Identifying Determinants of EGFR-Targeted Therapeutic Biochemical Efficacy Using Computational Modeling.

We modeled cellular epidermal growth factor receptor (EGFR) tyrosine phosphorylation dynamics in the presence of receptor-targeting kinase inhibitors (e.g., gefitinib) or antibodies (e.g., cetuximab) to identify systematically the factors that contribute most to the ability of the therapeutics to antagonize EGFR phosphorylation, an effect we define here as biochemical efficacy. Our model identifies distinct processes as controlling gefitinib or cetuximab biochemical efficacy, suggests biochemical efficacy is favored in the presence of certain EGFR ligands, and suggests new drug design principles. For example, the model predicts that gefitinib biochemical efficacy is preferentially sensitive to perturbations in the activity of tyrosine phosphatases regulating EGFR, but that cetuximab biochemical efficacy is preferentially sensitive to perturbations in ligand binding. Our results highlight numerous other considerations that determine biochemical efficacy beyond those reflected by equilibrium affinities. By integrating these considerations, our model also predicts minimum therapeutic combination concentrations to maximally reduce receptor phosphorylation.

For various malignancies, small-molecule inhibitors and antibodies that antagonize the function of oncogenic receptor tyrosine kinases are in use or in clinical trials. For the epidermal growth factor receptor (EGFR), ATP analog kinase inhibitors including gefitinib and erlotinib are approved for non–small cell lung carcinoma and pancreatic cancer,[1,2] and the ligand-competitive monoclonal antibody cetuximab is approved for head and neck and colorectal cancers.[3] While these therapeutics target the same receptor, there may be important determinants of their abilities to antagonize EGFR-initiated signaling beyond the competitive binding processes in which they participate, and those determinants may be unique for different therapeutic classes owing to the different steps of the receptor phosphorylation process at which the therapeutics act. Identifying such determinants may aid in the rational design of next-generation therapeutics targeting EGFR and could provide insight into the differential effectiveness of these therapeutics in vitro and in vivo (e.g., refs. 4,5,6).

Computational modeling represents a useful approach for systematically identifying processes that determine the abilities of therapeutics to antagonize EGFR signal-initiating capacity. Of course, a number of detailed kinetic models of EGFR signaling have been developed with varying levels of complexity (e.g., refs. 7,8,9,10,11). Surprisingly, none of these has been utilized to explore directly the determinants of the ability of different classes of EGFR-targeted therapeutics to interrupt EGFR-initiated signaling. For EGFR and other receptor tyrosine kinases, the well-known model of Cheng and Prusoff[12] has also been invoked to make inferences about therapeutic efficacy (e.g., ref. 13), but the simplicity of this model prevents a full analysis of all receptor-level processes that may influence therapeutic effects (e.g., receptor trafficking).

Here, we build upon a previous model of EGFR phosphorylation dynamics to identify systematically the key receptor-level processes that enable gefitinib and cetuximab to antagonize EGFR phosphorylation in the cellular context. We focus on determinants of EGFR phosphorylation since that is the initial step enabling EGFR to generate downstream signaling. We find that the processes that determine biochemical efficacy (defined here as ability to reduce EGFR tyrosine phosphorylation) extend beyond those involved in equilibrium EGFR-therapeutic binding and differ by therapeutic and ligand. For example, gefitinib and cetuximab are predicted to be more effective when EGFR activation is driven by amphiregulin (AR) than by epidermal growth factor (EGF) due to differences in affinity and time scales for receptor occupancy. EGFR tyrosine dephosphorylation rate is predicted to be a preferentially important determinant of gefitinib biochemical efficacy, while ligand binding rate is a preferentially important determinant of cetuximab biochemical efficacy, again due to differences in relevant process time scales. Our model also predicts how gefitinib and cetuximab can be most efficiently combined to reduce receptor phosphorylation maximally but minimize drug concentrations and redundant effects.

Results

Inhibition of receptor phosphorylation by gefitinib or cetuximab

The model considers the rate processes leading to EGFR phosphorylation in cell surface and interior compartments (). See for definitions and values of rate parameters. Reversibility of all processes is considered, allowing gefitinib and cetuximab to antagonize EGFR phosphorylation not only for already drug-bound receptors but through other rate processes, such as prolonging the dephosphorylated receptor state after receptors are acted upon by protein tyrosine phosphatases (). Throughout these results, we report therapeutic biochemical efficacy in terms of an IC50, defined as the therapeutic concentration required to reduce steady EGFR phosphorylation to half its value in the absence of therapeutic.

We begin by simulating inhibition curves for 10 ng/ml (1.6 nmol/l) EGF or equimolar AR for all ligand/therapeutic combinations (). For cetuximab and gefitinib, the predicted IC50 in the presence of EGF exceeds that for AR by roughly an order of magnitude (). This occurs, in part, because AR's lower affinity reduces receptor occupancy and the dimerization driving force. For either ligand, the predicted IC50 is larger for gefitinib than cetuximab. This occurs, in part, because the particular combinations of species concentrations and binding kinetics disfavor gefitinib's competition with ATP more than cetuximab's with ligand. Additional factors contribute to these differences, as will be discussed. To account for different ligand affinities, we repeated the analysis for a 100-fold increase in AR concentration (). This reduces, but does not eliminate, predicted IC50 differences ().

Effect of ligand and therapeutic binding kinetics on predicted IC50 values for gefitinib and cetuximab

Given that differences in ligand affinity do not fully explain predicted IC50 differences, we performed an analysis assuming constant affinities of ligand (based on EGF) and drug (gefitinib or cetuximab) but varying rate constants for ligand and drug binding and unbinding by an equal “cycling factor” (,). Faster ligand cycling on and off the receptor generally reduces predicted gefitinib and cetuximab IC50. For example, a 10-fold increase in EGF cycling from base values reduces gefitinib or cetuximab IC50 by ~25 or 40%, respectively. This occurs because of a reduced phosphorylation driving force as the time scale for ligand occupancy becomes similar or small compared to the time scale for ligand-bound receptors to become phosphorylated, as reflected by decreased EGFR phosphorylation in the absence of drugs with increasing ligand cycling (vertical grey scale bars in ).

, also show predicted effects of changing gefitinib or cetuximab cycling. Sufficient decreases in gefitinib cycling reduce gefitinib IC50 (), consistent with the notion that irreversible EGFR kinase inhibitors are more effective than reversible inhibitors.[14] This occurs because the receptor is increasingly less likely to rephosphorylate as the time scale with which it remains inhibitor-bound increases. Consistent with this, sensitivity to gefitinib cycling decreases as EGFR cycling through phosphorylated and unphosphorylated states slows (). In contrast, cetuximab's biochemical efficacy is relatively insensitive to changes in cetuximab cycling () because of competing effects. As cetuximab cycling increases, IC50 tends to decrease because cetuximab binds the receptor more slowly than ligand for the base parameters. That effect is offset, however, because the time scale for cetuximab dissociation from EGFR decreases and approaches that for receptor dephosphorylation as cetuximab cycling increases, which increases IC50. The modest net effect of cetuximab cycling on IC50 can be eliminated by reducing receptor dimerization and uncoupling rates () because cetuximab binding and dissociation steps are no longer rate limiting in the competitive processes described above that allow cetuximab cycling to influence IC50. Not surprisingly, IC50 values are also reduced by this parameter alteration.

IC50 sensitivity analysis

To identify other processes that determine IC50, we performed parameter sensitivity analyses. The predicted gefitinib IC50 in the presence of 1.6 nmol/l EGF is most sensitive to perturbations in parameters for ATP binding (k and k), gefitinib binding (k and k), EGFR phosphorylation (k), and EGFR dephosphorylation (k and k) (). Sensitivity to perturbations in ATP and gefitinib binding is anticipated because these parameters control gefitinib/ATP competition. Sensitivity to changes in k, k, and k arises because of the importance of receptor dephosphorylation and phosphorylation cycles in setting steady phosphorylation. The gefitinib IC50 in the presence of 1.6 nmol/l AR is sensitive to perturbations in ATP and gefitinib binding but relatively insensitive to perturbations in k, k, and k because 1.6 nmol/l AR does not promote substantial dimerization or phosphorylation. For 160 nmol/l AR, the number of dimers present at steady-state increases >20-fold, and the model predicts increased sensitivity to perturbations in parameters for ligand-receptor association and dissociation (k and k, respectively), k, k, and k.

For cetuximab, the IC50 in the presence of 1.6 nmol/l EGF is most sensitive to perturbations in k and k, rate constants for EGFR-cetuximab binding (k and k), and rate constants for EGFR internalization and sorting (k and k) (). Competition of cetuximab with ligand for EGFR binding explains sensitivity to cetuximab and EGF binding parameters. Sensitivity to k and k arises because cetuximab binds EGFR at the cell surface, and these parameters control EGFR distribution between the cell surface and interior. is insensitive to perturbations in k, k, or k because cetuximab indirectly disrupts receptor phosphate cycling by preventing receptor monomers from dimerizing. Relatively slow dephosphorylation is sufficient to reduce receptor phosphorylation in this context. For 1.6 nmol/l AR , we observe sensitivity mainly to the cetuximab binding parameters (), which arises because EGFR occupancy is so low that perturbations in AR binding constants cannot promote substantial competition with cetuximab. is relatively insensitive to perturbations in k and k because there is little EGFR internalization for this AR concentration. Increasing AR concentration sensitizes to ligand binding and trafficking parameters, as binding and endocytosis become more robust with the larger AR concentration ().

Note that parameter sensitivity results are not shown in for perturbations to EGFR, GRB2, or ATP concentrations because results for those simulations reflect effects already shown through variations in the parameters that control process steps in which those species are involved. For example, the relative importance of changing EGFR expression is reflected by results for perturbations in receptor dimerization parameters.

Kinetics of therapeutic-mediated reductions in EGFR phosphorylation

Our results suggest that some differences in gefitinib and cetuximab IC50 determinants arise because the kinetics with which phosphorylated receptors become dephosphorylated (and eventually rephosphorylated) in the presence of drugs influence IC50. This dependence arises because of the small time scales for the many reversible processes considered relative to receptor lifetime, and such effects can be observed in calculations of EGFR phosphorylation response to therapeutics. For example, the relative insensitivity of cetuximab IC50 to dephosphorylation kinetics can be elucidated by considering predicted receptor dephosphorylation kinetics in response to cetuximab versus gefitinib after an initial ligand pulse (). Gefitinib reduces EGFR phosphorylation more rapidly than an equimolar dose of cetuximab, as indicated by time scales for phosphorylated EGFR reductions (t50) of 0.2 and 7.7 min, respectively. These differences arise because cetuximab competes with relatively slow dimer uncoupling and ligand dissociation processes, while gefitinib competes with relatively rapid ATP dissociation. Thus, reducing EGFR internalization, to ensure EGFR access to cetuximab, and increasing ligand cycling, which promotes dimer uncoupling, produces nearly identical gefitinib and cetuximab t50 values (). For 1.6 nmol/l or 160 nmol/l AR, the predicted t50 values are similar for the therapeutics because AR cycles more rapidly than EGF (,).

To further identify processes that influence the time scales with which therapeutics reduce receptor phosphorylation, we performed parameter sensitivity analyses for t50 calculations (,). The t50 for 1.6 nmol/l EGF and 1 µmol/l gefitinib is sensitive to perturbations in k and k, k, k and k, k and k, k, and parameters for GRB2-EGFR binding (k and k) (). Sensitivity to k, k, and k is observed because GRB2 binding protects tyrosines from dephosphorylation and because the endosomal compartment is characterized by different kinetics for processes leading to receptor phosphorylation and dephosphorylation. The t50 for 1.6 nmol/l AR and 1 µmol/l gefitinib is most sensitive to perturbations in k, k and k and k. is less sensitive to perturbations in k than because of a reduced dimerization driving force in the presence of AR. For 160 nmol/l AR, sensitivity to perturbations in k increases but is still lower than that for 1.6 nmol/l EGF due to rapid AR dissociation.

The t50 for 1.6 nmol/l EGF and 1 µmol/l cetuximab is most sensitive to changes in k, k, k, k, k, k, and k (). Compared to , is less sensitive to perturbations in dephosphorylation parameters and more sensitive to perturbations in ligand binding parameters because ligand dissociation is more rate-limiting for cetuximab-mediated reductions in EGFR phosphorylation than tyrosine dephosphorylation. The t50 for 1.6 nmol/l AR and 1 µmol/l cetuximab is most sensitive to changes in k, k, k, k, and k. Since AR-EGFR dissociation is more rapid than EGF-EGFR dissociation, dephosphorylation is more rate-limiting for cetuximab-mediated reduction in EGFR phosphorylation in the presence of 1.6 nmol/l AR than 1.6 nmol/l EGF. For 160 nmol/l AR, is sensitive to perturbations in ligand binding parameters, k, GRB2 binding parameters, dephosphorylation parameters, and k. Increasing the AR concentration tends to promote receptor dimerization and phosphorylation, but does not promote receptor internalization as efficiently as 1.6 nmol/l EGF. Thus, remains sensitive to k perturbations.

We repeated this analysis for 50 nmol/l gefitinib or cetuximab to explore differences that may arise with drug concentrations at the lower end of those reported in vivo[15] (Supplementary Figure S1a,b). Relative sensitivity to perturbations in parameters for binding of therapeutics and binding processes with which therapeutic binding competes were increased at these lower drug concentrations due to the fact that drugs are in greater competition for binding to receptors when drug concentrations are reduced. Many of the other parameter sensitivities that were observed for 1 µmol/l drug concentrations were also observed here.

Predicted effects of gefitinib and cetuximab in combination

The clinical utility of combining cetuximab with erlotinib is the focus of ongoing clinical trials (e.g., clinicaltrials.gov ID: NCT00397384). Because our analysis highlights how gefitinib and cetuximab antagonize EGFR phosphorylation through different mechanisms, we used the model to predict the effects of combining cetuximab and gefitinib. For a particular cetuximab or gefitinib concentration, the model predicts that addition of the other therapeutic further decreases steady-state EGFR phosphorylation in the presence of EGF or AR (–). For our model structure, these effects are not synergistic (–). In fact, negative synergies are predicted for all combinations, resulting from redundant effects that are most apparent at high drug concentrations. The most efficient cotreatments would minimize receptor phosphorylation and redundant effects, while using the lowest drug concentrations to avoid off-target toxicity. With this in mind, we estimated combination efficiency by scaling pEGFR, synergy, and the logarithm of the total drug concentration between 0 and 1 and summing these values for each combination (–). This calculation provides new perspectives for how to combine cetuximab and gefitinib optimally. For example, consider the effects of increasing gefitinib concentration for a fixed cetuximab concentration at 1.6 nmol/l EGF. Starting from ~8 nmol/l cetuximab and 10−1 nmol/l gefitinib and increasing gefitinib, efficiency initially decreases until a ~20 nmol/l gefitinib because pEGFR levels are not significantly affected until that point. Beyond ~20 nmol/l gefitinib, efficiency increases beyond its starting point as pEGFR decreases. Efficiency eventually decreases again as drug effects become increasingly redundant. Similar effects occur for AR, but with shifts in efficiency values over the concentration space due to AR's differential ability to drive receptor phosphorylation.

Discussion

Our finding that the abilities of cetuximab and gefitinib to antagonize EGFR phosphorylation are determined by processes beyond those describing equilibrium drug binding motivates new consideration of optimal design strategies for EGFR-targeted therapeutics. To the extent that EGFR phosphorylation level correlates with clinical efficacy, these results also identify possible factors that could underlie the differential effectiveness of the therapeutics among patients. Of course, a number of limitations should be kept in mind in considering the implications of our results. Our analysis implicitly assumes that decreased EGFR phosphorylation will produce more effective therapeutic results. Of course, EGFR transduces signals through numerous pathways, and the integrated effects ultimately determine phenotypic outcomes.[16] Given that receptor–adaptor association is required for downstream signaling, however, computing the IC50 for EGFR-GRB2 complex formation may provide additional insight. Interestingly, the relatively rapid kinetics of EGFR-GRB2 binding,[17] which may not prevail for all EGFR adaptors, produces EGFR-GRB2 complex sensitivity results that are indistinguishable from those for phosphorylated receptor (Supplementary Figure S2a–d). Of course, our analysis also neglects the potential importance of antibody-mediated cytotoxicity and kinase inhibitor off-target effects. These limitations notwithstanding, a number of novel inferences can be drawn from our results.

Our identification of EGFR dephosphorylation kinetics as a key determinant of therapeutic biochemical efficacy is intriguing given that the activities of protein tyrosine phosphatases that regulate EGFR are altered in certain cancer settings.[18] For example, the receptor-like phosphatase protein tyrosine phosphatase receptor-type S (PTPRS) was found deleted in ~25% of head and neck squamous cell carcinomas.[19] PTPRS deletion was associated with elevated EGFR phosphorylation in tumor tissues, and PTPRS knockdown augmented resistance to erlotinib in head and neck squamous cell carcinomas cell lines. Interestingly, head and neck squamous cell carcinomas cell lines displaying cetuximab resistance also displayed decreased PTPRS expression. Our model does predict some cetuximab IC50 dependence on EGFR dephosphorylation kinetics, but it also predicts that other factors are stronger determinants of cetuximab's ability to reduce EGFR phosphorylation.

Our results also predict IC50 dependence on the rates of drug and ligand association and dissociation, even for constant affinities. Our prediction that slowing EGFR-gefitinib binding and dissociation cycling decreases IC50 is consistent with the observation that slower erlotinib cycling promotes growth inhibition of lung and brain cancer cells.[20] Importantly, Barkovich et al.[20] noted that slower erlotinib cycling did not correlate with reduced EGFR phosphorylation, possibly due to the relatively high concentrations of erlotinib required for an effect on cell growth. Our prediction that ligand association and dissociation kinetics affect IC50 suggests that different EGFR ligands, which may bind EGFR with different kinetics,[21] may result in different therapeutic IC50 values. Relative mRNA levels of different EGFR ligands generally vary among cells, as in gastric and colon cancer cell lines.[22] Thus, variable therapeutic responses among cells or tumors could be partially related to differential ligand expression profiles.

While our model predicts cetuximab IC50 sensitivity to k perturbations, only modest k sensitivity is predicted for gefitinib (). This occurs because cetuximab binds EGFR only at the cell surface, while gefitinib is available to EGFR in both cellular compartments. This is interesting to consider in light of findings that increased EGFR internalization, driven by ERK2 amplification, can increase the IC50 for WZ4002, an irreversible EGFR inhibitor, in PC9 cells.[23] The basis for this effect remains unknown, but it could result from lower protein tyrosine phosphatase activity against EGFR in the endosomal compartment versus the membrane in PC9 cells. In that scenario, increasing receptor internalization would increase gefitinib IC50. Interestingly, cetuximab resistance correlates with increased EGFR ubiquitination in colorectal cancer cells generated through prolonged cetuximab exposure,[24] which could also be related to EGFR internalization effects.[25] Other studies have linked impaired EGFR internalization with cetuximab resistance.[26] Such inconsistencies may occur because endocytosis perturbations can arise for a variety of reasons, with varied consequences for downstream signaling.

Methods

Model topology

A kinetic model of EGFR phosphorylation at a representative tyrosine was implemented using a framework similar to one previously described,[27] but with several alterations. The updated model includes kinetics for cetuximab binding to EGFR's extracellular domain and for intracellular GRB2 binding to the phosphorylated receptor, and assumes that GRB2-bound receptors internalize at experimentally measured rates for EGFR endocytosis.[27] Note that data for EGFR Y1068 dynamics are used for model training (described below), and that EGFR Y1068 is the primary GRB2 binding site in the EGFR cytoplasmic tail.[28] The model considers cell surface and interior compartments (), with the interior (endosomal) volume modeled as before.[27] In each compartment, EGFR monomers reversibly bind ligands and ATP and homodimerize. Ligands and ATP also reversibly bind receptor dimers. Dimerized, ATP-bound receptors undergo phosphorylation characterized by rate constants k or k, depending on receptor-ligand occupancy. In the surface compartment, phosphorylated receptors are dephosphorylated or bind GRB2, which plays a general adaptor role because of its signaling and endocytosis functions.[29,30] GRB2-bound receptors in the surface compartment irreversibly move to the endosome.[29] Dephosphorylation at the cell surface and in the cell interior are characterized by parameters k and k, respectively. Rules for model reactions are further explained in Supplementary Materials. Model parameters are provided in .

Asymmetric receptor dimers

In our previous model,[27] only symmetric receptor dimerizations were permitted (e.g., a ligand-bound EGFR could only dimerize with another ligand-bound EGFR) to limit model combinatorial complexity. In the updated model, we allowed for asymmetric dimerization with respect to ligand occupancy to reflect an updated structural understanding of dimers.[31]

EGFR-therapeutic binding

Gefitinib is assumed to compete with ATP regardless of EGFR localization. The model assumes that cetuximab binds only surface-localized non-ligand-bound EGFR monomers.[3] Cetuximab is modeled as a monovalent binder of EGFR to focus on a more straightforward comparison between drugs that compete with single ligand or ATP binding events in the extracellular or intracellular compartments, respectively, but the slightly enhanced binding affinity observed for the bivalent full-length antibody[32] was used in model parameterization. Note that monovalent cetuximab fragments potently reduce EGFR phosphorylation in cultured cells.[32] Cetuximab-bound species are permitted to internalize, but cetuximab dissociation is not permitted in the endosome by considering numerical issues. Given that EGFR–cetuximab dissociation and endosomal exit rate constants are of similar magnitude (), this assumption should not significantly affect model predictions.

The model allows cetuximab and gefitinib to antagonize phosphorylation through processes beyond the static sequestration of EGFR from entering the overall path leading to phosphorylation. For example, cetuximab can bind to phosphorylated receptors generated through uncoupling of phosphorylated dimers and dissociation of ligand (), preventing receptors from re-dimerizing and -phosphorylating after dephosphorylation. Similarly, gefitinib can bind phosphorylated receptors after ADP dissociation, antagonizing further rounds of phosphorylation ().

EGFR ligands

EGF binding constants were based on experimental measurements.[21,33] AR was assumed to dissociate from EGFR 100 times faster than EGF, based on studies suggesting that AR has a larger dissociation constant (K),[34] is 50–300 times less potent in cell growth assays,[35] and less efficiently promotes EGFR phosphorylation, CBL association, and ubiquitination.[36] Ligand binding affinities were assumed in the endosome due to the known effects of reduced pH in that compartment.[21] With the differences in ligand binding kinetics for EGF and AR, our model recapitulates published experimental findings that AR is much less efficient than EGF in promoting EGFR endocytosis,[37] with model-predicted specific rate constants for receptor endocytosis of 0.01 or 0.13 min−1 for 1.6 nmol/l AR or EGF, respectively.

Comparing therapeutics

For fixed concentration comparisons, we assumed 1 μmol/l or 50 nmol/l for gefitinib and cetuximab. 1 μmol/l significantly exceeds the binding constant of either therapeutic with EGFR (2.1 nmol/l for gefitinib and 5.2 nmol/l for cetuximab)[1,38] and is consistent with some reports of achievable therapeutic concentrations in vivo.[39,40] 50 nmol/l concentrations were used in some calculations to span the range of concentrations reported in vivo.[15]

Inhibition curves and IC50 calculations

We defined IC50 as the therapeutic concentration at which steady EGFR phosphorylation was reduced to half its value in the absence of therapeutic, a definition used in other studies (e.g., ref. 41). Inhibition curves were simulated by computing steady EGFR phosphorylation in the presence of ligand over a range of therapeutic concentrations. In making these calculations, we lumped all phosphorylated receptors regardless of binding partners or localization. EGFR degradation and synthesis were not considered due to the computationally intensive algorithm needed to determine the synthesis rate with the specific model structure implemented here.[27]

Pulse-chase curves and t50 calculation

To quantify the rate with which therapeutics reduce EGFR phosphorylation, we simulated 5 min treatments of cells with ligands followed by 1 μmol/l or 50 nmol/l therapeutic chases. t50 is defined as the time required for 50% of the maximum possible reduction in EGFR phosphorylation. For these calculations, EGFR degradation was not permitted in order to reach a steady state.

Sensitivity analysis

To quantify the relative importance of receptor-level processes in determining IC50 and t50, we computed sensitivities to model parameter perturbations. Sensitivity was defined as the absolute value of the difference in the logarithm of IC50 or t values between the perturbed and base parameter values, summed over all perturbations with parameters perturbed by 10- or 0.1-fold.

Model training

To capture realistic EGFR dephosphorylation kinetics, we fit k and k using our published data for EGFR Y1068 phosphorylation response to EGF, pervanadate, and gefitinib (Supplementary Figure S3a–c), as previously described.[27] Twenty fits were run, with small variations among results. The k and k values producing the lowest residual were chosen (). These values were slightly increased compared to those in our previous study,[27] due to the updated model's consideration of GRB2 binding to EGFR, which protects EGFR phosphotyrosines from dephosphorylation.

Representative cell

Cells were assumed to express 5.0 × 104 EGFR[42] and 2.1 × 105 GRB2.[43] ATP concentration was assumed to be 1 mmol/l.[44] EGFR internalization was assumed to be consistent with a specific endocytosis rate constant of 0.13 min−1,[45] using an algorithm described previously.[27]

Author Contributions.

C.S.M. and M.J.L. designed the research, analyzed the data, and wrote the manuscript. C.S.M. performed the research.

Conflicts of Interest.

The authors declared no conflicts of interest.

Study Highlights

Table 1

Model parameters