Developmental Plasma Binding and Blood-to-Plasma Ratios

Why Binding and Blood Partitioning Matter in Pediatric PBPK

A PBPK model must distinguish drug in plasma from drug in whole blood and from drug that is unbound. These are related, but they are not interchangeable. The distinction matters across pediatric ages because plasma protein concentrations, hematocrit, and drug partitioning into red cells can change during development. Their effects are drug-specific: a developmental change in binding does not imply the same change in unbound fraction or blood-to-plasma ratio for every compound.

The practical task is to use age-appropriate parameters and a consistent concentration basis. Plasma measurements can inform plasma binding, while a model that transports drug in whole blood needs blood-based concentrations and parameters. Confusing those bases can introduce errors into predicted distribution and clearance, even when each input value appears reasonable.

Definition: The plasma fraction unbound, \(f_{u,p}\), is the ratio of unbound drug concentration in plasma to total drug concentration in plasma. The blood-to-plasma ratio, \(R_b\), is the ratio of total drug concentration in whole blood to total drug concentration in plasma, \(R_b=C_b/C_p\). The blood fraction unbound, \(f_{u,b}\), is the ratio of unbound concentration in whole blood to total concentration in whole blood. Concentrations must refer to the same drug, sampling time, and relevant equilibrium conditions.

Developmental differences in albumin and alpha-1-acid glycoprotein can alter plasma binding, but the direction and size of the effect depend on a drug’s binding properties and other influences, including endogenous competitors. Hematocrit and red-cell partitioning contribute to \(R_b\); a change in hematocrit alone does not determine the direction of the change in \(R_b\). Age-specific measurements or justified parameter values are therefore preferable to applying one adult value across all ages.

Relating Plasma Binding to Whole-Blood Concentration

Suppose \(H\) is hematocrit, expressed as a fraction of whole-blood volume, and \(K_{RBC}=C_{RBC}/C_p\) is the ratio of drug concentration in red cells to that in plasma. Since whole blood consists of plasma and red cells, its total concentration is the volume-weighted average of those concentrations.

C_b=(1-H)C_p+H C_{RBC}

Dividing both sides by \(C_p\) gives the blood-to-plasma ratio. If unbound drug concentrations are equal in plasma and red cells at equilibrium, then the unbound concentration in blood is \(f_{u,p}C_p\). Dividing by total whole-blood concentration gives \(f_{u,b}\).

R_b=1-H+H K_{RBC} \qquad\text{and}\qquad f_{u,b}=\frac{f_{u,p}}{R_b}

The second relationship depends on the stated equilibrium assumption: unbound drug concentrations are equal across the plasma and red-cell phases. It should not be applied blindly when red-cell uptake is not at equilibrium, when measured concentrations are not comparable, or when the model uses a different definition of blood concentration. The first relationship also makes clear why \(R_b\) can change with age: either hematocrit, red-cell partitioning, or both may differ.

Worked Example: Converting Pediatric Plasma Binding to Blood Binding

Consider hypothetical measurements for a child: \(H=0.32\), \(K_{RBC}=1.50\), and \(f_{u,p}=0.080\). Assume equilibrium between unbound concentrations in plasma and red cells. Calculate \(R_b\) and \(f_{u,b}\).

First calculate the blood-to-plasma ratio:

R_b=1-H+H K_{RBC} =1-0.32+(0.32)(1.50) =0.68+0.48 =1.16

Then convert the plasma fraction unbound to a whole-blood fraction unbound:

f_{u,b}=\frac{f_{u,p}}{R_b} =\frac{0.080}{1.16} =0.06897 \approx 0.0690

Thus, under these assumptions, about 6.90% of total drug in whole blood is unbound. This is not the same as the plasma fraction unbound, which is 8.00%; the total whole-blood concentration also includes drug in red cells.

A useful binding model can help interpret why \(f_{u,p}\) may vary. For a single reversible binding site with protein concentration \(P\), association constant \(K_a\), and drug concentration low enough that binding sites are not appreciably saturated, the bound-to-unbound ratio is approximately \(K_aP\). The total-to-unbound ratio is then \(1+K_aP\), yielding:

f_{u,p}\approx\frac{1}{1+K_aP}

This approximation assumes a single binding class, equilibrium, and negligible site saturation. With multiple independent binding proteins at low drug concentration, a corresponding approximation is \(f_{u,p}\approx 1/(1+\sum_i K_{a,i}P_i)\). These expressions explain why a change in protein concentration can change binding, but they are not substitutes for drug-specific measurements when binding is complex or saturable.

Consequences for Distribution and Concentration Interpretation

At a specified total plasma concentration, \(C_p\), the unbound plasma concentration is \(C_{u,p}=f_{u,p}C_p\). Thus, a child and an adult with the same total plasma concentration can have different unbound concentrations if their fractions unbound differ. The unbound concentration is often the more relevant concentration for exchange with tissues, but plasma binding alone does not determine a distribution volume. Tissue binding, tissue composition, permeability, ionization, transport, and the model’s compartment structure also matter.

A simple equilibrium illustration shows the role of binding without implying that it is a complete tissue-distribution prediction. Assume passive equilibrium between plasma and one tissue, equal unbound concentrations in both, and a fixed tissue fraction unbound \(f_{u,t}\). Then \(f_{u,p}C_p=f_{u,t}C_t\), so the total tissue-to-plasma concentration ratio is \(C_t/C_p=f_{u,p}/f_{u,t}\). A change in \(f_{u,p}\) can therefore change this simplified ratio if tissue binding is held fixed. In a pediatric PBPK model, that conclusion must be assessed alongside age-related changes in tissue properties and body composition.

Worked Example: A Simplified Binding Contribution to Distribution

Suppose a hypothetical equilibrium model has a 3.0 L plasma compartment and a 10.0 L peripheral compartment. Assume passive equilibrium, \(f_{u,t}=0.020\), and no age change in tissue binding or compartment volumes. Compare two hypothetical plasma fractions unbound, 0.040 and 0.080. Under these deliberately simplified assumptions, \(K_{p}=C_t/C_p=f_{u,p}/f_{u,t}\), and the apparent total amount per plasma concentration is \(V_{\mathrm{app}}=V_p+V_tK_p\).

For \(f_{u,p}=0.040\):

K_p=\frac{0.040}{0.020}=2.00, \qquad V_{\mathrm{app}}=3.0\text{ L}+(10.0\text{ L})(2.00)=23.0\text{ L}

For \(f_{u,p}=0.080\):

K_p=\frac{0.080}{0.020}=4.00, \qquad V_{\mathrm{app}}=3.0\text{ L}+(10.0\text{ L})(4.00)=43.0\text{ L}

In this constructed example, greater plasma unbinding increases the tissue-to-plasma ratio and the apparent volume because tissue binding and volumes were held fixed. These numbers are not pediatric predictions: real tissue binding, composition, and distribution processes may also change with age.

The blood-to-plasma ratio affects the interpretation of concentrations as well as binding. If \(R_b=1.20\) and a plasma sample contains \(10.0\) mg/L, the corresponding whole-blood concentration under the same sampling conditions is \(12.0\) mg/L. Comparing a whole-blood observation directly with a plasma-based prediction would therefore create a 20% discrepancy even if the model otherwise described the drug correctly. Conversion is appropriate only when the ratio is applicable to the age, concentration range, and conditions of the data.

Implications for Hepatic Clearance

A blood-based well-stirred liver model provides a compact way to show how binding can influence predicted hepatic clearance. Let \(Q_H\) be hepatic blood flow and \(CL_{int}\) intrinsic clearance referenced to unbound drug concentration. The model assumes well-mixed liver blood, steady flow, linear elimination, and that only unbound drug is available for intrinsic elimination. With \(f_{u,b}\) relating unbound concentration to total inlet blood concentration, the model is:

CL_{H,b}=\frac{Q_H f_{u,b}CL_{int}}{Q_H+f_{u,b}CL_{int}}

This clearance is on a whole-blood concentration basis. If a plasma-based clearance is calculated from the same elimination rate and \(C_b=R_bC_p\), then \(CL_{H,p}=R_bCL_{H,b}\), provided the ratio applies consistently. Mixing a plasma-based clearance with blood-based flow or concentration parameters without conversion can yield an internally inconsistent calculation.

Worked Example: Binding and Blood-Based Hepatic Clearance

For a hypothetical drug in a child, let \(Q_H=90.0\) L/h, \(CL_{int}=120\) L/h, and \(f_{u,b}=0.040\). Assume the blood-based well-stirred model conditions hold. Calculate hepatic clearance.

The unbound intrinsic-clearance term is \((0.040)(120)=4.80\) L/h. Substitution gives:

CL_{H,b} =\frac{(90.0)(4.80)}{90.0+4.80} =\frac{432}{94.8} =4.56\text{ L/h}

If, in a second hypothetical age group, \(f_{u,b}=0.080\) while \(Q_H\) and \(CL_{int}\) remain fixed, then:

CL_{H,b} =\frac{(90.0)(0.080)(120)}{90.0+(0.080)(120)} =\frac{864}{99.6} =8.67\text{ L/h}

The modeled blood clearance increases in the second calculation because the unbound fraction is larger. This comparison isolates binding: it does not claim that hepatic flow or intrinsic clearance is actually unchanged across ages. Those parameters may also mature, and their effects must be represented separately.

The model also clarifies two limiting cases. When \(f_{u,b}CL_{int}\) is small relative to \(Q_H\), clearance is approximately \(f_{u,b}CL_{int}\) and is sensitive to changes in binding or intrinsic clearance. When \(f_{u,b}CL_{int}\) is large relative to \(Q_H\), clearance approaches \(Q_H\), so changing binding has less effect on clearance. These limits follow directly by comparing the denominator with its dominant term.

f_{u,b}CL_{int}\ll Q_H: \quad CL_{H,b}\approx f_{u,b}CL_{int}; \qquad f_{u,b}CL_{int}\gg Q_H: \quad CL_{H,b}\approx Q_H

Parameter Checks, Alternatives, and Limitations

Before using an age-specific \(f_{u,p}\) or \(R_b\), check that its basis matches the model and the data. Relevant diagnostics include whether plasma and whole-blood concentrations were measured at comparable times, whether the reported ratio varies across samples or concentrations, whether hematocrit and red-cell partitioning are plausible for the modeled age, and whether measured binding is consistent with the chosen protein-binding assumptions. A single ratio may be inadequate if partitioning is concentration-dependent or differs among age groups.

There are two main practical approaches. A model can use measured age-specific \(f_{u,p}\) and \(R_b\), which captures the observed net effects but may require data that are unavailable for some ages. Alternatively, it can estimate binding and \(R_b\) from protein concentrations, hematocrit, and drug-specific binding or red-cell partition parameters. That mechanistic approach makes assumptions more visible, but errors in any component can propagate into the result. Neither approach justifies treating adult parameters as universally applicable.

The equations here are limited representations. The blood-to-plasma relation assumes a meaningful whole-blood average and a defined red-cell concentration; the conversion to \(f_{u,b}\) relies on equal unbound concentrations. The binding approximations assume specified equilibrium and linearity conditions. The well-stirred clearance model does not represent every hepatic uptake, efflux, or spatial process. A mismatch between predictions and observations should therefore prompt checks of concentration basis and binding assumptions before concluding that ontogeny in enzyme capacity is responsible.

Common pitfall: “The child has a higher plasma fraction unbound, so the whole-blood fraction unbound must be higher by the same amount.” This ignores \(R_b\). Under the equilibrium relation, \(f_{u,b}=f_{u,p}/R_b\); a developmental change in red-cell partitioning can alter the conversion. Calculate or justify both quantities on the concentration basis used by the model.

Key takeaway: Pediatric binding and red-cell partitioning are distinct age-dependent inputs. Use \(f_{u,p}\) to relate total plasma concentration to unbound plasma concentration, use \(R_b\) to convert total plasma and whole-blood concentrations, and convert to \(f_{u,b}\) only under the stated equilibrium assumption.

Check Your Understanding

Answer each question, then compare your reasoning with the solutions below.

A hypothetical child has \(H=0.40\) and \(K_{RBC}=1.00\). Calculate \(R_b\). What does the result imply about total concentrations?
If \(f_{u,p}=0.060\) and \(R_b=1.20\), calculate \(f_{u,b}\) under equal unbound concentrations.
Why can a change in \(f_{u,p}\) affect a simplified tissue-to-plasma ratio without determining a real pediatric distribution volume by itself?
In the blood-based well-stirred model, what happens to \(CL_{H,b}\) when \(f_{u,b}CL_{int}\) is much smaller than \(Q_H\)?
A plasma concentration is 8.0 mg/L and the applicable \(R_b\) is 1.25. What whole-blood concentration corresponds to it?

Solutions. (1) \(R_b=1-0.40+(0.40)(1.00)=1.00\), so total blood and plasma concentrations are equal under this calculation. (2) \(f_{u,b}=0.060/1.20=0.0500\), or 5.00%. (3) Under passive equilibrium with fixed tissue binding, \(C_t/C_p=f_{u,p}/f_{u,t}\); a real pediatric distribution volume also depends on tissue properties, body composition, and other distribution processes. (4) Clearance is approximately \(f_{u,b}CL_{int}\), because the denominator is dominated by \(Q_H\). (5) \(C_b=R_bC_p=(1.25)(8.0)=10.0\) mg/L.