DDMODEL00000106: Krippendorff model for receptor-mediated endocytosis

  public model
Short description:
Model for receptor-mediated endocytosis (RME) proposed in Krippendorff et al., J Pharmacokinet Pharmacodyn 36(3):239-60, 2009. The model features saturable distribution into the receptor system and linear degradation, used as a PK model ("model B"). The model can be used for simulation; it is not possible to estimate all model parameters with the provided dataset. Data are from a PK study of Zalutumumab in Cynomolgus monkey (kindly provided by Genmab). The context of the data is described in more detail in Lammerts van Bueren et al, Cancer Res 66(15):7630-8, 2006.
PharmML (0.6.1)
  • Nonlinear pharmacokinetics of therapeutic proteins resulting from receptor mediated endocytosis.
  • Krippendorff BF, Kuester K, Kloft C, Huisinga W
  • Journal of pharmacokinetics and pharmacodynamics, 6/2009, Volume 36, Issue 3, pages: 239-260
  • Hamilton Institute, National University of Ireland Maynooth, Maynooth, Ireland.
  • Receptor mediated endocytosis (RME) plays a major role in the disposition of therapeutic protein drugs in the body. It is suspected to be a major source of nonlinear pharmacokinetic behavior observed in clinical pharmacokinetic data. So far, mostly empirical or semi-mechanistic approaches have been used to represent RME. A thorough understanding of the impact of the properties of the drug and of the receptor system on the resulting nonlinear disposition is still missing, as is how to best represent RME in pharmacokinetic models. In this article, we present a detailed mechanistic model of RME that explicitly takes into account receptor binding and trafficking inside the cell and that is used to derive reduced models of RME which retain a mechanistic interpretation. We find that RME can be described by an extended Michaelis-Menten model that accounts for both the distribution and the elimination aspect of RME. If the amount of drug in the receptor system is negligible a standard Michaelis-Menten model is capable of describing the elimination by RME. Notably, a receptor system can efficiently eliminate drug from the extracellular space even if the total number of receptors is small. We find that drug elimination by RME can result in substantial nonlinear pharmacokinetics. The extent of nonlinearity is higher for drug/receptor systems with higher receptor availability at the membrane, or faster internalization and degradation of extracellular drug. Our approach is exemplified for the epidermal growth factor receptor system.
Niklas Hartung, Zinnia Parra-Guillen
Context of model development: Mechanistic Understanding;
Model compliance with original publication: Yes;
Model implementation requiring submitter’s additional knowledge: No;
Modelling context description: To mechanisically understand the dynamics of receptor-mediated endocytosis;
Modelling task in scope: simulation;
Nature of research: Fundamental/Basic research;
Annotations are correct.
This model is not certified.
  • Model owner: Zinnia Parra-Guillen
  • Submitted: Dec 12, 2015 12:38:40 PM
  • Last Modified: Jul 15, 2016 10:12:13 AM
  • Version: 15 public model Download this version
    • Submitted on: Jul 15, 2016 10:12:13 AM
    • Submitted by: Niklas Hartung
    • With comment: Updated model annotations.
  • Version: 13 public model Download this version
    • Submitted on: Jun 13, 2016 9:50:19 AM
    • Submitted by: Niklas Hartung
    • With comment: Updated model annotations.
  • Version: 10 public model Download this version
    • Submitted on: Jan 18, 2016 1:37:33 PM
    • Submitted by: Niklas Hartung
    • With comment: Edited model metadata online.
  • Version: 6 public model Download this version
    • Submitted on: Dec 12, 2015 12:38:40 PM
    • Submitted by: Zinnia Parra-Guillen
    • With comment: Edited model metadata online.

Independent variable TIME

Function Definitions

proportionalError(proportional,f)=(proportional ×f)

Structural Model sm

Variable definitions

C_ex=(0.5 ×(((C2-Bmax)-Km)+(((C2-Bmax)-Km)2+((4 ×Km) ×C2))))
C_RS=(Bmax ×C_ex)(Km+C_ex)
dA1dTIME=(((q21 ×C_ex)-(q12 ×C1))-(CL_lin ×C1))
dA2dTIME=(((q12 ×C1)-(q21 ×C_ex))-(CL_RS ×C_RS))
Ypred=(1000 ×C1)

Initial conditions


Variability Model

Level Type





Parameter Model

EPS_YN(0.0,1.0) — DV

Observation Model

Observation Y
Continuous / Residual Data

Y=(Ypred+(proportionalError(RUV,Ypred) ×EPS_Y))

Estimation Steps

Estimation Step estimStep_1

Estimation parameters

Fixed parameters

  • POP_Km=5.0E-4
  • POP_Bmax=0.02875
  • POP_q12=1.505
  • POP_q21=3.01
  • POP_CL_lin=0.1925
  • POP_CL_RS=0.35
  • POP_V1=35
  • POP_V2=70

Initial estimates for non-fixed parameters

Estimation operations
1) Estimate the population parameters
    Algorithm SAEM

    Step Dependencies

    • estimStep_1