Predicting the F(ab)mediated effect of monoclonal antibodies in vivo by combining celllevel kinetic and pharmacokinetic modelling
Abstract
Celllevel kinetic models for therapeutically relevant processes increasingly benefit the early stages of drug development. Later stages of the drug development processes, however, rely on pharmacokinetic compartment models while celllevel dynamics are typically neglected. We here present a systematic approach to integrate celllevel kinetic models and pharmacokinetic compartment models. Incorporating target dynamics into pharmacokinetic models is especially useful for the development of therapeutic antibodies because their effect and pharmacokinetics are inherently interdependent. The approach is illustrated by analysing the F(ab)mediated inhibitory effect of therapeutic antibodies targeting the epidermal growth factor receptor. We build a multilevel model for antiEGFR antibodies by combining a systems biology model with in vitro determined parameters and a pharmacokinetic model based on in vivo pharmacokinetic data. Using this model, we investigated in silico the impact of biochemical properties of antiEGFR antibodies on their F(ab)mediated inhibitory effect. The multilevel model suggests that the F(ab)mediated inhibitory effect saturates with increasing drugreceptor affinity, thereby limiting the impact of increasing antibody affinity on improving the effect. This indicates that observed differences in the therapeutic effects of high affinity antibodies in the market and in clinical development may result mainly from Fcmediated indirect mechanisms such as antibodydependent cell cytotoxicity.
Keywords
Celllevel kinetics Pharmacokinetic models Therapeutic proteins EGFRIntroduction
Biotechnologically engineered proteins such as monoclonal antibodies (mAbs) have demonstrated their potential in therapies for cancer and other complex diseases [1]. Due to their ability to specifically bind targets, they allow to modulate specific cellular targets and signaling pathways. Various therapeutic proteins on the market use their binding specificity to inhibit cell surface receptors with critical biologic function. At the same time, many targeted receptor systems also constitute a degradation mechanism for such drugs because binding leads to endocytosis and ultimately degradation of the drug. A thorough understanding of the complex interplay between a drug’s pharmacokinetics and its effect is largely missing.
Empirical or semimechanistic compartmental models are typically used to analyze preclinical or clinical pharmacokinetic data of protein drugs [2, 3, 4, 5, 6]. In these models, the interaction of the drug with its target is represented by an empirical or semimechanistic term, accounting for the saturable degradation capacity of the target system. Further, models of target mediated drug disposition (TMDD) have been proposed as a general semimechanistic model for drugs that bind with high affinity and to a significant extent to a pharmacologic target such as an enzyme, receptor, or transporter [7, 8, 9]. This is accomplished by describing the target as an additional binding compartment.
In systems biology, detailed mechanistic models of targets at the cell level have proven valuable for identifying potent drug targets [10]. Such mathematical models allow identifying and ranking potential targets in cellular networks for achieving specific downstream effects [11, 12]. A recent prominent example is the use of a kinetic model to identify critical components in ErbB signaling pathways [13] and was the basis for the development of a therapeutic antibody that targets the ErbB3 receptor and is currently in Phase II clinical trials [14].
Linking pharmacokinetic and systems biology modelling approaches allows a multilevel description of the system as a whole. These kinds of systems pharmacology models are therefore increasingly advocated by researchers as well as regulators [15]. A combined model for a drugs’ pharmacokinetic and its cellular effect would be especially valuable for therapeutic proteins where drug effect and pharmacokinetics are inherently interdependent. As models of both, wholebody pharmacokinetics and cellular target dynamics, are becoming more abundant, the main bottleneck in developing multilevel systems pharmacology models is in how to interface the cellular and whole body layers levels.
The objective of this article is to develop a systematic approach to integrate the cellularlevel into compartment models of drug pharmacokinetics. Due to their important role in the treatment of cancer, we have developed a celllevel pharmacokinetic/pharmacodynamic model for antibodies antagonistically inhibiting the epidermal growth factor receptor (EGFR). The binding of one of its natural ligands to the EGFR results in the activation of signal transduction pathways that mediate a variety of cellular responses [16] which include cell proliferation, differentiation, survival, and angiogenesis [17]. We illustrate our approach by developing a celllevel PK/PD model for the antiEGFR therapeutic antibody zalutumumab in cynomolgus monkeys. The model integrates a compartment model developed based on in vivo plasma data for zalutumumab [6], and a receptor trafficking model based on in vitro data of the EGFR [18, 19, 20, 21, 22, 23, 24].
mAbs comprise a variable targetspecific F(ab) region and aconstant Fc region [4]. The targetspecific part recognizes the targeted protein, whereas the constant part is involved in different mechanism which determine the pharmacokinetics as well as trigger indirect therapeutic effects such as triggering antibodydependent cell cytotoxicity. Using our combined model and integrating preclinical pharmacokinetic data we have investigated in silico the impact of biochemical properties of antiEGFR antibodies on the F(ab)mediated inhibitory effect. This new kind of model allows to identify in silico opportunities and limitations for the optimization of biophysical properties of future therapeutic antibodies.
Theoretical
Compartment model of in vivo therapeutic antibody pharmacokinetics
Pharmacokinetic parameters determined in vivo by Lammerts van Bueren et al. [16]
Name  Definition  Value  Unit 

V_{pla}  Plasma volume  70  ml/kg 
V_{int}  Interstitial volume  35  ml/kg 
k_{pi}  Rate constant of plasmainterstitial transport  0.043  1/h 
k_{ip}  Rate constant of interstitialplasma transport  0.043  1/h 
k_{b}  Constant thatensures quasisteady state conditions  0.069  1/h 
B_{max,PK}  Wholebody capacity  2  mg/h/kg 
K_{M,PK}  Halfmaximal binding capacity in vivo  \(0.5 \cdot 10^{3}\)  mg/ml 
k_{el}  Elimination of EGFR by internalization and degradation  0.0055  1/h 
q_{pi}  Plasmainterstitial transport  \(V_{\rm pla}\cdot k_{\rm pi}\)  ml/h 
q_{ip}  Interstitialplasma transport  \(V_{\rm int}\cdot k_{\rm ip}\)  ml/h 
CL_{lin}  Targetindependent drug clearance  \(V_{\rm pla} \cdot {\rm k_{el}}\)  ml/h/kg 
In the above model of Lammerts van Bueren et al., the interaction of zalutumumab with its target (represented by the Michaelis Menten term) accounts for the nonlinear feedback of the receptor system on the mAb concentration in the interstitial space, known as receptor mediated endocytosis. With regard to drug effect, the above model does not allow us, however, to analyze the inhibitory effect of zalutumumab on the targeted receptors. Moreover, the Michaelis Menten interaction term is a hybrid parameter in the sense that it combines drug related properties—like binding and dissociation rate constants as well as internalisation rate constants—with receptor system parameters—like receptor synthesis, degradation and internalization [28]. As a consequence, the parameters B_{max PK} and K_{M,PK} are specific to zalutumuab. An analysis of the impact of changes in the drugreceptor interaction is not feasible with this model, nor is the study of the impact of different cell types, like normal and tumor cells, on the PK and PD of the therapeutic antibody. Both tasks, however, are feasible at the single cell level using kinetic models of the targeted receptor system.
Kinetic model of in vitro ligandreceptor interaction
where the SF_{unit} = 10^{9}/N_{avog} denotes a scaling factor from [#molecules] to [nmol] with \(N_{\rm avo}=6.02 \cdot 10^{23}\) 1/mol denoting Avogardo’s constant. We included those biological processes which are expected to have an impact on the PK of the drug and provide a possibility to link detailed systems biology model of downstream signalling pathway.
To study the inhibitory potential of a therapeutic antibody on a signalling pathway, realistic timedependent concentration time profiles are essential. As discussed, for many therapeutic antibodies, the targeted system also has an influence on the timecourse of the antibody via receptor mediated drug uptake and degradation. Hence, not only has the drug an effect on the receptor system, but also does the receptor system impact on the pharmacokinetics of the drug. As a consequence, we herein propose a novel approach based on integrating the singlecell level into compartment models of antibody PK.
Linking wholebody and singlecell level
On the wholebody level, the interaction of zalutumumab with its target is represented by a Michaelis Menten term that describes the apparent drugreceptor interactions. At the cellular level, this apparent interaction comprises several kinetic processes, including association and dissociation of the drugreceptor complex, internalization and subsequent degradation of the internalized drugreceptor complex. The assumption underlying our approach is that the apparent drugreceptor interaction on the wholebody level collectively represents the drugreceptor interaction of all relevant cells at the cellular level, i.e., all target–expressing cells that are exposed to the drug. The idea is then to replace the apparent drugreceptor interaction in the compartment model (1–3) by the detailed celllevel model (7–11), scaled from the singlecell to the wholebody level with the number of relevant cells. As a result of this integration process, we obtained a celllevel PK/PD model that allowed us to study the pharmacokinetics on the wholebody level and at the same time the inhibitory effect on the cellular level. For the integration, we determined (i) the apparent drugreceptor interaction of a single cell; and (ii) number of all relevant cells N_{cell} as the scaling factor that links the apparent drugreceptor interaction of a singlecell to the apparent drugreceptor interaction of the wholebody level.
Note that the maximal binding capacity B_{max cell} is only a function of the receptor system and independent of any drug properties, while the MichaelisMenten constant K_{M,cell} depends nonlinearly on both, receptor parameters as well as drug parameters. Due to the above relationship (14–15), we are able to explicitly compute the parameters B_{max cell} and K_{M,cell} based on the in vitro determined parameters k_{synR}, k_{degR}, k_{degRC}, k_{recyRi}, k_{onL}, k_{offL}, k_{degRL} of the singlecell model, the in vivo determined EGF concentration L, and the drugspecific parameters k_{onC}, k_{offC}, k_{degRC}.
Next, we present our approach based on a single cell type as a reference cell. We remark that the underlying compartment model including the linear clearance part was taken from the model by Lammerts van Bueren et al. as stated in Eqs. 1–3. In the second part of this article we then extend the celllevel PK/PD model to include multiple reference cell type (tumor and normal cells). Along the same lines, entire distributions of cell types could be integrated e.g., to account for spatial inhomogeneities as they are expected in solid tumors.
Celllevel pharmacokinetic/pharmacodynamic model
that describe the rate of change of the therapeutic antibody in plasma C_{pla} and in the interstitial space C_{int}, the free receptor R, the internalized receptor R_{i}, the drugreceptor complex RC, the EGF ligand in the interstitial space L and the ligandreceptor complex RL. Rather than just reestimating parameters of the singlecell PK/PD model, the above approach established a mechanistic link between the kinetic model of the receptor system at the singlecell level and the apparent term in the wholebody compartment model. As part of our approach, we provided a systematic way of determining an apparent drugreceptor model from a detailed celllevel description. This has been further elaborated in [28], where we have also shown that the reduced model (12–13) is a more appropriate description of the apparent drugreceptor interaction in the compartment model (1–3), since it eliminates the use of the artificial rate constant k_{b}.
Measures of receptor saturation, residual activity and inhibition
We analyzed the impact of mAb treatment of target cells with respect to three quantitative measures. The measures of transient response are illustrated in Fig. 2c and are defined as follows:
 The integral of inhibition: Cumulative EGF receptors that are not activated as a consequence of drug treatment. More formally, the integral of inhibition is defined as area under the curve of the active receptors with respect to their steady state pretreatment level RL^{*}, i.e.,$$ \begin{aligned} E = \int\limits_{0}^{\infty} (RL^{*}  RL(t)) dt. \end{aligned} $$(27)
 The peak inhibition: Maximal reduction in activated EGFR as a fraction of pretreatment level RL^{*}:$$ {\rm peak} = {\frac{RL^{*}  \min\{ RL\}}{RL^{*}}}. $$(28)
The duration of inhibition: Time needed to recover to 75% of the predrug level of activated receptors.
The chosen measures of inhibition resemble important characteristics of drug effect. For small molecule drugs, the integral of inhibition (exposure) is often related to the drug effect, while the peak inhibition or the duration of inhibition (measuring some threshold characteristics) are often related to the side effects.
Celllevel pharmacokinetic/pharmacodynamic model with normal and tumor cells
Methods
For the singlecell PK/PD model with normal cells only, the system is assumed to be in steady state prior to any drug administration, resulting in a number of free receptors R^{*}, active receptors RL^{*}, and zero drug–receptor complexes RC^{*} = 0. Similarly, for the model with normal and tumor cells, the steady state levels are defined by R_{N}^{*}, RL_{N}^{*}, and RC_{N}^{*} = 0, R_{T}^{*}, RL_{T}^{*}, and RC_{T}^{*} = 0.
Parameter values for the EGF receptor system
Name  Definition  Value  Unit  References 

k_{onL}  Ligand–receptor binding  \(7.2\cdot10^{2}\)  1/(nM\(\cdot\)min)  [20] 
k_{offL}  Ligand–receptor unbinding  0.34  1/min  [20] 
k_{degR}  Free receptor internalization  0.03  1/min  [20] 
k_{degRL}  Ligand–receptor complex internalization  0.03  1/min  [20] 
k_{R,N}  Receptor expression rate in normal cells  130  Receptors/min per cell  [20] 
k_{recyRi}  Free receptor recycling  \(5.8\cdot 10^{2}\)  1/min  [20] 
k_{degRi}  Free receptor degradation  \(2.2\cdot 10^{3}\)  1/min  [20] 
k_{onC}  Drug–receptor binding  k_{onL}  1/(nM\(\cdot\)min) 

k_{degRC}  Drug–receptor complex internalization  0.005  1/h  [6] 
MW_{mAbs}  Molecular weight  148000  Dalton (g/mol) 

Results
Predicting the inhibitory effect of the antiEGFR therapeutic antibody zalutumumab in cynomolgus monkeys
We determined a singlecell PK/PD model for the antiEGFR therapeutic antibody zalutumumab in cynomolgus monkeys. The model based on in vivo data for zalutumumab in cynomolgus monkeys [6], in vitro data of human fibroblast cells [29, 20] and determined drugreceptor affinities [35]. Importantly, our approach does not involve any fitting of parameters; all parameter values were either inherited from the original compartment model, determined in vitro, or explicitly calculated.
Evaluation against in vivo data
Dose (mg)  In vivo experiment  In silico prediction 

2  Not fully saturated  Max. 60 % saturated 
20  Fully saturated  100% saturated 
40  Fully saturated  100% saturated 
Predicting residual EGFR activity per cell
The celllevel PK/PD model then was used to predict the number of activated receptors over the duration of the treatment, which is difficult to examine in vivo. Our model predicted that the low dose (2 mg/kg) of antibody reduces the number of active receptors by about 35%. The steep initial decrease in receptor activation is followed by a recovery period secondary to a slow reduction of drug concentration (Fig. 3b). On the other hand, the higher dose (20 mg/kg) almost completely inhibited receptor activation for a period of about 20 days. The start of the recovery period coincided with the transition from saturated to linear pharmacokinetics between days 20 and 25. The model therefore suggests that changes in pharmacokinetics mays act as a biomarker for changes in the inhibitory response.
Comparing receptor saturation (25) with residual receptor activity (26), we found that both characteristics only corresponded initially, while at later points in time the receptor saturation underestimated the inhibitory effect of the antibody (e.g. compare with the 20 mg/kg dose after 50 days). This highlights the importance of adopting an integrated kinetic model to translate the binding of the drug into its actual inhibitory effect on receptor activation.
Impact of drug characteristics on receptor inhibition
One advantage of the celllevel PK/PD model is its ability to predict the impact of drug properties such as the dose, drugreceptor affinity, and drug induced receptor internalization on the inhibitory response under in vivo conditions. We assumed that the target independent PK distribution parameters V_{pla}, V_{int}, q_{pi} and q_{ip} do not change when changing properties of the F(ab) region. Since all the analyzed antibodies are either of IgG1 or IgG2 isotype, their targetindependent clearance was also assumed to be identical [36].
Affinity and dose
Affinities and isotypes of the different therapeutic antibodies against the EGFR. Values taken from Peipp et al. [35]
Antibody  Affinity/avidity (M)  Isotype 

Panitumumab  \(5\cdot 10^{11}\)  IgG2 
Cetuximab  \(4\cdot 10^{10}\)  IgG1 
IMC11F8  \(3\cdot 10^{10}\)  IgG1 
Nimotuzumab  \(1\cdot 10^{9}\)  IgG1 
Zalutumumab  \(7\cdot 10^{9}\)  IgG1 
Downregulation
Receptor downregulation denotes the druginduced process of the reducing the number of free receptor at the membrane that is available for binding to the natural ligand. Enforcing receptor downregulation by therapeutic antibodies is argued to be an important part of the drug effect [17]. In Fig. 4b–d, we predicted the inhibitory effect of antibodies with a 5fold and 10fold increased internalization rate constant (relative to the rate constant of zalutumumab) for different affinities and low and high doses. We found that for highaffinity antibodies, receptor downregulation only contributes to a negligible extent to the F(ab)mediated direct inhibitory effect. For medium affinity antibodies, however, an increased downregulation rate constant could increase the direct inhibitory effect to some extent.
Tumor cell specificity
Upregulation of EGFR expression and aberrant activation of EGFR has been shown in many human epithelial cancers, including those of the colon, lung, kidney, head and neck, breast, prostate, brain and ovary [38, 39, 40, 41, 42, 43]. The extent of overexpression also correlates with a poorer clinical outcome [44, 45].
Figure 5b compares the predicted transient inhibition for both alterations, increased synthesis rate and reduced internalization. For both alterations, the inhibitory ef fect is strong er for tumor cells than for cells with nor mal EGFR levels. Although both cell alterations resulted in similar steadystate activation levels, their responses to mAbs are remarkably different with cells with decreased receptor internalization showing a higher integral and duration of inhibition compared to cells with an increased synthesis of the receptor.
Discussion
The objective of this article was to develop a systematic approach to integrate the cellularlevel into compartment models of drug PK, and to apply the approach to analyze the F(ab)mediated inhibitory effect of therapeutic antibodies in cancer therapy.
Several mAbs on the market have a high receptor affinity in the subnM range, but the traditional design criterion that “the best binder makes the best drug” has been challenged [47, 48, 49]. Using our combined model we evaluated the effect of different affinities of antibodies targeting the EGFR. In cynomolgus monkeys, our celllevel PK/PD model predicts almost identical F(ab)mediated direct inhibitory effects for a range of antigenbinding affinities. Since current antiEGFR antibodies are located on the observed effect plateau, this relativizes the affinity amongst the properties that could be further tuned to optimize antibody efficacy.
A high affinity is thought to allow panitumumab to compete more effectively with EGF in binding to EGFR and to saturate EGFR in vivo at lower doses relative to mAbs with lower affinity [16]. This is not supported by our analysis, and instead our findings predict that the F(ab)mediated effect of panitumumab and cetuximab are comparable. This prediction of the model is in agreement with experimental results by Messersmith and Hidalgo [50]. We further investigated if this result is due to the specific values of the parameters we used to simulate the model by calculating an analytically solution of the integral of the effect. The analytical solution shows that the existence of an effect plateau is a generic feature of this drugtarget system and does not depend on specific parameter values. Therefore this result suggest that such an effect plateau might exist for other receptor systems with receptor trafficking.
Crombet et al. [48] argued that the low degree of adverse effects observed for Nimotuzumab in the clinics is due to its intermediate affinity compared to other antiEGFR antibodies. Their conclusions are based on a mathematical model that only takes into account receptor binding, but neglects the important process of receptor internalization and target specific degradation. Based on our singlecell PK/PD model for cynomolgus monkeys, we find that an intermediate affinity does not result in optimized tumor effect or specificity. Recently, Talavera et al. [51] suggested an alternative explanation for the low degree of adverse effects observed for Nimotuzumab.
Based on the existence of an effect plateau in the F(ab)mediated direct inhibitory effect, our findings suggest that the clinically observed differences among mAbs are likely to arise from Fcmediated indirect effects, such as the action of immune effector functions (such as antibody dependent cell mediated cytotoxicity or complement dependent cytotoxicity), rather than the direct antagonistic effect. This is consistent with a study of Bleeker et al. showing that effects in vivo of zalutumumab and cetuximab differed only by their ability to trigger such indirect effect and not by their direct inhibitory effect [25]. Possible extensions of the model could address the likelihood of triggering such Fcmediated indirect effects. Since the model predicts the time course of the different receptor species, it may serve as a starting point to estimate the proportion of bound antibody that are presented to the extracellular space and trigger Fcmediated immune effects.
Alterations of a number of kinetic processes can result in elevated EGFR levels. The combined systems biology/ pharmacokinetic model allows us to study two different tumor cell alterations with elevated EGFR levels resulting from (i) an increased receptor synthesis rate; and (ii) a decreased receptor internalization rate. Both types have been observed experimentally [46, 32, 34]. We found that receptor inhibition over time strongly depends on the underlying molecular alteration that caused the elevated EGFR level.
Our in silico studies show that the inhibitory effects at normal and tumor cells are correlated, and therefore support the hypothesis that the side effects may serve as a marker for the desired effect at the tumor cells. This is in line with experimental observations that the most common side effect of antiEGFR antibodies are cutaneous toxicities, affecting 45–100% of patients [52]. Since this skin rash follows from the inhibition of epidermal cells expressing normal levels of the EGFR, using the rash as a marker of drug activity and clinical outcome was proposed [53] and our theoretical study supports this.
The compartment model (1–3) describes the distribution of the drug to the target expressing cells. In this case we described distribution as reversible linear process as previously done when relating plasma concentration to potential pharmacodynamic effect [54]. However, processes such as convective movement, lymphatic circulation and filter effects can affect the distribution of antibodies. In these cases, detailed models for antibody distribution e.g. a two pore model (Rippe and Haraldsson, 1994, Physiological reviews) could be integrated into the model. Further, predictions of EGFR inhibition in tumor cells are limited to those malignant cells which are exposed to similar concentrations than normal cells, such as avascular metastases embedded in healthy tissue [55, 56]. In solid tumors, due to heterogeneous drug distribution, only malignant cells close to capillaries may be exposed to such concentration. Taken together, more detailed models of mAbs distribution, such as physiologically based pharmacokinetics models [57, 58], should be included in cases where distribution of the drug to target cells can not be described by reversible linear processes. The current model also predicts only the decrease in receptor activation rather than the actual biological response of the cell. While Knauer et al. [29] reported a linear dependence between the number of activated EGFR at steadystate and the cellular responses of fibroblasts and epithelial cells, other models describe a more complex relationship between receptor activation and downstream signalling [59].
Established models to study antibody pharmacokinetics include models of TMDD (e.g., Gibiansky et al. [8, 9]). Our celllevel PK/PD model has three important differences compared to TMDD models. First, the model includes the competition of natural ligands with the antibodies for the binding to the receptor. This allows us to study the change of the number of receptorligand complexes due to the drug treatment. Second, the model includes more details of the cellular mechanisms. For example, the internal pool of receptors and the recycling to the cell surface are part of the detailed receptor trafficking model, but not of current models of TMDD. We investigated if we could remove this pool together with receptor recycling to make the model more TMDDlike. However, we found this internal pool to be important to describe the initial PK without refitting of the experimentally derived parameters. Our findings support the hypothesis in [6] stating that “possibly, EGFR surface expression can temporarily be replenished with EGFR present in the cell”. Third, and most notably, our celllevel PK/PD model integrates in vitro determined parameter values instead of fitting all parameters to the in vivo data. This is useful to avoid overparamerization of the model, which has be reported to be a critical problem when using the original TMDD model [8].
Combining modelling approaches from pharmacokinetics and systems biology allows us to quantitatively analyse the dynamic interaction between drugs and biological systems [15]. One remaining question concerns the validation of multilevel models. We here used the approach to validate the model prediction using pharmacokinetic data while integrating an in vitro validated celllevel model. Furthermore, we validated the full model using available PK data together with limited PD data. Ideally however, validation should be done using datasets that integrate pharmacokinetic and celllevel data (e.g. receptor phosphorylation) from one source.
We envision that a celllevel PK/PD modeling approach will prove valuable in the emerging field of systems pharmacology. The use of more detailed systems biology models describing downstream signaling processes relevant to human diseases [13, 60, 61] may eventually allow to translate plasma drug concentration into responses of tumor cells.
Footnotes
 1.
We transformed the originally published system of difference equations [6, Supplement] into a corresponding continuous system of ordinary differential equations. The originally published equations in [6, Supplement] are identical to a certain discretization of the system of ODEs (1–3). The advantage of stating the system as continuous ODEs is that subsequently any numerical scheme can be used to solve them, in particular high accuracy ODE solver with adaptive step size control. See also [28].
Notes
Acknowledgments
The authors kindly thank Wim Bleeker (Genmab, Utrecht, The Netherlands) for providing the experimental plasma concentrationtime data shown in Fig. 3. B. K. and W. H. acknowledge fruitful discussions with Charlotte Kloft (Clinical Pharmacy, Freie Universität Berlin, Germany) and helpful comments on the manuscript from Richard Abadi (University of Manchester/UK), Ken R. Duffy (NUIM/Ireland), and Cormac Taylor (UCD/Ireland). W. H. and B.F. K. received funding from Merck Serono for their research.
Open Access
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References
 1.Meibohm B (2007) The role of pharmacokinetics and pharmacodynamics in the development of biotech drugs. In: Meibohm B (ed) Pharmacokinetics and pharmacodynamics of biotech drugs: principles and case studies in drug development. WileyVCH, WeinheimGoogle Scholar
 2.Dirks NL, Nolting A, Kovar A, Meibohm B (2008) Population pharmacokinetics of cetuximab in patients with squamous cell carcinoma of the head and neck. J Clin Pharmacol 48:267–78PubMedCrossRefGoogle Scholar
 3.Kuester K, Kovar A, Lüpfert C, Brockhaus B, Kloft C (2008) Population pharmacokinetic data analysis of three phase I studies of matuzumab, a humanised antiEGFR monoclonal antibody in clinical cancer development. Br J Cancer 98:9006CrossRefGoogle Scholar
 4.Mould DR, Sweeney KRD (2007) The pharmacokinetics and pharmacodynamics of monoclonal antibodies–mechanistic modeling applied to drug development. Curr Opin Drug Discov Devel 10:84–96PubMedGoogle Scholar
 5.Kloft C, Graefe EU, Tanswell P, Scott AM, Hofheinz R, Amelsberg A, Karlsson MO (2004) Population pharmacokinetics of sibrotuzumab, a novel therapeutic monoclonal antibody, in cancer patients. Invest New Drugs 22:3952CrossRefGoogle Scholar
 6.Lammerts van Bueren JJ, Bleeker WK, Bøgh HO, Houtkamp M, Schuurman J, van de Winkel JGJ, Parren PWHI (2006) Effect of target dynamics on pharmacokinetics of a novel therapeutic antibody against the epidermal growth factor receptor: implications for the mechanisms of action. Cancer Res 66:7630–8PubMedCrossRefGoogle Scholar
 7.Mager DE, Jusko WJ (2001) General pharmacokinetic model for drugs exhibiting targetmediated drug disposition. J Pharmacokinet Pharmacodyn 28:507–32PubMedCrossRefGoogle Scholar
 8.Gibiansky L, Gibiansky E, Kakkar T, Ma P (2008) Approximations of the targetmediated drug disposition model and identifiability of model parameters. J Pharmacokinet Pharmacodyn 35:573–591PubMedCrossRefGoogle Scholar
 9.Gibiansky L, Gibiansky E (2009) Targetmediated drug disposition model: relationships with indirect response models and application to population PKPD analysis. J Pharmacokinet Pharmacodyn 36:341–351PubMedCrossRefGoogle Scholar
 10.Hood L, Perlmutter RM (2004) The impact of systems approaches on biological problems in drug discovery. Nat Biotechnol 22:1215–7PubMedCrossRefGoogle Scholar
 11.Kitano H (2007) A robustnessbased approach to systemsoriented drug design. Nat Rev Drug Discov 6:202–10PubMedCrossRefGoogle Scholar
 12.Kreeger PK, Lauffenburger DA (2010) Cancer systems biology: a network modeling perspective. Carcinogenesis 31:2–8PubMedCrossRefGoogle Scholar
 13.Chen WW, Schoeberl B, Jasper PJ, Niepel M, Nielsen UB, Lauffenburger DA, Sorger PK (2009) Inputoutput behavior of ErbB signaling pathways as revealed by a mass action model trained against dynamic data. Mol Syst Biol 5:239PubMedGoogle Scholar
 14.Schoeberl B, Pace EA, Fitzgerald JB, Harms BD, Xu L, Nie L, Linggi B, Kalra A, Paragas V, Bukhalid R, Grantcharova V, Kohli N, West KA, Leszczyniecka M, Feldhaus MJ, Kudla AJ, Nielsen UB (2009) Therapeutically targeting ErbB3: a key node in ligandinduced activation of the ErbB receptorPI3K axis. Sci Signal 2:ra31PubMedCrossRefGoogle Scholar
 15.van der Graaf PH, Benson N (2011) Systems pharmacology: bridging systems biology and pharmacokineticspharmacodynamics (PKPD) in drug discovery and development. Pharm res 28:1460–1464PubMedCrossRefGoogle Scholar
 16.Jakobovits A, Amado R, Yang X, Roskos L, Schwab G (2007) From XenoMouse technology to panitumumab, the first fully human antibody product from transgenic mice. Nat Biotechnol 25:1134–1143PubMedCrossRefGoogle Scholar
 17.Mendelsohn J (2003) Status of epidermal growth factor receptor antagonists in the biology and treatment of cancer. J Clin Oncol 21:2787–2799PubMedCrossRefGoogle Scholar
 18.Fujita KA, Toyoshima Y, Uda S, Ozaki YI, Kubota H, Kuroda S (2010) Decoupling of receptor and downstream signals in the Akt pathway by Its lowpass filter characteristics. Sci Signal 3:ra56PubMedCrossRefGoogle Scholar
 19.Shankaran H, Resat H, Wiley HS (2007) Cell surface receptors for signal transduction and ligand transport: a design principles study. PLoS Comput Biol 3:e101PubMedCrossRefGoogle Scholar
 20.Starbuck C, Lauffenburger DA (1992) Mathematical model for the effects of epidermal growth factor receptor trafficking dynamics on fibroblast proliferation responses. Biotechnol Prog 8:132–43PubMedCrossRefGoogle Scholar
 21.Shankaran H, Wiley HS, Resat H (2007) Receptor downregulation and desensitization enhance the information processing ability of signalling receptors. BMC Syst Biol 1:48PubMedCrossRefGoogle Scholar
 22.Hendriks BS, Orr G, Wells A, Wiley HS, Lauffenburger DA (2005) Parsing ERK activation reveals quantitatively equivalent contributions from epidermal growth factor receptor and HER2 in human mammary epithelial cells. J Biol Chem 280:6157–6169PubMedCrossRefGoogle Scholar
 23.Hendriks BS, Opresko LK, Wiley HS, Lauffenburger DA (2003) Quantitative analysis of HER2mediated effects on HER2 and epidermal growth factor receptor endocytosis: distribution of homo and heterodimers depends on relative HER2 levels. J Biol Chem 278:23343–23351PubMedCrossRefGoogle Scholar
 24.Hendriks BS, Opresko LK, Wiley HS, Lauffenburger DA (2003) Coregulation of epidermal growth factor receptor/human epidermal growth factor receptor 2 (HER2) levels and locations: quantitative analysis of HER2 overexpression effects. Cancer res 63:1130–1137PubMedGoogle Scholar
 25.Bleeker WK, Lammertsvan Bueren JJ, van Ojik HH, Gerritsen AF, Pluyter M, Houtkamp M, Halk E, Goldstein J, Schuurman J, van Dijk MA, van de Winkel JGJ, Parren PWHI (2004) Dual mode of action of a human antiepidermal growth factor receptor monoclonal antibody for cancer therapy. J Immunol 173:4699–707PubMedGoogle Scholar
 26.Bastholt L, Specht L, Jensen K, Brun E, Loft A, Petersen J, Kastberg H, Eriksen JG (2007) Phase I/II clinical and pharmacokinetic study evaluating a fully human monoclonal antibody against EGFr (HuMaxEGFr) in patients with advanced squamous cell carcinoma of the head and neck. Radiother Oncol 85:24–8PubMedCrossRefGoogle Scholar
 27.Tang L, Persky A, Hochhaus G, Meibohm B (2004) Pharmacokinetic aspects of biotechnology products. J Pharm Sci 93:2184–2204PubMedCrossRefGoogle Scholar
 28.Krippendorff BF, Kuester K, Kloft C, Huisinga W (2009) Nonlinear pharmacokinetics of therapeutic proteins resulting from receptor mediated endocytosis. J Pharmacokinet Pharmacodyn 36:239–60PubMedCrossRefGoogle Scholar
 29.Knauer DJ, Wiley HS, Cunningham DD (1984) Relationship between epidermal growth factor receptor occupancy and mitogenic response. Quantitative analysis using a steady state model system. J Biol Chem 259:5623–31PubMedGoogle Scholar
 30.Brzeziński J, Lewiński A (1998) Increased plasma concentration of epidermal growth factor in female patients with nontoxic nodular goitre. Eur J Endocrinol 138:388–93PubMedCrossRefGoogle Scholar
 31.Masui H, Castro L, Mendelsohn J (1993) Consumption of EGF by A431 cells: evidence for receptor recycling. J Cell Biol 120:85–93PubMedCrossRefGoogle Scholar
 32.Lin C, Chen W, Kruiger W, Stolarsky L, Weber W, Evans R, Verma I, Gill G, Rosenfeld M (1984) Expression cloning of human EGF receptor complementary DNA: gene amplification and three related messenger RNA products in A431 cells. Sci Agric 224:843–8PubMedCrossRefGoogle Scholar
 33.Ullrich A, Ullrich A, Coussens L, Coussens L, Hayflick JS, Hayflick JS, Dull TJ, Dull TJ, Gray A, Gray A, Tam AW, Tam AW, Lee J, Lee J, Yarden Y, Yarden Y, Libermann TA, Libermann TA, Schlessinger J, Schlessinger J et al (1984) Human epidermal growth factor receptor cDNA sequence and aberrant expression of the amplified gene in A431 epidermoid carcinoma cells. Nature 309:418–425PubMedCrossRefGoogle Scholar
 34.Reddy CC, Wells A, Lauffenburger DA (1994) Proliferative response of fibroblasts expressing internalizationdeficient epidermal growth factor (EGF) receptors is altered via differential EGF depletion effect. Biotechnol Prog 10:377–84PubMedCrossRefGoogle Scholar
 35.Peipp M, Dechant M, Valerius T (2008) Effector mechanisms of therapeutic antibodies against ErbB receptors. Curr Opin Immunol 20:436–43PubMedCrossRefGoogle Scholar
 36.Morell A, Terry W, Waldmann T (1970) Metabolic properties of IgG subclasses in man. J Clin Invest 49:673–680PubMedCrossRefGoogle Scholar
 37.Yang X, Jia X, Corvalan J, Wang P, Davis C (2001) Development of ABXEGF, a fully human antiEGF receptor monoclonal antibody, for cancer therapy. Crit Rev Oncol Hematol 38:17–23PubMedCrossRefGoogle Scholar
 38.Sargent ER, Gomella LG, Belldegrun A, Linehan WM, Kasid A (1989) Epidermal growth factor receptor gene expression in normal human kidney and renal cell carcinoma. J Urol 142:1364–8PubMedGoogle Scholar
 39.Ogiso Y, Oikawa T, Kondo N, Kuzumaki N, Sugihara T, Ohura T (1988) Expression of protooncogenes in normal and tumor tissues of human skin. J Invest Dermatol 90:841–4PubMedCrossRefGoogle Scholar
 40.Sakai K, Mori S, Kawamoto T, Taniguchi S, Kobori O, Morioka Y, Kuroki T, Kano K (1986) Expression of epidermal growth factor receptors on normal human gastric epithelia and gastric carcinomas. J Natl Cancer Inst 77:1047–52PubMedGoogle Scholar
 41.van der Laan BF, Freeman JL, Asa SL (1995) Expression of growth factors and growth factor receptors in normal and tumorous human thyroid tissues. Thyroid 5:67–73PubMedCrossRefGoogle Scholar
 42.HenzenLogmans SC, van der Burg ME, Foekens JA, Berns PM, Brussée R, Fieret JH, Klijn JG, Chadha S, Rodenburg CJ (1992) Occurrence of epidermal growth factor receptors in benign and malignant ovarian tumors and normal ovarian tissues: an immunohistochemical study. J Cancer Res Clin Oncol 118:303–307PubMedCrossRefGoogle Scholar
 43.Terada T, Ohta T, Nakanuma Y (1994) Expression of transforming growth factoralpha and its receptor during human liver development and maturation. Virchows Archiv Int J Pathol 424:669–675CrossRefGoogle Scholar
 44.Mendelsohn J (2002) Targeting the epidermal growth factor receptor for cancer therapy. J Clin Oncol 20:1S–13SPubMedGoogle Scholar
 45.Grandis JR, Melhem MF, Gooding WE, Day R, Holst VA, Wagener MM, Drenning SD, Tweardy DJ (1998) Levels of TGFalpha and EGFR protein in head and neck squamous cell carcinoma and patient survival. J Natl Cancer Inst 90:824–32CrossRefGoogle Scholar
 46.Merlino G, Xu Y, Ishii S, Clark A, Semba K, Toyoshima K, Yamamoto T, Pastan I (1984) Amplification and enhanced expression of the epidermal growth factor receptor gene in A431 human carcinoma cells. Science 224:417PubMedCrossRefGoogle Scholar
 47.Rao BM, Lauffenburger DA, Wittrup KD (2005) Integrating celllevel kinetic modeling into the design of engineered protein therapeutics. Nat Biotechnol 23:191–4PubMedCrossRefGoogle Scholar
 48.Crombet T, Osorio M, Cruz T, Roca C, del Castillo R, Mon R, IznagaEscobar N, Figueredo R, Koropatnick J, Renginfo E, Fernández E, Alvárez D, Torres O, Ramos M, Leonard I, Pérez R, Lage A (2004) Use of the humanized antiepidermal growth factor receptor monoclonal antibody hR3 in combination with radiotherapy in the treatment of locally advanced head and neck cancer patients. J Clin Oncol 22:1646–54PubMedCrossRefGoogle Scholar
 49.Carter P (2001) Improving the efficacy of antibodybased cancer therapies. Nat Rev Cancer 1:118–129PubMedCrossRefGoogle Scholar
 50.Messersmith W, Hidalgo M (2007) Panitumumab, a monoclonal anti epidermal growth factor receptor antibody in colorectal cancer: Another one or the one?. Clin Cancer Res 13:4664PubMedCrossRefGoogle Scholar
 51.Talavera A, Friemann R, GómezPuerta S, MartinezFleites C, Garrido G, Rabasa A, LópezRequena A, Pupo A, Johansen RF, Sánchez O, Krengel U, Moreno E (2009) Nimotuzumab, an antitumor antibody that targets the epidermal growth factor receptor, blocks ligand binding while permitting the active receptor conformation. Cancer res 69:5851–5859PubMedCrossRefGoogle Scholar
 52.Lacouture ME (2006) Mechanisms of cutaneous toxicities to EGFR inhibitors. Nat Rev Cancer 6:803–12PubMedCrossRefGoogle Scholar
 53.PerézSoler R, Saltz L (2005) Cutaneous adverse effects with HER1/EGFRtargeted agents: is there a silver lining?. J Clin Oncol 23:5235–46PubMedCrossRefGoogle Scholar
 54.Agoram B (2007) Use of pharmacokinetic/pharmacodynamic modelling for starting dose selection in firstinhuman trials of highrisk biologics. Br J Clin Pharmacol 67:53–160Google Scholar
 55.Thurber GM, Schmidt MM, Wittrup KD (2008) Antibody tumor penetration: transport opposed by systemic and antigenmediated clearance. Adv Drug Deliv Rev 60:1421–1434PubMedCrossRefGoogle Scholar
 56.Thurber G, Schmidt M, Wittrup KD (2008) Factors determining antibody distribution in tumors. Trends Pharm Sci 29:57–61PubMedGoogle Scholar
 57.Urva S, Yang V, Balthasar J (2009) Physiologically based pharmacokinetic model for T84.66: a monoclonal antiCEA antibody. J Pharm Sci :1–19Google Scholar
 58.Davda JP, Jain M, Batra SK, Gwilt PR, Robinson DH (2008) A physiologically based pharmacokinetic (PBPK) model to characterize and predict the disposition of monoclonal antibody CC49 and its single chain Fv constructs. Int Immunopharmacol 8:401–13PubMedCrossRefGoogle Scholar
 59.Schoeberl B, EichlerJonsson C, Gilles ED, Mueller G (2002) Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors. Nat Biotechnol 20:370–5PubMedCrossRefGoogle Scholar
 60.Borisov N, Aksamitiene E, Kiyatkin A, Legewie S, Berkhout J, Maiwald T, Kaimachnikov NP, Timmer J, Hoek JB, Kholodenko BN (2009) Systemslevel interactions between insulinEGF networks amplify mitogenic signaling. Mol Syst Biol 5:256PubMedCrossRefGoogle Scholar
 61.Kholodenko BN (2006) Cellsignalling dynamics in time and space. Natl Rev Mol Cell Biol 7:165–76CrossRefGoogle Scholar