Cell‐specific responses to the cytokine TGF β are determined by variability in protein levels
2018; Springer Nature; Volume: 14; Issue: 1 Linguagem: Inglês
10.15252/msb.20177733
ISSN1744-4292
AutoresJette Strasen, Uddipan Sarma, Marcel Jentsch, Stefan Bohn, Caibin Sheng, Daniel Horbelt, Petra Knaus, Stefan Legewie, Alexander Loewer,
Tópico(s)Viral Infectious Diseases and Gene Expression in Insects
ResumoArticle25 January 2018Open Access Transparent process Cell-specific responses to the cytokine TGFβ are determined by variability in protein levels Jette Strasen Jette Strasen Berlin Institute for Medical Systems Biology, Max Delbrueck Center in the Helmholtz Association, Berlin, Germany Search for more papers by this author Uddipan Sarma Uddipan Sarma Institute of Molecular Biology (IMB), Mainz, Germany Search for more papers by this author Marcel Jentsch Marcel Jentsch Berlin Institute for Medical Systems Biology, Max Delbrueck Center in the Helmholtz Association, Berlin, Germany Department of Biology, Technische Universität Darmstadt, Darmstadt, Germany Search for more papers by this author Stefan Bohn Stefan Bohn Department of Biology, Technische Universität Darmstadt, Darmstadt, Germany Search for more papers by this author Caibin Sheng Caibin Sheng Berlin Institute for Medical Systems Biology, Max Delbrueck Center in the Helmholtz Association, Berlin, Germany Department of Biology, Technische Universität Darmstadt, Darmstadt, Germany Search for more papers by this author Daniel Horbelt Daniel Horbelt Institute for Chemistry and Biochemistry, Freie Universität Berlin, Berlin, Germany Search for more papers by this author Petra Knaus Petra Knaus Institute for Chemistry and Biochemistry, Freie Universität Berlin, Berlin, Germany Search for more papers by this author Stefan Legewie Corresponding Author Stefan Legewie [email protected] orcid.org/0000-0003-4111-0567 Institute of Molecular Biology (IMB), Mainz, Germany Search for more papers by this author Alexander Loewer Corresponding Author Alexander Loewer [email protected] orcid.org/0000-0002-8819-3040 Berlin Institute for Medical Systems Biology, Max Delbrueck Center in the Helmholtz Association, Berlin, Germany Department of Biology, Technische Universität Darmstadt, Darmstadt, Germany Search for more papers by this author Jette Strasen Jette Strasen Berlin Institute for Medical Systems Biology, Max Delbrueck Center in the Helmholtz Association, Berlin, Germany Search for more papers by this author Uddipan Sarma Uddipan Sarma Institute of Molecular Biology (IMB), Mainz, Germany Search for more papers by this author Marcel Jentsch Marcel Jentsch Berlin Institute for Medical Systems Biology, Max Delbrueck Center in the Helmholtz Association, Berlin, Germany Department of Biology, Technische Universität Darmstadt, Darmstadt, Germany Search for more papers by this author Stefan Bohn Stefan Bohn Department of Biology, Technische Universität Darmstadt, Darmstadt, Germany Search for more papers by this author Caibin Sheng Caibin Sheng Berlin Institute for Medical Systems Biology, Max Delbrueck Center in the Helmholtz Association, Berlin, Germany Department of Biology, Technische Universität Darmstadt, Darmstadt, Germany Search for more papers by this author Daniel Horbelt Daniel Horbelt Institute for Chemistry and Biochemistry, Freie Universität Berlin, Berlin, Germany Search for more papers by this author Petra Knaus Petra Knaus Institute for Chemistry and Biochemistry, Freie Universität Berlin, Berlin, Germany Search for more papers by this author Stefan Legewie Corresponding Author Stefan Legewie [email protected] orcid.org/0000-0003-4111-0567 Institute of Molecular Biology (IMB), Mainz, Germany Search for more papers by this author Alexander Loewer Corresponding Author Alexander Loewer [email protected] orcid.org/0000-0002-8819-3040 Berlin Institute for Medical Systems Biology, Max Delbrueck Center in the Helmholtz Association, Berlin, Germany Department of Biology, Technische Universität Darmstadt, Darmstadt, Germany Search for more papers by this author Author Information Jette Strasen1,‡, Uddipan Sarma2,‡, Marcel Jentsch1,3,‡, Stefan Bohn3, Caibin Sheng1,3, Daniel Horbelt4, Petra Knaus4, Stefan Legewie *,2 and Alexander Loewer *,1,3 1Berlin Institute for Medical Systems Biology, Max Delbrueck Center in the Helmholtz Association, Berlin, Germany 2Institute of Molecular Biology (IMB), Mainz, Germany 3Department of Biology, Technische Universität Darmstadt, Darmstadt, Germany 4Institute for Chemistry and Biochemistry, Freie Universität Berlin, Berlin, Germany ‡These authors contributed equally to this work *Corresponding author. Tel: +49 6131 39 21430; E-mail: [email protected] *Corresponding author. Tel: +49 6151 16 28060; E-mail: [email protected] Molecular Systems Biology (2018)14:e7733https://doi.org/10.15252/msb.20177733 PDFDownload PDF of article text and main figures. Peer ReviewDownload a summary of the editorial decision process including editorial decision letters, reviewer comments and author responses to feedback. ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InMendeleyWechatReddit Figures & Info Abstract The cytokine TGFβ provides important information during embryonic development, adult tissue homeostasis, and regeneration. Alterations in the cellular response to TGFβ are involved in severe human diseases. To understand how cells encode the extracellular input and transmit its information to elicit appropriate responses, we acquired quantitative time-resolved measurements of pathway activation at the single-cell level. We established dynamic time warping to quantitatively compare signaling dynamics of thousands of individual cells and described heterogeneous single-cell responses by mathematical modeling. Our combined experimental and theoretical study revealed that the response to a given dose of TGFβ is determined cell specifically by the levels of defined signaling proteins. This heterogeneity in signaling protein expression leads to decomposition of cells into classes with qualitatively distinct signaling dynamics and phenotypic outcome. Negative feedback regulators promote heterogeneous signaling, as a SMAD7 knock-out specifically affected the signal duration in a subpopulation of cells. Taken together, we propose a quantitative framework that allows predicting and testing sources of cellular signaling heterogeneity. Synopsis Single-cell measurements and mathematical modeling reveal that the levels of defined signaling proteins determine cell-specific responses to the cytokine TGFβ, leading to the decomposition of cells into classes with qualitatively distinct signaling dynamics and phenotypic outcome. Using live-cell microscopy and constrained dynamic time warping, signaling dynamics of thousands of cells are quantitatively compared and grouped into distinct signaling classes. A three-tiered mathematical modeling strategy describes heterogeneous single-cell responses and identifies sources of variability. Negative feedback regulators such as SMAD7 control the response in a cell-specific manner and fine-tune TGFβ signaling in a subpopulation of cells. Introduction Cells sense their surrounding using cell-surface receptors and signaling pathways that transmit the corresponding information from the cell membrane to the nucleus. Cellular signaling is able to quantitatively respond to fine-grained inputs, for example, during development, when morphogens precisely determine cell fates according to spatial localization (Gurdon et al, 1998). However, it remains poorly understood how mammalian cells encode and decode quantitative information about extracellular inputs. Recent studies have shown that temporal dynamics of pathway activity can contribute to specific information processing and determine cellular responses (Purvis & Lahav, 2013). To measure dynamics of cellular signaling, live-cell imaging of fluorescent reporters emerged as a powerful approach (Spiller et al, 2010). In addition to providing unparalleled temporal resolution, it allowed to follow signaling in thousands of individual cells over time. This revealed that genetically identical cells frequently respond in different ways to the same external stimulus. For p53, TNF-α, and NF-κB signaling, it has been demonstrated that due to non-genetic heterogeneity, the signaling dynamics of each individual cell determine the phenotypic response to extracellular stimulation (Geva-Zatorsky et al, 2006; Ashall et al, 2009; Spencer et al, 2009; Tay et al, 2010; Purvis et al, 2012; Lee et al, 2014). Further studies confirmed that precise information transmission is in general limited by non-genetic heterogeneity, leading to differences in differentiation programs (Chang et al, 2008; Goolam et al, 2016), drug resistance (Cohen et al, 2008; Sharma et al, 2010; Paek et al, 2016), and viral pathogenesis (Weinberger et al, 2005). Heterogeneity in signaling emerges from various molecular sources including cell cycle stage, external influences such as the microenvironment, or stochastic intracellular events (Loewer & Lahav, 2011; Snijder & Pelkmans, 2011). Stochasticity may arise due to the stochastic dynamics of biochemical reactions in a signaling pathway (Rand et al, 2012), or from noise in gene expression that leads to cell-to-cell variability in the concentrations of signaling proteins (Feinerman et al, 2008). We therefore need a quantitative time-resolved characterization of mammalian signaling systems at the single-cell level to understand and predict how each individual cell will respond to a given extracellular input. A crucial extracellular input during embryonic development, adult tissue homeostasis, and regeneration is the cytokine TGFβ (Schmierer & Hill, 2007; Heldin et al, 2009). TGFβ stimulation prevents uncontrolled tissue growth by inducing cell cycle arrest and apoptosis and can trigger epithelial-to-mesenchymal transition (EMT), a conversion of adherent epithelial cells into a migratory, mesenchymal phenotype (Gonzalez & Medici, 2014). TGFβ signaling is dysregulated during pathological conditions such as organ fibrosis and cancer. In tumorigenesis, the pathway plays a dual role: Many early-stage tumors evade the tumor-suppressive, cell cycle inhibitory role of TGFβ, whereas its EMT-promoting function frequently induces metastasis of late-stage tumors (Ikushima & Miyazono, 2010). Thus, a specificity switch from one cellular response to another can occur in TGFβ signaling. The underlying molecular changes are currently unclear and may involve changes in the expression of transcription factors (Mullen et al, 2011) and signaling proteins (Piek et al, 2001), or altered temporal dynamics of the pathway (Nicolás & Hill, 2003). TGFβ initiates signaling through binding to and activation of its serine/threonine kinase transmembrane receptors (TGFβRI and TGFβRII). Ligand binding triggers receptor-mediated phosphorylation of SMAD2/3, which then heterotrimerize with SMAD4, translocate to the nucleus and bind to target gene promoters for transcriptional regulation (Feng & Derynck, 2005). This results in gene expression changes including the downregulation of classical epithelial and cell cycle genes and upregulation of mesenchymal markers (Massagué, 2005). Additionally, TGFβ target genes include negative feedback regulators of the pathway. Previous experimental and theoretical studies quantitatively characterized the mechanisms shaping the temporal dynamics of SMAD signaling (Clarke & Liu, 2008; Schmierer et al, 2008; Zi et al, 2012). One important mechanism that limits the duration of the signal is the depletion of extracellular TGFβ due to internalization of receptor–ligand complexes, followed by lysosomal TGFβ degradation (Clarke et al, 2009; Zi et al, 2011). Internalization of signaling complexes may also deplete TGFβ receptors from the cell membrane (Vizan et al, 2013), thereby contributing to a refractory period in which cells are insensitive to further TGFβ stimuli (Vizan et al, 2013; Sorre et al, 2014). In the nucleus, phosphatases such as PPM1A revert the phosphorylation of SMAD2/3 and facilitate their export to the cytoplasm (Lin et al, 2006). Finally, transcriptional feedbacks acting at multiple levels including receptor deactivation (Valdimarsdottir et al, 2006; Wegner et al, 2012) or SMAD dephosphorylation (Wang et al, 2014a) contribute to signal termination. Previous quantitative analyses of SMAD signaling mainly focused on average behavior of a cell population at defined time points, whereas the long-term response at the level of individual cells is much less well characterized. Recent studies revealed that SMAD2-SMAD4 complex formation and nuclear translocation of fluorescently labeled SMAD proteins occur with pronounced cell-to-cell variability (Warmflash et al, 2012; Zieba et al, 2012). Heterogeneous signaling behavior at selected time points post-stimulation was shown to be partially related to cell density and cell cycle stage (Zieba et al, 2012). However, to understand how TGFβ signaling elicits defined responses in a cell-specific and concentration-dependent manner, we need to systematically characterize its dynamics on the single-cell level and integrate experimental measurements with quantitative mathematical models of the underlying molecular interactions. This would allow us to predict how individual cells react to a given input and to design targeted perturbations of the pathway to exploit its role in health and disease. To this end, we combined live-cell imaging of fluorescent SMAD2 and SMAD4 fusion proteins with automated image analyses to quantitatively characterize long-term dynamics of TGFβ signaling in individual cells. Based on clustering of thousands of time courses, we identified six cellular subpopulations with qualitatively distinct signaling behavior and concluded that the phenotypic response of an individual cell is determined by the temporal dynamics of SMAD nuclear translocation. We described the dynamics of these subpopulations and of the complete heterogeneous cell population using a quantitative modeling approach. This theoretical and experimental approach revealed that heterogeneity in signaling arises from varying levels of signaling proteins. A CRISPR/Cas9-mediated knock-out of SMAD7 confirmed our model prediction that a major part of the observed heterogeneity can be attributed to fluctuations in feedback proteins. Taken together, we present a framework to characterize the response of cellular subpopulations to external cues and to quantitatively model the underlying molecular mechanisms of signaling heterogeneity. Furthermore, our results place the cell-specific temporal dynamics of SMAD signaling as an important determinant of the variegated cell fates elicited by TGFβ stimuli. Results Quantitative imaging of SMAD nuclear translocation at the single-cell level A key step in TGFβ signaling is the translocation of SMAD transcription factor complexes from the cytoplasm to the nucleus. To monitor this translocation event in individual cells with high temporal and spatial resolution, we established a live-cell reporter system based on the breast epithelial cell line MCF10A, an established model for TGFβ signaling (Zhang et al, 2014). To this end, we generated a stable clonal cell line expressing a YFP-SMAD2 fusion protein under the control of a constitutive promoter as well as histone H2B-CFP as a nuclear marker (Fig 1A). Western blot analysis revealed that the amount of SMAD2-YFP fusion protein corresponds to approximately 50% of the endogenous SMAD2 protein (Fig 1B). We validated that this overexpression did not perturb the dynamics of SMAD2 signaling by monitoring TGFβ1-induced phosphorylation of endogenous SMAD2 in the parental and reporter cell lines (Figs 1C and EV1A). Furthermore, qPCR analysis revealed that the induction of well-characterized SMAD target genes in response to TGFβ1 stimulation remained essentially unchanged (Fig EV1B). Figure 1. Dynamics and variability of SMAD2 signaling in single cells A. Fluorescent reporter system to measure SMAD signaling dynamics in individual cells. SMAD2 was fused to the yellow fluorescent protein mVenus (YFP) under the control of the human ubiquitin C promoter (UbCp) with the selection marker G418 (Geneticin). As a nuclear marker, histone 2B (H2B) was fused to the cyan fluorescent protein mCerulean (CFP) under the control of UbCp with the selection marker hygromycin. B. Western blot analysis of endogenous and YFP-tagged SMAD2 in a stable clonal reporter cell line and the corresponding parental cell line. Cells were stimulated with 100 pM TGFβ1 and analyzed after 3 h. GAPDH was used as a loading control. C. Western blot analysis of SMAD2 activation in SMAD2-YFP reporter and parental MCF10A cells. Cells were stimulated with 100 pM TGFβ1, and SMAD2 phosphorylation was analyzed at indicated time points. GAPDH was used as a loading control. D, E. Live-cell time-lapse microscopy images of MCF10A cells expressing SMAD2-YFP following treatment with 100 pM TGFβ1 (D). White circles indicate the segmented nucleus, and the estimated cytoplasmic area is represented by red annuli. The indicated cell was tracked over 24 h and the corresponding nuclear-to-cytoplasmic (nuc/cyt) SMAD2-YFP ratio plotted over time (E). F. Time-resolved analysis of the SMAD2 nuclear to cytoplasmic localization for eight individual cells (thin lines) compared to the median nuc/cyt SMAD2 ratio of the entire population (thick line) upon stimulation with 100 pM TGFβ1. See Appendix Table S1 for number of cells analyzed. G. Median nuc/cyt SMAD2 ratio for reporter cells stimulated with 100 pM TGFβ1 and treated with TGBβRI kinase inhibitor (SB431542) at indicated time points. At all time points, SMAD2 nuclear translocation was dependent on TGFβ receptor activity. See Appendix Table S1 for number of cells analyzed. Download figure Download PowerPoint Click here to expand this figure. Figure EV1. Dynamics and variability of SMAD2 signaling in single cells A. Western blot analysis of SMAD2 activation in SMAD2-YFP reporter and parental MCF10A cells. Cells were stimulated with 100 pM TGFβ1 and SMAD2 phosphorylation was analyzed at indicated time points. GAPDH was used as a loading control. Independent experiments were quantified and normalized to maximum values. Error bars indicate standard deviation of biological repeats (n = 4). Note that phosphorylated YFP-SMAD2 was at background levels at 0.25 h presumably due to lower expression levels. B. Expression of SMAD target genes in parental and SMAD2 reporter cell lines. Expression kinetics of the SMAD target genes SMAD7, SnoN, and PAI-1 upon 100 pM TGFβ stimulation were measured by qPCR in the indicated cell lines. β-Actin was used as an internal control. Error bars indicate standard deviation of technical triplicates. C. Live-cell time-lapse microscopy images of H2B-CFP expression in MCF10A cells following treatment with 100 pM TGFβ. The same detail as in Fig 1D is shown. White circle indicates the segmented nucleus, and the estimated cytoplasmic area is represented by red annuli. D–F. The cell indicated in Fig 1D was tracked over 24 h. The mean nuclear (D) and cytoplasmic (E) fluorescence intensity of SMAD2-YFP as well as the nuclear fluorescence intensity of H2B-CFP (F) were measured upon 100 pM TGFβ stimulation. G. Reproducibility of SMAD2 translocation measurements. Median SMAD2-YFP ratios (solid lines) of cells plated in three independent glass bottom plates stimulated with 100 pM TGFβ at the same day and tracked over 24 h (biological triplicates). Shaded areas indicate 25th and 75th percentiles. See Appendix Table S1 for number of cells analyzed. H. Correlation between endogenously expressed SMAD2 and transgenic YFP-SMAD2. In the same individual SMAD2 reporter cells treated with 100 pM TGFβ for 1.5 h, nuclear endogenous SMAD2 was measured by immunofluorescence and compared to the nuclear fluorescence intensity from YFP-SMAD2. Both measures were highly correlated (Pearson's correlation, n = 7,300). I. Comparison of endogenous SMAD2 activation and SMAD2-YFP translocation. The nuc/cyt ratio of SMAD2-YFP upon 100 pM TGFβ stimulation was measured in reporter cells by time-lapse microscopy at the indicated time points (blue); phosphorylation of endogenous SMAD2 was measured in parental MCF10A cells by immunofluorescence (IF, red) under the same conditions. Data were normalized by minimum subtraction and division through the overall maximum. White and black dots indicate medians; boxes include data between the 25th and 75th percentiles; whiskers extend to maximum values within 1.5× the interquartile range; colored dots represent outliers. See Appendix Table S1 for number of cells analyzed. Download figure Download PowerPoint To measure SMAD2-YFP translocation in living cells, we performed time-lapse imaging over a 24-h time interval after a saturating TGFβ1 stimulus. In the example cell shown, SMAD2 predominantly located to the cytoplasm in the absence of TGFβ1 as expected and strongly accumulated in the nucleus within 1 h of stimulation (Fig 1D). After this initial response, SMAD2 relocalized to the cytoplasm, before it accumulated in the nucleus again about 5 h post-stimulation. Nuclear SMAD2 then remained elevated at varying levels throughout the experiment. As we aimed to compare SMAD2 dynamics in hundreds of cells, we employed automated image analysis to quantify the nuclear and cytoplasmic SMAD2 concentrations and expressed the signaling pathway activity as their ratio (nuc/cyt ratio, Figs 1E and EV1C–F, Appendix Fig S1 and Appendix II.A and II.B). This measure was robust against correlated fluctuations due to heterogeneity of transgene expression or measurement aberrations such as photobleaching and reproducible between biological replicates (Fig EV1G). We validated that changes in the nuc/cyt ratio of SMAD2 reflect the kinetics of receptor-mediated phosphorylation of endogenous SMAD2 (Fig EV1H and I). When cells divided during the duration of the experiment, we only followed one of the daughter cells and merged mother and daughter trajectories before and after division (see Appendix II.A). Using this approach, we observed substantial heterogeneity in the response to the saturating stimulus (Fig 1F). Most cells showed nuclear SMAD2 accumulation shortly after the initial stimulus. However, some cells immediately adapted to a low signaling plateau afterward, whereas others were characterized by renewed nuclear translocation of SMAD2. The average response of all cells in the population revealed signaling dynamics similar to biochemical measurements of cell populations in previously published studies (Inman et al, 2002; Clarke et al, 2009; Zi et al, 2011; Vizan et al, 2013). Importantly, nuclear translocation of SMAD2 was dependent on TGFβ receptor activity at all time points, as signaling was rapidly and synchronously terminated in all cells by the specific inhibitor SB431542 (Fig 1G; Inman et al, 2002). We observed comparable heterogeneous dynamics for SMAD4 nuclear translocation using a similarly engineered and validated reporter cell line (Appendix Fig S2). Dynamic features of SMAD signaling encode phenotypic responses Next, we investigated whether heterogeneous signaling was limited to saturating TGFβ1 concentrations or a characteristic feature of the pathway at all stimulus levels. We treated cells with varying TGFβ1 doses and quantified SMAD2 localization over a 24-h period. Interestingly, we again observed pronounced cell-to-cell variability (Fig 2A). At low stimulation levels, cells either showed almost no response to the input or transient nuclear SMAD2 accumulation over the first 5 h. At higher TGFβ1 concentrations, most cells showed an initial response to the input. However, the extent and duration of renewed nuclear SMAD2 translocation at later time points were highly variable: A single-cell response to 25 pM TGFβ1 could be transient and of limited amplitude, resembling trajectories typically observed upon stimulation with 5 pM TGFβ1 (Fig 2A). In essence, dynamic signaling responses were overlapping between input levels and therefore only partially determined by the strength of the extracellular stimulus. Figure 2. SMAD dynamics decompose into distinct signaling classes Time-resolved analysis of SMAD2 nuclear to cytoplasmic localization for varying stimulus levels. Nuc/cyt SMAD2 ratios for eight individual cells (thin lines) as well as the population median (thick line) are shown. See Appendix Table S1 for number of cells analyzed. Median nuc/cyt SMAD2 ratio of cells stimulated with varying concentrations of TGFβ1 over 24 h. See Appendix Table S1 for number of cells analyzed. Individual cells were clustered into six signaling classes according to their time-resolved nuc/cyt SMAD2 ratio using dynamic time warping (DTW). Each line represents the median over all cells of the indicated cluster. Cells stimulated with varying TGFβ1 concentrations as indicated in (B) were included in the analysis. Distributions of signaling classes depending on TGFβ dose. Silhouette plots of cells sorted according to TGFβ concentration (upper panel) or signaling classes (lower panel). Plots provide a graphical representation of how well the nuc/cyt SMAD2 ratios of each cell correspond to trajectories of other cells in its own group according to the cDTW measure. Positive silhouette scores indicate that SMAD2 responses are more similar to the own group, while negative scores signify that the corresponding trajectory is closer to any of the other groups. In general, signaling classes provide better separation than sorting according to stimulus levels. Cell proliferation shown as number of cell divisions per cell within 24 h after a TGFβ stimulus. Cells were sorted according to TGFβ concentrations (upper panel) or signaling classes (lower panel). Motility of each cell as summed distance covered between 20 and 24 h after stimulation with TGFβ (in pixel). Cells were sorted according to TGFβ concentrations (upper panel) or signaling classes (lower panel). White lines indicate median; boxes include data between the 25th and 75th percentiles; whiskers extend to maximum values within 1.5× the interquartile range; crosses represent outliers. See Appendix Table S1 for number of cells analyzed. Download figure Download PowerPoint TGFβ is known to control cell fate in a dose-dependent manner (Schmierer & Hill, 2007). Accordingly, we find that changing the TGFβ1 stimulus alters the median SMAD2 response and expression levels of selected target genes in cell populations (Figs 2B and EV2A and B). How does the SMAD pathway encode dose-dependent information despite the strong cellular heterogeneity observed in our single-cell measurements? We hypothesized that phenotypic responses are determined by the individual pattern of SMAD translocation in a given cell rather than by the amount of ligand applied to a population. To quantify pair-wise differences between single-cell time courses, we used dynamic time warping (DTW), a method for non-linear alignment in the time domain, which is frequently employed in speech analysis (Sakoe & Chiba, 1978). Compared to simpler metrics such as Euclidean distance, DTW is more robust against distortions in the time domain and therefore emphasizes dynamic patterns while preserving differences in amplitudes (Fig EV2C). To improve its applicability to biological systems, we modified DTW by introducing an elastic constraint on stretching a given time series (cDTW, see Appendix Fig S3 and Appendix II.C for more information on cDTW implementation and performance). Click here to expand this figure. Figure EV2. Clustering heterogeneous SMAD translocation dynamics using dynamic time warping A, B. Dose-dependency of SMAD target gene expression. Parental MCF10A cells were stimulated with varying concentrations of TGFβ and SMAD7 (A) and PAI-1 (B) expression was measured by qPCR at indicated time points. Error bars indicate standard deviation of technical triplicates. C. Illustrative comparison of Euclidian distance and dynamic time warping (DTW). In the left panel, three single-cell trajectories (red, blue, and black) with similar Euclidian distances are shown (see table). DTW performs a non-linear alignment in time (middle panel) that compensates the temporal shift of the peaks in the red and blue trajectory (cyan lines). This leads to a lower DTW distance score compared to the DTW distance between the red and black or blue and black trajectories, which remain almost unchanged (see table). D. Dissimilarity matrix calculated pair-wise by cDTW of single-cell trajectories treated with varying TGFβ doses. Strength of the TGFβ stimulation increases from top left to bottom right. E. Heat map of single-cell time courses sorted according to hierarchical clustering. The corresponding dendrogram is shown on top. F. Optimal number of clusters. For different cluster numbers, jump size is calculated using sum of square errors of cDTW scores as a measure of intra-cluster dispersion. Jump size reaches maxima at three and six clusters, indicating that these are good choices for cluster number. G–J. Direction-resolved analysis of cell motility in TGFβ-stimulated cells. The angle and distance of each cell movement were determined and averaged for 0–30 h (upper panel) and 30–60 h (lower panel) after stimulation with varying concentrations of TGFβ (see Appendix II.F for details). Cells are grouped according to stimulation levels (G) or signaling classes (H). Changes in cell motility are more pronounced at later time points after stimulation. Unidirectional movements (angle = 0) of TGFβ-stimulated cells 30–60 h after treatment were normalized by the mean movement of unstimulated cells in the same time period and analyzed according to stimulus level (I) or signaling classes (J). Changes in cell motility are express as median fold change; error bars indicate 95% confidence intervals from permutation testing. Signaling dynamics allow better stratification of cellular outcomes compared to stimulus levels. See Appendix Table S1 for number o
Referência(s)