Byun, J. H. | Search bioRxiv

bioRxiv2026

Derivation and theoretical validation of fractional quasi-steady state approximation (fQSSA) for target-mediated drug disposition models with memory effects

Standard target-mediated drug disposition (TMDD) models are widely used to describe nonlinear pharmacokinetics driven by high-affinity drug-target interactions. However, their reliance on instantaneous binding limits their ability to capture delayed and history-dependent dynamics observed in vivo. Here, we introduce a fractional TMDD model that incorporates memory effects through a fractional derivative, thereby generalizing the standard TMDD (sTMDD) framework. Although this fractional TMDD (fTMDD) formulation increases modeling flexibility, it also exacerbates parameter identifiability challenges under typical experimental conditions where only drug concentration data are available. To address this limitation, we derive a fractional quasi-steady-state approximation (fQSSA) that reduces model dimensionality while preserving essential nonlinear and memory-dependent pharmacokinetic dynamics. We further establish an explicit validity condition that quantifies the approximation error of both fTMDD and fQSSA without requiring numerical simulation. This condition reveals that the initial drug-to-target ratio is the primary determinant of QSSA validity, whereas the fractional order has a comparatively minor influence. Application of the proposed framework to recombinant human erythropoietin (rhEPO) data demonstrates that fractional dynamics play a population-dependent role, improving model performance in adults but not in infants. Together, this work provides the first systematic derivation of a QSSA framework for fractional TMDD models, along with rigorous and computable applicability conditions. Our results establish a principled foundation for incorporating memory effects into pharmacokinetic modeling and offer a generalizable framework for nonlinear PK-PD systems involving binding-mediated dynamics. Author summaryMany drugs interact strongly with their biological targets, leading to complex and nonlinear pharmacokinetics that are commonly described using target-mediated drug disposition (TMDD) models. However, these models assume that drug-target interactions occur instantaneously, which limits their ability to capture delayed and history-dependent behaviors observed in real biological systems. In this study, we develop a new modeling framework that incorporates such memory effects by extending TMDD models using fractional calculus. To make the model more practical and computationally efficient, we derive a simplified version based on a quasi-steady-state approximation (QSSA) and provide a clear mathematical condition that determines when this simplification is valid. Our analysis shows that the accuracy of the simplified model is primarily controlled by the initial ratio of drug to target, while the influence of memory effects is comparatively smaller. When applied to experimental data for erythropoietin, our model reveals that memory effects are important in adults but negligible in infants, suggesting that these effects may reflect underlying physiological differences. Overall, this work provides a systematic and interpretable framework for incorporating memory effects into pharmacokinetic modeling, with potential applications to a wide range of drug systems involving complex binding dynamics.

pharmacology and toxicology↗

bioRxiv2026

Real world data based evaluation of a novel target-mediated drug disposition approximation model

Target-mediated drug disposition (TMDD) models have been widely used to describe nonlinear pharmacokinetic profiles driven by high-affinity, low-capacity drug-target binding. A pTMDD model, derived by applying the Pade approximation of the quasi-steady-state (QSS) model (qTMDD) was previously proposed. Although pTMDD model showed a comparable estimation accuracy while maintaining computational efficiency, further validation in realistic clinical scenarios and comprehensive performance evaluations have been needed to assess its practical applicability. Here, we evaluated the pTMDD model using five clinical datasets and extended the previous study that focused on simulations. Using the full TMDD as a reference, the approximation models were compared in terms of the parameter estimation results (parameter estimates, relative standard error values and model diagnostics) and computational efficiency (estimation and bootstrap runtimes). The pTMDD model, previously validated in simulation settings, also preserved the estimation accuracy while reducing the computation time of the clinical data. Both pTMDD and qTMDD remained close to the full TMDD model, whereas Michaelis-Menten TMDD (mTMDD) model showed substantial discrepancies especially at low doses, including biased estimates for key TMDD-related parameters (e.g., kdeg, kint, krec, and kup) and higher objective function values. Moreover, pTMDD was faster than qTMDD in four of the five cases compared to the full TMDD. The time savings were particularly pronounced for larger datasets, supporting the computational efficiency of pTMDD. Q2PCONV, an R Shiny application that converts NONMEM code from qTMDD to pTMDD, was also developed, thereby making this new approximation more accessible to researchers. The findings support pTMDD as a practical alternative to existing TMDD approximation models. Author SummaryTarget-mediated drug disposition (TMDD) models describe a high-affinity, low-capacity binding between drug and its target. To avoid overparameterization, approximation models have been used. The two primary models are Michaelis-Menten model (mTMDD), which is accurate only at high doses, and Quasi-steady-state (qTMDD), which is accurate in wider ranges but requires longer runtime. We have proposed a new approximation model named pTMDD. Here, we evaluated pTMDD using five real clinical trial datasets to assess its practical usefulness. pTMDD produced parameter estimates closer to those from the full TMDD model and showed lower uncertainty than both the full TMDD and mTMDD models. In terms of computational efficiency, pTMDD reduced estimation time by an average of 11% and bootstrap time by an average of 6% relative to qTMDD across cases. In addition, we also developed an R shiny application to help researchers apply pTMDD in practice. Our work supports pTMDD as a practical and efficient tool for TMDD modeling in drug development.

pharmacology and toxicology↗