relative to exit gives a lower intracellular concentration than plasma unbound concentration. If entry and exit are balanced symmetrically for passive diffusion, the ratio is one; a ratio different from one requires an explanation such as active transport, ionization and pH gradients, or another maintained concentration gradient. Permeability measurements alone do not establish the steady-state ratio unless the transport model and its other processes are specified.

Worked Example: Estimating Intracellular Concentration With Net Efflux

For a hypothetical compound, let \(C_{u,p}=0.30\ \mu\mathrm{mol/L}\). Suppose the effective entry coefficient is \(k_{\mathrm{in}}=0.12\ \mathrm{h}^{-1}\), and the effective exit coefficient is \(k_{\mathrm{out}}=0.30\ \mathrm{h}^{-1}\). Assume constant plasma unbound concentration and a steady state described by the transport balance above.

At steady state, the intracellular-to-plasma unbound ratio is:

\frac{C_{u,i}}{C_{u,p}} =\frac{k_{\mathrm{in}}}{k_{\mathrm{out}}} =\frac{0.12\ \mathrm{h}^{-1}}{0.30\ \mathrm{h}^{-1}} =0.400

Therefore:

C_{u,i}=0.400(0.30\ \mu\mathrm{mol/L}) =0.120\ \mu\mathrm{mol/L}

The effective coefficients imply an intracellular unbound concentration below plasma unbound concentration. This is a steady-state estimate, not a claim that the concentration is reached immediately. If both coefficients were reduced by the same factor, the steady-state ratio would be unchanged even though membrane access would be slower.

Two Routes to an Estimate, and Their Limitations

There are two common calculation routes. When paired tissue and plasma measurements and tissue binding data are available, use \(K_{p,uu}=K_pf_{u,t}/f_{u,p}\). When a mechanistic transport balance is justified and its effective entry and exit coefficients are known, use \(C_{u,i}/C_{u,p}=k_{\mathrm{in}}/k_{\mathrm{out}}\) at steady state. These routes need not give identical answers if they represent different tissues, conditions, or biological processes. They should not be combined as if each were an independent correction factor unless the model defines how they relate.

Approach	What it estimates	Main requirement or limitation
Total plasma concentration alone	A measured plasma amount, not intracellular unbound exposure	Does not account for plasma binding, tissue distribution, or membrane access
\(K_p\) with unbound fractions	An unbound tissue-to-plasma ratio	Requires relevant tissue partition and tissue binding measurements; tissue homogenate may not identify intracellular free concentration
Steady-state transport balance	An intracellular unbound-to-plasma unbound ratio under a specified transport model	Requires effective entry and exit parameters and a valid steady-state assumption

A reported tissue total concentration can be high because of nonspecific tissue binding or sequestration, even when the unbound concentration near an intracellular target is low. Conversely, a low plasma unbound concentration may still produce substantial target-site exposure if the tissue unbound-to-plasma ratio is high. Thus total plasma concentration alone can mis-rank compounds or conditions when binding and transport differ.

Worked Example: Same Total Plasma Concentration, Different Target-Site Estimates

Two hypothetical drugs each have total plasma concentration \(5.0\ \mu\mathrm{mol/L}\). For drug A, \(f_{u,p}=0.10\), \(K_p=1.0\), and \(f_{u,t}=0.050\). For drug B, \(f_{u,p}=0.020\), \(K_p=2.0\), and \(f_{u,t}=0.040\). Assume each set of fractions and partition values applies to its target-bearing tissue.

For drug A:

C_{u,p,A}=0.10(5.0)=0.500\ \mu\mathrm{mol/L}

K_{p,uu,A}=1.0\frac{0.050}{0.10}=0.500 \qquad\Longrightarrow\qquad C_{u,i,A}\approx0.500(0.500)=0.250\ \mu\mathrm{mol/L}

For drug B:

C_{u,p,B}=0.020(5.0)=0.100\ \mu\mathrm{mol/L}

K_{p,uu,B}=2.0\frac{0.040}{0.020}=4.00 \qquad\Longrightarrow\qquad C_{u,i,B}\approx4.00(0.100)=0.400\ \mu\mathrm{mol/L}

Although the drugs have the same total plasma concentration, the estimated intracellular unbound concentration is \(0.250\ \mu\mathrm{mol/L}\) for A and \(0.400\ \mu\mathrm{mol/L}\) for B. This comparison does not establish which drug has the greater pharmacological effect; it shows only that total plasma concentration does not determine target-site unbound concentration when binding and tissue partitioning differ.

Diagnostics, Failure Modes, and Practical Interpretation

Before using an estimate in a mechanistic model, check whether the inputs actually support it. A mismatch in tissue, species, sampling condition, or concentration range can invalidate the calculation even when the arithmetic is correct. Also check units: \(f_{u,p}\), \(f_{u,t}\), and \(K_p\) are dimensionless, so multiplying them by a concentration must leave concentration units unchanged. In the transport balance, \(k_{\mathrm{in}}/k_{\mathrm{out}}\) is dimensionless because both coefficients have units of inverse time.

Check binding estimates. Unbound fractions may depend on assay conditions, concentration, and the composition of the biological matrix. Do not assume a fraction measured in one matrix applies to another without justification.
Check the tissue definition. A homogenized tissue measurement combines extracellular and intracellular material and may include residual blood. It is not automatically a measurement of concentration at the target.
Check for active transport or gradients. If transporters, ionization, or pH differences are important, passive equality of unbound concentrations is not a suitable assumption. A steady-state ratio may depend on these processes and may change across conditions.
Check whether the system is at the modeled condition. A steady-state partition ratio should not be used as though it describes every changing exposure condition. A permeability barrier can delay access even when the eventual ratio is unchanged.
Check concentration dependence. Saturable transport or binding can make a single ratio inappropriate across a dose range.

A frequent mistake is to multiply total plasma concentration by \(K_p\) and call the result intracellular active concentration. That calculation gives total tissue concentration under the definition of \(K_p\); it does not account for either plasma or tissue binding and does not show that the measured tissue reflects the target-bearing cells. Another mistake is to treat low permeability as proof of a lower equilibrium concentration. Low permeability can limit the rate of access, but a reduced steady-state ratio requires an appropriate mechanism or measured evidence.

Key takeaway: Start with plasma unbound concentration, then use a tissue unbound partition ratio or an explicitly stated transport balance to estimate intracellular unbound concentration. Interpret the result as an estimate conditional on its tissue, binding, transport, and steady-state assumptions—not as a direct consequence of total plasma concentration.

Check Your Understanding

Answer each question, then compare with the solutions below.

A hypothetical drug has \(C_{\mathrm{tot,p}}=12.0\ \mu\mathrm{mol/L}\) and \(f_{u,p}=0.050\). What is \(C_{u,p}\)?
A tissue has \(K_p=2.0\), \(f_{u,t}=0.020\), and \(f_{u,p}=0.040\). Calculate \(K_{p,uu}\). If \(C_{u,p}=0.300\ \mu\mathrm{mol/L}\), estimate the tissue unbound concentration.
In the steady-state transport balance, what is \(C_{u,i}/C_{u,p}\) if \(k_{\mathrm{in}}=0.08\ \mathrm{h}^{-1}\) and \(k_{\mathrm{out}}=0.20\ \mathrm{h}^{-1}\)?
Why can two drugs with identical total plasma concentrations have different intracellular unbound concentrations?

Solutions. (1) \(C_{u,p}=0.050(12.0)=0.600\ \mu\mathrm{mol/L}\). (2) \(K_{p,uu}=2.0(0.020/0.040)=1.00\); therefore \(C_{u,t}=1.00(0.300)=0.300\ \mu\mathrm{mol/L}\). (3) At steady state, \(C_{u,i}/C_{u,p}=k_{\mathrm{in}}/k_{\mathrm{out}}=0.08/0.20=0.400\). (4) Their plasma unbound fractions, tissue binding, tissue partitioning, or transport can differ, so the conversion from plasma total to intracellular unbound concentration need not be the same.