Research ArticleCell Biology

Short-term cellular memory tunes the signaling responses of the chemokine receptor CXCR4

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Science Signaling  09 Jul 2019:
Vol. 12, Issue 589, eaaw4204
DOI: 10.1126/scisignal.aaw4204

Remembering the past for CXCR4 signaling

Activation of the chemokine receptor CXCR4 by its ligand CXCL12 enables cancer cells to disseminate and metastasize. Spinosa et al. performed imaging analysis and computational modeling to analyze signaling responses mediated by CXCR4 at the single-cell level. CXCR4 can signal through the kinases Akt and ERK. The authors found that exposing cells to different growth-promoting stimuli before CXCL12 altered the activity of upstream kinases (PI3K and Ras) or of a common downstream kinase complex (mTORC1) to bias CXCR4 signaling through either Akt or ERK. Furthermore, kinase inhibitors that are clinically used to treat cancer increased the likelihood of CXCR4 activation of Akt and/or ERK, suggesting that such drugs may inadvertently promote pro-metastatic CXCR4 signaling.

Abstract

The chemokine receptor CXCR4 regulates fundamental processes in development, normal physiology, and diseases, including cancer. Small subpopulations of CXCR4-positive cells drive the local invasion and dissemination of malignant cells during metastasis, emphasizing the need to understand the mechanisms controlling responses at the single-cell level to receptor activation by the chemokine ligand CXCL12. Using single-cell imaging, we discovered that short-term cellular memory of changes in environmental conditions tuned CXCR4 signaling to Akt and ERK, two kinases activated by this receptor. Conditioning cells with growth stimuli before CXCL12 exposure increased the number of cells that initiated CXCR4 signaling and the amplitude of Akt and ERK activation. Data-driven, single-cell computational modeling revealed that growth factor conditioning modulated CXCR4-dependent activation of Akt and ERK by decreasing extrinsic noise (preexisting cell-to-cell differences in kinase activity) in PI3K and mTORC1. Modeling established mTORC1 as critical for tuning single-cell responses to CXCL12-CXCR4 signaling. Our single-cell model predicted how combinations of extrinsic noise in PI3K, Ras, and mTORC1 superimposed on different driver mutations in the ERK and/or Akt pathways to bias CXCR4 signaling. Computational experiments correctly predicted that selected kinase inhibitors used for cancer therapy shifted subsets of cells to states that were more permissive to CXCR4 activation, suggesting that such drugs may inadvertently potentiate pro-metastatic CXCR4 signaling. Our work establishes how changing environmental inputs modulate CXCR4 signaling in single cells and provides a framework to optimize the development and use of drugs targeting this signaling pathway.

INTRODUCTION

Preexisting cellular states, rather than stochasticity, dictate the ability of individual cells to signal in response to an input stimulus (1). Because of variations in preexisting states, individual cells within a population exhibit heterogeneous activation of signaling pathways, and subsets of cells expressing the target receptor fail to signal at all in response to uniform input of a specific ligand (28). The fact that extracellular ligand may not activate signaling through a target receptor confounds reliability of biomarkers based on protein expression instead of function for selection of targeted drugs. Additional heterogeneity in signaling outputs arises because cells adapt signaling responses based on changes in environmental conditions over time, indicating that context shapes plasticity in preexisting cellular states. Context-dependent flexibility and intercellular heterogeneity in signaling allow single cells to survive under stressful conditions, hampering the ability to treat cancer and other diseases in which subpopulations of cells drive critical steps in pathogenesis. Discovering mechanisms that shift cells to states that are more or less responsive to receptor signaling promises to improve the ability to control cell behaviors for therapy and optimize responses to molecularly targeted drugs.

We focused on identifying mechanisms underlying responsiveness of cells to signal through chemokine receptor CXCR4 and its ligand, CXCL12. CXCL12-CXCR4 binding is essential for normal development and also promotes cancer initiation and metastasis in more than 20 different malignancies (911). We previously observed that only a small subset of CXCR4-positive cells migrates toward a uniform gradient of CXCL12 (12), making this ligand-receptor pair an ideal model to investigate cellular states controlling heterogeneous signaling. The CXCR4 inhibitor balixafortide has shown promising results in a phase 1 clinical trial as an adjuvant therapy for advanced metastatic breast cancer (13), reinforcing the need to understand signaling through this receptor to help identify patients likely to respond to this therapy and potential causes for treatment failure. CXCR4 activates the downstream effector kinases Akt and extracellular signal–regulated kinase (ERK), which mediate cell proliferation, survival, and chemotaxis (14). Akt and ERK are components of the most commonly activated oncogenic signaling pathways [phosphatidylinositol 3-kinase (PI3K)/Akt/mammalian target of rapamycin (mTOR) and mitogen-activated protein kinase (MAPK)] in cancer (14, 15). Thus, understanding how cells edit responsiveness to CXCR4 signaling to Akt and ERK will advance our understanding of cell signaling and inform clinical applications of CXCR4-targeted therapies.

We combined single-cell fluorescent reporters and single-cell computational modeling to identify mechanisms through which changes in environmental conditions modulate CXCL12-CXCR4 signaling. Recent signaling inputs shift the intracellular state based on extrinsic noise in PI3K, Ras, and mTORC1, generating a short-term cellular memory that regulates subsequent CXCR4-mediated signaling to Akt and ERK. The computational model predicted how intersections among genetic mutations in pathway components, growth factor–induced cellular memory, and kinase inhibitors tune the ability of cells to signal through CXCR4. These data provide previously unidentified insights into how cells adapt to dynamic changes in environmental conditions and how clinical treatments alter cell states and signaling by CXCR4.

RESULTS

Growth factor conditioning potentiates subsequent CXCR4 signaling

CXCL12 signaling through CXCR4 activates the MAPK and PI3K pathways (Fig. 1A). These pathways activate ERK and Akt, respectively. To capture CXCR4 signaling to ERK and Akt in single cells, we stably expressed fluorescent reporters that measured the activities of these kinases [kinase translocation reporters (KTRs)] (16, 17). KTRs reversibly translocate from nucleus to cytoplasm based on the phosphorylation of a specific substrate for each kinase. Quantifying the ratios of fluorescence intensities in cytoplasm to nucleus provides analog, independent measurements of kinase activity for ERK and Akt in single cells. Reporter-expressing breast cancer cells stably expressed histone 2B fused to mCherry (H2B-mCherry) to mark the cell nuclei and enable image segmentation and analysis and CXCR4 fused to a blue fluorescent protein (CXCR4-mTagBFP), allowing us to identify levels of tagged CXCR4 in each cell (fig. S1A).

Fig. 1 Conditioning cells with a growth stimulus potentiates subsequent CXCR4 signaling.

(A) CXCL12 binds to CXCR4 and elicits downstream Akt and ERK activation. Separate kinase translocation reporters (KTRs) for Akt (Aquamarine) and ERK (mCitrine) were stably expressed in breast cancer cells. Phosphorylation and dephosphorylation of the kinase substrate drive the reporter into the cytoplasm or nucleus, respectively. (B) Cells were conditioned for 4 hours with or without growth stimuli or kinase inhibitors. Single-cell, time-lapse imaging was performed for 10 min before and 50 min after addition of CXCL12 (10 ng/ml). Single-cell time tracks (control conditioning, n = 347 cells; FBS conditioning, n = 312 cells) show CXCR4-dependent activation of Akt and ERK in MDA-MB-231 breast cancer cells quantified as log2 of cytoplasmic-to-nuclear ratio (C/N) of fluorescence intensities for each KTR in individual cells and displayed on a pseudocolor scale. (C) Quantification of Akt and ERK activation in cells conditioned with FBS before CXCL12 stimulation (control conditioning, n = 347 cells; FBS conditioning, n = 312 cells). Strong activation was defined by ≥1 increase in log2(C/N) unit. (D) Quantification of Akt and ERK activation in cells conditioned with FBS for 4 (n = 312 cells) or 7 (n = 367 cells) hours compared to control conditioning (n = 347 cells) before CXCL12 stimulation. (E) Quantification of Akt and ERK activation in cells that were conditioned with various concentrations of epidermal growth factor (EGF) for 4 hours before CXCL12 stimulation [control conditioning, n = 347 cells; EGF conditioning (1 ng/ml), 354 cells; EGF conditioning (10 ng/ml), 370 cells; EGF conditioning (30 ng/ml), 358 cells].

Using live-cell imaging to quantify the dynamics of Akt and ERK KTRs in single cells, we observed heterogeneous CXCR4 signaling in MDA-MB-231 breast cancer cells treated with CXCL12 (10 ng/ml) as the only stimulus (fig. S1B). Single-cell responses ranged from strong activation of both Akt and ERK to undetectable signaling despite expression of CXCR4 (Fig. 1B). MDA-MB-231 cells typically exhibited greater activation of Akt than ERK because mutant KRas and BRaf (18) in these cells constitutively drive ERK signaling, reducing the dynamic range for activation by CXCR4.

Because cells under normal physiological conditions signal in the context of multiple signaling inputs, we hypothesized that treatment of cells with a different growth factor would generate a short-term memory (19) that modified subsequent CXCL12-CXCR4 signaling. To test this hypothesis, we conditioned cells for 4 hours with fetal bovine serum (FBS) before adding CXCL12. FBS conditioning produced a transient increase in Akt activity that resolved essentially to baseline within 4 hours, returning cells to an imaging appearance indistinguishable from control (fig. S1C). Single-cell time tracks showed that FBS conditioning increased the number of MDA-MB-231 cells by fourfold with strong activation of Akt in response to CXCL12 (Fig. 1, B to D). FBS conditioning also reduced the number of nonresponding cells by 50%. Conditioning with FBS did not substantially alter the activation of ERK by CXCL12-CXCR4 signaling likely due to the constitutive activation of this kinase in MDA-MB-231 cells (Fig. 1, B to D). Extending FBS conditioning to 7 hours before adding CXCL12 produced only a twofold increase in cells with strong activation of Akt and did not change the number of nonresponding cells, establishing a time-dependence aspect to the cellular memory of previous signaling inputs and identifying 7 hours as a near end point for this form of cell signaling memory (Fig. 1D). We next examined the extent to which conditioning with epidermal growth factor (EGF) modified subsequent CXCL12-CXCR4 signaling responses. Similar to FBS, conditioning with various concentrations of EGF transiently activated Akt and ERK, but the activities of these kinases returned to baseline within 4 hours. Subsequent addition of CXCL12 increased the number of cells with strong CXCR4-mediated activation of Akt, in a manner proportional to the concentrations of EGF used for conditioning (Fig. 1E). Regardless of experimental condition, CXCL12 did not activate Akt or ERK signaling in cells lacking CXCR4-BFP (fig. S1, D and E), indicating that these cells express little to no endogenous CXCR4 as we reported previously (20). The amount of CXCR4-BFP on single cells did not account for intercellular heterogeneity in signaling, and conditioning did not alter expression or localization of the fluorescent receptor (fig. S1D). These data demonstrate that previous growth stimuli tune responses of cells to CXCR4 signaling through a mechanism downstream of the receptor.

Computational modeling predicts single-cell signaling dynamics

The intracellular state of cells downstream of receptors involves a complex network of signaling components that is difficult to intuit with experiments alone. We hypothesized that conditioning with growth factors changed the intracellular state, thereby altering subsequent CXCR4 signaling. To uncover mechanisms that control the responsiveness of cells to CXCL12-CXCR4 beyond what experiments could alone provide, we used ordinary differential equations to construct a computational single-cell conditional signaling model (CSM) of CXCR4-mediated activation of Akt and ERK. Two key features of experimental signaling data informed the construction of the CSM. First, the lack of correlation between basal activity and CXCL12-mediated activation of either kinase in single cells (fig. S2, A to C) indicated that different regulators controlled basal kinase activity versus responses of single cells to CXCL12. Second, a trend between activation of Akt and ERK by CXCR4 in single cells (fig. S2, A to C) suggested that a component common to both PI3K and MAPK pathways regulated the responsiveness of both kinases. We constructed the framework of the CSM based on these experimental observations and previously published data (Fig. 2A and fig. S3, A to C).

Fig. 2 The computational conditional signaling model (CSM) predicts CXCR4-mediated Akt and ERK signaling responses, establishing a framework for understanding the range of heterogeneous signaling data.

(A) The CXCL12-CXCR4 interaction elicits G protein signaling to activate Akt and ERK but can be restrained by negative feedback and cross-talk mechanisms. mTORC1 functions as a central regulator of signaling because it can inhibit the activation of both Akt and ERK. Extrinsic noise in phosphatidylinositol 3-kinase (PI3K), Ras, and mTORC1 promotes activation of Akt and/or ERK in the absence of CXCR4-mediated signaling. Signaling kinetics cover a range of time scales with thicker arrows and lines qualitatively indicating faster reaction rates. A complete list of differential equations, initial conditions, and parameters is available in tables S1 to S5. (B) To encompass heterogeneous signaling responses of single cells in both Akt and ERK, we varied extrinsic noise parameters for PI3K, Ras, and mTORC1 in the CSM. By running combinations of these three parameters, we generated a model library of >12,000 predicted paired Akt and ERK responses. We performed a least-square fit of experimentally determined Akt and ERK responses from the KTRs to predicted responses to derive the PI3K, Ras, and mTORC1 extrinsic noise parameters that best describe each single cell in the experiments.

In addition to CXCR4 signaling outputs (Fig. 2A), the CSM included extrinsic noise to account for signaling heterogeneity in a cell population (2, 5, 2124). In this context, extrinsic noise refers to preexisting cell-to-cell differences in kinase activity. We used the two observations in the experimental data described above to determine the components of the signaling pathways that needed to contain extrinsic noise. PI3K, Ras, and mTORC1 constituted the main sources of heterogeneity in CXCR4 signaling because our data suggested that basal levels of upstream activators of Akt (PI3K) and ERK (Ras), as well as a downstream regulator common to both pathways (mTORC1), varied from cell to cell. In addition, PI3K, Ras, and mTORC1 have roles external to CXCR4 signaling relating to confluency, metabolism, or local mitogenic signals (22, 2527). Heterogeneity was mathematically incorporated in the CSM in the form of a conditional term on these three pathway components (fig. S4) that set the baseline activities of Akt and ERK in each cell in the absence of any stimulation. We used the CSM with various combinations of extrinsic noise parameters for PI3K, Ras, and mTORC1, referred to as the conditional signaling state, to generate a library of predicted Akt and ERK signaling responses to CXCL12, independent of the presence and type of conditioning stimulus (Fig. 2B). We used this library of predicted signaling behavior as a framework for understanding the heterogeneous signaling data seen in experiments.

Maps of the signaling landscape reveal that conditional signaling states control CXCR4 responsiveness

The CSM captured the paired signaling behavior of Akt and ERK in single cells across the range of responses measured experimentally in the population (Fig. 3A). We used the CSM to generate a map of the signaling landscape displaying the conditional signaling states that permit CXCR4 activation of Akt and ERK (fig. S4). The signaling landscape reflected individual CSM simulations at all combinations of conditional signaling states. The Akt and ERK signaling landscape predicted by the CSM contains areas in which cells can activate one kinase, both kinases, or neither (Fig. 3B and fig. S5). Generally, the highest CXCR4 activation of Akt occurred in those conditional signaling states with low PI3K and mTORC1 activity. By comparison, the conditional signaling states with high PI3K, low Ras, and low mTORC1 activities showed greatest CXCR4 signaling to ERK (Fig. 3B). The CSM predicted the cellular states that were permissive for CXCR4 signaling.

Fig. 3 The CSM captures heterogeneous single-cell signaling responses seen in experiments and reveals the conditional signaling states controlling responsiveness to CXCR4 signaling.

(A) Responses from the model library match experimentally determined control and FBS conditioned single-cell (control conditioning, n = 347 cells; FBS conditioning, n = 312 cells) CXCR4 signaling to Akt and ERK. Greater than 95% of cells fit the matching criteria. The gray dashed line identifies when CXCL12 was added (10-min time point). Images were taken every 2 min for 60 min. (B) Akt or ERK responses through CXCR4 as affected by different combinations of extrinsic noise parameters for PI3K (orange), Ras (green), and mTORC1 (blue) during simulation. Plots show a 2D plane of the entire 3D signaling landscape generated by varying three parameters (kPI3K, kRas, and kmTORC1) combinatorially. Green and orange dashed lines denote the value on the third axis.

MDA-MB-231 cells occupy tunable conditional signaling states

The CSM provides a framework to organize complex signaling behavior and extract conditional information from cell populations. We constructed occupancy maps to illustrate distributions of experimental cells in the CSM signaling landscape. Under control conditioning, MDA-MB-231 cells occupied a region of the signaling landscape with moderate PI3K, Ras, and mTORC1 activities (Fig. 4A). Akt and ERK signaling responsiveness from Fig. 3B is shown as the underlay on the occupancy maps and illustrates regions of the signaling landscape containing cells in which CXCR4 activates Akt and/or ERK. When conditioned with FBS for 4 hours before CXCL12 stimulation, MDA-MB-231 cells shifted to a region of the signaling landscape with lower PI3K and mTORC1 activities, which favored CXCR4-mediated activation of Akt (Fig. 4B). Using the CSM-predicted Akt and ERK signaling behaviors that matched the experimental data, the percentage of cells activating Akt in response to CXCL12 increased after FBS conditioning compared to control (Fig. 4C). Conditioning with three different concentrations of EGF also decreased PI3K and mTORC1 activities in a dose-dependent manner compared to control (fig. S6, A and B). We conclude that conditioning cells with growth factors alters the conditional signaling states consistent with a decrease in PI3K and mTORC1 activity. These shifts in conditional signaling state provide a mechanism underlying the ability of growth factor conditioning to enhance numbers of cells responding to CXCL12 and amplitude of signaling to Akt.

Fig. 4 FBS conditioning shifted the conditional signaling state of MDA-MB-231 breast cancer cells to a region more permissive to CXCL12-CXCR4 signaling to Akt.

(A to C) Occupancy maps (normalized to contain 1 × 106 cells) illustrate combinations of extrinsic noise parameters (conditional signaling state) corresponding to regions of 3D signaling landscape (CSM output) where experimental cells most frequently match. Contour lines display numbers of cells out of 1 × 106. Occupancies were summed in the third dimension for purposes of viewing the map in two dimensions. Cyan and yellow underlays illustrate regions of responsiveness for Akt and ERK, respectively. Green and orange lines illustrate the specific Ras and PI3K planes, respectively, corresponding to the responsiveness underlays. Occupancy maps are shown for MDA-MB-231 cells that received control conditioning (A) or FBS conditioning (B) before CXCR4 stimulation. (C) Quantification of cells with each signaling response. We defined responses in the computational model as >5 nM increases in kinase activity for Akt or ERK.

Vari-068 and SUM-159 cells occupy tunable conditional signaling states distinct from MDA-MB-231 cells

In contrast to MDA-MB-231 cells, many breast cancers harbor mutations in upstream activators of Akt (28). We tested the CSM on cells with constitutive activation of signaling to Akt, which we expected to occupy different conditional states in the signaling landscape than MDA-MB-231 cells. In patient-derived Vari-068 cells with mutant phosphatase and tensin homolog (PTEN), CXCR4 signals primarily through ERK rather than Akt (fig. S6C), which is distinct from MDA-MB-231 cells. Vari-068 cells occupy a region of the signaling landscape with high PI3K and moderate Ras (Fig. 5A). Because PTEN degrades phosphatidylinositol-3,4,5-phosphate (PIP3) and a loss-of-function mutation in PTEN is present in Vari-068 cells, the model represented Vari-068 cells as having high PI3K activity. When conditioned with FBS for 4 hours before the addition of CXCL12, Vari-068 cells shifted to a region of the signaling landscape with lower mTORC1 but similar PI3K and Ras activities (Fig. 5B). Cells in this state showed potentiated ERK signaling (Fig. 5C and fig. S6C). These results define a signaling paradigm in which mTORC1 controls overall cellular permissiveness for CXCR4 signaling, and conditioning with growth factors reduces mTORC1-mediated restraint mechanisms on ERK and Akt signaling. Conditioning breast cancer cells with growth factors decreases PI3K and mTORC1 activity to potentiate subsequent CXCR4-mediated signaling to Akt and ERK but cannot overcome activating mutations in upstream components of these pathways. Genetic mutations define the subset of conditional signaling states available to cells, but conditioning with growth factors further tunes the signaling state of any single cell.

Fig. 5 Genetic mutations set the subset of conditional states available to cells, but these states can be tuned to further edit signaling behavior.

(A) Occupancy map shown as contour lines is a 3D histogram, which (normalized to contain 1 × 106 cells) illustrates combinations of extrinsic noise parameters (conditional signaling state) corresponding to regions of the 3D signaling landscape (CSM output) where experimental cells most frequently match. Cyan and yellow underlays illustrate regions of responsiveness for Akt and ERK, respectively. Green and orange lines illustrate the specific Ras and PI3K planes, respectively, corresponding to the responsiveness underlays. Occupancy map shown for patient-derived Vari-068 cells (which have an inactivating mutation in PTEN) that received control conditioning before CXCR4 stimulation. (B) Occupancy map shown as contour lines (normalized to contain 1 × 106 cells) illustrates combinations of extrinsic noise parameters corresponding to regions of the 3D signaling landscape where experimental cells most frequently match. Cyan and yellow underlays illustrate regions of responsiveness for Akt and ERK, respectively. Green and orange lines illustrate the specific Ras and PI3K planes, respectively, corresponding to the responsiveness underlays. Occupancy maps are shown for patient-derived Vari-068 cells that received FBS conditioning before CXCR4 stimulation. (C) Quantification of cells with each signaling response. We defined responses from the computational model as >5 nM increases in kinase activity for Akt or ERK.

We next investigated the extent to which CXCR4 signals to Akt and ERK in cells with activating mutations in both PI3K and MAPK pathways. Similar to Vari-068 cells, CXCR4 in SUM-159 cells, which have constitutively active HRas (an upstream activator of ERK) and PI3K, signals primarily to ERK rather than to Akt (Fig. 6, A and B, and fig. S6C), indicating that the ERK pathway remains inducible in the presence of an upstream activating mutation. SUM-159 cells occupy a region of the signaling landscape with high PI3K activity due to the activating mutation in this kinase and moderate Ras and mTORC1 activities (Fig. 6A). The CSM revealed that, despite activating mutations in both MAPK and PI3K pathways, the PI3K/Akt pathway generally dominated and was almost uninducible by CXCL12 in these cells. Signaling in breast cancer cells with genetic mutations in Akt, ERK, or both is therefore tuned both by these mutations and by growth factor availability. A summary cartoon illustrates the conditional states of the breast cancer cell types we tested, showing how genetic mutations and growth factor conditioning stimuli shift cell signaling states to various regions of the signaling landscape (Fig. 6C). Genetic mutations dictate the subset of conditional signaling states available from the set of all possible states predicted from the CSM, and growth factor availability further tunes the states within that subset that single cells will occupy.

Fig. 6 SUM-159 cells occupy conditional signaling states with ERK responsiveness.

(A) Occupancy map shows where experimental cells most frequently match model predictions. Cyan and yellow underlays illustrate regions of responsiveness for Akt and ERK, respectively. Green and orange lines illustrate the specific Ras and PI3K planes, respectively, corresponding to the responsiveness underlays. Occupancy map is shown for SUM-159 cells (which have activating mutations in both ERK and Akt) that received control conditioning. (B) Summary of the percentage of cells with each signaling response. We defined responses from the computational model as >5 nM increases in kinase activity for Akt or ERK. (C) A summary of how genetic mutations and growth factor conditioning interact to tune cellular responsiveness in Akt and ERK by shifting the conditional signaling state at the single-cell scale. CA, constitutive activation; lof, loss of function.

MEK inhibition potentiates subsequent CXCR4-mediated Akt signaling in a subset of cells

We applied the CSM to predict the responsiveness of cells treated with two therapeutic agents relevant to CXCR4 signaling, the MAPK kinase (MEK) inhibitor trametinib and the mTORC1 inhibitor ridaforolimus. The CSM predicted that conditioning with trametinib would block ERK signaling but potentiate CXCR4 signaling to Akt in a subset of cells (fig. S7, A and B). In the CSM, inhibiting MEK decreases ERK-mediated mTORC1 activation and releases restraint on mTORC2 to activate Akt. A simulated dose response of trametinib conditioning revealed that larger doses of trametinib increased the activation of Akt in MDA-MB-231 cells (Fig. 7A). We experimentally confirmed the CSM predictions, demonstrating that conditioning MDA-MB-231 cells with trametinib for 4 hours heterogeneously potentiated CXCR4 signaling to Akt (Fig. 7B). Difference maps illustrate areas of change of peak activation with inhibitor conditioning compared to control (Fig. 7C). The CSM revealed that cells exhibiting enhanced Akt signaling after trametinib conditioning were those with low PI3K and mTORC1 activity, which corresponded to cells in states predisposed to be highly responsive to CXCL12 with control conditioning. By comparison, CXCR4 signaling in other, nonresponsive states was not affected by trametinib (Fig. 7C). Trametinib-treated cells occupied regions of the signaling landscape similar to those of cells that received control conditioning, confirming that the simulated inhibitor treatment did not shift conditional signaling states and only affected responsiveness at each state.

Fig. 7 Computational modeling correctly predicts that trametinib conditioning potentiates subsequent CXCR4-mediated Akt signaling in a subset of MDA-MB-231 cells.

(A) The CSM predicts Akt (left) and ERK (right) signaling dynamics at simulated concentrations of trametinib conditioning that inhibit 50 or 90% of MEK activity relative to control before CXCR4 stimulation. The predicted signaling dynamics denoted by the red and blue dots correspond to different conditional signaling states and correspond to the dots in (C). (B) The CSM accurately predicts single-cell experimental CXCR4-mediated Akt and ERK signaling dynamics for trametinib conditioning (n = 447 cells) on MDA-MB-231 cells (control conditioning, n = 429 cells). Trametinib conditioning was modeled as a 50% decrease in the rate of MEK-mediated phosphorylation of ERK, consistent with noncompetitive inhibition kinetics. (C) Difference maps show the CSM-predicted change in peak Akt activation between the control conditioned and trametinib-conditioned cells at each conditional signaling state. Shaded gray surface contours show regions in signaling landscape with conditional signaling states that position trametinib-conditioned cells for the listed increases in peak Akt activation (nM). Contour lines display numbers of cells out of 1 million occupying conditional signaling states after matching experimental trametinib-conditioned cells to the CSM. Green and orange lines illustrate the specific Ras and PI3K planes, respectively, of the CSM corresponding to the responsiveness underlays. Red dots indicate conditional signaling states that were permissive to Akt signaling under control conditioning. Blue dots indicate conditional states that were not permissive to Akt signaling under control conditioning. The red and blue dots from (C) correspond with those in (A).

mTORC1 inhibition potentiates subsequent CXCR4-mediated Akt and ERK signaling

A simulated dose response of ridaforolimus conditioning potentiated CXCR4 signaling to both Akt and ERK in MDA-MB-231 cells in a dose-dependent manner (Fig. 8A and fig. S7C). In the CSM, inhibition of mTORC1 releases restraint on both mTORC2 and Ras, thereby activating both Akt and ERK. Difference maps indicated enhanced CXCR4 signaling to Akt in cells with low PI3K activity, and all cells exhibited enhanced ERK signaling (Fig. 8B). We experimentally confirmed CSM predictions, demonstrating that conditioning MDA-MB-231 cells for 4 hours with ridaforolimus potentiated CXCL12-dependent activation of both Akt and ERK (fig. S7D). Again, the conditional signaling states of ridaforolimus-treated cells were similar to those of cells that received control conditioning. These data establish that targeted kinase inhibitors can potentiate CXCR4 signaling in subpopulations of cells.

Fig. 8 Computational modeling correctly predicts that conditioning with the mTORC1 inhibitor ridaforolimus potentiates subsequent CXCR4-mediated Akt and ERK signaling in MDA-MB-231 cells.

(A) The CSM predicts Akt (left) and ERK (right) signaling dynamics at simulated concentrations of ridaforolimus conditioning that inhibit mTORC1 activity by 50 or 90% relative to control before CXCR4 stimulation. The predicted signaling dynamics denoted by the red and blue dots correspond to cells able to respond and not respond in Akt under control conditioning, respectively. (B) Difference maps show the CSM-predicted change in peak Akt (left) and peak ERK (right) activation between the control conditioned and ridaforolimus-conditioned cells at each conditional signaling state. Shaded gray surface contours show regions in signaling landscape with conditional signaling states that position ridaforolimus-conditioned cells for the listed increases in peak activation (nM). Contour lines display numbers of cells out of 1 million occupying conditional signaling states after matching experimental ridaforolimus-conditioned cells to the CSM. Green and orange lines illustrate the specific Ras and PI3K planes, respectively, of the CSM corresponding to the responsiveness underlays. The red and blue dots from (B) correspond to those in (A). The CSM-predicted signaling dynamics are from 50% inhibition of mTORC1.

DISCUSSION

Rather than representing hard-wired pathways that always generate the same output, signaling networks in single cells produce heterogeneous responses shaped by changing environmental conditions and signaling inputs. Our work demonstrates that, although cells adapt signaling based on short-term memories of previous inputs, these adaptations are predictable on the basis of a specific set of rules. We used one parameter set to simulate single-cell paired Akt and ERK signaling dynamics for entire populations of cells and introduced heterogeneity by adding extrinsic noise to only three pathway components: PI3K, Ras, and mTORC1. The ability of the CSM to predict heterogeneous basal states and responsiveness of single cells in multiple breast cancer cell types with only extrinsic noise in three pathway components suggests that the model captures the major drivers of CXCR4 signaling to Akt and ERK.

Local intracellular and extracellular conditions tune signaling responses in individual cells. As a consequence, gradients of growth factors or kinase inhibitors in vivo may drive heterogeneous signaling outcomes. We showed that conditional effects such as genetic mutations, growth factors, and kinase inhibitors all collectively tuned responsiveness of cells to CXCL12-CXCR4 signaling and activation of Akt and ERK. We propose that cells exist on a signaling landscape based on conditional states. The signaling landscape, which accounts for CXCR4 signaling dynamics at all possible cellular conditional states, defines the output of the CSM. Genetic mutations force cells into distinct regions within the signaling landscape. Conditioning cells with growth factors allows cells to shift within these regions to potentiate signaling, whereas conditioning with kinase inhibitors modifies the cell signaling potential in each state but preferentially affects cells already existing in states poised to signal. We showed that trametinib potentiated only subsequent CXCR4-mediated Akt signaling in cells with low PI3K and mTORC1 activities, which constituted a small fraction of cells in the population. As an active enzyme, even modest increases in Akt signaling and function in small numbers of cells can drive the pathogenesis of processes critical to cancer progression (29), making behaviors of “outlier” single cells relevant for disease and therapy.

We built the CSM to explore the entire design space (the single-cell signaling landscape) potentially occupied by experimental cells. By mapping experimental cells onto the signaling landscape, we assigned mechanisms for heterogeneous CXCR4 signaling responses observed in experiments and discovered how conditioning tuned these responses. The CSM predicted that trametinib would produce not only the expected outcome of suppressing ERK but also the off-target consequence of enhancing CXCR4-mediated activation of Akt. Similarly, we predicted that ridaforolimus would potentiate both Akt and ERK signaling, two pathways that promote cancer growth and metastasis. These results highlight how targeted cancer therapies may potentiate CXCR4 signaling, a driver of tumor growth and metastasis, and how our computational model can predict such outcomes.

Cell signaling networks contain central nodes that store integrated information about multiple inputs and use this information to regulate responses to new signaling inputs. Our data indicate that mTORC1 functions as one of these central nodes, holding information about previous signaling to control subsequent activation of Akt and ERK. Although negative regulation of ERK by mTORC1 remains poorly characterized in literature, our CSM and single-cell imaging experiments demonstrate this as a crucial mechanism that drives coordinate regulation of Akt and ERK.

Although robust and predictive, the computational model we present here points to additional research opportunities relevant to heterogeneity in single-cell signaling. To establish heterogeneity among cells, the CSM incorporated extrinsic noise in three pathway components: PI3K, Ras, and mTORC1. However, specific molecular mechanisms driving noise in these pathway components remain to be identified. The cell cycle plays a role in cell signaling variability (30), but other environmental inputs likely also shape signaling responsiveness, such as hypoxia, pH, metabolism, energy levels, or other signaling stimuli. Mathematically, the source of the noise in our model is embedded in a first-order kinetic rate constant. Understanding the causes of extrinsic noise in these molecules will highlight potential approaches to tune CXCR4 signaling for therapy. This work focused only on the tunability of CXCR4 signaling. Because our data suggest that signaling heterogeneity can originate downstream of receptors, we posit that other signaling pathways can be tuned by a similar mechanism. In integrated three-dimensional (3D) environments with mixed cellular composition, we predict that cells will occupy some signaling states in the CSM-predicted signaling landscape that remain unoccupied in 2D monocultures. Because the equations in the CSM unrelated to extrinsic noise describe kinetic reactions independent of cellular geometry, we expect that the model will predict behaviors in mixed cell environments and complex tissues. We realize that environmental context may alter the initial conditions of some model species, such as CXCR4 abundance. Our future studies will advance into 3D environments and mouse models of cancer, where heterogeneous CXCR4 signaling responses are critical to mechanisms of metastasis and response to targeted therapies.

MATERIALS AND METHODS

Cell culture

We cultured the breast cancer cell lines MDA-MB-231, which express constitutively active KRAS and BRaf (18), and SUM-159, which express constitutively active PI3K and HRAS (18), as described previously (31). Vari-068 cells (a gift from S. Merajver, University of Michigan) are patient-derived, triple-negative breast cancer cells adapted to cell culture. These cells have an inactivating mutation in PTEN. We cultured these cells as described previously (32). In the conditioning phase of our experiments, we cultured control cells in low (1%) FBS media to suppress proliferation, thereby reducing the effects of cell cycle on signaling heterogeneity.

Fluorescent reporter construction

We constructed the KTR plasmid, pHAEP, in a PiggyBac transposon vector with CAG promoter based, in part, on plasmid pHGEA (a gift from K. Aoki, Okazaki Institute for Integrative Bioscience) (30). To optimize two-photon imaging of KTR reporters for Akt and ERK, we fused the kinase substrates to fluorescent proteins Aquamarine (33) and mCitrine (34), respectively, and replaced the histone 2B marker with mCherry to improve brightness and photostability. We also replaced the internal ribosomal entry site to blasticidin resistance marker with a P2A sequence, followed by a puromycin resistance marker. We assembled the plasmid using HiFi assembly (New England BioLabs, Ipswich, MA, USA) with synthetic double-stranded DNA fragments (GenBlocks, IDT, Coralville, IA, USA) or double-stranded DNA amplified from pHGEA as illustrated in fig. S1A. We constructed the CXCR4-mTagBFP2 (Evrogen, Moscow, Russia) in lentiviral expression vector pLVX-Ef1α (Clontech/Takara, Kusatsu, Shiga, Japan).

Cell engineering

To generate cells stably expressing the pHAEP construct, we cotransfected each cell line with the pHAEP transposon and Super PiggyBac transposase vector (System Biosciences, Palo Alto, CA, USA) using FuGene HD (Promega, Milwaukee, WI, USA). We selected batch populations of stable cells with puromycin (4 μg/ml). For MDA-MB-231 and SUM-159 cells, we transduced cells stably expressing the pHAEP reporter with lentiviral vector for CXCR4-mTagBFP and sorted mTagBFP-positive cells by flow cytometry.

Time-lapse two-photon microscopy and image processing

To prepare cells for time-lapse microscopy, we seeded cells (1.2 × 105 MDA-MB-231 cells, 6.5 × 104 SUM-159 cells, or 2.0 × 105 Vari-068 cells) in 35-mm dishes with a 20-mm glass bottom (Cellvis, Mountain View, CA, USA) in 2 ml of imaging base media [FluoroBrite Dulbecco’s Modified Eagle Medium (A1896701; Thermo Fisher Scientific, Waltham, MA USA), 1% GlutaMax, 1% PenStrep, and 1% sodium pyruvate] supplemented with 10% FBS (HyClone). For SUM-159 cells, we also added 0.05% insulin (I9278; Sigma-Aldrich) and 0.01% hydrocortisone (10 mg/ml, 70% ethanol/water). Forty-eight hours after seeding, we changed to 1% FBS in imaging base media for all cell types. On the next day, 4 hours before imaging, we conditioned cells by adding 200 μl of FBS (final concentration, 10%), EGF (final concentration, 1, 10, or 30 ng/ml) (R&D Systems, Minneapolis, MN, USA), ridaforolimus (final concentration, 10 nM) (Selleck Chemicals, Houston, TX, USA), or trametinib (final concentration, 100 nM) (Selleck Chemicals) to their existing media. For extended conditioning, we added 200 μl of FBS 7 hours before imaging.

We imaged cells with an Olympus FVMPE-RS upright microscope, 25× near-infrared-corrected objective, and four-channel detection (blue, cyan, yellow, and red) with a live-cell imaging chamber (Okolab, San Bruno, CA, USA). Laser settings were as follows: mTagBFP2 excitation at 800 nm, laser power 6%; Aquamarine and mCitrine excitation at 920 nm, laser power 6%; and mCherry excitation at 1040 nm, laser power 11%. We optimized the fluorophores, optical filters, and scan protocol to achieve negligible cross-talk between detector channels. We acquired four emission channels with pairs of detectors separated by a 552-nm dichroic mirror. We collected blue (channel 1) and cyan (channel 2) emissions with the following filters and dichroic mirror: channel 1, 435/50 nm; channel 2, 480/40 nm; and a 485-nm dichroic mirror. We collected yellow (channel 3) and red (channel 4) emissions (light >552 nm) with the following filters and dichroic mirror: channel 3, 540/40 nm; channel 4, 641/75 nm; and a 596-nm dichroic mirror. The microscope is equipped with tunable IR laser and a fixed 1040-nm laser. We acquired initial images of CXCR4-BFP with simultaneous excitation at 800 nm (mTagBFP) and 1040 nm (mCherry). We then immediately acquired repeated scans using sequential excitation by line at 920 (Aquamarine and mCitrine) and 1040 nm (mCherry). We acquired images as a multiarea time lapse scanned every 2 min for four images before addition of CXCL12 (final concentration, 10 ng/ml) and every 2 min thereafter for a total of 1 hour. We developed custom MATLAB code to automatically segment cells, calculate the KTR cytoplasmic-to-nuclear ratio (C/N) in each cell, measure intensity of CXCR4-mTagBFP, and track individual cells. The segmentation algorithm identified nuclei with adaptive thresholding, followed by watershed segmentation. The extended minima from the nuclear watershed were used to seed watershed segmentation of a mask of the combined KTR channels, which yielded cytoplasmic segmentation in good agreement with the contours of individual cells in confluent monolayers. Nuclei were used for tracking individual cells during the time-lapse imaging. For KTR reporters, we calculated the ratio of median fluorescence intensities in the cytoplasm to the nucleus (C/N), expressed as the log2 of the C/N, and output data as pairs of Akt and ERK KTR measurements for each cell with a complete time track (generally 300 to 500 cells per image). For cells engineered to express CXCR4-mTagBFP, we only used cells with detectable blue fluorescence for computational modeling. We discarded from the analysis the small number of cells undergoing mitosis during imaging because we could not track identities of these cells throughout the entire time course of an experiment.

Computational model: Receptor dynamics

We constructed a computational CSM of CXCR4-mediated Akt and ERK signaling using ordinary differential equations to generate predicted signaling outcomes. The CSM contains receptor, signaling, and reporter dynamics. A schematic including all connectivity in the CSM is drawn in fig. S3 (A to C). All equations, parameters, and initial conditions can be found in tables S1 to S5.

Receptor dynamics (CXCR4 trafficking after CXCL12 stimulation) are as described previously (3537). Briefly, CXCL12 in the extracellular space binds to CXCR4. Upon receptor phosphorylation and β-arrestin recruitment to the plasma membrane, the receptor-ligand complex is internalized, trafficked to endosomes, and destined for degradation. Because β-arrestin is an adapter protein ubiquitously involved in desensitizing many different GPCRs [heterotrimeric GTP-binding protein (G protein)–coupled receptors] (38, 39), we assume that it is in large excess and do not model it explicitly. CXCR4 not bound to CXCL12 can be internalized upon phosphorylation and β-arrestin recruitment, but the receptor is recycled to the cell surface rather than degraded.

Computational model: Signaling dynamics

The CXCR4-CXCL12 complex promotes signaling through Akt and ERK in a mechanism involving feedback loops and cross-talk that restrain signaling. The model includes a cascade of events leading to the phosphorylation of ERK and both the Thr308 and Ser473 sites in Akt needed for full activation (4042). The PI3K/Akt pathway is initiated when CXCL12-CXCR4 complexes, whether phosphorylated or not, promote G protein activation (43). To account for both ligand-independent and non–CXCL12-induced G protein activation, we incorporated a basal rate of G protein activation. Activated G proteins organize subunits of PI3K into their active state (44). Activated PI3K phosphorylates the membrane lipid PIP2 to form PIP3 (44, 45). PIP3 has two major roles in Akt signaling. First, it activates PDK1 by binding and forming a complex. The active form of PDK1 recruits and phosphorylates Thr308 in Akt, phosphorylated or not at Ser473 (45, 46). The Ser473 site in Akt is activated by a separate kinase, mTORC2. We assumed that the phosphorylation of either site in Akt is independent of the phosphorylation of the other, consistent with Pezze et al. (46). mTORC2 activation is generally thought to be PI3K dependent (47, 48). In our model, we proposed that mTORC2 is activated and recruited to the plasma membrane by PIP3, the second role for this lipid in the model and consistent with the results of Gan et al. (49). mTORC1 opposes mTORC2 formation (50). Although many studies have emphasized the importance of mTORC1 opposing PI3K formation through IRS-1 and thus halting mTORC2 formation (51, 52), mTORC1 can more directly inhibit mTORC2 formation. The subunit on mTORC2 that promotes docking to PIP3 and thus mTORC2 activation, mSIN1, is phosphorylated and inactivated by a target of mTORC1, activated and phosphorylated S6K (53, 54). This phosphorylation event detaches mSIN1 from mTORC2, preventing mTORC2 from attaching to the plasma membrane and becoming activated (55). These dynamics closely follow uncompetitive inhibition. Therefore, we model the activation of mTORC2 with PIP3 acting as the enzyme, inactive mTORC2 as the substrate, and mTORC1 as an uncompetitive inhibitor. Akt phosphorylated at both Thr308 and Ser473 and phosphorylated ERK promote mTORC1 activation (27, 56, 57). This activation involves many species, including TSC1/2 and RHEB, which were not modeled here explicitly for simplicity. Instead, we assumed that Akt phosphorylated at both Thr308 and Ser473 and phosphorylated ERK promote the activation of mTORC1.

The MAPK signaling pathway is initiated with the activation of Ras by active G proteins (58). Because mTORC1 can oppose the activation of Ras (59), we incorporated this relationship in our model. Without mTORC1 inhibition of Ras activation, the model did not accurately recapitulate coordinate regulation of Akt and ERK dynamics. Ras promotes activation of the Raf/MEK complex (60). MDA-MB-231 cells also have a Raf mutation, for which we accounted with a GPCR-independent Raf activation reaction and by setting this parameter to 0 when modeling cells without this mutation. In addition, Raf is inhibited by active Akt (61). Activated Raf/MEK promotes the phosphorylation of ERK (62). Other previously reported negative feedback mechanisms, such as feedback from ERK to Sos, Raf, and MEK, were lumped into ERK activation rate constants and were not included explicitly in the CSM because they were not required to reproduce critical behaviors seen in our experiments.

Computational model: Reporter dynamics

To connect active kinase concentrations (Akt phosphorylated at both Thr308 and Ser473 and phosphorylated ERK) to their respective reporters in the CSM, we use a set of published ordinary differential equations (16). Briefly, the reporters exist in two locations, the nucleus or cytoplasm, and have two states in both locations, phosphorylated or unphosphorylated. The reporters are phosphorylated and dephosphorylated according to Michaelis-Menten kinetics and are transported between nucleus and cytoplasm by mass action kinetics. To determine the C/N in individual cells in our model, we calculated the ratio of each reporter (phosphorylated and unphosphorylated) in the cytoplasm to the nucleus, and we expressed this variable in log2 format. The single-cell C/N of each reporter was the output of our model.

Computational model: Extrinsic noise

Extrinsic noise is now appreciated as a major driver of cell signaling heterogeneity (22, 25, 27, 63). In the CSM, extrinsic noise encompassed cellular conditions driven by mutations, metabolism, mitogenic signals, or any other external force acting on signaling components. The model incorporated extrinsic noise in three molecules, PI3K, Ras, and mTORC1, to predict the heterogeneous single-cell CXCR4-mediated Akt and ERK responses. A first-order rate constant for each of these molecules describes their activation independently of CXCR4 signaling. One important assumption of this approach is that the extrinsic noise rate parameters were constant over the time frame of our experiments. We believed that this assumption was reasonable because CXCR4 signaling activated PI3K, Ras, and mTORC1 dynamically by the explicit mechanisms in the CSM rather than by the extrinsic noise terms, which incorporated signaling not due to CXCR4 stimulation. Values for the extrinsic noise rate constants for PI3K, Ras, and mTORC1 could not be compared directly because they depended on the inactive states of each respective kinase, which existed in different concentrations in the cell. Because we modeled the activation of all kinases from their respective inactive states in the ERK and Akt signaling cascades, the concentration of each active kinase approached the total concentration of each kinase in the cell as the extrinsic noise rate parameter increases.

Computational model: Solution and calibration

The CSM was solved using MATLAB function ode15s. At the start of a simulation, the model was run in the absence of CXCL12 to calculate the steady-state concentrations of all model species. Next, a dose of CXCL12 was given and downstream signaling dynamics occurred as described above and by the differential equations in tables S2 and S3.

First-pass model parameters were obtained from literature as documented in table S4. We performed Latin hypercube sampling (64) as a search strategy for efficient parameter selection using the first-pass model parameters and a ±50% variation to find a suitable baseline parameter set. We used moderate values for extrinsic noise parameters and performed a least-square fit to calibrate the model to the mode cell in the experiment with control conditioned MDA-MB-231 cells treated with CXCL12 (10 ng/ml) to find a baseline parameter set that could span the range of responses using only variation in extrinsic noise rate parameters. We then used the same baseline parameter set for every cell in all of our simulations and varied only the three extrinsic noise rate parameters to generate signaling heterogeneity.

Determining the conditional signaling state of experimental cells

By varying the extrinsic noise parameters for PI3K, Ras, and mTORC1, we used the CSM to generate over 12,000 possible CXCR4-mediated Akt and ERK responses. To determine the conditional state of cells in our experiments, we calculated the residuals of each paired Akt and ERK experimental cell response to each of the predicted paired Akt and ERK responses from the CSM. We determined the conditional state of each experimental cell from the predicted cell to which it shared the minimum squared residual. In this manner, each individual experimental cell was now associated with a set of extrinsic noise parameters (kPI3K, kRas, and kmTORC1) that defined the conditional signaling state of that cell predicted by the CSM. Occupancy maps in Figs. 4 to 6 and fig. S6B are an illustration of the probability of experimental cells occupying a conditional state in the CSM. For each cell in an experiment, we calculated a fit score, which was the reciprocal of the sum of the squared residuals for experimental Akt and ERK KTRs compared with the simulated Akt and ERK KTR at each conditional state in the CSM. We normalized fit scores for each experimental cell to their sum over all CSM conditional states. We set a lower bound (0.0005), below which fit scores were set to 0. We calculated the probability of occupancy of each CSM conditional state as the sum of the fit scores for all cells under that condition, normalized to the sum of fit scores for all cells to all CSM conditional states. For illustration purposes, these values were multiplied by 1 million cells.

SUPPLEMENTARY MATERIALS

stke.sciencemag.org/cgi/content/full/12/589/eaaw4204/DC1

Fig. S1. KTRs report concentration- and time-dependent CXCR4 signaling in response to FBS.

Fig. S2. There is a trend between Akt responsiveness and ERK responsiveness, but initial Akt and ERK activity are poorly correlated with responsiveness in each respective kinase.

Fig. S3. CSM for CXCR4 signaling to ERK and Akt.

Fig. S4. Differential equations for the three species containing extrinsic noise terms in the computational model.

Fig. S5. Extrinsic noise parameters for PI3K, Ras, and mTORC1 produce a highly differentiated signaling landscape of basal activity and CXCR4 responsiveness to ERK and Akt.

Fig. S6. Conditional states of cells shift in the context of different conditioning times, stimuli, and genetic mutations.

Fig. S7. Computational modeling of responses to the MEK inhibitor trametinib and the mTORC1 inhibitor ridaforolimus shows concentration-dependent, context-specific effects on the activation of Akt and ERK by CXCR4 in MDA-MB-231 cells.

Table S1. CSM species descriptions and initial conditions.

Table S2. CSM rate equations.

Table S3. CSM differential equations.

Table S4. CSM parameter values.

Table S5. CSM parameters for modeling kinase inhibition.

References (6575)

REFERENCES AND NOTES

Acknowledgments: We thank E. Nash (University of Michigan) for technical assistance. Funding: The authors acknowledge funding from NIH Microfluidics in Biomedical Sciences Training Program NIBIB T32 EB005582 (to P.C.S.), as well as NIH grants R01CA196018 (to J.J.L. and G.D.L.), U01CA210152 (to G.D.L.), and R37CA222563 (to K.E.L.). Author contributions: P.C.S., J.J.L., G.D.L., and K.E.L. conceptualized the study. B.A.H., J.M.B., and K.E.L. provided reagents. P.C.S., B.A.H., D.L.M., and K.E.L. performed experiments and analyzed data. P.C.S., G.D.L., and K.E.L. wrote the manuscript. All authors edited the manuscript before submission. Competing interests: G.D.L. receives research funding and serves on the scientific advisory board for Polyphor. The other authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper or the Supplementary Materials. All cell lines, DNA constructs, and custom MATLAB code including the computational model and image processing files require a material transfer agreement from the University of Michigan.
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