Expression and function of EPOR in the NSCLC cell line H838

We previously showed that the NSCLC cell line H838 expresses the EPOR at the mRNA and protein level, albeit at rather low levels [10]. To more robustly detect EPO-induced phosphorylation of signaling components and expression of target genes in this cell line, we stably expressed high levels of HA-tagged human EPOR (HA-hEPOR) in H838 cells by retroviral transduction (H838-HA-hEPOR). The amount of EPOR protein present in the human lung cancer cell line H838 and its derivative H838-HA-hEPOR was determined by immunoprecipitation followed by quantitative immunoblotting and compared to the amount present in mouse CFU-E cells (Fig 1A). A protein band in the immunoblot that corresponds to the EPOR was detected in the analyzed cell types. As shown in S1A and S1B Fig, the hEPOR levels in H838-HA-hEPOR cells were increased 170-fold compared to H838 cells. The shift in molecular weight of the EPOR in H838-HA-hEPOR cells is most likely due to the HA-tag introduced into the EPOR. For absolute quantification of receptor expression levels, signal intensities of purified protein standards of mouse or human GST-tagged EPOR [34] were used to establish calibration curves and to subsequently estimate the number of EPOR molecules per cell (S1D Fig). As shown in S1 Table, H838-HA-hEPOR cells harbor 620 000 ± 200 000 hEPOR molecules per cell, H838 cells 3 600 ± 1 200 hEPOR molecules per cell and CFU-E cells 4 300 ± 2 200 mEPOR molecules per cell.

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Fig 1. Functional and signaling-competent EPOR in the NSCLC cell line H838 and CFU-E cells.

(A) Left panel: H838 and H838 cells stably overexpressing HA-tagged human EPOR (H838-HA-hEPOR) were either left untreated (-) or stimulated with 10 U/ml EPO beta (+). Cells were lysed after 10 min and hEPOR proteins were subjected to immunoprecipitation (IP, MAB 307, R&D) and phosphorylated (p) EPOR (4G10, Merck Millipore) and total EPOR (C-20, Santa Cruz) were detected by quantitative immunoblotting (IB). The complete immunoblot is shown in S1 Fig. Right panel: murine (m) CFU-E cells were either left untreated (-) or stimulated with 5 U/ml Epo alfa (+). Cells were lysed after 10 min and mEPOR proteins were subjected to IP (M-20, Santa Cruz). pEPOR (4G10, Merck Millipore) and total EPOR (M-20, Santa Cruz) were detected by IB with chemiluminescence by CCD camera. The experiment was performed in biological triplicates. (B) H838 and H838-HA-hEPOR cells were treated with the indicated doses of EPO beta. Cells were lysed after 10 min and JAK2 proteins were subjected to IP. pJAK2 and total JAK2 were detected by IB with chemiluminescence by CCD camera. (C) H838 and H838-HA-hEPOR cells were treated with the indicated doses of EPO beta. Cells were lysed after 20 min and STAT5 proteins were subjected to IP. The degree of phosphorylation of STAT5 was measured with mass spectrometry. For H838 cells, the average degree of STAT5 phosphorylation based on biological duplicates is shown. (D) H838 and H838-HA-hEPOR cells were treated for three days with 5 mg/l cisplatin or left untreated. Additionally, cells were treated with 10 U/ml EPO beta and the cell viability was measured with CellTiter-Blue assay. The error bars represent standard deviation of biological replicates (n ≥ 5). The experiment was performed on two independent days (second replicate in S4 Fig). (E) H838-HA-hEPOR cells expressing the Casper3-GR FRET-based sensor (H838-HA-hEPOR-Casper3-GR) were treated with 5 mg/l cisplatin, EPO beta, a combination of both or left untreated. Staurosporine (10 μM) was used as positive control for induction of apoptosis. Casper3-GR FRET signal was measured by life-cell imaging for 60 hours. Caspase-3 activity was determined based on the green-to-red ratio and normalized to the untreated control (n = 2, second replicate in S5 Fig).

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To assess the activation of signal transduction we examined ligand-induced phosphorylation of the EPOR (Fig 1A). H838 and H838-HA-hEPOR cells were treated for 10 min with 10 U/ml EPO beta and CFU-E cells for 10 min with 5 U/ml EPO alfa or were left untreated. In each case, a band in the immunoblot corresponding to the phosphorylated EPOR was detectable in the treated samples, but was absent in the unstimulated controls. The amount of pEPOR in H838-HA-hEPOR upon stimulation with 10 U/ml EPO beta was only approximately 12-fold increased compared to H838 (S1C Fig), indicating that in cells expressing elevated levels of the EPOR such as H838-HA-hEPOR possibly the transport of the receptor to the plasma membrane or phosphorylation of the EPOR by JAK2 might be limiting. S2A and S2B Fig show that EPO alfa and EPO beta activate EPO-induced signaling at a comparable extent.

Further, we examined EPO-induced JAK2/STAT5 survival signaling in the NSCLC cell line H838 and its derivative H838-HA-hEPOR because it had been reported that EPO induces survival signaling via the JAK2/STAT5 pathway in CFU-E cells [19]. In H838 cells, pJAK2 was detected upon stimulation with 100 U/ml and in H838-HA-hEPOR an EPO dose-dependent increase in JAK2 phosphorylation was observed (Fig 1B). Because the latent transcription factor STAT5 is a key mediator of the JAK2/STAT5 signaling pathway, we determined the degree of STAT5 phosphorylation by mass spectrometry in H838 and H838-HA-hEPOR cells treated with different doses of EPO beta (Fig 1C). The highest degree of STAT5 phosphorylation was observed at 10 U/ml EPO beta, with approximately 60% of STAT5 in H838-HA-hEPOR cells being phosphorylated and 3% in H838 cells. As quantified in S2C and S2D Fig and summarized in S1 Table both H838 and H838-HA-hEPOR harbor approximately 1 200 JAK2 and 90 000 STAT5 molecules compared to 24 000 JAK2 and 20 000 STAT5 molecules in CFU-E. To also consider the cytoplasmic and nuclear volume of the cell types analyzed, trypsinized cells were analyzed by fluorescence microscopy and the diameter of the cell and of the nucleus was determined (S3A and S3B Fig). CFU-E cells with a cell volume of 700 μm³ and a nuclear volume of 300 μm³ are much smaller compared to H838 cells that have a cell volume of around 14 000 μm³ and a nuclear volume of around 2 000 μm³. The respective volumes were utilized to convert number of molecules per cell into cell type-specific initial concentrations, which are summarized in S1 Table.

To test whether EPO influences survival and may reduce cisplatin-induced apoptosis in NSCLC cells, H838 and H838-HA-hEPOR cells were treated with 5 mg/l of the chemotherapeutic agent cisplatin in combination with 10 U/ml EPO beta or were left untreated for three days. Cell viability was measured every 24 hours by the CellTiter-Blue assay (Fig 1D, S4 Fig). In untreated proliferating H838 and H838-HA-hEPOR cells, a two- to three-fold increase in cell numbers was observed. No significant impact of EPO beta on cell viability was detected during this observation period. The treatment of H838 and H838-HA-hEPOR with 5 mg/l cisplatin reduced cell viability or at least decreased proliferation compared to the untreated control. Interestingly, co-treatment with 10 U/ml EPO beta decreased the impact of cisplatin in H838 and H838-HA-hEPOR at each time point. While there was some variability in the response of these cells to cisplatin, the rescue effect induced by EPO beta was consistent. To validate these findings, the Casper3-GR FRET (fluorescence resonance energy transfer)-based sensor was expressed in H838-HA-hEPOR (H838-HA-hEPOR-Casper3-GR) and caspase-3 activity, a key indicator for apoptotic responses, was measured by life-cell imaging in a time-resolved manner (Fig 1E, S5 Fig). As a positive control 10 μM staurosporine was applied that is known to rapidly induce caspase-3. Indeed, the effect of staurosporine was observed within 5 hours upon treatment whereas in untreated cells no peak of caspase-3 activation was detected. Upon treatment with 5 mg/l cisplatin the maximum peak of caspase-3 activity was reached at around 24 hours followed by a strong signal decrease due to cells undergoing apoptosis. Upon co-treatment with 10 U/ml or 500 U/ml EPO the amplitude of the cisplatin-induced maximal caspase-3 activation showed an EPO dose-dependent reduction, which is in line with the cell viability assay, and a peak shift to around 15 hours. Treatment with EPO alone did not induce caspase-3 activation.

Concluding, we demonstrated that, similar to CFU-E, the EPOR expressed in H838 cells was capable of activating the JAK2/STAT5 signaling cascade. Further, in line with the observation that EPO-induced activation of JAK2/STAT5 signaling correlates with survival signaling [19], we showed in co-treatment experiments that EPO reduces the extent of cisplatin-induced apoptosis in H838 and H838-HA-hEPOR cells and thus exhibits a rescuing effect in the lung cancer cell line and its derivative. Due to the similarity of the core signaling components, it is difficult to predict cell type-specific differences in the signaling network based only on experimental observations. We developed a systematic mathematical modeling approach for the unbiased identification of cell type-specific differences with the aim to propose strategies to exclusively target the lung cancer cells but not the erythroid progenitor cells.

Development of a strategy to identify cell type-specific parameters

To predict cell type-specific model parameters between two different cell types, we propose an ODE-based mathematical modeling strategy in combination with a L₁ regularization method. To show that this approach is capable to identify these parameter differences, first an in silico model with simulated data was investigated. The exemplary mathematical model mimics a two-step phosphorylation cascade in two different cell types, in which a protein (Protein) is irreversibly converted into a phosphorylated protein (pProtein) with rate k₁ followed by another phosphorylation step resulting in a doubly phosphorylated protein (ppProtein). This second step can be reversed by a dephosphorylation reaction (Fig 2). The ppProtein and its intermediate pProtein equilibrate depending on the ratio of the forward (k₂) and backward reaction (k₃). The corresponding differential equation system is given by:

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Fig 2. Example model with simulated data for two different cell types.

The process diagram of a two-step phosphorylation reaction (Protein→pProtein→ppProtein) is shown according to Systems Biology Graphical Notation. The ODE was numerically solved over time for two cell types that differ in the initial protein concentration ([Protein]_{t = 0}) and in one kinetic rate (k₃). The initial concentrations of the phosphorylated compounds were set to zero ([pProtein]_{t = 0} = [ppProtein]_{t = 0} = 0). The second phosphorylation step is reversible and the dephosphorylation rate (k₃) was assumed to be cell type-specific. The parameters for the phosphorylation steps (k₁, k₂) are the same for both cell types. Simulated data points are depicted as black dots, and the grey shading indicates the standard deviation (σ = 0.1) of the simulated measurement errors. Model trajectories are displayed as black lines.

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The model structure and the parameters k₁ and k₂ were chosen to be identical for cell type 1 and cell type 2. In contrast, the following two parameters were set as cell type-specific: The rate k₃ was set to 0.5 min^-1 in cell type 1 and 0.1 min^-1 in cell type 2 and the parameter [Protein]_{t = 0} was defined as 1 nM in cell type 1 and 2 nM in cell type 2. The initial concentration of pProtein and ppProtein at t = 0 min were assumed to be zero in both cell types.

The ODE solution was calculated using the D2D software [31] and data (black dots) were simulated by adding normally distributed noise (σ = 0.1) (Fig 2). The model trajectories are depicted as black lines and the shading represents the noise distribution. To approximate a realistic setting, only two proteins were assumed to be measurable and sampling time points were not equal. Hence, data was available for Protein (n = 21) and ppProtein (n = 10).

To estimate parameters and identify cell type-specific differences given only by the model structure and the simulated data, the model was parameterized with parameter p_i for cell type 1 and r_i ∙ p_i for cell type 2, with r_i denoting fold-changes between both cell types. After calculating the maximum likelihood estimates individually for cell type 1 and 2, the regularization weight λ of the constrained likelihood was scanned. Here, ℒ_{cell type 1} and ℒ_{cell type 2} denote the likelihood (i.e. the negative two-fold log-likelihood) of the respective cell type and the last term regularizes the fold-changes r_i of parameters between the cell types. If the parameter p_i is the same in both cell types, r_i = 1 and the regularization term is zero. To obtain the regularization path for all parameters, we gradually increased λ from 10⁻⁴ to 10⁴ and re-estimated the constrained likelihood at each step.

With increasing regularization weight λ, the number of cell type-specific parameters decreased until all parameters were independent from the cell type (Fig 3A). To determine the optimal regularization weight λ, i.e. to statistically evaluate the minimum number of cell type-specific parameters that are necessary for the model to sufficiently describe the data (parsimonious model), the likelihood ratio test was utilized. The L₁ regularization was used to select cell type-specific parameters. To reduce bias, the parameters of the non-regularized parsimonious model were then estimated in a second step. The likelihood ratio test statistic D = ℒ_λ − ℒ_full was used, where ℒ_full denotes the likelihood of the full model with only cell type-specific parameters (M) and ℒ_λ the likelihood of a model with N cell type-specific parameters that were selected for a given λ. If D < χ²_dof,α, the smaller model cannot be rejected based on the χ²-distribution for a given confidence level α and degrees of freedom (dof = M − N).

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Fig 3. L₁ regularization recovers cell type-specific parameters.

(A) The dependency of the predicted number of cell type-specific parameters and the regularization weight λ is shown. (B) The likelihood ratio test was performed for each number of cell type-specific parameters. If the test statistics (blue), i.e. the mismatch between data and model, is larger than the statistical threshold (red dashed), the regularization weight λ was too large hence the model was rejected. The crossing of the blue and the dashed red line corresponds to the parsimonious model (dashed black line). (C) The regularization path of the four parameters fold-changes is shown. The regularization-dependent parameter differences are indicated with shades of red (higher in cell type 1) to blue (higher in cell type 2). The asterisks indicate the identified parameter differences. (D) Model trajectories and simulated data for three exemplary scenarios. The dashed green line shows the dynamics for only cell type-specific parameters. In contrast, the blue line displays the model trajectories for no cell type-specific parameters, which is unable to describe the simulated data. Finally, the parsimonious model (solid red) is able to describe the simulated data with only two relevant cell type-specific parameters recovering the simulated parameter differences.

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In Fig 3B, the test statistic D is shown by a solid blue line and the statistical threshold based on the likelihood ratio test is shown as a dashed red line. The crossing point of both lines defines the parsimonious model, in which only relevant parameters are defined as cell type-specific. The so-called regularization path shown in Fig 3C indicates the fold-changes between cell type 1 and cell type 2 for all parameters at a given regularization weight. The colors red or blue show whether a parameter is larger in cell type 1 or 2, respectively. The regularization path is also shown in S6A Fig as a line plot. In our example, the parsimonious model that is indicated by the vertical dashed line (Fig 3A, 3B and 3C) has two cell type-specific parameters. These two parameters were the rate k₃ and the initial concentration of Protein [Protein]_{t = 0}, which could be reconstructed from the example model as cell type-specific (indicated with asterisks in Fig 3C and S6A Fig). We determined the relative difference and by a profile likelihood approach [35] the corresponding confidence interval (S6B Fig): [Protein]_{t = 0} is larger in cell type 2 by a factor of 1.88 ± 0.17 (true value is 2) and k₃ is larger in cell type 1 by a factor of 4.71 ± 1.20 (true value is 5).

To illustrate how well individual models that differ in the number of cell type-specific parameters can describe the simulated data, model trajectories of three different scenarios were plotted with the simulated data (Fig 3D). The model with only cell type-specific parameters (green dashed line), which is the largest model and has the highest degree of freedom, was capable to describe all data sets. The smallest model with no cell type-specific parameters (blue dashed line) was not in statistical agreement with the simulated data, because e.g. for both cell types the species “ppProtein” was not correctly described. In line with the likelihood ratio test, the parsimonious model with only relevant cell type-specific parameters (solid red line) described the simulated data to a comparable extent as the model with only cell type-specific parameters.

In sum, the L₁ regularization was able to reconstruct cell type-specific parameters for simulated data using a single scan of the regularization weight λ, suggesting that our implementation for dynamic ODE-based mathematical modeling in combination with L₁ regularization is appropriate to reveal differences between two different cell types.

Generalized mathematical model structure of the EPO-induced JAK2/STAT5 signaling pathway in CFU-E and H838 cell types

To pinpoint cell type-specific differences in EPO-induced JAK2/STAT5 signaling in CFU-E cells and H838 & H838-HA-hEPOR cells by the approach introduced above, the previously published mathematical model of EPO-induced JAK2/STAT5 signaling in murine CFU-E cells [19] was used as reference model structure: The JAK2/STAT5 model for mCFU-E cells described the EPO-induced JAK2 activation in the EPOR-JAK2 complex, the subsequent phosphorylation of the EPO receptor, attenuation by the phosphatase SHP1, the activation of the transcription factor STAT5 by the EPOR-JAK2 complex and the STAT5 transport from cytosol into and out of the nucleus, as well as the induced transcription and translation of the negative feedback regulators SOCS3 and CIS. To describe EPO-induced JAK2/STAT5 signaling in human H838 and H838-HA-hEPOR cells, a generalized model structure was developed by adding the following components to the reference model: (i) Basal RNA activation rates were included, because we observed that basal CISH mRNA and SOCS3 mRNA is also reduced by inhibiting transcription (S7A and S7B Fig). (ii) A dephosphorylation step of nuclear phosphorylated (np) STAT5 was included to be able to distinguish dephosphorylation and nuclear export of STAT5 [36]. (iii) The regulation of the SOCS3 promotor binding activity by npSTAT5 was described by a Hill coefficient to allow non-linear transcriptional activity. In addition, the receptor phosphatase SHP1 that is known to be restricted to hematopoietic cells was substituted by the general term PTP (Fig 4).

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Fig 4. Generalized mathematical model structure of the EPO-induced JAK2/STAT5 signaling pathway.

The process diagram of the EPO-induced JAK2/STAT5 signaling pathway model is shown according to Systems Biology Graphical Notation. The binding of the ligand EPO to its cognate receptor results in the phosphorylation of first JAK2 and then of the EPOR (pEPORpJAK2). STAT5 is recruited by pEPOR and phosphorylated by pJAK2 and translocates to the nucleus where it induces the transcription of the negative feedback regulators CISH mRNA and SOCS3 mRNA. Protein tyrosine phosphatase (PTP) regulates the dephosphorylation of the EPOR-JAK2 complex.

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The generalized model structure was parameterized based on cell type-specific quantitative data. First, the model was calibrated by directly implementing cell type-specific quantities for H838 and H838-HA-hEPOR cells such as cellular and nuclear volumes and the initial concentrations of the EPOR as well as JAK2 and STAT5 together with their respective experimental error (summarized in S1 Table). As the ratio of the EPOR and JAK2 was different for H838 and H838-HA-hEPOR cells possibly resulting in a saturation of the phosphatase in H838-HA-hEPOR cells, distinct properties were assumed for the phosphatase PTP in H838-HA-hEPOR cells. Except for this difference and the number of receptors on the surface as shown in S1 Fig, the JAK2/STAT5 signaling models for H838 and H838-HA-hEPOR cells were parameterized identically. Therefore, H838 and H838-HA-hEPOR cells were treated as the same cell type but with different conditions.

To calibrate the model for CFU-E cells, quantitative data of the reference model [19] was reutilized (open circles in Fig 5). For the NSCLC cell line H838 and its derivative H838-HA-hEPOR, quantitative time-resolved data was generated (black closed circles in Fig 5). For H838 cells, the dynamics of pEPOR, pJAK2 and pSTAT5 and the expression of CISH mRNA upon stimulation with 10 U/ml EPO beta were determined. For H838-HA-hEPOR cells, the amount of total and phosphorylated STAT5, pEpoR, pJAK2 and the expression of CISH and SOCS3 mRNA were measured upon stimulation with 10 U/ml EPO beta. While the temporal changes of pEPOR were similar in CFU-E, H838-HA-hEPOR and H838 cells, the dynamics of CISH mRNA was more transient in CFU-E cells, while pSTAT5 was more sustained in H838-HA-hEPOR cells than in H838 cells. SOCS3 mRNA, on the other hand, was more sustained in CFU-E cells than in H838-HA-hEPOR cells. Thus, we observed substantial differences in the dynamics of signaling components in the three cell types analyzed. We performed a multitude of additional measurements with different conditions (S7 Fig). The basal expression levels of CISH mRNA and SOCS3 mRNA were determined for CFU-E and H838-HA-hEPOR cells by applying the transcription inhibitor actinomycin D. Time- and dose-resolved protein quantification was performed by quantitative immunoblotting and relative mRNA quantification by qRT-PCR. The degree of STAT5 phosphorylation (pSTAT5) was measured for both the lung cancer cell line and its derivative by quantitative mass spectrometry.

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Fig 5. Model selection.

The model trajectories for a selection of key pathway components are shown for CFU-E, H838 and H838-HA-hEPOR cells. This includes expression of the EPOR targets CISH mRNA and SOCS3 mRNA measured by qRT-PCR as well as pEPOR, pJAK2 and cytoplasmic STAT5 data measured by quantitative immunoblotting. The amount of pSTAT5 was determined by either mass spectrometry or quantitative immunoblotting. The closed circles represent experimentally measured data in H838 and H838-HA-hEPOR cells. CFU-E data previously published [19] are shown as circles. The lines depict the three applied model strategies: dashed green (only cell type-specific parameters), dashed blue (no cell type-specific parameters) and solid red (parsimonious model, only relevant cell type-specific parameters). The parsimonious model describes the data similarly to the model with only cell type-specific parameters, whereas the trajectories of the model without cell type-specific parameters are not in line with the experimental data, e.g. for SOCS3 mRNA in CFU-E and for pSTAT5 in H838. All data sets, replicates and trajectories of the parsimonious model are shown in S8 and S9 Figs.

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The generalized model structure comprised 25 kinetic parameters and 3 initial concentrations (the EPOR-JAK2 complex, STAT5 and PTP at time point 0). Assuming that all kinetic parameters and initial concentrations were cell type-specific (i.e. different parameters for CFU-E and for H838 & H838-HA-hEPOR cells), this model was calibrated based on the experimental data of CFU-E (516 data points) using 83 additional observation parameters and of H838 and H838-HA-hEPOR cells (625 data points) using 77 additional observation parameters. For global optimization of the likelihood, a multi-start deterministic strategy was applied [37]. The model could describe all data sets of the cell types tested, shown representatively by the model trajectory of the model with only cell type-specific parameters (dashed green line in Fig 5). Concluding, we identified a model structure that was able to describe the data sets of EPO-induced JAK2/STAT5 signaling in CFU-E, H838 and H838-HA-hEPOR cells.

L₁ regularization identifies cell type-specific parameters

Our experimental observations suggested that core reactions of the pathway operate comparable in the different cell systems. We therefore tested whether it is possible to identify cell type-independent and cell type-dependent parameters to establish a parsimonious model. The parsimonious model is defined as the model with the smallest number of cell type-specific parameters that is still compatible with the experimental data. To infer cell type-specific parameters, the L₁ regularization strategy was applied while parameterizing the mathematical model based on the experimental data established for the different cell types. We tested the 25 kinetic parameters and the initial concentrations of PTP, while the initial concentrations of the EPOR-JAK2 complex and STAT5 were fixed to the measured values (S1 Table). As expected, by increasing the regularization weight the number of cell type-specific parameters was gradually decreased (Fig 6A). In analogy to the example (Fig 3), the parsimonious model was determined using the likelihood ratio test (blue line in Fig 6B). The statistical threshold corresponding to a significance level α = 0.05 is shown by the red dashed line. At the crossing point of these two lines, the parsimonious model with relevant cell type-specific parameters is defined and depicted by the dashed black vertical line in all panels of Fig 6. The parsimonious model with the minimal number of cell type-specific parameters (red line, Fig 5) resulted in trajectories describing the data and showed similar performance as the model with only cell type-specific parameters (dashed green line, Fig 5). On the contrary, the model with only cell type-independent parameters (dashed blue line, Fig 5) was not capable of representing the dynamics of the data as evidenced e.g. by the difference of the model trajectory and the experimental data of SOCS3 mRNA. The parsimonious model simultaneously described all experimental data measured in CFU-E (S8 Fig), H838-HA-hEPOR (S9A and S9B Fig) and H838 (S9B and S9C Fig).

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Fig 6. Identification of cell type-specific differences.

(A) The number of cell type-specific parameters in dependency of the regularization weight λ is shown. (B) The likelihood ratio test statistics was calculated for each regularization weight λ, resulting in a nested sub-model with a number of cell type-specific parameters that is smaller compared to the full model. If the test statistics (blue) is larger than the statistical threshold (red dashed), the model reduction step was rejected. The crossing of the blue and the dashed red line corresponds to the parsimonious model (dashed black line). (C) The regularization path of the 26 parameters is shown. The regularization-dependent parameter differences are indicated with shades of red (higher in CFU-E) to blue (higher in H838 & H838-HA-hEPOR). The asterisks depict the identified parameter differences.

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Seven relevant cell type-specific parameters are highlighted with an asterisk in the regularization path of the 26 parameters in Fig 6C and in an alternative representation in S10A Fig. We ensured significance by calculating the confidence intervals of these parameter differences (S10B Fig). Table 1 provides a description of the 26 parameters and the model-predicted differences between CFU-E cells and H838 & H838-HA-hEPOR cells. The cell type-specific parameters predicted to have higher values in CFU-E cells (depicted in red, Fig 6C) were the CISH mRNA turnover rate (CISHRNAturn), the activation rate of the EPOR by JAK2 (EPORactJAK2) and the activation rate of JAK2 by EPO (JAK2actEPO). In contrast, the parameters that were predicted to have higher values in the H838 & H838-HA-hEPOR cells (depicted in blue, Fig 6C) were the parameter inversely defining the delay in SOCS3 mRNA production (SOCS3RNAdelay), the SOCS3 promoter activity (SOCS3prom) the import rate of pSTAT5 into the nucleus (STAT5imp) and the deactivation rate of STAT5 in the nucleus (nSTAT5deact).

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Table 1. Parameters and identified cell type-specific differences.

https://doi.org/10.1371/journal.pcbi.1005049.t001

The parameter that showed strongest evidence for a difference between both cell types was the parameter regulating npSTAT5-induced SOCS3 promoter activity (SOCS3prom) (Fig 6C). The model predicted a linear correlation of the SOCS3 mRNA production rate and the concentration of npSTAT5 for CFU-E cells (S11A Fig). In contrast, the same prediction analysis for H838 & H838-HA-hEPOR cells indicated a threshold behavior of the SOCS3 mRNA production rate with respect to npSTAT5. The analysis showed that in these cells a certain amount of activated STAT5 has to be present in the nucleus to induce SOCS3 mRNA synthesis (S11B Fig). To test whether this difference between cell types can be explained by differences in promoter binding elements or epigenetic modifications, the human and murine SOCS3 promoter was analyzed for STAT5 binding sites. Indeed, the murine promoter contains four STAT5 binding sites, whereas the human harbors only two (S11C Fig). Additionally, we performed methylation analyses and demonstrated that the SOCS3 promoter is accessible in both CFU-E and H838 cells (S11C Fig).

Taken together, the selected parsimonious model could simultaneously describe the data sets of CFU-E, H838 and H838-HA-hEPOR cells. Seven relevant cell type-specific parameters were identified and three of these parameters had higher values in CFU-E cells and four had higher values in H838 & H838-HA-hEPOR cells.

Validation of the predicted cell type-specific models

The parsimonious model predicted several cell type-specific parameters comprising mRNA processing: the turnover rate of the CISH mRNA, the SOCS3 promoter activity and the SOCS mRNA delay parameter. Therefore, we selected mRNA processing as a biological process that can be measured experimentally and is connected to parameters identified by the model as cell type-specific for experimental validation of the parsimonious model. We hypothesized that by the application of the transcriptional inhibitor actinomycin D the dynamics of CISH mRNA and SOCS3 mRNA would be altered in a cell type-specific manner.

First, the dynamics of CISH mRNA and SOCS3 mRNA were predicted for CFU-E and H838-HA-hEPOR cells for 300 min upon treatment with EPO (black) or EPO in combination with actinomycin D (blue) (Fig 7). We proposed by experimental design that the transcriptional inhibitor should be applied at the predicted peak of mRNA expression upon EPO stimulation, which was after 60 min for CFU-E cells treated with 5 U/ml EPO alfa and after 30 min for H838-HA-hEPOR stimulated with 10 U/ml EPO beta (blue arrows in Fig 7). To assess the uncertainty of the model dynamics, the prediction profile likelihood [38, 39] was utilized. The shading with dotted lines indicates the 1σ confidence interval. The EPO-induced dynamic of CISH mRNA and SOCS3 mRNA was predicted to show a transient peak followed by a new steady state in both cell types. Addition of actinomycin D was predicted to result in a more dramatic decrease after the treatment and a steady state that is lower compared to EPO treatment alone. The SOCS3 mRNA in H838-HA-hEPOR cells was predicted to even decrease below the starting level after around two hours.

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Fig 7. Experimental validation of the cell type-specific CISH and SOCS3 mRNA parameters.

The parsimonious model was employed to predict the dynamics of CISH mRNA and SOCS3 mRNA upon treatment with a transcriptional inhibitor. The mRNA dynamics in CFU-E stimulated with 5 U/ml EPO alfa alone (black) or with transcriptional inhibition after 60 min (blue) was predicted. Additionally, the mRNA dynamics in H838-HA-hEPOR stimulated with 10 U/ml EPO beta alone (black) or with transcriptional inhibition after 30 min (blue) was predicted. Shadings surrounded by dotted lines depict uncertainty of the prediction. CFU-E cells were stimulated with 5 U/ml EPO alfa and either additionally treated with 1 μg/ml actinomycin D, to inhibit transcription, at 60 min (blue arrows) or left untreated. The H838-HA-hEPOR cells were either stimulated with 10 U/ml EPO beta alone (black) or additionally with 1 μg/ml actinomycin D at 30 min (blue arrows). The mRNA was extracted at the indicated time and the SOCS3 and CISH mRNA levels were measured with qRT-PCR. Experimental data are depicted as closed circles. The experiment was performed in triplicates and one representative example is shown.

https://doi.org/10.1371/journal.pcbi.1005049.g007

To experimentally validate these predictions, H838-HA-hEPOR and CFU-E cells were treated either with 10 U/ml EPO beta or 5 U/ml EPO alfa alone (black dots) or in combination with 1 μg/ml actinomycin D (blue dots) at the predicted time points of either 60 min (CFU-E) or 30 min (H838-HA-hEPOR). The dynamics of CISH mRNA and SOCS3 mRNA were measured by qRT-PCR. Unknown experiment-specific offset and scaling parameters were estimated from this validation data. As shown in Fig 7, the experimentally measured CISH mRNA and SOCS3 mRNA (dots) were in line with the model predictions (lines with shadings).

In summary, the model predicted cell type-specific differences in the dynamics of the SOCS3 and CISH mRNA could be experimentally validated. Therefore, the parsimonious model and the uncovered cell type-specific differences were used to recommend strategies to specifically target JAK2/STAT5 signaling in H838 cells.

Mathematical model predicts cell type-specific drug targets

To identify potential targets in the EPO-induced JAK2/STAT5 signaling pathway, a sensitivity analysis was performed for CFU-E and H838 cells. The area-under-curve of npSTAT5 at 60 min was taken as read out (Κ), because we previously could correlate this to survival of CFU-E cells [19]. A control coefficient was calculated for each model parameter (p_i) in both cell types [23]. The larger the absolute value of the control coefficient, the larger is the influence of a parameter to the simulated biological readout. If a control coefficient is positive, a decrease of the parameter induces a decrease in the area-under-curve of npSTAT5. Interestingly, we observed not only that several parameters exerted major control over npSTAT5, but also that the control coefficients of these parameters differed between CFU-E and H838 cells (S12 Fig). We identified six parameters that had a larger control coefficient for JAK2/STAT5 signaling in H838 cells than on CFU-E cells and thus could represent suitable therapeutic targets (indicated with asterisks in S12 Fig): The activation rate of STAT5 by pEPOR, the activation rate of JAK2 by EPO, the activation rate of STAT5 by pJAK2, the activation rate of the EPOR by pJAK2, the SOCS3 mRNA turnover rate and the deactivation rate of PTP. The inhibition of these parameters would diminish the npSTAT5 level and thus the STAT5-mediated survival in the H838 cells more than in CFU-E cells.

The cell type-specific parameters and the predicted therapeutic targets are summarized by a color code in the process diagram of the JAK2/STAT5 pathway (Fig 8). Cell type-specific differences in the parameter values are depicted in the upper part of each reaction square: Red indicates that the parameter had higher values in CFU-E cells, purple that the parameter value was higher in H838 and H838-HA-hEPOR cells and colorless that there is no difference between cell types. The predicted therapeutic targets are marked in blue in the lower part of each reaction square. Most of the differences were related to the receptor-kinase complex and the shuttling of STAT5. Interestingly, the potential drug targets identified by the sensitivity analysis did not entirely overlap with cell type-specific differences in parameter values. Parameters with a higher control coefficient in H838 cells than in CFU-E cells were either related to the activation of the JAK2-EPOR complex and its control of STAT5 phosphorylation or SOCS3 mRNA degradation. The shuttling of STAT5 was in fact cell type-specific, but the control coefficient had a higher value in CFU-E cells (S12 Fig), meaning that CFU-E cells would be particularly sensitive for inhibitors and npSTAT5 levels would decrease in the erythroid progenitor cells and not, as intended, in the lung cancer cells.

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Fig 8. Sensitivity and differences.

The process diagram of the EPO-induced JAK2/STAT5 signaling pathway model is shown according to Systems Biology Graphical Notation. Identified parameter fold-changes between CFU-E and H838 cells are shown in red (higher in CFU-E: JAK2actEPO, EPORactJAK2, CISHRNAturn) or purple (higher in H838: STAT5imp, nSTAT5deact, SOCS3prom, SOCS3RNAdelay). Parameters with a more effective inhibition in H838 cells are shown in light blue (JAK2actEPO, EPORactJAK2, STAT5actJAK2, STAT5actEPOR, STAT5imp, STAT5exp, SOCS3RNAturn). The area-under-curve of npSTAT5 at 60 min after stimulation was used as read-out to calculate the sensitivities.

https://doi.org/10.1371/journal.pcbi.1005049.g008

Based on these results, the model suggests inhibitors for the receptor complex, e.g. a JAK2 inhibitor, as optimal drugs to diminish the EPO-induced JAK2/STAT5 signaling specifically in H838 cells while the CFU-E cells would continue to benefit from EPO treatment.

In sum, we demonstrate that the approach of ODE-based mathematical modeling in combination with L₁ regularization is an appropriate method to identify cell type-specific differences and suitable therapeutic targets.

NSCLC cell line and its derivative and cell culture conditions

Human lung adenocarcinoma cell line H838 was purchased from ATCC (CRL-5844) and cultivated in Dulbecco's modified Eagle's Medium (DMEM, Lonza) supplemented with 10% fetal calf serum (Gibco), 100 μg/ml streptomycin (Gibco) and 100 U/ml penicillin (Gibco). The Phoenix ampho packaging cell line [57] was cultured in DMEM (Gibco) supplemented with 10% fetal calf serum, 100 μg/ml streptomycin (Gibco) and 100 U/ml penicillin (Gibco). For the EPOR overexpressing cell line (H838-HA-hEPOR) 1.5 μg/ml puromycin (Sigma) was added. As growth factor depletion medium DMEM without phenol-red (Lonza) supplemented with 1 mg/ml BSA (Sigma), 100 μg/ml streptomycin (Gibco), 100 U/ml penicillin (Gibco) and 2 mM L-glutamine (Gibco) was used. All cells were cultivated at 37°C, 5% CO₂ and 95% relative humidity.

Generation of stably transduced H838 cells

Generation of the retroviral expression vectors pMOWS-GFP [58] and pMOWS-HA-hEPOR [59] have previously been described. To generate pMOWS-Casper3-GR, the Casper3-GR cassette of the vector pCasper3-GR (evrogen, #FP971) was cut out with the restriction enzymes BamHI and NotI and subcloned into the retroviral expression vector pMOWS [58], in which the puromycin resistance cassette was replaced with a neomycin resistance cassette.

Transfection of Phoenix ampho cells was performed by calcium phosphate precipitation. Transducing supernatants were generated 24 hours after transfection by passing through a 0.45 μm filter and supplemented with 8 μg/ml polybrene (Sigma). Stably transduced H838 cells were selected in the presence of 1.5 μg/ml puromycin (Sigma) 48 hours after transduction for H838-GFP and H838-HA-hEPOR and for the H838-HA-hEPOR-Casper3-GR cell line in the presence of additional 400 μg/ml G418 (Sigma).

Surface expression of the EPOR in H838-HA-hEPOR cells was verified by flow cytometry. H838-HA-hEPOR cells were detached with Cell Dissociation Solution (Sigma) according to the manufacturer’s instructions and stained with anti-HA antibody (Roche) diluted 1:40 in 0.3% PBS/BSA for 20 min at 4°C. Cells were washed with 0.3% PBS/BSA and incubated with secondary Cy5-labeled antibody against rat (Jackson Immuno Research), diluted 1:100 in 0.3% PBS/BSA, for 20 min at 4°C in the dark. After washing samples with 0.3% PBS/BSA, propidium iodide (BD Biosciences) was added to exclude dead cells. Canto II (BD Bioscience) was used for sample analysis. The expression of the Casper3-GR sensor and GFP was verified by life cell imaging.

Isolation of TER119⁻ erythroid progenitor cells at the CFU-E stage from murine fetal livers

All animal experiments were approved by the governmental review committee on animal care of the state Baden-Württemberg, Germany (reference number DKFZ215). At E13.5 Balb/c mouse embryos were dissected from the uteri of female mice euthanized by CO₂ inhalation. Fetal livers were resuspended in PBS/0.3% BSA and passed through a 40-μm cell strainer (BD Biosciences). Fetal liver cells (FLCs) were treated with 9 ml Red Blood Cell Lysis Buffer (Sigma-Aldrich) to remove erythrocytes. For sorting TER119⁻ erythroid progenitors, FLCs were incubated with rat antibodies against the following surface markers: GR1, CD41, CD11b, CD14, CD45R/B220, CD4, CD8 and Ter119 (BD Pharmingen), and 42.2.2 for 30 min at 4°C. After washing, cells were incubated for 30 min at 4°C with anti-rat antibody-coupled magnetic beads and negatively sorted with MACS columns according to the manufacturer's instructions (Miltenyi Biotech). Sorted CFU-E cells were cultivated for 12–14 hours in Panserin 401 (PAN-biotech) supplemented with 50 μM β-mercaptoethanol and 0.5 U/ml EPO alfa. Before the experiments, cells were growth factor-depleted for 60 min.

RNA extraction, cDNA synthesis and quantitative Real-Time-PCR

Total RNA was extracted using the miRNeasy Mini Kit (QIAGEN) according to the manufacturer’s instructions. cDNA was generated from 1 μg of total RNA using High Capacity cDNA Reverse Transcription Kit (Applied Biosystems) according to the manufacturer’s instructions. cDNA templates were analyzed by quantitative Real-Time-PCR (qRT-PCR) on a LightCycler 480 (Roche Applied Science) cycler using the LightCycler 480 Probes Master with final 0.4 μM primer and 0.2 μM FAM-labeled hydrolysis probes (Universal Probe Library, Roche Applied Science). Crossing point values were calculated using the second-derivative-maximum method of the LightCycler 480 Basic Software (Roche Applied Science). Quantitative RT-PCR efficiency correction was performed for each setup individually. Concentrations were normalized using the geometric mean of β-glucuronidase (GUSB) and esterase D (ESD) for the NSCLC cell line and its derivative and hypoxanthine-guanine phosphoribosyltransferase (HPRT) for the CFU-E cells. Primers were designed using the UniversalProbe Library Assay Design Center (Roche Applied Science).

UPL Probes and primer sequences for murine samples were CISH_for 5′-gacatggtcctttgcgtaca-3′ CISH_rev 5′-atgccccagtgggtaagg-3′ probe#1, SOCS3_for 5′- gctggtactgagccgacct-3′ SOCS3_rev 5′-aacttgctgtgggtgaccat-3′ probe#83, and HPRT_for 5′-tcctcctcagaccgctttt-3′ HPRT_rev 5′-cctggttcatcatcgctaatc-3′ probe#95. UPL Probes and primer sequences for human samples were CISH_for 5′-agccaagaccttctcctacctt-3′ CISH_rev 5′-tggcatcttctgcaggtgt-3′ probe#20, SOCS3_for 5′-agacttcgattcgggacca-3′ SOCS3_rev 5′-aacttgctgtgggtgacca-3′ probe#36, ESD_for 5′-ttagatggacagttactccctgataa-3′ ESD_rev 5′-ggttgcaatgaagtagtagctatgat-3′ probe#27 and GUSB_for 5′-cgccctgcctatctgtattc-3′ GUSB_rev 5′-tccccacagggagtgtgtag-3′ probe#57.

CellTiter-Blue viability assay

H838 and H838-HA-hEPOR cells were seeded in a 96-well plate at a density of 10 000 cells/well for three days. Before the experiment, cells were growth factor-depleted for 14–16 hours. To measure the viability of cells, CellTiter-Blue Viability Assay (Promega) was applied according to the manufacturer’s instructions. Incubation with the dye for 60 min was followed by measurement of the fluorescence with the infinite F200 pro Reader (TECAN). A blank well containing culture medium but no cells was measured as background.

Caspase-3 apoptosis assay

For the caspase-3 activity assay, H838 cells overexpressing HA-hEPOR and additionally expressing the FRET-based Casper3-GR sensor (H838-HA-hEPOR-Casper3-GR) were seeded in 8-well plates at a density of 20 000 cells/well. 24 hours after seeding, cells were growth factor-depleted for 16 hours and then treated with 5 mg/l cisplatin (Teva) or left untreated. Cells were imaged on an environment-controlled microscope (Zeiss LSM 710) and GFP and RFP intensity was determined. Images were acquired every 20 min for 64 hours.

Determination of cellular and nuclear volumes

H838-GFP cells were amplified to a density of 80% and growth factor-depleted for 14–16 hours. The cells were trypsinized with 0.025% Trypsin/EDTA/PBS (Invitrogen) for 5 min and resuspended in DMEM (Lonza) and Hoechst (H33342) (final concentration 1 μg/ml) was added. The cells were imaged on an environment-controlled microscope (Zeiss LSM 710) and the data was analyzed with Fiji software [60].

Quantitative immunoblotting

For the detection of the EPOR, JAK2 and STAT5, 800 000 H838 and H838-HA-hEPOR cells, respectively, were seeded three days in advance in a 10-cm plate and washed three times with DMEM without additives and then kept for 3 hours in DMEM with 1% penicillin/streptomycin, 2 mM L-glutamine (Gibco) and 1 mg/ml BSA. The cells were stimulated with 10 U/ml EPO beta (Roche) and lysed with 500 μL 1.25x NP-40 lysis buffer (1.25% NP-40, 187.5 mM NaCl, 25 mM Tris pH 7.4, 12.5 mM NaF, 1.25 mM EDTA pH 8.0, 1.25 mM ZnCl₂ pH 4.0, 1.25 mM MgCl₂, 1.25 mM Na₃VO₄, 12.5% glycerol) supplemented with aprotinin and AEBSF (Sigma). The cell debris was removed by centrifugation and the supernatant was used for determination of protein concentration (BCA Protein Assays, Thermo Fisher). Immunoprecipitations (IP) were performed consecutively with first antibodies against hEPOR (MAB 307, R&D) and JAK2 (06–255, Merck Millipore) and then with antibodies against STAT5A/B (C-17, Santa Cruz) using protein A sepharose beads. The immunoprecipitates were loaded to a 10% polyacrylamide gel and transferred to a nitrocellulose membrane (Schleicher & Schuell). The membranes were blocked with 5% BSA for 1 hour and successively incubated with a phosphotyrosine antibody (4G10, Merck Millipore). To remove antibodies, membranes were treated with β-mercaptoethanol and SDS and subsequently incubated with an anti-hEPOR antibody (C-20, Santa Cruz), an anti-JAK2 antibody (06–255, Merck Millipore) or an anti-STAT5 antibody (C-17, Santa Cruz). Secondary horseradish peroxidase-coupled antibodies were obtained from GE Healthcare or Dianova. Detection was performed using ECL substrate (GE Healthcare) and acquired with the CCD camera-based ImageQuant LAS 4000 (GE Healthcare). For quantification, the ImageQuant TL version 7.0 software (GE Healthcare) was used.

For the detection of mEPOR in mCFU-E cells, the cells were growth factor-depleted for 3 hours and 1×10⁷ cells shaking in 250 μl were stimulated for 10 min with 5 U/ml EPO alfa (Janssen-Cilag). The cells were lysed by addition of 250 μL 2x NP40 lysis buffer. IP was performed using an anti-mEPOR antibody (M-20, Santa Cruz) and protein A sepharose. For phosphorylated mEPOR, the phosphotyrosine antibody (4G10, Merck Millipore) was used. For total mEPOR anti-mEPOR antibody (M-20, Santa Cruz) was applied.

Determination of protein abundances

For determination of protein abundances different recombinant fusion proteins were synthesized using a pGEX-2T vector (GE Healthcare). GSTΔhEPOR and GSTΔmEPOR consist of the complete cytoplasmic part of the respective receptor fused N-terminally to a GST tag leading to proteins of 52 214 Da mass for hEPOR and 52 309 Da for mEPOR. GSTΔJAK2 and GSTΔSTAT5 were constructed as described previously [61]. Briefly, in GSTΔJAK2 the tag is fused N-terminally to the kinase domain of murine JAK2 starting from L549 leading to a 94 572 Da fusion protein with 95% consensus to human JAK2. GSTΔSTAT5 consist of the N-terminal end of murine STAT5B starting from F332 which leads to a fusion protein of 78 432 Da with 97% consensus to hSTAT5B.

The concentrations of the recombinant proteins were determined using a BSA standard curve on a Coomassie-stained SDS-PAGE gel (SimplyBlue SafeStain, Invitrogen). Different amounts of the respective calibrators were added to the cell lysate. IP and immunoblotting was performed with the indicated total antibodies. The linear calibration curve based on the intensities of the recombinant protein was estimated with SigmaPlot (V12.5) and the endogenous signal was interpolated to calculate the corresponding number of molecules. The cell number was counted in parallel with a Neubauer improved counting chamber.

Mass spectrometry

For mass spectrometry experiments, at least 1.5×10⁷ H838 or H838-HA-hEPOR cells were used per time point. Treatment, lysis and IP conditions are described above. IPs were separated by 10% SDS-PAGE and gels were stained with SimplyBlue SafeStain (Invitrogen). STAT5A (90.6 kDa) and STAT5B (89.9 kDa) containing bands were excised between around 75 and 100 kDa (according to Precision Plus Protein marker, Bio-Rad) then destained, reduced (DTT, Sigma), alkylated (IAA, Sigma) and digested with trypsin gold (Promega). To ensure robust and accurate degree of phosphorylation analysis of Tyr694 (STAT5A) and Tyr699 (STAT5B) we applied an internal standard peptide mixture (One-source peptide-/phosphopeptide ratio standard) with defined ratio of labelled peptide and its phosphorylated counterpart. Starting from the in-house synthesized stable isotope labelled phosphopeptide A-[V+6Da]-D-G-pY-V-K-P-Q-I-K (identical for STAT5A and STAT5B) the standard mixture was generated by (i) dividing peptide dilution into two aliquots (ii) quantitative dephosphorylation of one of the aliquots (iii) remixing of dephosphorylated and untreated aliquot (described in detail [62]). The standard was spiked into the samples during tryptic digestion. All mass spectrometry sample preparation steps from lysis to standard addition have been previously described in more detail [63]. Following peptide extraction and concentration of eluates, samples were desalted and purified using C18 ZipTips (Merck Millipore). Samples were measured by nanoUPLC (nanoAcquity, Waters) coupled to an LTQ-Orbitrap XL mass spectrometer (Thermo Fisher). LC separations were performed on a 75 μm × 150 mm C18 column with 1.3 μm particle size (Waters) using a water/acetonitrile based gradient up to 40% acetonitrile within 60 min. Intensities of native and labelled STAT5 peptide and phosphopeptide pairs were analyzed manually using Xcalibur 3.0.63 (Thermo Fisher).

Analysis of the SOCS3 promoter and DNA methylation measurement

Genomatix Genome Analyzer was used for promoter analysis (www.genomatix.de). Promoter retrieval was performed by Genomatix Gene2Promoter (ElDorado 12–2013) and the transcription factor binding site analysis was performed using the Genomatix Overrepresented TFBS pipeline combining Genomatix MatBase and MatInspector based on Matrix Family Library Version 9.1. Sequence alignment was performed using the Genomatix Multiple Alignment pipeline based on DiAlign professional TF Release 3.1.5 (June 2011).

H838 and CFU-E cells were cultivated as described above. Genomic DNA was extracted with the DNeasy Tissue Kit (Qiagen) according to the manufacturer's instructions and bisulfite converted using the EZ DNA Methylation kit (Zymo Research). Amplicons spanning the entire SOCS3 promoter region were designed and used to amplify this region from bisulfite-treated DNA (S2 Table). For MassARRAY EpiTYPER assay (Agena Bioscience), the PCR products were transcribed in vitro, cleaved by RNase A and subjected to matrix-assisted laser desorption ionization time-of-flight mass spectrometry to quantitatively assess methylation levels of CpG dinucleotides [64].

Model simulation and parameter estimation

The ODE system consisted of 23 states, with 20 initial values that were implicitly dependent on kinetic parameters through steady-state assumptions, two initial values with prior knowledge available, and one initial value with prior knowledge only available for CFU-E, which was estimated for H838 & H838-HA-hEPOR. To obtain a numerical solution of the ODE system the solver CVODES was applied [65]. For CFU-E cells, 23 model variants representing experimental conditions were implemented, and 36 for H838 & H838-HA-hEPOR cells, respectively. For numerical efficiency, the ODE system and solver were compiled as C-executables, supplying calculation of states as well as sensitivities, and solved in a parallelized manner for all conditions. Data2Dynamics [31] was utilized to facilitate the automatic derivation of conditions and sensitivity equations. The ODE system was re-parameterized to disentangle internal concentrations from relative measurements and to decouple modules of the signaling network with different scales. Relative and absolute tolerances of the ODE solver were set to 10⁻⁶.

For parameter estimation, all three cell types CFU-E, H838 and H838-HA-hEPOR were initially implemented separately. To achieve global optimization, a multi-start deterministic optimization strategy was used [37] with 1000 initial parameter vectors for each cell type. Each single optimization was performed using the MATLAB implementation of the trust-region method (lsqnonlin) [66]. The algorithm was set to terminate an optimization run if the proposed step size is smaller than 10⁻⁶. To account for flat regions in the parameter space, the termination criterion based on change of the objective function was omitted. A noise parameter was assumed for each experimental technique, observable and cell type. For intensity-based measurements, a log-normal error model was used, where σ is relative to the observation [67]. For degree of phosphorylation data obtained by mass spectrometry, a constant error model was assumed. Kinetic parameters, initial concentrations, observation parameters and error model parameters were estimated simultaneously based on the data [37]. Parameters were estimated in log-space and values between 10⁻⁵ and 10³ were initially allowed. If an estimate was located at the boundary of the parameter space, the respective boundaries were enlarged. Efficiencies of inhibitors were limited to a maximum of one (100% efficiency), and the accuracy of degree of phosphorylation data obtained by mass spectrometry was restricted to a maximum of 5%.

For CFU-E cells, 516 data points were used to estimate a total of 109 parameters. 1000 parameter estimation runs were started from random points of the parameter space. The global optimum was found in 9.0% of parameter estimation runs. Likewise for H838, 204 data points were used to estimate 54 parameters. Here, the global optimum was found in 5.2%. For H838-HA-hEPOR, 407 data points were used to estimate 75 parameters with the global optimum reached in 0.7% of all optimization runs. These results suggested that the global optimum was discovered for all cell types.

L₁ regularization and uncertainty analysis

The comprehensive model taking all cell types into account had a total of 216 parameters that were estimated based on 1141 data points. The parameters were estimated independently for CFU-E and H838 & H838-HA-hEPOR cells, and the corresponding fold-change was L₁-regularized. Residuals and sensitivities were passed to the optimizer. To account for discontinuities of the L₁ regularization gradient, optimization steps were truncated in the derivatives by preventing to cross zero at each step. To facilitate convergence, derivatives of the L₁ regularization residuals were set to zero if their contribution was smaller than the respective gradient of the log-likelihood. The re-parameterization to decouple modules of the signaling network was performed with CFU-E as reference point for H838 & H838-HA-hEPOR. For generating the regularization path, the regularization strength was scanned in log-space from 10⁻⁴ to 10⁴. Regularization was only used for selection of parameter differences, while for model selection the un-regularization solution was used for unbiased parameter estimates. The threshold for model selection was calculated using likelihood ratio test statistics (α = 0.05), i.e. by the inverse cumulative density function of the χ²-distribution with the difference of number of parameters between full and reduced model as degrees of freedom.

The profile likelihood was calculated to assess the standard deviation of the parameter ratios [35]. To conservatively estimate the standard deviation based on asymmetric confidence intervals, the maximum of the log₁₀ difference between maximum likelihood estimate and lower/upper limit of the confidence interval was used to approximate σ.

Modeling framework, examples and data are open source and publicly available at www.data2dynamics.org.