# DDMODEL00000106: Krippendorff model for receptor-mediated endocytosis

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.
 Format: PharmML (0.6.1) Related Publication: .hiddenContent {display:none;} 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 Affiliation: Hamilton Institute, National University of Ireland Maynooth, Maynooth, Ireland. Abstract: 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. Contributors: 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;
 Validation Status: Annotations are correct. Certification Comment: This model is not certified.
• Model owner: Zinnia Parra-Guillen
• Submitted: Dec 12, 2015 12:38:40 PM
##### Revisions
• Version: 15
• Submitted on: Jul 15, 2016 10:12:13 AM
• Submitted by: Niklas Hartung
• With comment: Updated model annotations.
• Version: 13
• Submitted on: Jun 13, 2016 9:50:19 AM
• Submitted by: Niklas Hartung
• With comment: Updated model annotations.
• Version: 10
• Submitted on: Jan 18, 2016 1:37:33 PM
• Submitted by: Niklas Hartung
• With comment: Edited model metadata online.
• Version: 6
• 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

$C1=A1V1$
$C2=A2V2$
$C_ex=(0.5 ×(((C2-Bmax)-Km)+(((C2-Bmax)-Km)2+((4 ×Km) ×C2))))$
$C_RS=(Bmax ×C_ex)(Km+C_ex)$
$dA1dTIME=(((q21 ×C_ex)-(q12 ×C1))-(CL_lin ×C1))$
$dA2dTIME=(((q12 ×C1)-(q21 ×C_ex))-(CL_RS ×C_RS))$
$Ypred=(1000 ×C1)$

Initial conditions

$A1=0$
$A2=0$

### Variability Model

Level Type

DV

residualError

ID

parameterVariability

### Parameter Model

Parameters
$POP_Km$ $POP_Bmax$ $POP_q12$ $POP_q21$ $POP_CL_lin$ $POP_CL_RS$ $POP_V1$ $POP_V2$ $RUV$
$EPS_Y∼N(0.0,1.0)$ — DV
$Km=POP_Km$
$Bmax=POP_Bmax$
$q12=POP_q12$
$q21=POP_q21$
$CL_lin=POP_CL_lin$
$CL_RS=POP_CL_RS$
$V1=POP_V1$
$V2=POP_V2$

### Observation Model

#### Observation YContinuous / Residual Data

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

### 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

$RUV=0.1$
##### Estimation operations
1) Estimate the population parameters
Algorithm SAEM

### Step Dependencies

• estimStep_1