Computational Modeling Implicates Protein Scaffolding in p38 Regulation of Akt

Abstract

Cells process environmental cues by activating intracellular signaling pathways with numerous interconnections and opportunities for cross-regulation. We employed a systems biology approach to investigate intersections of kinase p38, a context-dependent tumor suppressor or promoter, with Akt and ERK, two kinases known to promote cell survival, proliferation, and drug resistance in cancer. Using live, single cell microscopy, multiplexed fluorescent reporters of p38, Akt, and ERK activities, and a custom automated image-processing pipeline, we detected marked heterogeneity of signaling outputs in breast cancer cells stimulated with chemokine CXCL12 or epidermal growth factor (EGF). Basal activity of p38 correlated inversely with amplitude of Akt and ERK activation in response to either ligand. Remarkably, small molecule inhibitors of p38 immediately decreased basal activities of Akt and ERK but increased the proportion of cells with high amplitude ligand-induced activation of Akt signaling. To identify mechanisms underlying cross-talk of p38 with Akt signaling, we developed a computational model with subcellular compartmentalization of signaling molecules by scaffold proteins. Dynamics of this model revealed that subcellular scaffolding of Akt accounted for observed regulation by p38. The model also demonstrated that differences in the amount of scaffold protein in a subcellular compartment captured the observed single cell heterogeneity in signaling. Finally, our model suggests that reduction in kinase signaling can be accomplished by both scaffolding and direct kinase inhibition. However, scaffolding inhibition can potentiate future kinase activity by redistribution of pathway components, potentially amplifying oncogenic signaling. These studies reveal how computational modeling can decipher mechanisms of cross-talk between the p38 and Akt signaling pathways and point to scaffold proteins as central regulators of signaling dynamics and amplitude.

1. Introduction

Cells respond to environmental and internal cues using dynamic, intersecting networks of kinases. Kinases regulate fundamental aspects of normal physiology and disease, including differentiation, metabolism, and drug resistance. Previous research reveals substantial cell-to-cell heterogeneity in kinase activation, even among isogenic cells responding to an identical stimulus ^1–3. Heterogeneity arises from both intrinsic randomness in the chemical reactions in kinase pathways and extrinsic variability in protein expression levels and cellular organization^4–6. Understanding mechanisms that establish and regulate heterogeneity among cells offers the potential for more effective cancer treatments, as treatments that “miss” some cells due to their heterogeneity may fail^6–8.

The p38 mitogen activated protein kinase, which controls processes including stress responses and cell death decisions, has been studied extensively in the context of cancer with mixed, frequently hard-to-predict results⁹. For instance, Zhang et. al. found that inhibiting p38 could produce pro-survival or pro-death effects on colorectal cancer cells depending on the level of a phosphatase in the cells¹⁰. p38 suppressed mitogenic activity of ERK in cells with high levels of phosphatase PP2AC, so inhibiting p38 allowed activation of ERK to increase cancer cell growth. With low PP2AC, inhibition of p38 resulted in downstream suppression of mTORC1, a kinase complex necessary for proliferation of cells. Chen et al. found that in breast cancer cell lines, sensitivity to p38 inhibition depended on p53 status¹¹. Cells with wild-type p53 showed sensitivity to p38 inhibition, while cells with mutant p53 resisted inhibitors of p38. Miura et al. demonstrated that the balance between p38 and JNK (another stress related kinase) predicted apoptosis in individual cells¹. Cells with cells with high p38 survived due to inhibition of JNK. Thus, effects of p38 on cell survival are complex, contingent on other cellular processes, and heterogeneous in populations of individual cells.

p38 affects other cell signaling pathways, including kinases ERK and Akt^3,9,12,13. Breast cancers commonly show increased activation of ERK and Akt, which drive oncogenic processes including unregulated proliferation, drug resistance, migration, and metastasis¹⁴. Even cells with constitutively active ERK or Akt pathways exhibit substantial variability in kinase activity, highlighting the need to determine non-genetic sources of ERK and Akt heterogeneity^2,15. p38 intersects with ERK and Akt pathways through several mechanisms that depend on cellular context and mutational status. p38 inhibits mTORC1 by activating a negative regulator, tuberous sclerosis complex 1/2 (TSC1/2)^10,16. Both ERK and Akt signal through mTORC1 to drive cell growth and proliferation. p38 increases transcription and translation of phosphatases, such as PP2A that inhibits components of ERK and Akt signaling pathways¹³. p38-ERK-Akt cross-talk also occurs through scaffolding on proteins such as EEA1 or HSP27^17–19. By bringing signaling proteins into close proximity, scaffolding increases rates of kinase reactions and may protect kinases from negative regulation by phosphatases^20,21. These regulatory mechanisms are not mutually exclusive, and specific pathways and/or extent of regulation may vary among cell types or even individual cells.

We previously demonstrated marked heterogeneity in ERK and Akt signaling in single cells and developed a computational model that defined how pre-existing cell states regulate variations among cells ^2,15. Based on known intersections with ERK and Akt, we hypothesized that p38 regulates pre-existing cell states and heterogeneity in ERK and Akt signaling. Using multiplexed live-cell signaling reporters for ERK, Akt, and p38 and automated image processing, we revealed unprecedented single-cell relationships among the pathways^22,2322,23. We discovered that p38 activity negatively correlates with activation of ERK and Akt in response to chemokine CXCL12 and epithelial growth factor (EGF). Inhibiting p38 potentiated subsequent activation of Akt and ERK in subsets of cells, demonstrating an unexpected mode of cross-talk among pathways. Using our validated computational model of EGF/CXCL12 signaling to ERK and Akt, we tested several hypotheses to explain interconnections of p38 with activation of Akt and ERK. We developed a novel computational model including subcellular compartmentalization of signaling proteins to explain the observed behavior. Our model suggests that p38 indirectly regulates Akt through scaffold proteins that control subcellular compartmentalization of kinases, underscoring critical functions of protein scaffolding in signaling outputs of cells.

2. Results

2.1. Measuring multiplexed kinase activity in thousands of single cells over time

We first measured kinase dynamics in single cells after various perturbations to p38, ERK, and Akt. To acquire these measurements, we used multiplexed fluorescent kinase translocation reporters (KTRs) to simultaneously measure activities of p38, ERK, and Akt in living cells^22,23. KTRs reversibly translocate between the cytoplasm and the nucleus based on the specific activity of their upstream kinase, providing a quantitative, dynamic imaging readout (Figure 1A). The KTR construct also encodes a nuclear marker, H2B-mCherry, for automated image processing and analysis of thousands of single cells tracked over time. We stably expressed KTRs in MDA-MB-231 breast cancer cells. While mutations in these cells cause constitutive activation of ERK, we previously observed heterogeneity in both basal ERK and Akt activities and responses to CXCL12 and ERK ^2,15. We quantified activities of ERK and Akt under basal conditions and in response to EGF or CXCL12 based on the ratio of fluorescence intensities of each KTR in the cytoplasm versus nucleus (cytoplasmic to nuclear ratio, or CNR) (Figure 1B). This automated workflow allows us to extract matched, quantitative p38, ERK, and Akt trajectories over time for hundreds of individual cells in different experimental conditions.

Figure 1: Baseline and ligand-stimulated heterogeneity in ERK, Akt, and p38 measured with a multiplexed fluorescent reporter system|.

A) Schematic showing reversible translocation of a kinase translocation reporter (KTR) and the multiplexed reporters expressed in MDA-MB-231 cells. B) Experimental schematic showing a single stimulus added to cells expressing KTRs C) Mean and single cell dynamics for each reporter after addition of 10 ng/ml EGF. Each subplot shows the response of the same two cells measured by different reporters. Two representative cells are shown. Data are presented as the log base 2 of the cytoplasmic to nuclear ratio (CNR) of fluorescence intensities for each reporter. D) Same as in (C) but with 10 ng/ml CXCL12 stimulus.

2.2. p38 activity predicts responses of Akt to ligands

We stimulated MDA-MB-231 cells with 10 ng/ml CXCL12 or EGF, both of which activate ERK and Akt pathways. Using live cell imaging, we quantified single-cell ERK, Akt, and p38 activities before and after stimulation and calculated changes in activity of each kinase in response to a ligand. We found marked heterogeneity in cell responses, such that mean cell behavior and individual cell behavior could be quite different (Figures 1C and 1D). Responding cells show increases in CNR within minutes and remain active for at least an hour. EGF produced a higher mean amplitude of Akt response than CXCL12. Mutations in MDA-MB-231 cells constitutively activate ERK, elevating basal activity and dampening overall fold-change in CNR in response to stimulation. Cells showed minimal activation of the p38 reporter after treatment with either ligand. For both ligands, single cell data suggest that cells with higher pre-stimulus p38 levels (red lines) responded less to stimulation.

To further investigate to what extent p38 levels affect ligand responses in single cells, we first sorted cell tracks exposed to each stimulus by their Akt response as quantified by the difference between the Akt log₂(CNR) before and after stimulus. Kymographs of signaling activity show that cells with higher Akt responses to EGF (near top of kymograph) (Figure 2A) or CXCL12 (Figure 2B) had lower pre-stimulus levels of p38. We also observed that pre-stimulus p38 log₂(CNR) also negatively correlated with ERK responses to EGF, but not CXCL12. Thus, lower basal activity of p38 in a cell generally correlated with increased ligand-induced activation of both Akt and ERK.

Figure 2: Heterogeneous p38 states predict Akt responses to EGF and CXCL12 |.

A,B) Color maps showing single cell responses in each reporter channel over time after 10 ng/ml EGF (A) or 10 ng/ml CXCL12 (B). Each row is a single cell with the y-axis listing numbers of cells. Each column is a single time point. The thick black bars separate kinase channels. The dashed line indicates time of adding a ligand. We sorted color maps by Akt response, which is calculated as the difference in Log2(CNR) before and after stimulus. In (A), N = 546 cells, and in (B), N = 346 cells. C, D) Plotting initial p38 log2(CNR) against change in Akt (C) or ERK (D) CNR for single cells shows an inverse correlation for p38 with Akt response to EGF (m = −0.724, p = 1.48×10⁻¹⁹) and CXCL12 (m = −0.461, p = 3.37×10⁻⁴⁸). P38 has a strong inverse correlation with ERK response to EGF (m = −0.878, p = 1.96×10⁻¹⁴) but a weaker correlation for CXCL12 (m = −0.12, p = 8.99×10⁻¹²). In both (C) and (D), EGF conditions correspond to N = 546 cells and CXCL12 conditions correspond to N = 346 cells.

2.3. p38 perturbations affect subsequent ligand responsiveness

To further explore how p38 affects responses to ligands, we activated or inhibited p38 (p38 perturbation) and then tracked cell responses to a subsequent ligand stimulus. We activated p38 with anisomycin and inhibited the kinase with SB203580 or doramapimod (also known as BIRB-796). The two inhibitors have different off-target effects and bind to different sites of p38²⁴, so we reasoned that observing similar effects with both drugs could be attributed to p38 inhibition (p38i). For our experiments, we applied a p38 perturbation to cells for 4 – 6 hours and then added CXCL12 or EGF (Figure 3A). This approach allowed us to image the immediate impact of a p38 perturbation (stimulus 1) on all three signaling pathways and subsequent responses to CXCL12 or EGF (stimulus 2) in single cells.

Figure 3: p38 perturbation affects later response to a stimulus |.

A) Experimental protocol for p38 perturbation preconditioning. First, cells are exposed to p38 inhibition or activation followed several hours later by treatment with EGF or CXCL12. B) Distributions of Akt responses caused by p38 perturbation prior to stimulating cells with EGF or CXCL12. Akt response was calculated by subtracted post-p38 perturbation levels of Akt from pre-p38 perturbation levels of Akt for each cell. C) Correlation coefficients between Akt activation and pre-stimulus p38 amount for stimulation with CXCL12 or EGF (related to figure 2C,D). D) Tertiles of Akt responses to CXCL12 or EGF were calculated based on unperturbed stimulus responses. Then, we stratified responses in conditions with p38 perturbations into strong, medium, and weak responses based on unperturbed response thresholds.

First, we quantified effects of p38 perturbation on ERK, Akt, and p38 prior to stimulation with CXCL12 or EGF. p38 activation (p38a) and inhibition affected p38 levels as expected (Figure S1). Both inhibitors of p38 caused strong deactivation of ERK and Akt in cells, while anisomycin caused activation of ERK and Akt (Figure 3B and Figure S2). Because of the reduced dynamic range of ERK signaling in MDA-MB-231 cells we focused subsequent analysis predominantly on Akt.

We next analyzed the response to CXCL12 or EGF after p38 perturbation. We calculated cell response to CXCL12 or EGF by subtracting the log₂(CNR) after stimulus addition from the log₂(CNR) prior to addition. Without a p38 perturbation, cells showed a moderate or strong negative correlation between initial p38 activity and fold-change in Akt in response to CXCL12 or EGF (stimulus 2), respectively. Perturbing p38 (stimulus 1) decreased the negative correlation between p38 status and Akt response to CXCL12 or EGF (Figure 3C). We also quantified how strongly EGF or CXCL12 stimulated increases in Akt log₂(CNR) without a p38 perturbation and defined consistent thresholds for weak, medium, and strong responders. We then applied those same thresholds to conditions with a p38 perturbation. For CXCL12, we found that p38 inhibition and activation generally increased and decreased the magnitude of Akt responses, respectively (Figure 3D). Thus, while inhibition of p38 immediately reduces ERK and Akt kinase activities, inhibiting p38 also elevates percentages of cells responding strongly to EGF and CXCL12.

2.4. Computational modeling supports role of scaffolding proteins in regulating p38-Akt cross-talk

We next sought to identify what biological mechanism might explain our observed signaling behaviors. Specifically, we focused on how p38i could reduce basal Akt while still permitting subsequent treatment with EGF to “reset” Akt to similar levels compared to uninhibited cells. We focus on Akt here because mutations in MDA-MB-231 cells cause constitutive activation of ERK. We considered several models of p38i-Akt cross-talk, including the possibility that p38 influences mTORC1, a kinase we previously showed inhibited ligand-dependent activation and Akt¹⁵. Literature reports ^10,16 suggest that p38 inhibits mTORC1, so we would expect p38i to increase mTORC1 activity and inhibit ERK and Akt ligand response. However, we observe the opposite effect. We also considered that basal p38 activity could affect the balance of phosphatases in the cell¹², potentially by suppressing JNK^1,25. p38i could allow JNK to reactivate and induce transcription of Akt-specific phosphatases. In this model, the phosphatases would persist in the cell after EGF or CXCL12 stimulation and inhibit activity after ligand addition. Thus, to fit our observations, the phosphatases would need to degrade rapidly upon addition of EGF or CXCL12, which to our knowledge is not described by any mechanism. Finally, we considered that instead of affecting molecules that directly phosphorylate or dephosphorylate Akt pathway components, p38 might control subcellular localization of these pathway components. There are multiple mechanisms of subcellular localization, but we focused on scaffolding molecules that support basal Akt activity^17,18. Inhibiting p38-dependent scaffolding would inhibit Akt but still enable later ligand-induced signaling to pull more pathway components into scaffolded signaling complexes.

To investigate our hypothesis that p38-dependent scaffolding regulates Akt, we developed the subcellular organization of kinase signaling model (SOKS), a kinetic model that explicitly considers the impact of scaffolding on signaling (Figure 4A, B). We modeled four compartments within the cell corresponding to: 1) p38 scaffolded activity; 2) EGF receptor (EGFR) scaffolded activity; 3) scaffolded activity in the rest of the cell; and 4) a free (unscaffolded) compartment. We assumed that scaffolding rates were the result of second-order kinetics dependent on the number of available sites at each location and the amount of free kinase. A compartment-specific amount of upstream activator (representing mTORC2/PDK1 for Akt) catalyzes phosphorylation of unphosphorylated kinase. Phosphorylated kinase is subject to first order dephosphorylation. Dephosphorylation occurs relatively slowly in scaffolded compartments but rapidly in the free compartment, consistent with the suggested role of scaffolds in protecting pathway molecules from dephosphorylation²⁰. We model p38 inhibition by decreasing the number of sites and upstream activator in the p38 scaffolded compartment, and the addition of ligand by increasing the number of sites and upstream activator in the receptor bound compartment. Finally, we explicitly considered the dynamics of KTRs in our model, with KTRs phosphorylated by the sum of active kinase in all four compartments. Figure 4C shows fits of the model to the Akt log2(CNR) averaged over all cells at each timepoint following p38 perturbation with SB203580 (p38i) and then stimulation with EGF. Rapid inhibition and somewhat slower recovery of Akt following p38i is caused by descaffolding of Akt at a particular subcellular location with subsequent slower redistribution of pathway components (such as PI3K or mTOR) to other locations. EGF activation proceeds independent of previous p38i exposure because p38i frees pathway components and facilitates more kinase activation in the EGF compartment (figure 4D). Having shown that the SOKS model captures the trends present in mean cell behavior, we next used the model to investigate single cell behaviors.

Figure 4: Subcellular organization of kinase signaling (SOKS) model|.

A) Schematic showing the four compartments considered in the model. The p38-scaffolded compartment includes an unknown scaffold protein. B) Close-up schematic of model reactions showing how kinase binding sites and upstream activators affect compartment translocation and kinase activation reaction rates. C) Comparison of mean Akt dynamics after exposure to p38 inhibition and EGF with model runs with and without preconditioning with SB203580 (p38i). D) Dynamics of each individual pathway component in the model run from C. +p38i indicates time of p38i SB203580 addition, while +EGF indicates time of EGF addition.

2.6. Modeling Heterogeneous Single-Cell Behaviors

To explain single-cell variability in responses to p38 inhibition and subsequent EGF exposure, we hypothesized that differences in the number of scaffold sites in each compartment (receptor scaffolded, free, p38 scaffolded, and rest of cell) could drive differences in response to each stimulus. We varied the total number of sites in each of the four compartments to create nearly 20,000 distinct parameter sets and corresponding SOKS model runs. We then calculated the absolute difference at each time point between each model run and each measured single-cell Akt time track to identify the model run (and thus the numbers of sites) most closely corresponding to each experimental cell (figure 5A). We observed similar distributions of model fit and experimental data for pre-p38i, post-p38i, pre-EGF, and post-EGF states (Figure 5B), further demonstrating that the model captures variability at key points in cell trajectories.

Figure 5: Modeling identifies drivers of heterogeneous responses|.

A) Kymograph showing experimental Akt Log2(CNR) compared with the best fit model curve for each individual cell. Dashed lines correspond to each of the times shown in panel B, and solid line separates experimental and model curves. In A, N = 658 experimental cell tracks. B) Distribution of experimental and model-fit curves at each time indicated in panel A. C) Contour plots showing the distribution of model scaffolding parameters that best fit the experimental cells. Distributions are shown as probability distributions in 3D space summed over each axis. Red, green, and blue points overlaid on contours represent sample cell trajectories shown in D. The red point represents the mean parameter set used in figure 4C. D) 3 sample model cell tracks (solid lines) and the best fit experimental cells (dashed lines). +p38i indicates time of p38i SB203580 addition, while +EGF indicates time of EGF addition.

To determine how effectively our model captures single cell heterogeneity, we compared the difference between experimental time tracks and their best fitting model track. Approximately 90% of cells differed from their model matches by less than 0.1 log₂(CNR) units per time point. To contextualize this number, we quantified the time point to time point changes in log₂(CNR) values in unperturbed cells, when log₂(CNR) measurements reflect measurement noise and endogenous cellular processes that we do not model. In unperturbed cells, ~90% of time point to time point changes measured less than 0.1 log₂(CNR), indicating that our fits are accurate to the level of experimental noise (figure S3). Thus, the SOKS model suggests that differences in single cell signaling arise from subcellular compartmentalization and variations in available scaffold sites in different compartments among cells rather than overall levels of signaling molecules.

2.7. Compartmentalization of signaling molecules drives signaling heterogeneity

We next sought to use the correspondence between experimentally measured cells and model runs to quantify the distribution of scaffold components in our experimental population. The model fits for each individual cell were defined by 3 different parameter values (one for each compartment site). Therefore, we were able to place each cell within a 3-dimensional parameter space (see methods) and visualize the resulting probability distribution (figure 5C). The model fits reveal that single cells occupy a wide range of sites in each compartment. We quantify the median, 25^th, and 75^th percentile of the scaffold concentrations in table 1. In constructing the model we assumed that he number of sites in the rest of the cell compartment, which represents scaffolded cellular activity everywhere except the receptor- and p38-scaffolded compartments, greatly exceeded the two defined compartments (Figure 4). This assumption was made because Akt regulates many different cellular processes and must be shared among signaling complexes in multiple pathways²⁶. Our comparison between model and experimental individual cells suggests that this is a valid assumption. We can also compare how representative the mean cell parameters are of single cell parameters by examining the parameter distributions. Our model suggests that some cells have 3 times as many EGFR-scaffolded sites or p38-scaffolded sites than the mean cell (Figure 5C, red dot), implying the existence of subsets of cells with different responses to EGF stimulus or p38 inhibition.

Table 1:

Statistics of scaffold distribution fits (shown in figure 5C)

Compartment	25th percentile	Median	75th percentile
Rest of cell sites	2.6 μM	2.8 μM	3.3 μM
p38 sites	22 nM	42 nM	62 nM
EGFR sites	37 nM	95 nM	154 nM

To more clearly visualize effects of changing the distribution of scaffold sites in each compartment, we simulated three different scaffold distributions corresponding to the red, green, and blue points in figure 5C. The simulated dynamics for each simulated scaffold distribution are shown in figure 5D. We also show the best fitting cell for each simulation in figure 5D to demonstrate that simulated behaviors match real cells. Cells with more p38-scaffolded reaction sites (figure 5D, green and blue) showed greater susceptibility to p38 inhibition than the mean cell (red). Cells with more EGFR-scaffolded sites (figure 5D, blue) responded more strongly to EGF (red). Our model explains a potentially clinically interesting subpopulation of cells. Cells with more p38 and EGFR sites will initially respond strongly to p38 inhibition, which appears to limit oncogenic signaling. However, p38i will also potentiate the response of these cells to EGF.

2.8. Comparing scaffold perturbations with signaling pathway perturbations

We next asked whether our model could reveal important differences between pharmacologic inhibition of kinases and scaffold proteins. We reasoned that pre-clinical compounds could demonstrate inhibition of a particular clinical target (such as Akt) by directly inhibiting the activity of a protein catalytically involved in the Akt pathway or by interfering with scaffolding that facilitates Akt activation. In high-throughput screening assays, these effects could be indistinguishable. However, catalytic inhibition and scaffolding inhibition might have different, clinically relevant, effects on ligand-responsive signaling. Our work here suggests that scaffolding inhibition may redistribute scaffold components (figure 4D). Redistributing signaling components could modify the activity of a specific kinase based on the site of activity or amplify later signaling, while directly inhibiting catalytic activity of an upstream signaling component is more likely to limit kinase activation at any subcellular location.

To study this idea with our computational model, we assumed that catalytic inhibition would manifest as a reduction in upstream activator species in all 4 compartments we model because a small molecule inhibitor would diffuse freely to all subcellular locations (methods). Meanwhile, inhibition of a scaffold would manifest as a reduction in scaffold molecules in the rest of the cell compartment because the this compartment represents many different scaffolds within the cell. Thus, we defined percent of inhibition as the amount of scaffold or upstream activator we inhibited upon addition of p38i. We ran our model in each of these conditions and simulated subsequent addition of 10 ng/ml EGF (Figure 6A, B). We found that both types of inhibition decreased levels of phosphorylated Akt, although with different kinetics and levels of recovery. At equal percent inhibition in amount of scaffold or upstream activator, kinase inhibition decreased levels of phosphorylated Akt to a greater extent than scaffold inhibition both immediately after inhibition and after subsequent EGF treatment (Fig. 6A, B). We next quantified the change in phosphorylated Akt after EGF addition at each level of inhibition. Our model shows that scaffold inhibition potentiates later responses to EGF, while kinase inhibition does not (Fig 6C). Thus, our model suggests that kinase and scaffold inhibition can have similar immediate effects but may have divergent and potentially clinically detrimental effects.

Figure 6: Comparing modeled kinase and scaffold inhibition|.

We simulated two different types of inhibition targeting one type of scaffold or targeting an upstream activator everywhere in the cell. We modeled inhibition and subsequent exposure to 10 ng/ml EGF. ppAkt dynamics after varying levels of scaffold (A) or kinase (B) inhibition. C) Comparison of change in Akt activity after EGF stimulation for different levels of inhibition with each type of inhibitor shown in A and B.

3. Discussion

Kinase signaling pathways form highly interconnected networks in cells. The complexity of these networks represents a pivotal obstacle to identifying regulators of basal signaling states and predicting responses to ligands or targeted inhibitors. Cross-talk between pathways constitutes a major cause of complexity in cell signaling²⁷. Cross-talk may be direct when signaling pathways share common components or effectors, a situation that points clearly to potential for competition or coordinated regulation. Pathway cross-talk also may occur indirectly through processes such as compartmentalization of molecules by scaffolding proteins or sequential effects of one pathway on subsequent activation of another. Understanding causes and consequences of pathway cross-talk is essential to anticipate how stimuli shape cell behaviors and to devise effective therapies.

In this work, we focused on cross-talk of p38, a central hub for cell stress responses, with Akt and ERK, two kinases that regulate processes including proliferation and survival in normal and malignant cells. Using fluorescent reporters and time-lapse microscopy to quantify activities of p38, ERK, and Akt in individual living cells, we observed substantial heterogeneity in kinase activities under basal conditions and response to environmental inputs. By analyzing single cell data, we discovered that basal activity of p38 correlated inversely with fold-change increases in Akt or ERK following treatment with CXCL12 or EGF. Inhibiting p38 decreased ligand-independent basal activities of Akt and ERK and the negative correlation between basal p38 levels and ligand-stimulated fold-change in Akt and ERK. Remarkably, p38 inhibitors potentiated subsequent ligand-stimulated activation of Akt, revealing an unanticipated disconnect between basal and ligand-dependent signaling.

To identify potential mechanisms for cross-talk of p38 with Akt, we developed a computational model (SOKS) that explicitly considers signaling occurring in multiple subcellular compartments. This model points to cross-talk arising from a system where p38 inhibition prevents pre-stimulus signaling from occurring in one subcellular compartment but does not destroy any signaling components or cause synthesis of any negative regulators of signaling. Thus, ligand stimulation after p38i can increase fold-change in Akt activation because cells have greater amounts of free signaling components to scaffold by the ligand-receptor complex and/or downstream components. We simulated our model with a range of binding sites in multiple subcellular compartments. Using the set of simulated kinase dynamics, we reproduced single-cell Akt dynamics and determined the distribution of scaffold sites within experimental cells that would account for measured experimental data. The distribution of scaffold sites helps explain heterogeneous Akt responses to multiple sequential stimuli and reveals subpopulations of cells which demonstrate high levels of signaling potentiation after p38 inhibition. Finally, we used our model to explore differences between kinase inhibition and scaffold inhibition. Our model suggests that both scaffold and kinase inhibition can initially decrease activity of an oncogenic kinase like Akt. However, scaffold inhibition can potentiate later signaling. This may be particularly relevant in high-throughput screens, where lead compounds are identified based on their ability to inhibit a kinase.

Spatial localization of subsets of proteins within a cell is increasingly recognized as a common mechanism employed to control outputs of numerous signaling pathways^28–31. Compartmentalizing signaling proteins in a defined site, such as an organelle, facilitates interactions with other specific molecules in a pathway, increasing reaction kinetics and reducing effects of negative regulators^20,29,32. In response to a new ligand or drug, rapid changes in protein localization allow cells to respond without the delays involved in synthesizing new proteins or targeting proteins for degradation. Compartmentalization of signaling molecules also restricts interactions with proteins in other sites, thereby controlling flow of information and signaling outputs²⁶. Scaffold proteins define a class of proteins commonly used by cells to assemble and compartmentalize components of signaling pathways^33,34. Scaffold proteins may assemble signaling complexes at defined structures in a cell, such as the cell membrane, endosomes, or the cytoplasm. Past studies have discovered several scaffold proteins that can localize p38 or components of its signaling pathway to different sites in a cell³³. As revealed by our computational model, compartmentalization of kinases by mechanisms such as scaffolds provides one mechanism for cross-talk of p38 with Akt signaling.

Controlling scaffold proteins remains experimentally challenging, making computational models essential for understanding how scaffolds regulate fundamental aspects of signaling pathways. A prior Monte Carlo simulation model investigated how assembling proteins on a scaffold altered kinetics of signaling³⁵. Scaffolds allowed a broad range of kinase activation over time, permitting both early and late responses to stimuli. Concentrations of scaffolds that produced the broadest duration of signaling also maximized amplitude of kinase activation. By comparison, our data proposed that scaffold proteins accounted for effects of p38 inhibitors to increase fold-change increases in kinase activity without a requirement for altering kinetics of pathway activation. Using ordinary differential equations to model a generic scaffold in mitogen activated protein kinase (MAPK) signaling, Levchenko et. al also concluded that scaffolds regulate specificity and amplitude of kinase signaling²⁰. That work demonstrated that optimal conditions for maximal signaling amplitude depend on concentrations of kinases and scaffold protein rather than binding constants, making the output independent of specific scaffold protein. Unlike these and other computational models of scaffolds in signaling³⁶, we designed our model to fit signaling outputs at the level of single cells, illuminating potential causes of heterogeneity of signaling amplitudes among cells in a population.

While many different small molecule inhibitors of p38 have been developed and tested in several different types of cancer, these trials have failed consistently³⁷. Unmanageable toxicities account for many of the failures. However, context-dependent functions of p38 as a tumor suppressor or promoter contribute to ongoing challenges in targeting this kinase⁹. Our results emphasize the context-dependent nature of p38 on activation of Akt, a kinase known to promote tumor initiation and progression in multiple malignancies. Two different inhibitors of p38 reduced basal activity of Akt in the absence of stimulation with a ligand. Unexpectedly, inhibitors of p38 potentiated strong activation of Akt by CXCL12 and EGF in subsets of cells. Since CXCL12 and EGF both increase tumor-enhancing processes including proliferation, angiogenesis, migration, and metastasis, enhancing CXCL12 or EGF signaling to Akt potentially could drive tumor progression^38,39. Many drivers of tumor growth and metastasis activate Akt, so inhibiting p38 may promote oncogenic signaling by multiple signaling pathways and lead to treatment failure.

While our computational model calls attention to critical functions of subcellular compartmentalization in signaling pathways, we do not define specific scaffold protein(s) or mechanisms of spatial localization that regulate cross-talk of p38 with the Akt pathway. As revealed by our computational model, compartmentalization of kinases by mechanisms such as scaffolds provides one mechanism for cross-talk of p38 with Akt signaling. Our model could also invoke other mechanisms of subcellular compartmentalization which are known to be regulated by p38. For instance, p38 can regulate mitochondrial morphology, and mitochondrial membranes are known to serve as sites of Akt activation^26,40–42. Our model predicts Akt dynamics based on a concentration of kinase sites associated with each compartment, but not the specific cause of changes in site concentration. Thus, we are unable to definitively distinguish between changes in scaffolding due to p38 regulation of a scaffold protein like HSP27 or due to p38 regulation of a whole membrane or organelle like the mitochondria. However, EGF-induced recovery of signaling occurs rapidly. Therefore, our results are more consistent with a mechanism of subcellular localization that can be rapidly reversed. Future research will address potential molecular mechanisms of compartmentalization and effects of experimentally shifting spatial localization of p38 on activation of Akt. We also will further analyze specific effects of p38 on setting heterogeneity of signaling responses in single cells. While the computational model considered p38 as a single entity, four different isoforms of this kinase have been identified. Various isoforms have overlapping and some unique functions, although the compounds we used in this work inhibit all isoforms of p38.

Our systems biology approach establishes the framework essential to further decipher interconnections among p38, Akt, and ERK signaling in response to a variety of biochemical ligands and/or inhibitors of these pathways. We also provide a new computational platform that can be adapted to investigate potential effects of scaffold proteins and subcellular compartmentalization of signaling molecules in other pathways. Importantly, our approach advances computational modeling of compartmentalization of signaling molecules to the level of single cells, enabling studies focused on heterogeneity of responses to the same environmental conditions. Systems biology studies at the level of single cells ultimately may improve the ability to identify and target “outlier” cells that currently evade therapy.

Methods

Cell culture

We originally obtained MDA-MB-231 cells from the ATCC (Manassas, VA, USA). We cultured MDA-MB-231 cells as described previously^2,15. We cultured cells in DMEM (ThermoFisher, Waltham, MA USA) 10% fetal bovine serum, 1% glutamax, 1% penicillin/streptomycin, and plasmocin prophylactic (InvivoGen, Toulouse, France) in a humidified incubator maintained at 37°C and 5% CO2.

Stable expression of KTRs in cells

We previously reported a PiggyBac transposon vector (Systems Biosciences, Palo Alto, CA, USA) co-expressing KTRs for Akt and ERK, mCherry fused to histone 2B (H2B-mCherry) for nuclear localization, and puromycin for selection of stable cells². To add the p38-mTagBFP2 KTR, we linearized plasmid pHAEP² with EcoN1 and inserted two synthetic DNA fragments encoding P2A-p38 KTR²³ and mTagBFP2-P2A (Evrogen, Moscow, Russia) using NEBuilder HiFi DNA Assembly (NEB, Ipswich MA, USA). See Supplement 1 for full vector sequence. We verified the final construct by DNA sequencing and visualization of expected blue fluorescence from the reporter when transiently transfected into cells. We generated MDA-MB-231 cells stably expressing the 3X KTR reporter by co-transfecting cells with a 3:1 ratio of 3X KTR reporter to Super PiggyBac transposase (Systems Biosciences) and selecting cells with 5 μg/ml puromycin (ThermoFisher) as described².

Cell imaging

For time-lapse microscopy, we seeded MDA-MB-231 cells in 96-well glass bottom plates (Cellvis, Mountain View, CA, USA) at 2,750 cells per well in 100 μl of complete imaging media (FluoroBrite DMEM [ThermoFisher], 1% GlutaMax, 1% PenStrep, 1% Sodium Pyruvate, and 10% FBS). After 36 hours, we washed each well with warmed PBS before adding 100 μl of starve imaging medium (1% rather than 10% FBS). 12 hours after changing the medium, we moved cells to the on-stage incubator of an EVOS M700 microscope (ThermoFisher) and equilibrated cells for 1 hour at 37°C, 5% CO2, and 20% humidity. For each experiment, we configured imaging parameters to minimize light exposure to cells. We captured images approximately every 5 minutes for the duration of the experiment, using mCherry, CFP, and YFP cubes. As indicated in figure legends, we treated cells with CXCL12, EGF (both from R&D Systems, Minneapolis, MN), p38 inhibitors, or anisomycin (all from SelleckChem, Houston TX, USA) without removing the plate from the microscope incubator.

Image processing

After acquisition, images were processed automatically using custom MATLAB code as described previously^2,15. Briefly, we identify nuclei in the mCherry images using adaptive thresholding. We then expand the nuclear mask to identify cytoplasmic pixels and calculate the average over each region of interest. We then calculate the log₂ of the ratio between the cytoplasmic and nuclear intensity and present this value as the cytoplasmic to nuclear intensity ratio (CNR) at each time point. Cells are connected between time points by identifying nuclei in time t+1 that best overlaps with each nucleus in time t.

Computational modeling

We developed a series of models with increasing complexity that allowed for kinases to be segregated in different numbers of compartments via scaffolding mechanisms. We found that a model including three scaffolded and one free (unscaffolded) signaling compartment was able to capture kinase activity before p38 inhibition, the decrease and subsequent recovery of activity, and EGF response. Each compartment included a concentration of active and inactive kinase and upstream kinase activator. For 3 of the compartments, associated with p38-scaffolded, EGFR-scaffolded, and activation at kinases scaffolded in the rest of the cell,scaffold sites were also tracked, while the unscaffolded compartment did not include scaffold sites.

The model included 4 types of reactions: 1) second order translocation of active or inactive kinase from the unscaffolded compartment and each of the three scaffolded compartments, which is dependent on the number of scaffold sites available in each compartment; 2) second order activation of inactive kinase in each compartment, which is dependent on the amount of upstream activator in each compartment; 3) first order deactivation of kinase in all 4 compartments; and 4) translocation of active or inactive kinase from scaffolded compartments to the unscaffolded compartment. Scaffolded kinase must translocate to the unscaffolded compartment before entering another compartment, meaning that the unscaffolded compartment was shared by the other three compartments. KTR dynamics were added to the model as previously reported, where the KTR was activated by the sum of active kinase in all 4 compartments, consistent with reports that local activation of an ERK FRET reporter also activates a KTR for the ERK pathway⁴³. While previous work has focused on complex interactions between receptors and kinases upstream of ERK and Akt, our model simplifies these factors by considering only the concentration of a direct upstream kinase activator, for PDK1 as an activator for Akt. The concentration of both scaffolds and upstream activator proteins are controlled as model variables. Model species are listed in Table S1, model reactions are listed in Tables S2 and S3, and final model parameters are listed in Table S4. The differential equations used are listed in Table S5.

Parameter estimation

To estimate model parameters, we first cast each reaction as a first order reaction by lumping reaction rate constants with scaffold or upstream activator concentrations as necessary. This led to a system of 20 first-order reactions (10 forward and 10 backward) between 8 total components, inactive and active kinase in each of 4 compartments. By framing the problem in this way, we were able to solve the system algebraically by adding constraints to the model representing assumptions and experimental observations about the system. We solved these equations and constraints using MATLAB. We included several trivial constraints, including the definition of equilibrium constants and defining rate constants as non-negative. The nontrivial constraints we used are summarized in table 1. We solved for the amount of active kinase at steady state after p38i had been applied, since this value enabled us to assume that kinase activation in both the p38- and EGFR-dependent compartments was effectively zero. Furthermore, we assumed that the number of sites in each compartment, and upstream activator in each compartment was constant, enabling us to cast second order reactions as first order reactions. Finally, we assumed active kinase levels corresponding to our experimentally measured levels during the time after p38 addition, but before EGF addition. Specifically, we fit to the population average 30 minutes after SB203580 addition. This enabled us to assume that there was relatively little active kinase scaffolded by p38 or EGFR.

After acquiring analytical solutions for first order reaction rates, we converted first order reactions corresponding to p38 regulated scaffolding, kinase activation at p38 scaffolded sites, EGF regulated scaffolding, and kinase activation at EGFR regulated sites into second order reactions by explicitly introducing model terms for the concentration of active sites in the EGFR compartment, the p38 compartment, and the rest of cell compartment, along with the variables corresponding to the effects of p38i and EGF. We also introduced parameters to affect p38 and EGFR scaffolding and reaction rates, which were varied over the course of a simulation to simulate the effects of adding p38i or EGFR.

To run the model, we assumed that p38 inhibition and subsequent EGF activation modified rate constants associated with p38 scaffolding and activation or EGFR scaffolding and activation, respectively. Thus, for the first phase of the model, corresponding to the time prior to p38i addition, we set the parameters p38sitemult and p38catmult to 19.71 and 6.63, respectively, and decreased them to 1 after p38i was added. Similarly, when EGF was added, we increased the parameters EGFsitemult and EGFcatmult from 1 to 3.12 and 258, respectively.

To identify these parameters, we performed Latin Hypercube Sampling^45,46 on parameters defining the effects of EGF and p38, as well as the concentrations of sites and upstream activators in each compartment and identified parameters that best fit the dynamics of the average cell response to p38i and subsequent EGF by identifying the parameter set with the lowest mean squared error from the measured experimental data. Parameter values are presented in table S4.

Fitting single cell behaviors

To fit single cell behaviors, we started from the mean parameter set. We varied the number of base sites in each of the three compartments (receptor scaffolded, p38 scaffolded, and rest of cell) around the mean parameter set. Each parameter set sits in a 3-dimensional space where each axis is one parameter value. Using each of these parameter sets, we ran the SOKS model to steady state, then simulated adding p38i (SB203580) and then three hours later adding 10 ng/ml EGF, then running the model for another two hours. We thus simulated kinase dynamics for each combination of sites.

We next fit each cell within the 3-D parameter space.² We calculated the residual between each model run and each single-cell Akt trajectory. Given experimental noise, we sought to identify regions of parameter space (as opposed to a single parameter set) likely to be occupied by each cell. Therefore, we defined a residual cutoff based on the above which experimental trajectories could not be matched with model trajectories. This cutoff resulted in 623 of 658 cells (95%) being matched with at least one model run. For a single cell, we assigned the probability of that cell matching a parameter set based on the normalized inverse residual of each experimental trajectory with residual below the cutoff. We repeated this procedure for each cell to develop the parameter distributions shown in figure 5.

Simulating kinase and scaffold inhibition

To model kinase inhibition (figure 6) we decreased the levels of the upstream activator species in all compartments in the model by the values indicated in figure 6. This represents the activity of a relatively specific small molecule kinase inhibitor targeting a kinase such as MEK or PI3K. We assume that such a perturbation would affect upstream activator molecules everywhere in the cell equally. To model scaffold inhibition, we assumed that the inhibitor we model would affect one or more of the scaffolds represented by the rest of cell compartment (which aggregates the activity of all scaffolds other than the unknown p38-dependent scaffold and EGFR). We thus decreased the amount of scaffold present in the rest of cell compartment by the amount indicated in figure 6.

Quantifying limits of model fits based on measurement noise

We calculate a baseline level of measurement noise from image processing, image capture, and intrinsic cellular fluctuations. We do not differentiate between true measurement noise and biologically meaningful fluctuations due to, for example, signaling activity or cell cycle progression. To determine measurement noise, we calculated the change in Akt log₂(CNR) for the first 5 timepoints (i.e.before any additions) of 3 different experiments that have identical conditions. These times represent the cells at “steady-state” where the only contribution to changes in Akt log₂(CNR) should be due to measurement noise. We then calculate the cumulative distribution of changes in Akt log₂(CNR) and present them in figure S3a (colored lines). We also present the error per timepoint calculated for each experimental single cell Akt log₂(CNR) trajectory, showing that it is comparable to the noise in our determination of Akt log₂(CNR) (figure S3a, black line).

Table 2:

Constraints used to solve for reaction rates in first-order model.

Constraint	Value	Source/justification
Total kinase	800 nM Akt	Previous work2
Active kinase in rest of cell compartment	32 nM	Measured kinase activity after p38i (this work, figure 4C)
Active kinase at p38 scaffolded site after p38 inhibition.	0.1 nM	Assumed no activity scaffolded by p38 after inhibition
Active kinase scaffolded by EGFR	0.1 nM	Assumed no activity prior to EGF stimulus
Rapid dephosphorylation in unscaffolded compartment	K4 = 1000	Assumed based on phosphatase susceptibility for unscaffolded kinase20
More kinase is scaffolded in rest of cell compartment than p38 or EGFR specific sites	K1Q = 2	Assumed
Low levels of scaffolding in p38 or EGFR scaffold after p38i, before EGF	K1E = 0.1, K1S = 0.1	Assumed
Half-life for deactivation is between 5 and 10 minutes	k1r, k2r, k3f = 0.1 min−1 for all 3 loops	Measured kinase activity after p38i (this work)
Reaction rates around a loop must be equal in either direction.	K1s*K2s*K3s*K4 = 1	Microscopic reversibility44

Using these constraints, the reaction rates were fully determined and could be solved analytically using MATLAB.