Selection of drug concentrations.

For each drug, the concentration was chosen by literature review or experimental dose response measurements by western blot. The low dose was selected to reduce activity on a known target by 50%. We also used a high dose, which was defined as double the absolute concentration of the low dose.

Molecular measurements.

Cells were collected at 8 time points after drug addition in logarithmic progression (10, 27 and 72 minutes and 3, 9, 24, 48, and 67 hours). The temporal proteomic response of the cells to the different conditions was derived using reverse phase protein array (RPPA) measurements in 124 total and phospho-protein levels [19] from minimally three biological replicates across two data sets. Antibodies were selected to broadly cover signaling pathways with known involvement in cancer (e.g., AKT, ERK, and JAK/STAT pathways).

Phenotypic measurements.

We used live cell imaging to follow A2058 cells as they responded to drug treatment (Incucyte, Essen BioScience, Ann Arbor, MI, U.S.A.). We acquired GFP, mCherry, and phase images of all conditions every 3 hours for 72 hours following drug addition. Cell number was determined at each time point by counting using image segmentation software (Incucyte), which identified the transgenic H2B-mCherry fluoraphore. Apoptosis was determined by image segmentation and counting of the GFP channel, which measured a Caspase-3/7 fluorescent activity reagent (Essen BioScience). Data were sub-sampled to select time points that closely matched collection of the proteomic data (1, 3, 9, 24, 48, and 67 hours).

Agreement of experimental results with literature.

As most of the selected drugs have well described signaling effects, i.e., kinase substrates whose activity is directly affected by the drugs (S1 Table), we asked whether each drug elicited the expected molecular changes. The drugs that target MEK, AKT, and JNK, resulted in the expected decrease of their known targets ERK1/2-pT202/T204, AKT-pS473/pT308, and CJUN-pS73, respectively (S2 Fig). RAF and mTOR inhibition did not result in a strong decrease in their direct targets (MEK1/2-pS217/221 and S6K-pT389, respectively), but they did significantly decrease signaling in further downstream nodes ERK1/2-pT202/T204 and S6-pS235/236. For the STAT3 and SRC inhibitors, the proteins’ highest-ranked responders are not known to be downstream targets, but may be indirectly affected via multiple steps, signaling feedback or crosstalk.

The live-cell imaging data (see Materials and methods) revealed the bromodomain inhibitor CPI203 (BET inhibitor) to be the most potent drug, at the chosen concentrations, in terms of both decrease in cell growth and increase in apoptosis after three days of treatment (S1 Table, S1 Fig). These data are in agreement with results on the effect of this inhibitor class in the drug-resistant melanoma cell line SkMel-133, which also strongly impaired cell growth in response to the bromodomain inhibitor JQ1 in combination with MEK and ERK inhibitors in our earlier work [4].

Network models.

To model the cellular processes, we used the previously proposed nonlinear multiple input–multiple output model [4, 20, 21]. This model has the ability to capture a wide range of biological and kinetic effects, and has been applied to diverse biological problems including to predict the effect of novel drug combinations [4, 6]. (1) The time-dependent variable describes the dynamics of node i (in our context a protein level or measured phenotype) and the impact of a perturbation on node i (e.g., the application of a single drugs or drug combinations) in experimental condition μ. Here, w_ij denotes the interaction between the nodes i and j (more specifically, molecules, phenotypes, drugs or processes). Intuitively, w_ij > 0 corresponds to activation of node i by node j, and w_ij < 0 to inhibition. The prefactor α_i quantifies the rate at which node i returns to its initial state x_i = 0. The sigmoidal transfer function tanh is used to cap the reaction rates and to account for saturation and noise. Consequently, the prefactor ε_i > 0 determines the dynamic range of node i as values of tanh are limited to the one-dimensional unit ball [−1, 1]. To obtain data-derived network models, we used Eq 1 and constrained its parameters to the proteomic and phenotypic measurements in 54 drug combination conditions and at 8 time points. Our full model contained 124 molecular and two phenotypic nodes. For a complete description of the model equations, see Materials and methods.

Model selection and error estimation.

Datasets were subdivided into training, validation and test sets (gray, green and blue boxes, respectively, in Fig 3 top left). The training sets contained all data from single-drug experiments; the validation and test sets were constructed such that (i) they contain all pairwise drug combinations and (ii) every drug has the same number of occurrences in both sets. Model parameter estimation was performed on the training dataset. We varied the regularization parameter λ on a linear grid and trained 10 network models per grid value. As expected, higher values of λ resulted in sparser networks with fewer interactions (Fig 3 top right, magenta) and higher error on the training data (Fig 3 bottom left, gray). The optimal regularization strength was selected using the validation dataset by (i) Bayesian Information Criterion (BIC) computed on the training set (Fig 3 top right, gray) and (ii) by residual sum of squares (RSS) (Fig 3 bottom left, green). This regularization parameter was determined to be λ* = 3 for both the BIC and RSS metric (Fig 3, bottom left). The same result was obtained when using Pearson’s correlation coefficient (S4 Fig). We studied the accuracy of the final models on the independent test dataset (Fig 3 bottom right). The resulting generalization error for optimal λ* on left-out data had a mean of 0.181 across the 10 models and of 0.118 for phenotypic data alone, and the corresponding Pearson correlation coefficient between model prediction and the experimentally measured data was 0.54 (molecular and phenotypic) and 0.79 for the phenotypic data alone. The correlation was found to be higher in the later time points of molecular and phenotypic data. In particular, the Pearson correlation coefficient between predictions and measurements of the combined molecular and phenotypic data was 0.71 on the combined last three time points (24, 48, and 67 hours) and 0.74 for the last time point alone (S5 Fig). Hence, the inferred temporal model had the highest accuracy at the 67-hour time point. We conclude that the method for network modeling has a reasonably accurate predictive power, especially for predictions in the 24–67 hour range and that the models are useful for predicting the effects of new perturbations as hypotheses. Reasonable accuracy means that an affordable number of experiments would lead to a positively validated result (a ‘hit’) that can be advanced to pre-clinical investigation.

Analysis of network models.

We used the optimal regularization parameter λ* = 3 to infer 101 network models on all available data. To have reasonable diversity, the models were inferred without using prior information, i.e., known biological interactions. Several key model interactions agreed with interactions reported in the literature. The inferred effect of selected drugs on proteins (Fig 4) was in agreement with known drug–protein interaction patterns (e.g., MEKi inhibits the phorphorylation of ERK1/2 at T202/Y204 and RAFi inhibits MEK1/2 phorphorylation at S217/221) as well as unknown interactions (e.g., PKCi inhibits phorphorylation of CREB at S133). In addition, these model-derived drug–protein effects were in agreement with the observed drug effects from single-drug RPPA measurements (S2 Fig).

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Fig 4. Model-inferred effect of drugs on proteins and phospho-proteins.

The effect of drug treatment on (phospho-)protein levels is captured as edges between drugs (colored circles) and proteins (gray circles) in the model (represented by the drug–(phospo-)protein interaction strength d_il from Eq 2). Some of the edges are well known (e.g., MEKi inhibits ERK1/2-pT202/T204) and some appear to be novel or indirect (e.g., inhibitory effect of PKCi on CREB-pS133). Based on the distribution of edge values over the 101 network models, only the strongest drug–protein edges are displayed for visualization purposes (85th percentile for positive/activating interactions and 15th percentile for negative/inhibiting interactions, by absolute value).

https://doi.org/10.1371/journal.pcbi.1007909.g004

Saturation effects of drugs are taken into account by the model using the open parameter δ_i. For values of 0 < δ_i < 1, we have an almost linear drug effect; values of δ_i > 1 do not result in any significant change as drug concentrations increase. For the case of PKC and SRC inhibitors, we find a δ_i in the linear range, i.e., that a doubling of the low dose results in almost the double response, while RAF and JNK inhibitors have almost reached saturation, i.e., no significant difference between the drug effect in low and high dose of the drugs (S3 Fig).

Predicted effect of drug perturbations and nomination of targets for drug testing.

Using the 101 inferred network models, we predicted the phenotypic response (cell growth and apoptosis) as a function of network node inhibition (proteins and phospho-proteins). In particular, we systematically simulated a wide spectrum of inhibition strengths (c^pert) targeting every molecular node (Eq 7) and the phenotypic response according to Eq 8 at t = 72 h (see Materials and methods). The mean resulting dose response curves across all models when inhibiting each molecular node was used to estimate the half maximal effective concentrations (EC₅₀) for cell growth (S6 Fig) and apoptosis (S7 Fig). We further used these EC₅₀ concentrations to simulate the effect of pairwise combination perturbations of the 124 proteins and phospho-proteins on each phenotypic node independently across all models.

The predicted phenotypic responses were averaged across all models and the first 20 unique nodes were selected from the highest ranking combinations (Fig 5 left: cell growth reduction, right: apoptosis increase). In total, we predicted cell growth and apoptosis for 124 ⋅ 123 = 15, 252 conditions for 101 networks, resulting in 1, 540, 452 simulated responses (S8 and S9 Figs).

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Fig 5. Model predicts the effect of combination perturbations and suggests optimal inhibitor combinations.

The top 20 × 20 predictions of pairwise inhibition of molecular nodes (i.e., proteins and phospho-proteins) that decrease cell growth (bottom left, blue) and increase apoptosis (bottom right, red). Cell growth and apoptosis were computed for each target combination. These values were log₂-transformed, normalized to the unperturbed steady state, and the average value over 101 network model predictions is presented (diagonal represents predictions for inhibition of single targets). Combinations nominated for drug testing are highlighted by dark-rimmed squares. For complete heatmaps of all tested predictions, see S8 and S9 Figs.

https://doi.org/10.1371/journal.pcbi.1007909.g005

The most effective predicted combination for decreasing cell number was found to be inhibition of phospho-tyrosine at position 992 on EGFR together with phospho-serine at positions 636/639 on IRS1 (Fig 5 left). Simultaneous inhibition of the protein IRS1 together with reduction of phospho-serine at positions 636/639 on IRS1 was found to the most effective combination for increasing apoptosis (Fig 5 right). Note that predicted perturbation of IRS1 alone had the nearly the same effect on apoptosis as in the combination.

EGFR is involved in growth signaling through the RAS/MEK pathway, and EGFR-pY992 is an activating auto-phosphorylation site at the receptor [22]. There are many available drugs that specifically inhibit EGFR and are expected to decrease EGFR-pY992, for example the drugs lapatinib [23], gefinitib, and erlotinib. Inhibitors of EGFR alone do not have a strong anti-proliferative effect in melanoma cell lines [24].

IRS1 transmits signals from IGFR to PI3K/AKT. The protein can be inhibited by the compound NT157 [25], which has two mechanisms of action: 1) reduce IGF1 signaling through dissociation of IRS1 from the IGF1 receptor, and 2) reduce levels of IRS1 by phosphorylation at serine sites that lead to proteosomal degradation [25]. IRS1-pS636/639 is one such serine phosphorylation site [25]. The inhibitor NT157 is reported to first increase IRS1-pS636/639, which induces degradation of IRS1 (within hours) [25]. It has been reported that NT157 inhibits proliferation in the RAF inhibitor resistant melanoma cell line A375, both through reduced IGF1-signaling and reduced STAT3-signaling [26]. The inhibitor NT157 has also been shown to increase the tyrosine-phosphorylation 1172 at EGFR in the melanoma cell line A375 [27]. Using an EGFR inhibitor to abrogate this increase in EGFR-pY1172 after NT157 treatment may provide a mechanism for increased drug efficacy. In summary, simultaneous inhibition of IRS1 and EGFR is predicted to both reduce cell growth and increase apoptosis. In theory, this effect can be achieved by using the drugs NT157 (IRS1 inhibitor) and gefitinib (EGFR inhibitor).

Bayesian information criterion.

Assuming independent and identically distributed model errors drawn from a normal distribution, the maximum loglikelihood can be expressed in terms of the minimum , where is the parameter set that maximizes the likelihood function. We use the following simplified definition of the Bayesian information criterion, BIC, where k is the number of non-zero model parameters and n is the number of data points used in the parameter estimation. The number of non-zero parameters is a function of the regularization applied via λ, i.e., k = k(λ). We select the optimal regularization parameter λ as the minimum of the BIC, where we omitted contributions from constants that are dependent on the number of data points n. For the current data set, the optimal regularization parameter is found as λ* = 3 for the Bayesian information criterion (Fig 3 top right). The Akaike information criterion did not have a clear minimum.

Dataset division.

In addition to selecting λ using the Bayesian Information Criterion, the optimal regularization parameter λ* is evaluated by splitting the data into a training dataset to estimate the model parameters, a validation dataset to determine an optimal λ, and a test dataset to evaluate model performance. The training set is chosen to contain all single drug conditions, and the test sets are chosen as a split between all combinations of drugs (Fig 3 top left). As with the Bayesian Information Criterion, the optimal regularization parameter is found to be λ* = 3 (Fig 3 bottom left).

Selection of inhibition strength for in silico combination perturbations.

We assume the solution of Eqs 7 and 8 at t = 72 h to have the following shape when molecular node i is perturbed with a single in silico inhibitor applied with concentration , where and represent the maximum and minimum change in each phenotype, respectively. is the concentration of the in silico inhibitor specifically targeting molecular node i. n and c are open parameters. n is the Hill coefficient and c is the in silico-derived 50%-effect concentration, EC₅₀. In our framework, we focus on the effect on cell growth and apoptosis by single molecular node inhibition. As the data are all log₂-normalized to control data, and so the equation above simplifies to, (9) with and (see S6 and S7 Figs for the mean individual dose response of apoptosis and cell growth as a function of inhibiting single molecular nodes). These in silico-derived EC₅₀ are subsequently used for molecular node inhibition simulations. These simulations are systematically carried out such that all single and pairwise molecular nodes are perturbed, and their effect on cell growth and apoptosis is calculated (Fig 5).

The scale of concentration in the simulations, and hence the estimated in silico EC₅₀ concentration (parameter c in Eq (9), S6 Fig), is expressed in arbitrary units, but can nevertheless be related to the experimental EC₅₀ concentration. This can be done by equalising the estimated in silico and experimentally determined EC₅₀ values. This assumes however that the inhibitor used in the experiments is of perfect specificity.

Numerical solution and simulation of model equations and systematic perturbations.

The above specified ordinary differential equations were numerically solved with a second-order Runge–Kutta method with two stages and a fixed step size in a Python environment. As a quality check, these results were compared with those using the ode15s solver for stiff differential equations in MATLAB R2018a (Mathworks, Natick, MA, U.S.A.) and were in agreement.

Molecular measurements in response to perturbation.

The melanoma cell line A2058 was seeded in 6-well plates at 50,000 cells per well. Each biological replicate was run on separate occasions. The physical difficulties and logistical complexity of the experiments required that each time point be run in batches with the early time points being harvested immediately and the late time points being setup immediately following time point harvesting. Perturbed cells were lysed in CLB1 buffer (Bayer Technology Services, Leverkusen, Germany; now NMI TT Pharmaservices, Reutlingen, Germany). For Dataset 1, we performed a 4-fold dilution series of the samples using the Biomek FXP Laboratory Automation Workstation (Beckman Coulter Inc., Brea, CA, U.S.A.) automatic pipetting system in one technical replicate [19]. For Dataset 2, [a single lysate sample was printed twice (technical replicate)] each lysate sample was printed at the respective protein concentration in two technical replicates. Diluted samples were printed onto tantalum pentoxide-coated glass chips and then blocked with an aerosol BSA solution. The protein array chips are then washed in double-distilled H₂O and dried before measurement. For the immunoassay, we incubated the chips with primary antibodies for 24 hours followed by 2.5 hours incubation with Alexa Fluor-647 conjugated secondary antibody detection reagents. Antibodies are diluted in CAB1 buffer (Bayer Technology Services, Leverkusen, Germany). The immuno-stained chips were imaged using the ZeptoREADER (Zeptosens/Bayer, Witterswil, Switzerland). The ZeptoView 3.1 software (Zeptosens/Bayer, Witterswil, Switzerland) was used to output the reference net spot fluorescence intensity, RNFI. Included standard global and local normalization of sample signal to the reference BSA grid is used.

Sample lysis and RPPA chip layout and analysis.

All experimental perturbations and sample preparations were carried out in the Sander lab. Cell lysate was aliquoted into multiple samples, and RPPA measurement using the zeptosens platform was carried out in both the Sander lab (MSKCC, Dataset 1) and the Pawlak lab (NMI TT Pharmaservices, Dataset 2).

Differences between each dataset.

Dataset 1 consists of 71 antibody measurements of three biological replicates at eight time points (10 min, 27 min, 72 min, 3 h, 9 h, 24 h, 48 h, 67 h). For Dataset 1, each RFI data point, , was derived from a four-spot protein dilution series of 0.2, 0.15, 0.1, and 0.05 . Dataset 2 consists of 86 antibody measurements of three biological replicates at (a) eight time points for biological replicate 1 and (b) two time points (48 h, 67 h) for biological replicate 2 and 3. For Dataset 2, protein lysate was diluted to 3 μg/μl, when concentration was higher than 3.4 μg/μl, and each RFI data point was derived from the mean of two measured spots. Median-centered protein factors, determined for each sample by NMI TT Pharmaservices, were used to normalize protein content.

Similarities between each dataset.

All data were acquired from the same RPPA platform (Zeptosens/Bayer, Witterswil, Switzerland). 33 antibodies were measured in both datasets as controls, which resulted in 71 + 86 − 33 = 124 unique antibodies. After outlier detection and loading normalization (see above), the median of the three biological replicates from Dataset 1 and the median of the data (one biological replicate in six time points and three biological replicates in two time points) from Dataset 2 was combined and used in the downstream analysis and modeling steps.

Fluorescence signal evaluation.

Each spot measured on the Zeptosens array corresponds to the relative concentration of a specific protein or phospho-protein in a single condition. This value is detected by measuring the secondary antibody fluorescence that is bound to the (phospho)protein-specific antibody. The relationship between this signal and the absolute concentration of the (phospho-)protein is assumed to be linear in the observed range, i.e., given constant exposure times across all the experimental conditions and time points in each antibody measurement. In Dataset 1, for each (phospho-)protein i one measures four antibody fluorescence signals , , and , corresponding to the four serial dilutions of cell lysate , , and . These values are referred to as Referenced Net spot Fluorescence Intensity (RNFI). This allows to quantify the degree of “non-linearity” of the signal by computing the discrepancy between linear fit and actual signal. Assuming a linear dependency, then , the fitting parameters are found in a least-squares estimation, where, For ideal profiles, i.e., without intercept or , we have (and consequently, ). A single value, the Referenced sample Fluorescence Intensity (RFI), corresponding to the linear fit of the 4-spot array corresponding to the mean concentration value, , is chosen, Zeptosens calls the RFI using the reference concentration of the total protein content per spot (). This concentration was chosen to be roughly the protein content of a eukaryote cell. Ideally, the concentrations for each sample are , but in practice c_i varies due to experimental uncertainties. We could estimate a posteriori the actual protein loading quantification with the reference loading chip and subsequently adjust for each sample by setting . For Dataset 2, we adopt this strategy and use on-chip measured median-centered protein factors determined from protein stain assays. However, for Dataset 1 we had no measurements of the protein loading and therefore applied double-median normalization (see [39]) for protein loading normalization.

Spotting error detection.

For Dataset 1, due to stochastic sampling, low concentrations or saturated sample, as well as occasional robotic errors, some lysate spots in the serial dilutions do not follow the expected linear and monotonically decreasing dilution profile. We identify outliers that deviate strongly from the linear interpolation of the RNFI values using the Cook’s distance [43]. We then use a Cook’s distance of 0.8 as cutoff. For Dataset 2, the spotting quality appeared to be more consistent and no spotting error removal was required.

Protein loading normalization.

Occasionally, samples have total protein concentrations that deviate from the optimal loading concentration. To normalize for this uneven loading in the we perform double-median normalization (sometimes referred to as “loading control”) as described in [44]. For Dataset 1, the log₂-transformed and normalized value for the i-th antibody in time-point k and under experimental condition μ is then calculated as, Here, denotes the linear raw data of antibody i measured in time point k under experimental condition μ, the median of the log₂-transformed values in each antibody across time points and experimental conditions and its median absolute deviation. In Dataset 2, in contrast to Dataset 1, we have an estimate on the relative deviation from the target protein loading concentration in each sample of 0.3 μg/μl. The observed protein loading was lower and found to have a median concentration of 0.22 μg/μl). Based on these measurements, we normalize each lysate sample by the corresponding on-chip measured median-centered protein factors.

Data normalization.

Before applying any further modeling and inference, we subtract the log₂-transformed and double-median normalized RPPA data in the DMSO control condition (without perturbation) from all previously log₂-transformed and double-median normalized RPPA data, :

Cell line.

Cell line A2058 with H2B-mCherry was thawed, tested for mycoplasma, and passaged twice prior to testing. The cell line was passaged fewer than 15 times and screened with the compounds within a month of thawing. The cell line was passaged and cultured on DMEM media with 10% FBS and 1% Penicillin/Streptomycin.

Screening protocol.

Cells were harvested, counted, and deposited into 384 well plates at a total volume of 50 μl per well with a t₀ seeding density of 750 cells/well using a Thermo Multidrop Combi dispenser (Thermo Fisher Scientific, Waltham, MA, U.S.A.). Cells were immediately placed into the Incucyte microscope culture and allowed to attach and proliferate for 24 hours. Four compounds (NT157, CAS285986, gefitinib, SB203580) were dissolved into 10 mM solutions two hours prior to dosing. The compounds were dispensed into the previously seeded 384 well plates using a HP D300e Digital Dispenser 24H after cell seeding in a dose matrix testing each concentration point of each drug in combination with each concentration point of the other drugs, with three of the drugs (NT157, gefitinib, and SB203580) titrated from 0.01 μM to 10 μM and CAS285986 titrated from 0.075 μM to 75 μM. The plates were then placed back into the Incucyte and cell measurements were recorded every 3 hours for 96 hours.