Pubertal Changes in Enzyme and Transporter Activity

Why Puberty May Matter in Pediatric PBPK

A pediatric simulation can represent development by age, body size, or a developmental characteristic such as puberty stage. These are related, but they do not answer the same biological question. Age indexes elapsed development; size describes growth; puberty stage characterizes a developmental process that may coincide with changes in some enzyme or transporter systems. A model that uses only age or size can miss a stage-associated pattern. A model that adds puberty stage without adequate evidence can instead encode noise, duplicate an existing maturation effect, or imply a biological change that was not demonstrated.

The relevant evidence is system-specific. An observed difference in enzyme abundance, catalytic activity, or transporter function does not automatically establish a corresponding difference in drug clearance. The substrate, tissue, assay, other clearance pathways, and the direction of transporter action all matter. In PBPK, the question is therefore not simply whether activity differs by stage, but whether the evidence supports a defensible change to the relevant model parameter and improves predictions for the intended population.

What Counts as Evidence?

Evidence may come from tissue measurements, in vitro assays, probe-substrate pharmacokinetics, or clinical data interpreted with a mechanistic model. Each measures a different link in the chain. Abundance is not identical to catalytic activity; activity measured for one substrate is not necessarily interchangeable with activity for another; and a change in one pathway may have a small effect on total clearance if other pathways dominate. For transporters, an increase in activity can increase uptake into a tissue or increase efflux out of it, with different consequences for tissue exposure and systemic disposition.

A useful evidence review asks whether puberty stage was measured directly or inferred from age, whether the age and size distributions overlap across stages, and whether the measured endpoint is relevant to the simulated pathway. It also checks assay conditions, sample size, uncertainty, and consistency across data sources. Longitudinal observations can help distinguish within-person developmental change from differences between groups, although they still require suitable measurements and interpretation. Cross-sectional comparisons may be informative, but stage groups that differ substantially in age or size cannot cleanly isolate a stage association.

The earlier material on enzyme maturation, body-size scaling, age-dependent enzyme capacity, transporter ontogeny, and enzyme–transporter co-maturation provides the components that a puberty-stage representation must complement. The key modeling decision here is whether stage explains a supported pattern beyond those components, rather than being used as a substitute for them.

Three Ways to Represent Development

For comparison, let \(a\) denote age, \(W\) body weight, and \(S\) a recorded puberty stage. Let \(C\) be a model output such as a simplified enzyme-mediated capacity, scaled relative to an adult reference \(C_{\mathrm{adult}}\). The following equations illustrate alternative covariate choices; they are not replacements for the tissue and flow equations of a full PBPK model.

An age-only function can be appropriate when the available evidence supports age as a sufficient predictor for the intended simulation. A size-only representation may describe body-size scaling, but it cannot distinguish children of similar size who differ in stage. A stage term can represent a residual stage pattern, but requires enough data to estimate it and a clear reference stage. If stage groups are represented by categories, a set of stage-specific multipliers is often more defensible than assuming that each one-stage increase produces the same increment. The combined formula is a simplifying illustration; in a PBPK model, scaling organ quantity and enzyme activity must be defined consistently to avoid multiplying the same size effect twice.

Deriving a Stage Multiplier From Matched Comparisons

A simple justification for a stage multiplier follows from comparing observations at similar age and size. Suppose a measured activity \(A\) is represented as a baseline \(A_0\), an age contribution, a size contribution, and a stage multiplier:

For two individuals or groups matched on age and size, the terms \(A_0\), \(M_{\mathrm{age}}(a)\), and \((W/W_{\mathrm{ref}})^b\) are the same. Dividing the later-stage prediction by the earlier-stage prediction cancels those common terms:

If the earlier stage is the reference, set \(P(S_{\mathrm{earlier}})=1\). The observed matched activity ratio then estimates the later-stage multiplier. This argument depends on the matching assumption: if age, size, assay conditions, or other relevant factors differ, the ratio cannot be attributed to stage alone. It also assumes the multiplicative form is a reasonable representation over the comparison being made.

Comparing Representations in a Simulation

A fair comparison uses the same population, drug assumptions, and simulation design, changing only the developmental representation under evaluation. Consider a simplified hypothetical comparison of predictions against four held-out, normalized observations. The observed values are 0.60, 0.68, 0.80, and 0.95. An age-only model predicts 0.63, 0.70, 0.77, and 0.82; a model with a supported stage term predicts 0.61, 0.69, 0.81, and 0.93. For these values, the root mean squared error (RMSE) is the square root of the mean squared prediction error.

Diagnostics, Pitfalls, and Limits

Before retaining a stage term, check whether each relevant stage is represented by enough observations and whether the comparisons have meaningful overlap in age and size. If nearly all younger children are in one stage and nearly all older children are in another, a model may be unable to distinguish an age pattern from a stage pattern. Also check that stage is measured consistently, the assay or clinical endpoint maps to the pathway in the model, and the direction of the simulated change agrees with the biological role of the enzyme or transporter.

Compare predictions and residuals across stages, not only a single overall error statistic. A lower training error after adding stage is expected to be possible because the expanded model has more flexibility; it is not sufficient evidence of improvement. Use held-out or otherwise independent evidence when available, and examine whether estimates are sensitive to sparse stage groups or the choice of stage coding. For transporters, evaluate the relevant tissue and transport direction rather than assuming that “higher activity” means lower plasma concentration.

Common mistake: “The later-stage group has higher activity, so puberty increases clearance by the same percentage.” This reasoning skips the possibility that the groups differ in age, size, assay characteristics, or other pathways, and it equates measured activity with systemic clearance. The correction is to treat the observed difference as evidence for a testable, pathway-specific model term; isolate it as far as the data allow; then evaluate its effect on PBPK predictions and uncertainty.

No single representation is best for every enzyme, transporter, substrate, or age range. Stage-specific covariates are limited by measurement quality, sparse data, and overlap with other developmental variables. A simple age-only or size-only model may be preferable when stage evidence is weak or when the intended application does not justify the added complexity. Conversely, a well-supported stage term can improve biological specificity when it explains relevant information beyond the other components.