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Systems Modeling Identifies Divergent Receptor Tyrosine Kinase Reprogramming to MAPK Pathway Inhibition ALLISON M. CLAAS, 1 LYLA ATTA, 1 SIMON GORDONOV, 1 AARON S. MEYER, 2 and DOUGLAS A. LAUFFENBURGER 1 1 Department of Biological Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA; and 2 Department of Bioengineering, Jonsson Comprehensive Cancer Center, Eli and Edythe Broad Center of Regenerative Medicine and Stem Cell Research, University of California, Los Angeles, Los Angeles, CA 90095, USA (Received 22 May 2018; accepted 17 July 2018; published online 26 July 2018) Associate Editor Michael R. King oversaw the review of this article. Abstract Introduction—Targeted cancer therapeutics have demon- strated more limited clinical efficacy than anticipated, due to both intrinsic and acquired drug resistance. Underlying mechanisms have been largely attributed to genetic changes, but a substantial proportion of resistance observations remain unexplained by genomic properties. Emerging evi- dence shows that receptor tyrosine kinase (RTK) reprogram- ming is a major alternative process causing targeted drug resistance, separate from genetic alterations. Hence, the contributions of mechanisms leading to this process need to be more rigorously assessed. Methods—To parse contributions of multiple mechanisms to RTK reprogramming, we have developed a quantitative multi-receptor and multi-mechanistic experimental frame- work and kinetic model. Results—We find that RTK reprogramming mechanisms are disparate among RTKs and nodes of intervention in the MAPK pathway. Mek inhibition induces increased Axl and Her2 levels in triple negative breast cancer (TNBC) cells while Met and EGFR levels remain unchanged, with Axl and Her2 sharing re-wiring through increased synthesis and differing secondary contributing mechanisms. While three Mek inhibitors exhibited mechanistic similarity, three Erk inhibitors elicited effects different from the Mek inhibitors and from each other, with MAPK pathway target-specific effects correlating with Erk subcellular localization. Further- more, we find that Mek inhibitor-induced RTK reprogram- ming occurs through both BET bromodomain dependent and independent mechanisms, motivating combination treat- ment with BET and Axl inhibition to overcome RTK reprogramming. Conclusions—Our findings suggest that RTK reprogramming occurs through multiple mechanisms in a MAPK pathway target-specific manner, highlighting the need for comprehen- sive resistance mechanism profiling strategies during phar- macological development. KeywordsTriple negative breast cancer, EGFR, Her2, Met, Axl, Mek inhibition, Erk inhibition, BET inhibition. ABBREVIATIONS RTK Receptor tyrosine kinase BET Bromodomain and extra-terminal domain TNBC Triple negative breast cancer MAPK Mitogen-activated protein kinase TKI Tyrosine kinase inhibitor PCA Principal component analysis ELISA Enzyme linked immunosorbent assay MEKi Mek inhibitor BETi BET inhibitor AXLi Axl inhibitor LLOQ Lower limit of quantitation INTRODUCTION Detailed genetic understanding of molecular cancer drivers has enabled the development of targeted cancer therapeutics. Well-characterized cancer targets such as mutant EGFR in non-small cell lung cancer (NSCLC) and the BCR-Abl fusion gene in chronic myelogenous leukemia (CML) led to initial breakthroughs, 12,31,37 and success via this approach has continued to expand as more than 150 targeted therapeutics have been ap- proved to date by the FDA to treat various cancer subtypes. 48 Unfortunately, sustained therapeutic effi- cacy has been limited by the emergence of drug resis- tance. Enabled by broadening availability of advanced Address correspondence to Douglas A. Lauffenburger, Depart- ment of Biological Engineering, Massachusetts Institute of Tech- nology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA. Electronic mail: [email protected] Cellular and Molecular Bioengineering, Vol. 11, No. 6, December 2018 (ȑ 2018) pp. 451–469 https://doi.org/10.1007/s12195-018-0542-y 1865-5025/18/1200-0451/0 ȑ 2018 The Author(s) 451

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  • Systems Modeling Identifies Divergent Receptor Tyrosine KinaseReprogramming to MAPK Pathway Inhibition

    ALLISON M. CLAAS,1 LYLA ATTA,1 SIMON GORDONOV,1 AARON S. MEYER,2

    and DOUGLAS A. LAUFFENBURGER 1

    1Department of Biological Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge,MA 02139, USA; and 2Department of Bioengineering, Jonsson Comprehensive Cancer Center, Eli and Edythe Broad Center of

    Regenerative Medicine and Stem Cell Research, University of California, Los Angeles, Los Angeles, CA 90095, USA

    (Received 22 May 2018; accepted 17 July 2018; published online 26 July 2018)

    Associate Editor Michael R. King oversaw the review of this article.

    AbstractIntroduction—Targeted cancer therapeutics have demon-strated more limited clinical efficacy than anticipated, dueto both intrinsic and acquired drug resistance. Underlyingmechanisms have been largely attributed to genetic changes,but a substantial proportion of resistance observationsremain unexplained by genomic properties. Emerging evi-dence shows that receptor tyrosine kinase (RTK) reprogram-ming is a major alternative process causing targeted drugresistance, separate from genetic alterations. Hence, thecontributions of mechanisms leading to this process need tobe more rigorously assessed.Methods—To parse contributions of multiple mechanisms toRTK reprogramming, we have developed a quantitativemulti-receptor and multi-mechanistic experimental frame-work and kinetic model.Results—We find that RTK reprogramming mechanisms aredisparate among RTKs and nodes of intervention in theMAPK pathway. Mek inhibition induces increased Axl andHer2 levels in triple negative breast cancer (TNBC) cellswhile Met and EGFR levels remain unchanged, with Axl andHer2 sharing re-wiring through increased synthesis anddiffering secondary contributing mechanisms. While threeMek inhibitors exhibited mechanistic similarity, three Erkinhibitors elicited effects different from the Mek inhibitorsand from each other, with MAPK pathway target-specificeffects correlating with Erk subcellular localization. Further-more, we find that Mek inhibitor-induced RTK reprogram-ming occurs through both BET bromodomain dependentand independent mechanisms, motivating combination treat-ment with BET and Axl inhibition to overcome RTKreprogramming.Conclusions—Our findings suggest that RTK reprogrammingoccurs through multiple mechanisms in a MAPK pathwaytarget-specific manner, highlighting the need for comprehen-

    sive resistance mechanism profiling strategies during phar-macological development.

    Keywords—Triple negative breast cancer, EGFR, Her2, Met,

    Axl, Mek inhibition, Erk inhibition, BET inhibition.

    ABBREVIATIONS

    RTK Receptor tyrosine kinaseBET Bromodomain and extra-terminal domainTNBC Triple negative breast cancerMAPK Mitogen-activated protein kinaseTKI Tyrosine kinase inhibitorPCA Principal component analysisELISA Enzyme linked immunosorbent assayMEKi Mek inhibitorBETi BET inhibitorAXLi Axl inhibitorLLOQ Lower limit of quantitation

    INTRODUCTION

    Detailed genetic understanding of molecular cancerdrivers has enabled the development of targeted cancertherapeutics. Well-characterized cancer targets such asmutant EGFR in non-small cell lung cancer (NSCLC)and the BCR-Abl fusion gene in chronic myelogenousleukemia (CML) led to initial breakthroughs,12,31,37

    and success via this approach has continued to expandas more than 150 targeted therapeutics have been ap-proved to date by the FDA to treat various cancersubtypes.48 Unfortunately, sustained therapeutic effi-cacy has been limited by the emergence of drug resis-tance. Enabled by broadening availability of advanced

    Address correspondence to Douglas A. Lauffenburger, Depart-

    ment of Biological Engineering, Massachusetts Institute of Tech-

    nology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.

    Electronic mail: [email protected]

    Cellular and Molecular Bioengineering, Vol. 11, No. 6, December 2018 (� 2018) pp. 451–469https://doi.org/10.1007/s12195-018-0542-y

    1865-5025/18/1200-0451/0 � 2018 The Author(s)

    451

    http://orcid.org/0000-0002-0050-989Xhttp://crossmark.crossref.org/dialog/?doi=10.1007/s12195-018-0542-y&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1007/s12195-018-0542-y&domain=pdf

  • genome sequencing technologies, genetic mechanismsof drug resistance have been widely identified—com-monly mutation or amplification in the target itself oralternate proteins.14,35,36,41 However, emerging evi-dence is showing that non-genetic mechanisms alsocontribute significantly to drug resistance, such that asubstantial proportion of resistance cannot be readilyattributed to genetic lesions. For instance, target andalternative receptor tyrosine kinases (RTKs) can ex-hibit enhanced activities via increased expression evenin the absence of gene amplification,4,10,35,46,49 includ-ing by means of modulated ligand binding and/orreceptor oligomerization.25,50,52 Due to the manyRTKs that may contribute to resistance, monitoringcoordinated changes in RTK networks, termed ‘‘RTKreprogramming’’, has become important for evaluatingcancer drug resistance.10,13,45

    While identification of mutation or amplification ofthe target protein can lead to improved second andthird line inhibitors that have advantageous properties,such as alternate binding motifs, covalent binding, orthe combination of antibodies and small moleculeinhibitors,26,40 elucidation of additional activatedproteins, whether alternative RTKs or downstreamsignaling molecules, can guide combination treatmentwith inhibitors against a second target. When geneexpression networks are broadly altered, it may beuseful to employ epigenetic inhibitors, such as bro-modomain and extra-terminal domain (BET) in-hibitors, to limit the dynamic response of numerouspotential targets simultaneously.9

    A highly relevant clinical application representing amajor unmet treatment need is triple negative breastcancer (TNBC), which is an aggressive diseaseaccounting for approximately 15% of invasive breastcancers and is defined as progesterone receptor (PR)negative, estrogen receptor (ER) negative, and Her2negative.38 Although lacking traditional markersidentified in breast cancer, the EGFR inhibitor erloti-nib has been shown to have subtype specificity forbasal/TNBC.21 Furthermore, 37% of patient samplesclassified as TNBC overexpress EGFR.38 However, ina phase II study of Cetuximab for EGFR inhibition incombination with carboplatin for treatment of TNBC,fewer than 20% of patients responded to treatmenteven though they had EGFR activation prior totreatment. Analysis of pre- and post-treatment biopsysamples found that the EGFR pathway was upregu-lated in 81% of pre-treatment samples and eight ofthirteen patients retained high EGFR pathwayexpression in the presence of EGFR inhibition, indi-cating pathway maintenance downstream of EGFR.5

    As the MAPK pathway is one of the major signaltransduction pathways downstream of EGFR thatpromotes growth and survival, it has been studied for

    its role in TNBC. In fact, approximately 80% ofTNBCs have amplification in EGFR, KRAS, orBRAF proteins, providing a rationale for targeting theMAPK pathway.27 Further, TNBC cell lines are pref-erentially sensitive to Mek inhibition supportingMAPK inhibition in TNBC.23

    Despite this compelling rationale, pre-clinical andclinical evidence indicates that TNBC cells undergoRTK reprogramming, limiting response to Mek inhi-bition.13,34 While RTK reprogramming has been de-scribed as a transcriptionally regulated event,13,45 workfrom Miller et al. demonstrated abrogation of RTKectodomain shedding as an alternative mechanism.34

    With multiple competing, or more likely complemen-tary, hypotheses found in different studies, a need isclear for a more integrative perspective on how mul-tiple mechanisms may concomitantly contribute todrug resistance even through a particular phenomenonsuch as dynamic alterations in RTK levels.

    Our work here accordingly aims to develop anintegrative framework based on quantitative experi-mentation and a computational model that quantifiescontributions of non-genetic mechanisms to many al-tered RTK levels in parallel. By leveraging non-specificcell labeling and antibody specific measurements wehave developed a methodology that is amenable tosystems level characterization and provides robustestimates for parameters that are historically cumber-some to measure directly. We apply this framework inthe context of drug resistance to MAPK inhibition inTNBC to clarify the absolute contributions of com-peting processes. In doing so, we show that Axl andHer2 levels increase following Mek inhibition not onlythrough increased synthesis but also through sec-ondary mechanisms, including decreased proteindegradation and endocytosis. Additionally, receptordegradation and endocytosis decreased broadly withonly context-specific quantitative effects on RTK levelsand decreased proteolytic shedding does not quanti-tatively contribute to altered cellular RTK levels.Furthermore, we identify differences in the RTKreprogramming response to Mek inhibitors vs. Erkinhibitors. Taken together, we have identified integra-tive, RTK specific, and MAPK inhibitor-specific RTKreprogramming responses in TNBC.

    RESULTS

    Integrative Model Quantifies Mechanistic CellularProcesses and Basal Cell State

    We used the model structure depicted in Fig. 1 todescribe the mechanistic processes of interest govern-ing protein levels and subcellular localization. Briefly,

    CLAAS et al.452

  • RTKs are either on the cell surface, intracellular (en-dosomal/lysosomal/nuclear), or free ectodomains arecirculating in the extracellular environment (super-natant). Zeroth order protein synthesis adds protein tothe cell surface, while first order rate constants governtransport between the compartments by proteolyticshedding, endocytosis, recycling, and degradation.

    To inform the model, both end point and time-course experiments were performed to capture pro-cesses manifesting over both fast and slow time scalesand provide additional unique model information. Assummarized in Fig. 2, end point measurements aremade by treating cells for 24 h. Lysate and supernatantsamples are quantified with a multi-plexed bead-basedELISA and recombinant protein standard. Time-course measurements are pulse-chase experiments,whereby cell surface proteins are non-specifically la-beled with a cleavable, cell impermeable biotin. Aftervarying incubation times from 5 to 90 min to facilitatelabeled protein trafficking, cells are either lysed inwhole or after the cell surface biotin label is stripped,yielding an internal pool of labeled protein. Samplesare then measured by total protein pull-down withprimary antibodies in a multi-plexed bead-based ELI-SA and labeled protein detection with a streptavidinconjugate, permitting relatively straightforward multi-plexing. This technique combines biotinylation non-specificity of binding to essentially all accessible sur-

    Psyn

    kdeg

    kendkrec

    kshed

    rf

    ri

    rs

    FIGURE 1. Model schematic. Axl (blue), Met (orange), EGFR(green), and Her2 (purple) receptors exist in one of threecompartments: Cell surface (rs), intracellular (combinedendosomal, lysosomal, nuclear) (ri), or freely circulating inthe extracellular medium (rf). Psyn represents net proteinsynthesis, the sum of transcriptional and translationalregulation, kdeg represents protein degradation from theinternal compartment, kshed represents proteolytic sheddingof cell surface extracellular domains, and kend and krecrepresent endocytosis and recycling to and from the internalprotein pool (i.e., endosomes) respectively.

    Time-course experiment: Measure fast RTK kinetics

    Total labeled RTK (rt(t))

    Internal labeled RTK (ri(t))

    Add treatment, Internalize for t= 5, 20, 45, 75, 90

    minutes

    Lysate RTK (rt, t=24) Supernatant RTK (rf, t=24)

    End-point experiment: Measure 24 hour lysate and supernatant accumulation

    Remove media, wash cells

    Add treatment for 24 hours

    Label with cell impermeable biotin

    Cleave cell surface biotin

    - +

    Collect lysate and supernatant

    Measure via multiplexed immunoassay

    Quantify with recombinant

    standard curve MFI

    Concentration

    MFI

    Concentration

    Measure via adapted multiplexed immunoassay

    FIGURE 2. Experimental methodology for measuring varying RTK levels and kinetics. (left) End point experiment workflowwhereby after 24-h treatment lysate and supernatant samples are collected and measured by bead-based ELISA with a recombinantprotein standard. (right) Time-course experiment workflow whereby cell surface proteins are non-specifically labeled with biotin,labeled proteins are trafficked over varying time points, and surface biotin is either cleaved or un-cleaved. Samples are measuredwith an adapted bead-based ELISA. Colors represent two proteins measured simultaneously and independently.

    Systems Modeling for MAPK Induced RTK Reprogramming 453

  • face proteins with antibody specificity to selectivelyquantify those proteins of particular interest. Fur-thermore, the direct labeling and measurement of theprotein of interest allows us to characterize the basalcell state in addition to perturbation effects (as op-posed to traditional methods dependent on a labelledligand or antibody binding effects), further increasingthe applicability of this methodology.

    To characterize the basal cell state of MDAMB231TNBC cells, we collected end point and time-coursemeasurements for Axl, Met, EGFR, and Her2 incontrol treated cells (Figs. 3a and 3b). Axl, Met, andEGFR are highly expressed at levels on the order of105–106 molecules/cell, consistent with values charac-terized previously for EGFR in cancer cell lines.44 Wealso found high supernatant levels of Axl and Met,ranging from ~ 1 to 6% of lysate levels shed per hourrespectively, highlighting the rapid turnover of proteinthrough proteolytic shedding. Furthermore, we ob-serve different RTK kinetics, with biotinylated Metlevels turning over the most rapidly and internal Axllevels accumulating to the highest relative level.

    We utilized Bayesian statistics to calculate the pos-terior probability for model parameters, identifyingparameter distributions accounting for experimentalvariability which provides a more comprehensivecharacterization than single point estimates. Further-more, we leveraged prior distributions to enable esti-mation of biologically relevant parameter regimeswithout over-constraining parameters based on litera-ture values from different proteins, cell lines, or envi-ronmental contexts. Parameter estimation was firstperformed via a deterministic direct search algorithmwith 100 semi-random start sites identified by latinhypercube sampling (see ‘‘Materials and Methods’’).While we observe start site dependent local optima foroptimized negative log(posterior) values across RTKs,we also observe a convergence to what we presume tobe the global minimum posterior value (Fig. 3c). Assuch, deterministic optimization yields our presumedglobal optimum parameter set. To address parametervariability and generate distributions as opposed tosingle point estimates, we used an adaptive metropolisalgorithm to generate the full parameter posteriordistributions describing the experimental data(Fig. 3d).

    -8 -5-3-10

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    (a) (b)

    (c) (d)

    FIGURE 3. Quantitative experiments and parameter estimation define MDAMB231 cell basal state. (a) End point samplequantification for total lysate (left) and supernatant (right) samples for control treated MDAMB231 cells. mean 6 standarddeviation, n = 12. (b) Time-course measurement of total biotin labeled RTK (left) and internal biotin labeled RTK (right) samples forcontrol treated MDAMB231 cells. mean 6 standard deviation, n = 18. (c) Optimized posterior value from deterministicpatternsearch algorithm for 100 start sites determined by latin hypercube sampling and ordered by increasing -log(posterior)values. (d) Parameter posterior distributions from adaptive metropolis algorithm. Data are summed from 4 independent chains,100,000 iterations each, minus 20,000 step burn-in period. Psyn has units of molecules cell

    21 min21 and kdeg, kend, krec, and kshedhave units of min21. Blue—Axl, orange—Met, green—EGFR, purple—Her2.

    CLAAS et al.454

  • Generally, parameter values across RTKs forendocytosis, recycling, degradation and synthesis wereconsistent with published literature values forEGFR15,17,18,22,39,51 and Axl endocytosis and recyclingrates were similar to those estimated from a model ofligand-receptor interaction and trafficking.33 In addi-tion to estimated values consistent with literature re-ports, we find relatively narrow distributions forparameter estimates with the methodology developedhere. Compared to traditional trafficking measurementmethods that depend on radioactive or fluorescentlylabeled ligands and treatment with broad-spectruminhibitors which are often toxic to the cells, we wereable to achieve constrained parameter estimates withexperiments that are readily accessible, extendable, andavoid using inhibitors that may introduce off-targeteffects.

    Of note, EGFR degradation and synthesis havelimited comparability to literature values as a conse-quence of low identifiability and strong parametercovariation which was not observed with other recep-tors and treatments. Furthermore, we observe aroughly uniform distribution for Her2 kshed althoughthere was no Her2 measured in the supernatant. This isa result of assuming the supernatant measurement canbe any value less than the lower limit of quantitation(LLOQ) such that the Her2 kshed distributions hereinrepresent biologically plausible shedding rates thatwould yield un-detectable supernatant levels consistentwith our experimental measure. While EGFR kinetics,and Her2 kinetics to a lesser extent, have been well-documented in the literature, we have gained insightshere into the basal cellular behavior of the less studiedAxl and Met receptors.

    To validate the ability of our experimental andcomputational framework to quantitate cellularmechanistic processes, we used two perturbations withknown cellular effects. First, cells were stimulated withEGF which is known to internalize EGFR and Her2and down-regulate lysate levels.22,39,44 Indeed, EGFRand Her2 lysate levels were decreased after 24 hwhereas Axl and Met levels remained unchanged(Supplemental Fig. 1a). Additionally, receptor inter-nalization was increased for EGFR and Her2 and theendocytosis (kend) parameter distribution wasincreased for cells stimulated with EGF (SupplementalFigs. 1b, 1c). Second, cells were treated with batimas-tat, a broad-spectrum metalloprotease inhibitor whichhas been used to decrease proteolytic shedding of Axland Met.34 Axl and Met lysate levels were increasedafter 24 h with batimastat treatment with a concomi-tant decrease in the supernatant levels, consistent withmodel estimations of decreased kshed (SupplementalFig. 2). For both cases and all other treatments usedherein, we find good agreement between experimental

    data and simulated data generated from randomlysampling 10% of parameter sets (i.e., sampling fromadaptive metropolis steps, maintaining parametercovariate relationships) for both end point data(Figs. 4a and 5a, Supplemental Figs. 1a, 2a, 6a, 7a)and time-course data (Supplemental Figs. 1b, 2b, 3, 4).This provides confidence that the parameter posteriordistributions on which we draw biological conclusionsnot only fit the data well but also reflect the underlyingsources of variability in the data. Together, these twoexamples highlight the ability of the methodology tocapture and quantify known RTK specific perturba-tions.

    Mek Inhibitors Alter Axl and Her2 Levels ThroughDistinct Integrative Mechanisms

    Three Mek inhibitors, selumetinib, binimetinib, andPD0325901, were tested for their induction of RTKreprogramming. To allow for compound dependentdownstream effects (i.e., viability, RTK reprogram-ming), we used concentrations that were 100 timesgreater than the reported in vitro IC50 values for targetinhibition. We find that the three compounds havedifferent IC50 values in MDAMB231 cells, althoughthe selected concentration values result in similar in-hibitory effects (Supplemental Fig. 5).

    After 24-h treatment, MDAMB231 and SUM159cells had increased Axl and Her2 lysate levels anddecreased Axl and Met supernatant accumulation rel-ative to lysate levels (represented as percent shed)(Fig. 4a, Supplemental Fig. 6a). Parameter distribu-tions underlying the treatment induced changes areshown in Fig. 4b and Supplemental Fig. 6b. Lookingacross RTKs, we observe multiple trends in compar-ison to control treatment. First, we see a decrease inendocytosis (kend) across all inhibitors and RTKs.Second, Axl and Met degradation (kdeg) and shedding(kshed) are decreased across Mek inhibitors and to agreater extent in MDAMB231 cells. Third, Axl andHer2 synthesis (Psyn) are increased across inhibitors.Although the mechanisms described here (endocytosis,degradation, etc.) represent fundamental cellular pro-cesses, the identification of RTK specific effects indi-cates underlying molecular details, such as mediatorproteins and their abundance, activity, or co-localiza-tion, are likely driving the mechanism context depen-dency.

    While changes in broad parameter distributions areinformative as to how cellular processes are changing,we wished to quantitate how these changes translatedto changes in RTK abundance. To quantitate the effectof treatment-induced parameter distribution changes,lysate levels were predicted using the mean parametervalues for control treatment and singly substituting

    Systems Modeling for MAPK Induced RTK Reprogramming 455

  • mean parameter values for each treatment. The modeltherefore allows one to predict the quantitative con-tribution of individual parameter mean changes rela-tive to the entire treatment induced changes for totalprotein levels. For Her2, we find that protein synthesisis the dominant driver of increased lysate levels, al-though decreased endocytosis has secondary contri-butions as well (Fig. 4b, Supplemental Fig. 6b). Axl,on the other hand, is equally governed by the increasedprotein synthesis and decreased degradation rates,with smaller contributions from decreased endocytosis.Her2 mRNA levels have been reported to increase with

    Mek inhibition;13 however, Axl levels have not beenreported to have significantly altered mRNA levels13,34

    (unpublished in-house data). Two hypotheses areconsistent with both pieces of data, the first thatmRNA to protein levels do not always correlate well30

    such that small, statistically insignificant mRNAchanges could yield significant protein changes, andthe second that protein synthesis control occurs post-transcriptionally.

    Although these model predictions are based onmean parameter values, we assessed the contributionsof parameter variability to model predictions using

    AxlParameterdistribution

    -2.4 -2.1 -1.9 -1.7

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    -2.3 -2.2 -2.1 -2

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    -13 -9 -5.5 -1.9

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    -4.2 -4 -3.7 -3.5

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    2.4 2.6 2.8 3log10(Parameter)

    Psyn

    MetParameterdistribution

    -2 -1.8 -1.6 -1.5

    -2.3 -2.1 -2 -1.8

    -4.2 -3.3 -2.3 -1.3

    -3.3 -3.1 -2.9 -2.7

    2.9 3.1 3.2 3.4log10(Parameter)

    EGFRParameter

    distribution

    -14 -10 -6.1 -2.1

    -2.5 -2.3 -2.1 -1.9

    -2.1 -1.8 -1.5 -1.2

    -5.4 -5.2 -5.1 -4.9

    -7.7 -4.1 -0.57 3log10(Parameter)

    Her2Parameter

    distribution

    -1.8 -1.6 -1.5 -1.3

    -2.7 -2.6 -2.4 -2.3

    -13 -9.2 -5.4 -1.6

    -5.8 -5.1 -4.3 -3.6

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    AxlPrediction

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    Axl Met EGFR Her20.5

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    ControlSelumetinibBinimetinibPD0325901

    .. ****** * * * * *

    (a)

    (b)

    FIGURE 4. Mek inhibitors increase Axl and Her2 lysate levels and alter multiple parameter estimations. (a) (left panel) End pointlysate measurements and (right panel) end point percent shed (rf/rt) levels normalized to the mean control treated value forMDAMB231 cells treated for 24 h with three Mek inhibitors. Points indicate experimental data (n = 12) and shaded bars representthe range of simulated data from resampling 10% of parameter sets. Asterisk indicates p < 0.01 and ÆÆ indicates p < 0.05 with a two-sample t test with Bonferroni multiple hypothesis correction. (b) Parameter posterior distributions (summed for 4 independentchains, 100,000 iterations each, 20,000 step burn-in time) for control and Mek inhibitor treated cells and predicted protein level foldchange relative to control treatment (red dots indicate observed treatment fold change). Psyn has units of molecules cell

    21 min21

    and kdeg, kend, krec, and kshed have units of min21. Black—control, blue—selumetinib, orange—binimetinib, green—PD0325901.

    CLAAS et al.456

  • 10,000 randomly sampled control and treated param-eter sets (Supplemental Fig. 8). We find the distribu-tion of predicted changes for the conclusions drawnabove to have little to no overlap with an unchangedvalue of 1, providing support for the predictivecapacity in the presence of parameter variability.

    Surprisingly, we saw that the decreases in prote-olytic shedding had only quantitatively minor pre-dicted effects on lysate levels in the cell line modelstested here, although it has previously been shown toserve as a biomarker for poor patient progression freesurvival in melanoma patients treated with Mek and

    Braf inhibitors.34 Further study in systems with higherlevels of shed protein will be needed to gain a betterunderstanding of if and when proteolytic shedding is amajor contributor to drug resistance. Importantly, ourresult here does not eliminate a potential role of pro-teolytic shedding in other models and our analysisframework highlights the importance of quantitativemodeling for distinguishing between correlative andcausative changes. Additionally, our methodologyidentifies a yet un-studied contributor to Mek inhibitorinduced RTK reprogramming, decreased proteindegradation and endocytosis.

    AxlParameterdistribution

    -2.2 -1.9 -1.7 -1.5

    kdeg

    -2.3 -2.2 -2.1 -1.9

    kend

    -12 -8.5 -5.1 -1.7

    krec

    -4 -3.8 -3.6 -3.4

    kshed

    2.2 2.5 2.7 2.9log10(Parameter)

    Psyn

    MetParameterdistribution

    -2 -1.7 -1.5 -1.3

    -2.4 -2.2 -2 -1.8

    -4 -3 -2.1 -1.1

    -3.3 -3.1 -2.9 -2.7

    2.9 3.1 3.3 3.4log10(Parameter)

    EGFRParameter

    distribution

    -13 -9.5 -5.7 -1.9

    -2.6 -2.4 -2.1 -1.9

    -1.9 -1.6 -1.3 -1.1

    -5.4 -5.2 -5 -4.8

    -7.5 -4 -0.48 3log10(Parameter)

    Her2Parameter

    distribution

    -1.7 -1.5 -1.3 -1.1

    -2.7 -2.5 -2.3 -2.1

    -13 -9.1 -5.2 -1.3

    -5.8 -5 -4.3 -3.6

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    AxlPrediction

    0.51

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    ControlUlixertinibDEL-22379GDC-0994

    ..(a)

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    FIGURE 5. Erk inhibitors have compound dependent parameter changes that vary from Mek inhibition. (a) (left panel) End pointlysate measurements and (right panel) end point percent shed (rf/rt) levels normalized to the mean control treated value forMDAMB231 cells treated for 24 h with three Erk inhibitors. Points indicate experimental data (n = 12) and shaded bars represent therange of simulated data from resampling 10% of parameter sets. Asterisk indicates p < 0.01 and ÆÆ indicates p < 0.05 with a two-sample t test with Bonferroni multiple hypothesis correction. (b) Parameter posterior distributions (summed for 4 independentchains, 100,000 iterations each, 20,000 step burn-in time) for control and Mek inhibitor treated cells and predicted protein level foldchange relative to control treatment (red dots indicate observed treatment fold change). Psyn has units of molecules cell

    21 min21

    and kdeg, kend, krec, and kshed have units of min21. Black—control, blue—ulixertinib, orange—DEL-22379, green—GDC-0994.

    Systems Modeling for MAPK Induced RTK Reprogramming 457

  • Erk Inhibitors Have Compound Dependent Effectsthat Vary from Mek Inhibitors

    To compare the RTK reprogramming effect fol-lowing inhibition of the MAPK pathway at differentpoints, we similarly tested three Erk inhibitors, ulix-ertinib, DEL-22379, and GDC-0994. When comparedto Mek inhibitors, we see that only one of the Erkinhibitors, ulixertinib, increased Axl and Her2 lysatelevels in MDAMB231 cells and had no effect inSUM159 cells (Fig. 5a, Supplemental Fig. 7a). Addi-tionally, ulixertinib increases Met and EGFR levels inMDAMB231 cells, showing differences from Mek in-hibitors. These increases are primarily driven byincreased synthesis of all RTKs with an absence ofdecreased protein degradation and endocytosis(Fig. 5b). Interestingly, ulixertinib and GDC-0994 areboth Erk TKIs whereas DEL-22379 is an Erk dimerinhibitor. Not only do we see different responseswithin TKIs, but these responses, as well as Mek in-hibitors, are further different from DEL-22379, indi-cating that variations in Erk dimerization is not

    driving the observed differences seen here (Fig. 5,Supplemental Fig. 7).

    MAPK Pathway Has Target-Specific RTKReprogramming

    We utilized principal component analysis (PCA) toidentify the greatest variation across cell lines and in-hibitors (scores) and the variables (loadings) con-tributing to these changes. PCA was performed withtwo different variable definitions: (1) mean parametervalues (Figs. 6a and 6b) and (2) predicted proteinchange (Figs. 6c and 6d). In both cases, there is a clearseparation between Mek and Erk treated samples, withErk inhibitor treated samples more similar to controltreated. Axl and Her2 synthesis (Psyn), Axl, Her2 andMet endocytosis (kend), and Axl, Met, and Her2degradation (kdeg) are among the loadings of largestmagnitude and with directionality consistent withMek-Erk score separation in both PCA analyses,indicating they are major drivers of the MAPK targetspecific RTK reprogramming response observed.

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    FIGURE 6. Principal component analysis identifies separation of Mek and Erk inhibitors and cell type specific responses. (a) and(b) Scores and Loadings plots respectively for PCA analysis where mean parameter values were used as variables. (c) and (d)Scores and Loadings plots respectively for PCA analysis where predicted protein fold change values were used as variables. InScores plots, circles indicate control treated samples, squares indicate Mek inhibitor treated samples, and diamonds indicate Erkinhibitor treated samples. Filled symbols indicate MDAMB231 cells while open symbols indicate SUM159 cells. In Loadings plots,variables are color coded by RTK (blue—Axl, orange—Met, green—EGFR, purple—Her2) and mechanistic processes are labeledaccordingly.

    CLAAS et al.458

  • We further observe cell type specific effects as a shiftfrom Control/Erk to Mek treatment along principalcomponent 1 for MDAMB231 cells and along princi-pal component 2 for SUM159 cells. Whereas Mek in-hibitors alone decrease endocytosis (kend) inMDAMB231 cells, both Mek and Erk inhibitors de-crease endocytosis in SUM159 cells. Alternatively, Metprotein synthesis (Psyn) is decreased with Mek inhibi-tion and unaffected with Erk inhibition in SUM159cells and unaffected with both Mek and Erk inhibitionin MDAMB231 cells. Cell specific responses are notsurprising, especially considering their varying geneticbackground (MDAMB231- Kras mutant,23 PIK3CAwild type42 SUM159- Hras mutant, PIK3CA mutant),3

    although further study is needed to address contribu-tions of these genetic factors to the varying RTKreprogramming phenotypes observed.

    Mek and Erk inhibitors had different effects on Erkphosphorylation where Mek inhibitors decreased Erkphosphorylation (T202/Y204) and Erk inhibitors didnot (Fig. 7, Supplemental Fig. 9). Two hypotheses forphosphorylation site effects are around Erk dimeriza-tion and subcellular localization. As we have alreadyobserved protein levels and parameter distributionswith an Erk dimer inhibitor, DEL-22379, that varyfrom those of Mek and Erk TKIs, it is unlikely thatdifferences in Erk dimer formation in a phospho-sitedependent manner describe the observed Mek and Erkinhibitor differences. However, Erk nuclearlocalization is decreased specifically with Mek inhibi-tion (Fig. 7, Supplemental Fig. 9), consistent with therole of Erk phosphorylation on nuclear transport.7

    Mek and BET Inhibition Have Differing Effects,Motivating Combination Treatment and Sensitizing

    Cells to Axl Inhibition

    In the case of cellular RTK reprogramming wherebyno single alternate target exists for combinationtreatment, the use of epigenetic regulators to preventthe transcriptional response has been postulated andtested in certain models.8,45 In TNBC cell lines, Mekinduced RTK reprogramming was reported to actthrough de-stabilization of Myc, inducing transcrip-tion of proteins that are normally repressed.13 JQ1, aBET bromodomain inhibitor, was developed to inhibitthe recognition of acetylated lysine residues by BETfamily proteins and not only has shown some speci-ficity for Myc driven genes11 but other genetic targetsas well.2,43 Additionally, JQ1 was found to be effectiveat inhibiting viability in TNBC cell lines in vitro andin vivo43 as was previously seen for Mek inhibitors.23

    Although both Mek and BET inhibition are methodsof perturbing Myc genetic regulation it is unclearwhether their mechanism of action is redundant and

    thus is of interest to compare the RTK rewiringresponse for both treatments alone and in combina-tion. Furthermore, Mek inhibitor increased Her2 levelswere primarily driven by protein synthesis while Axllevels were only driven in part. Through combinationtreatment with Mek and BET inhibition (with the ca-veat that JQ1 has target specificity that may not in-clude Her2 and Axl), we can test the model predictionsfor the quantitative synthesis role for Her2 and Axland expect that combination treatment would returnHer2 levels to baseline whereas Axl levels would re-main elevated.

    Whereas both Mek inhibition (selumetinib) andBET inhibition (JQ1) had anti-proliferative and anti-migratory effects alone, combination treatment furtherinhibited both processes (Fig. 8a). Interestingly, Her2lysate levels were increased with Mek but not BETinhibition yet the combination of the two reduced Her2levels back to baseline (Fig. 8b). This finding indicatesthat the Mek inhibitor-induced Her2 transcriptionbecomes BET dependent whereas basal transcription isnot. On the other hand, Mek inhibition and BETinhibition both increased Axl levels, resulting in sus-tained high Axl protein and phosphorylation levels(data not shown) with combination treatment. Com-bined, this further sensitized cells to inhibition withR428, an Axl inhibitor, whereby R428 had no anti-proliferative effect in combination with either Mek or

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    Systems Modeling for MAPK Induced RTK Reprogramming 459

  • BET inhibitor alone but does in the combined back-ground of Mek + BET inhibition. Together, these re-sults not only support the use of Mek and BETinhibitors in combination due to their non-overlappingand context-dependent effects on RTK reprogram-ming, but further support combination inhibition ofAxl in this context.

    DISCUSSION

    An integrative, multi-receptor model developed hereexpands our knowledge of targeted cancer therapy-induced RTK reprogramming by providing mecha-nistic insights into the underlying processes responsiblefor changes in RTK levels. Previous work has de-scribed the RTK reprogramming phenotype as atranscriptionally regulated event,13,45 putting thespotlight on BET inhibitors as viable treatment op-tions to prevent resistance onset. Our work addition-ally identifies the presence of non-synthesis mediatedchanges in protein levels, the therapeutic implicationsfor which have yet to be explored in greater detail.

    We describe divergent RTK reprogramming phe-notypes between Mek and Erk inhibitors, indicatingthat Mek and Erk inhibitors should not be consideredinterchangeable. Assuming that both Mek and Erkinhibitors decrease Erk kinase activity, differencescould be driven by Erk phosphorylation dependent

    cellular localization, protein binding, or alternate Meksubstrates. While we have not assessed differences inErk binding to target proteins with Mek or Erk in-hibitors, we have observed decreased Erk nuclearlocalization following Mek but not Erk inhibition. Inaddition to the traditional role of Erk substrate phos-phorylation, Erk has been found itself to be associatedwith chromatin,24,32 potentially acting as a transcrip-tion factor to link subcellular localization and proteinsynthesis variations with Mek and Erk inhibitors.Further studies characterizing Erk DNA binding withMek and Erk inhibitors may help shed light on thishypothesis. Interestingly, Erk TKIs had a less pro-nounced effect on RTK reprogramming in the recep-tors studied here than Mek inhibition, which may bedesired when considering a therapeutic option, yet cellproliferation was largely insensitive to Erk inhibition.Characterizing the RTK reprogramming in cells thatare sensitive to Erk inhibition may help to understandif adaptation and efficacy are intrinsically connectedwithin the MAPK pathway or if Erk inhibition main-tains minimal effects on RTK reprogramming. Anexpansion of our knowledge of the molecular targetssusceptible to RTK reprogramming may help charac-terize ideal targets within a pathway.

    In addition to protein synthesis, the processes ofendocytosis, degradation, and proteolytic shedding arelargely decreased with Mek inhibition relative to con-

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    FIGURE 8. Mek and BET inhibitor combinations improve response and sensitize cells to Axl inhibition. (a) Phenotypic drugresponse for MEKi (selumetinib, 1.5 lM), BETi (JQ1, 0.2 lM), and AXLi (R428, 1 lM) in MDAMB231 cells. Proliferation (black) andMigration (grey) responses, represented by either % confluence of the entire well or of the wound respectively, were measured forvarying single and combination treatments. Proliferation measurement was after 100 h and migration measurement was after 24 h.Mean 6 standard deviation with n = 8. (b) Lysate levels in molecules/cell for RTKs when treated with control, MEKi, BETi, orMEKi 1 BETi in MDAMB231 cells. Points indicate experimental data (n = 12) and crosses indicate mean values. Asterisk indicatesp < 0.01 and ÆÆ indicates p < 0.05 determined by pairwise t tests with Bonferroni correction.

    CLAAS et al.460

  • trol treatment and Erk inhibition. While these pro-cesses constitute post-synthesis mechanisms with re-spect to controlling RTK levels, it is plausible that theproteins governing these processes themselves aretranscriptionally altered with MAPK inhibition.Interestingly, Mek has been shown to bind and phos-phorylate heat shock factor 1 (HSF1), facilitating nu-clear localization and transcription of heat shockproteins which are involved in a wide array of cellularprocesses including vesicular transport and proteindegradation.20,47 As an effect upstream of Erk activity,HSF1 is an intriguing candidate protein for broadlyaffecting cellular processes such as endocytosis anddegradation with Mek inhibition alone. As alteredtrafficking and degradation were a surprising outcomeof the model predictions that spanned across RTKs, itwill be important to continue to study these processeslinked to drug resistance. As regulators of cellularhomeostasis, characterizing the molecular playersresponsible for the adaptive response as well as iden-tifying the extent that proteins not looked at in thisstudy are affected by these processes will continue toexpand our understanding of systems level changeswith targeted therapeutics.

    While BET inhibitors are being clinically evaluatedas monotherapies, limited pre-clinical evidence showsbenefit for their use in combination to overcome RTKreprogramming resistance.45 However, molecularunderstanding for rational combinations with BETinhibitors is currently limited. Although JQ1 wasoriginally described to preferentially inhibit Myctranscriptional networks in multiple myeloma,11 newstudies identify additional pathway effects for BETinhibition in alternate model systems.2,43 Furthermore,BET inhibitors not only inhibit transcription of BETactivated genes, but they also induce transcription ofBET repressed genes. As such, the molecular details oftreatment with BET inhibitors or Mek inhibitors aloneare not fully characterized and we have limited abilityto predict combination treatments to attenuate RTKreprogramming and the subsequent resistance. To thispoint, both Mek and BET inhibitors have been de-scribed to affect transcriptional networks by inhibitingMyc, either by de-stabilization and protein degrada-tion or reducing transcription and interrupting Myc-adaptor-chromatin interactions respectively. Yet thecombination of the two has a larger anti-proliferativeand anti-migratory response than either alone.

    Furthermore, BET inhibition has no effect on Her2levels when used alone but reduces Her2 levels incombination treatment with Mek inhibition, indicatingMek inhibitor induced BET dependency. Axl, how-ever, is increased by both Mek inhibition and BETinhibition, retaining high levels with combinationtreatment such that cells are further inhibited by the

    addition of an Axl inhibitor. Following our hypothesis,this data indicates a Mek inhibitor induced loss of Erktranscriptional repression for Her2 and Axl whosenewly active transcription is mediated in a BETdependent and independent manner respectively. Ta-ken together, this indicates a lack of redundancy in thecellular targets and provides rationale for combiningthe two treatments, although relief of repressed tran-scriptional targets remains an issue for drug resistance.The suitability of these combinations will likely becontext dependent and further study is needed toidentify the governing rules.

    Although our focus here is on RTK levels, there isan underlying assumption that these altered levels areindicative of increased signaling activity, promoting acell survival response to MAPK inhibition. As Mekinhibition leads to increases in Axl and Her2 phos-phorylation13,34 and we have found that increased Axllevels with Mek and BET inhibition correspond to acontext dependent anti-proliferative effect of Axlinhibition, we believe our characterization of RTKlevels is a suitable surrogate measurement. We havealso limited our study to four RTKs and two cell lines.While these comparisons have enabled interesting in-sights regarding RTK specific responses, integrativemechanisms, and Mek vs. Erk inhibitor variableresponses, studies of a larger scale of both proteins andcell lines will further the understanding and implica-tions of these trends for improved selection of combi-nation treatments. Fortunately, the combination ofnon-specificity of cell surface biotinylation and anti-body mediated specificity for experimental measure-ments coupled to a generalized model structuregrouping complex protein dependent processes (i.e.,ligand induced receptor dimerization/heterodimeriza-tion) into representative processes was purposeful tofacilitate the adaptation to further proteins of interestwithout requiring detailed a priori understanding. Apotential limitation of the lumped parameters, how-ever, is that they may represent multiple underlyingrates. For instance, EGFR and Her2, knownheterodimerization partners, have been shown tointernalize at different rates when homo- orheterodimerized,22 the combination of which will becaptured with our model. The model and methodologycould be extended to include a cross-linking protocolwith different capture and detection antibodies for theheterodimerization partners to explicitly quantify theendocytosis rate to de-convolve the lumped parameterto provide better granularity if it were desired.

    In summary, we have shown that using a model toextract mechanistic meaning from quantitative experi-ments allows us to understand the cellular processesaltered by MAPK inhibition. We have further utilizedmodel predictions to quantitate the effects of individual

    Systems Modeling for MAPK Induced RTK Reprogramming 461

  • cellular process changes with inhibition, identifyingmultiple processes contributing to the RTK repro-gramming phenotype. In doing so, we identified RTKdependent, integrative responses that varywith differentMAPK target inhibitors. Taken together, the resultspropose a more complex picture of RTK reprogram-ming whereby no single mechanistic change, such asprotein synthesis, alters RTK levels but there is a dy-namic, integrative response. Increased understandingand accounting of this complexity will undoubtedlyimprove rational combination treatment selection toovercome resistance to targeted cancer therapies.

    MATERIALS AND METHODS

    Cell Culture, Reagents, and Compounds

    MDAMB231 cells were purchased from ATCC andgrown in DMEM (Gibco) media supplemented with10% FBS, 1% Pen/strep, and 1% Glutamax Supple-ment (Thermo Fisher) and maintained at 37 �C in 5%CO2. SUM159 cells were purchased from AsterandBioscience and grown according to manufacturer’ssuggestion. Recombinant human EGF was used at10 nM. Batimastat (BB94, Tocris Bioscience) was usedat 10 lM. Selumetinib (AZD6244, Selleck Chem) wasused at 1.5 lM. Binimetinib (Mek162, ARRY-162,Selleck Chem) was used at 1.2 lM. PD0325901 (Sel-leck Chem) was used at 33 nM. Ulixertinib (BVD-523,VRT752271, Selleck Chem) was used at 30 nM. DEL-22379 (Selleck Chem) was used at 5 lM. GDC-0994(Selleck Chem) was used at 30 nM. JQ1 (Tocris Bio-science) was used at 0.2 lM. R428 (BGB324, SelleckChem) was used at 1 lM. DMSO at matched con-centrations was used as all controls.

    Cell Lysis and Supernatant Collection

    Prior to lysis, 200 lL of the cellular supernatant wastransferred to a 96 well v-bottom plate. Cells werelysed with 50 lL NP40 lysis buffer (20 mM Tris–HCl,150 mM NaCl, 2 mM EDTA, 1% NP40, 10% Glyc-erol, pH 7.4). Plates were shaken for 15 min at~ 8000 rpm at 4 �C. Lysates were transferred to a 96well v-bottom plate and lysates and supernatant sam-ples were clarified by centrifugation for 15 min at~ 23009g. Samples were stored at � 20 �C prior touse.

    Luminex Reagents and Antibody-Bead Coupling

    Capture antibodies for Axl, Met, EGFR, and Her2were purchased from R&D Systems (MAB154,MAB3581, AF231, and MAB1129 respectively).

    Biotinylated detection antibodies for Axl, Met, EGFRand Her2 were purchased from R&D Systems(BAF154, BAF358, BAF231, and BAF1129 respec-tively). Streptavidin Phycoerythrin (SAPE) was pur-chased from Biorad (cat. no. 171304501). Assaydiluent and washing buffer used in all steps was 0.1%BSA + 0.1% Tween20 in 19 PBS.

    100 lL MagPix beads (Luminex Corp.) were cen-trifuged at 10,0009g for 2 min and the supernatantwas discarded. EDC (N-(3-dimethylaminopropyl)-N¢-ethylcarbodiimide, Sigma) and S-NHS (N-hydroxy-sulfosuccinimide, Pierce) were dissolved in diH20 to50 mg/mL. Beads were incubated with 80 lL activa-tion buffer (100 mM NaH2PO4 pH 6.3), 10 lL EDC,and 10 lL S-NHS for 20 min dark at room tempera-ture shaking at ~ 900 rpm. The mixture was cen-trifuged at 10,0009g for 2 min and the supernatantwas discarded. Antibodies were diluted to 0.1 mg/mLin 100 lL coupling buffer (50 mM HEPES, pH 7.4)and incubated with the bead suspension, overnightshaking, at 4 �C. The following day beads were washed39 and resuspended in 1 mL 1% BSA + 1% Tween20in 1x PBS and stored at 4 �C.

    Luminex Bead-Based ELISA Procedure

    Capture antibodies were each diluted 759 into assaydiluent (0.1% BSA + 0.1% Tween20 in 19 PBS) and25 lL was added to each well in a 384 well Optiplate(Perkin Elmer). The plate was briefly centrifuged at2009g for 1 min and washed 39 with 80 lL washbuffer (0.1% BSA + 0.1% Tween20 in 19 PBS).Samples were added to each well according to thefollowing dilutions. End point measurement lysateswere diluted at both 259 and 109 in assay diluent to afinal volume of 25 lL per well with data selected forfurther use based on location in the log-linear range ofthe standard curve. Supernatants were supplementedwith 5% solution volume 0.1% BSA in 19 PBS to afinal volume of 50 lL. Standard curves were preparedat matched volumes and diluent concentrations as allsamples. Samples were incubated with the captureantibody beads overnight shaking at ~ 8000 rpm at4 �C. The following day the plate was centrifuged at2009g for 1 min and washed 39 with 80 lL washbuffer. Detection antibody was diluted 10009 intoassay diluent and 15 lL was added to each well. Theplate was centrifuged at 2009g for 1 min, incubated atroom temperature for 1 h, and washed 39 with 80 lLwash buffer. SAPE was diluted 1009 into assay diluentand 15 lL was added to each well. The plate wascentrifuged at 2009g for 1 min, incubated shaking atroom temperature for 15 min, and washed 39 with80 lL wash buffer. After the final wash 60 lL assaydiluent was added to each well. Samples were read on a

    CLAAS et al.462

  • Flexmap 3D machine (Luminex Corp) according tomanufacturer’s protocol.

    Time-Course Experiments

    Cells were seeded at 50,000 cells/well and SUM159cells were seeded at 18,750 cells/well in 48 well platesovernight. The following day cells were washed 19with PBS and 125 lL of 0.5 mg/mL Sulfo-NHS-SS-Biotin (Pierce) was added to each well and incubatedfor 1 h at 4 �C with gentle agitation. Cells were washed19 with PBS followed by addition of treatment andincubated at 37 �C for 5, 20, 45, 75, or 90 min. Fol-lowing incubation, cells were washed 19 with Reduc-ing Buffer (50 mM Tris, 150 mM NaCl, pH 8.6) andcells were either stripped with the addition of 20 mMsodium 2-mercaptoethanesulfonate (MESNA, Sigma)or non-stripped with Reducing buffer and incubatedfor 1 h at 4 �C with gentle agitation. The strippingreaction was quenched by addition of 40 mMIodoacetamide (IAA, Sigma) for 10 min at 4 �C withgentle agitation. Cells were washed 19 with PBS andlysed. Lysates were measured for total biotin signal(surface un-stripped with MESNA) and internal biotinsignal (surface stripped with MESNA) with an adaptedLuminex protocol, eliminating the detection antibodystep. Independent experimental replicates were nor-malized to the mean of the measured total biotin signalat the first time point.

    End Point Experiments

    MDAMB231 cells were seeded at 50,000 cells/welland SUM159 cells were seeded at 18,750 cells/well in48 well plates overnight. The following day controlsand treatments were added to 6 replicate wells for 24 h.Following treatment, supernatant and lysate werecollected. Axl, Met, EGFR, and Her2 levels weresimultaneously quantified in samples by bead-basedELISA (Luminex Corp) with recombinant proteinstandards (R&D systems).

    Absolute Receptor Quantification

    End point measurements were converted from themeasured mean fluorescence intensity (MFU) toabsolute quantity (mr) in pg by five-parameter logisticregression to a recombinant protein standard. Subse-quently, measurements were converted to receptorconcentration (r, molecules/cell) through the followingrelationship:

    r ¼ mr � dil � protcell � navgcprot �MWRTK � vlys

    ð1Þ

    where dil is the fraction of the total lysate and super-natant measured respectively, cprot is the concentrationof total protein in the lysate as measured by BCA as-say, MWRTK is the molecular weight of the recombi-nant protein standard, vlys is the volume of lysatecollected, navg is Avogadro’s number, and protcell is theprotein content per cell, estimated here as 300 pg/cellas reported for HeLa cells.29

    For absolute quantification, DMSO control treatedsamples were collected on three separate days (bio-logical day replicates), on two separate plates each day(biological plate replicates), with 3 replicate wells perplate (technical plate replicates). Lysate and super-natant samples were collected and measured forMDAMB231 and SUM159 cells on 3 independentbead-based ELISA plates, with individually preparedreagents, including standard curves, on each plate. Onplate standard curves were averaged and on platesamples were converted based on the mean standardcurve. Absolute RTK quantification was calculated asthe median RTK quantitation value (across biologicalday, plate and technical replicates) in a given condition(cell line, lysate vs. supernatant). For subsequentmeasurements, the offset was calculated as the foldchange between the DMSO control in-experimentmedian value to the absolute quantitation value. Thisoffset was applied to individual experimental pointsacross all treatments, effectively shifting the experi-mental data to account for variations in the standardcurve.

    Surface Fraction Assay

    Cells were seeded overnight at the above describeddensities. The following day media was changed andcells were incubated at 37 �C for 24 h. Subsequently,cells were washed 19 with PBS and 125 lL of 0.2 mg/mL cell permeable NHS-SS-Biotin (Pierce) was addedto each well and incubated for 1 h at 4 �C with gentleagitation. Cells were then washed 19 with ReducingBuffer (50 mM Tris, 150 mM NaCl, pH 8.6) and cellswere either stripped with the addition of 20 mM so-dium 2-mercaptoethanesulfonate (MESNA, Sigma) ornon-stripped with Reducing buffer and incubated for1 h at 4 �C with gentle agitation. The stripping reac-tion was quenched by addition of 40 mM Iodoac-etamide (IAA, Sigma) for 10 min at 4 �C with gentleagitation. Cells were washed 19 with PBS and lysed.Lysates were measured for total biotin signal (notstripped with MESNA) and internal biotin signal(surface stripped with MESNA) with an adapted Lu-minex protocol, eliminating the detection antibodystep.

    Systems Modeling for MAPK Induced RTK Reprogramming 463

  • Cell Viability Assay

    MDAMB231 cells were seeded at 2500 cells/welland SUM159 cells were seeded at 2000 cells/wellovernight in 96 well plates. The following day treat-ments were added and cells were incubated for 72 h at37 �C and 5% CO2. Viability measurements were madeusing CellTiter-Glo Luminescent Cell Viability Assay(Promega) per manufacturer’s suggestions.

    Proliferation Assays

    MDAMB231 cells were plated at 2500 cells/well in96 well plates overnight. The following day treatmentswere added and cells were incubated for 100 h at 37 �Cand 5% CO2. Plates were measured for percent con-fluence in the well using the IncuCyte Zoom Systemand Software (Essen Bioscience).

    Migration Assays

    MDAMB231 cells were plated at 25,000 cells/well in96 well plates overnight. The following day, a woundwas made with a 96-well WoundMaker (Essen Bio-science) and wells were washed twice with 19 PBS.Treatments were added to wells and plates were mea-sured for percent confluence in the wound using theIncuCyte ZOOM System and Software (Essen Bio-science) at 24-h post treatment.

    Cell Fixation, Staining, and ImmunofluorescenceImaging

    Cells were seeded onto 35 mm glass-bottom disheswith MDAMB231 cells at 100,000 cells/dish andSUM159 cells at 50,000 cells/dish overnight. On thesecond day treatments were spiked into the media for4 h. Media was aspirated then cells were covered with4% formaldehyde diluted in PBS at 37 �C for fixation.After 15 min at room temperature plates were rinsed inPBS. Cells were then covered with ice-cold 100% me-thanol for permeabilization. After 15 min at � 20 �Cthe methanol was aspirated and the plates rinsed inPBS. Blocking was performed in Odyssey BlockingBuffer (PBS) for 60 min and then the buffer aspirated.The primary antibodies used were diluted (1:400 p-p44/42 MAPK (Erk1/2) [Thr202/Tyr204] and p44/42MAPK (Erk1/2) [L34F12]) in Odyssey Blocking Buffer(PBS) and incubated overnight at 4 �C. Cells wereagain rinsed in PBS. Fluorochrome-conjugated sec-ondary antibodies used were diluted (1:200 Donkeyanti-Mouse IgG Fluor 594, Donkey anti-Rabbit IgGFluor 488) in Odyssey Blocking Buffer (PBS). DAPIwas used to stain the nuclei for segmentation purposes(1:10,000). After 1 h at room temperature in the dark,

    cells were aspirated and rinsed in PBS before imaging.Imaging was performed on a Nikon Ti spinning diskConfocal Microscope with wide-field at 20x.

    Immunofluorescence Image Processing and Analysis

    To analyze single-cell immunostaining of Erk andpErk, images were processed and analyzed as followsusing in-house MATLAB scripts (Mathworks, Inc).Images were exported at the microscope-acquired bitdepth using Nikon Elements software. Cell nuclei werefirst localized and segmented using point-sourcedetection1 with a 2D Gaussian standard deviation of 6pixels from the DAPI images, and segmented objectssmaller than 42 lm2 were empirically categorized asdebris and removed. For cell body segmentation, theErk immunostained images were used. The Erk-stainedimages were first retrospectively flat-field corrected toremove uneven illumination by first generating a flat-field image. This image was generated by averaging allErk-stained images on a pixel-by-pixel basis andapplying a 100 9 100 pixel median filter to the aver-aged image. Each Erk image was then divided on apixel-by-pixel basis by the flat-field image. Cell bodieswere then segmented using the flat-field corrected Erk-stained images by combining the overlap in fore-grounds of intensity-based Otsu thresholding andCanny edge detection masks, followed by morpho-logical closing of objects using a disk structural ele-ment of 2 pixels, and removal of all mask spur pixels.Putative cell body objects not overlapping with at leastone pixel of the segmented nuclei mask were consid-ered debris and removed. Touching cells were splitfrom each other using a propagation algorithm28 partof the CellProfiler tool.6 Nuclei centers detected duringthe localization stage above were used as seeds to splitnuclei objects using propagation with a regularizationparameter of 5. Segmented and split nuclei were thenused as seeds for the cell body mask, whereby cellbodies were split using propagation with a regulariza-tion parameter of 0 to fully utilize intensity variation inthe objects to split touching cells. To analyzeimmunostaining signal intensities in the nucleus andcytoplasm of cells, local segmentation of nuclei wasfirst performed by Otsu-based thresholding of theDAPI signal within each segmented cell body croppedimage individually. The locally-segmented nuclearmasks were eroded using a disk structural element of 2pixels, to minimize the chance of including cytoplasmregion pixels in the nuclei masks. The cytoplasmregions were defined as the cell body masks excludingthe locally-segmented nuclei mask regions for each cell.For nucleus, cytoplasm, and whole-cell (nu-cleus + cytoplasm) compartments for each cell, mean

    CLAAS et al.464

  • pixel intensity was computed in the immunostainedimages.

    Model Structure

    The model schematic is shown in Fig. 1 wherebyreceptors exist in 1 of 3 compartments: Cell surface(rs), intracellular (combined endosomal, lysosomal,nuclear) (ri), or freely circulating in the extracellularmedium (rf). Movement between compartments isgoverned by the following processes: newly synthesizedprotein inserted to the cell membrane (Psyn), proteindegradation from the internal protein pool (lysosomalor proteasomal pathways) (kdeg), proteolytic cleavageof protein ectodomains from the cell surface to freelycirculating the supernatant (kshed), endocytosis fromthe cell surface to the internal compartment (kend), andrecycling from the internal pool to the cell surface(krec). These parameters are semi-mechanistic in thatthey lump more detailed processes, such as receptor-ligand binding and interaction with trafficking ordegradation mediated proteins, to give an overviewrate of the entire process. Based on mass actionkinetics, we describe the system as:

    dridt ¼ kendrs � krec þ kdeg

    � �ri ð2Þ

    drsdt ¼ Psyn þ krecri � kend þ kshedð Þrs ð3Þ

    drfdt ¼ kshedrs ð4Þ

    with units of molecules cell�1 min�1 for Psyn and min�1

    for kdeg, kend, krec, and kshed. As the end point experi-ments measure lysate and supernatant quantities,Eq. (4) is used to quantitate supernatant measureswhile drt/dt = dri/dt + drs/dt is used to quantitate ly-sate measures. The time-course data is assumed to notmeasure protein synthesis as it is a pulse-chase exper-iment, altering Eq. (3) above to become

    drsdt ¼ krecri � kend þ kshedð Þrs ð5Þ

    Measured quantities in the time-course experiment areri(t) (total labeled biotin internal to the cell with time)and rt(t) (total labeled biotin in the whole cell withtime), where drt/dt = dri/dt + drs/dt.

    Bayesian Inference for Parameter Estimation

    In order to estimate the parameters for the model inFig. 1, we simultaneously fit to both steady state andtime-course data to capture the redundancy inparameters between data types. We undertake anapproach that allows us to generate full parameterprobability distributions, as opposed to a single best fit

    parameter set. Additionally, we incorporate expectedvalues for a given parameter through setting a priordistribution as opposed to single literature-based val-ues, allowing the results to reflect known quantitationfor RTK mechanisms without constraining the resultto any single RTK or condition. These goals areachieved using Bayes Theorem,

    P HjXð Þ ¼ P XjHð ÞP Hð ÞP Xð Þ ð6Þ

    Which states that the posterior probability distribution(P HjXð Þ) is proportional to the product of the likeli-hood of the data (P XjHð Þ) and the prior probabilitydistribution (P Hð Þ) for a given parameter. P Xð Þ is theprobability of the data which we do not calculate asP HjXð Þ is calculated as a ratio between step i andi + 1. Operating in log space and assuming that log-transformed data is normally distributed, we calculatethe data likelihood for any given parameter set as:

    log Likelihoodð Þ ¼ LL ¼X

    e

    X

    t

    X

    r

    �bye;t � ye;t;r� �2

    2r2e

    � log reð Þ �1

    2log 2pð Þ

    ð7Þ

    where by is the simulated value, y is the experimentaldata, and LL values are summed over experiment typee (end point vs. time-course, supernatant vs. lysate,internal vs. total biotin), time points t (when applica-ble), and replicates r. Sigma (rÞ is the standard devi-ation of the data for experiment type e, where themedian value from all cell lines, receptors, and treat-ments is used as a set value for any given experimenttype.

    Prior Distribution Selection

    The prior distribution for kshed was approximateddirectly by the end point experimental data. Assumingrs is time invariant, integrating Eq. (4) and rearrangingidentifies

    kshed ¼ rfrtfsDt ð8Þ

    where Dt is the duration of the end point experimentand fs is the protein surface fraction. Surface fractionwas measured using a cell permeable, cleavable biotinlinker (NHS-SS-Biotin). Based on this in-house data(Supplemental Fig. 10), fs was modeled to havemean = 0.85 and standard deviation = 0.1 withboundary conditions at [0, 1]. Similarly, rf and rs havemean and standard deviation values from 12 replicatemeasures. Using 10,000 iterations, random values weredrawn for fs, rf and rs from their associated normaldistributions to calculate a data-based distribution for

    Systems Modeling for MAPK Induced RTK Reprogramming 465

  • kshed. The distribution calculated for kshed was thenrepresented as a mean and standard deviation. As rswas found to change with treatment, we evaluated analternative extreme assumption whereby rt linearlyapproaches its treatment induced end point measure-ment and numerically integrated Eq. (4) with a time-dependent rs. We found kshed estimates indistinguish-able from those calculated above, indicating rsdynamics have a negligible effect on kshed estimation.

    As the Her2 supernatant measurement was unde-tected, the value rf was instead represented by a uni-form distribution from 1 to 89 molecules cell�1 h�1

    and randomly sampled as for the distributions formeasured data. The LLOQ was calculated to be 89molecules cell�1 h�1 by finding the lowest point in thestandard curve greater than 5 times the averagebackground value and whose back-fit value was within20% of the real value. From the resulting uniformdistribution for Her2 kshed, minimum and maximumvalues were used as the lower and upper bounds of auniform distribution used for the prior distribution.

    With the exception of Her2 kshed, prior values werecalculated assuming log transformed parameter valueswere normally distributed, such that

    log Priorð Þ ¼P

    p� ðblp�lpÞ

    2

    2r2p� log rp

    � �� 12 log 2pð Þ ð9Þ

    where p are different parameters (kdeg, kend, etc.), blp isthe current test parameter value, lp is the prior dis-tribution mean parameter value, and rp is the priordistribution standard deviation. kshed values for lp andrp were as calculated above, whereas the other lpvalues were estimated from the literature to be as fol-lows: 10�2 for kdeg,

    15,18 kend,17,22,51 krec

    17 and 102 forPsyn.

    39 Values were based on low end estimates asobserved for EGFR as it is most commonly reportedfor the ligand stimulated case. rp values were set to 10

    2

    yielding wide priors, reflecting our lack of knowledgeof the true parameter value for any given protein orcondition.

    Parameter distributions were first estimated for thecontrol treated case, after which the prior distributionsto be used for comparative treatments were updated toreflect the mean of these distributions. The controlestimated parameter distribution standard deviationwas expanded by twofold which we found optimal tomaintain the goodness of fit to new data while mini-mizing parameter non-normality.

    Non-parametric priors included surface fractionand initial conditions. Surface fraction values withmean = 0.85, standard deviation = 0.1 and bound-ary conditions at [0, 1] were used as for kshed calcula-tion. For end point data, initial supernatantconcentrations, rf,0, were assumed to be zero due to

    media washout and initial lysate concentrations, rt,0,had a prior distribution representing the mean andstandard deviation of the control treated case. Initialconditions for time-course data had mean values equalto that of the t = 5 time point with standard deviationvalues = 10 to allow for any dynamic changesbetween t = 0 and 5 min.

    Sequential Deterministic and Stochastic OptimizationImplementation

    We used a multi-step parameter estimation work-flow to optimize global optimization as well as gener-ate statistically based parameter distributions. First,we performed global optimization in Matlab (Math-works) using the built-in patternsearch function using100 parameter start sites generated using latin hyper-cube sampling. Upper and lower parameter boundswere set to [� 6,0] for kdeg, kend, krec, and kshed and [0 5]for Psyn, reflecting expansions on the prior distribu-tions selected. The parameter set across all optimizedstart sites yielding the minimum objective functionvalue was assumed to be the global optimum. Second,we performed local optimization for distribution cal-culation in Matlab (Mathworks) by altering the mh-sample function to represent an adaptive metropolisalgorithm19 for improved trace walk convergence. Theadaptive metropolis function was run with initialcovariance C0 = 0.01 for t0 ¼ 100, scaling termsd= 0.2, and e = 10

    �20. Initial start site was semi-randomly generated for 4 chains by drawing a randomstart site from a normal distribution with mean of theglobal minimum parameter value and 5% coefficient ofvariation and run for 100,000 iterations. Chain con-vergence was assessed visually and by Gelman Rubinconvergence criteria 16 assuming random start siteswithin a local environment instead of for global opti-mization. The first 20,000 steps were discarded as theburn-in period.

    Predicted Lysate Levels

    Control and treatment parameter distributions werereduced to mean values. Starting with the controltreated parameter vector, each parameter mean for thetreated case is individually substituted into the controlvector and total lysate levels were simulated thennormalized to the control treated lysate level to rep-resent the treatment single parameter induced foldchange.

    CLAAS et al.466

  • Principal Component Analysis (PCA)

    PCA was performed in Matlab (Mathworks) usingthe pca function where the rows of the data blockrepresent the cell lines and inhibitor treatments. Col-umns of the data block were performed in two differ-ent ways. First, the columns used were mean parameterdistribution values for all parameters and all RTKsmeasured. Second, the columns used were the pre-dicted lysate level changes for a given parameter andRTK. Unchanged variables were determined by ran-domly sampling 10% of parameter values from controland treated distributions, generating a difference dis-tribution, and calculating the smaller of the fraction ofsamples above or below zero, representing a metric fordistribution overlap. An arbitrary cutoff value wasused such that distributions with more than 25%overlap with control were set to the control meanparameter value or set to predicted lysate fold changeof one for the respective variable definition. Columnswere z-score normalized across treatments for indi-vidual cell lines and then analyzed together to accountfor variations in absolute parameter magnitude acrosscell lines.

    ELECTRONIC SUPPLEMENTARY MATERIAL

    The online version of this article (https://doi.org/10.1007/s12195-018-0542-y) contains supplementarymaterial, which is available to authorized users.

    ACKNOWLEDGMENTS

    This work was partially funded by NIH GrantsR01-CA96504, U54-CA217377, and the Institute forCollaborative Biotechnologies through grantW911NF-09-0001 from the U.S. Army Research Of-fice; the content of the information does not necessarilyreflect the position or the policy of the Government,and no official endorsement should be inferred.

    CONFLICT OF INTEREST

    Authors A.M.C., L.A., S.G., A.S.M., D.A.L. de-clare no conflict of interest.

    HUMAN AND ANIMAL RIGHTS

    No human studies were carried out by the authorsfor the article. No animal studies were carried out bythe authors for this article.

    OPEN ACCESS

    This article is distributed under the terms of theCreative Commons Attribution 4.0 International Li-cense (http://creativecommons.org/licenses/by/4.0/),which permits unrestricted use, distribution, andreproduction in any medium, provided you giveappropriate credit to the original author(s) and thesource, provide a link to the Creative Commons li-cense, and indicate if changes were made.

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