Topography of epithelial-mesenchymal plasticity

Abstract

The transition between epithelial and mesenchymal states has fundamental importance for embryonic development, stem cell reprogramming, and cancer progression. Here, we construct a topographic map underlying epithelial-mesenchymal transitions using a combination of numerical simulations of a Boolean network model and the analysis of bulk and single-cell gene expression data. The map reveals a multitude of metastable hybrid phenotypic states, separating stable epithelial and mesenchymal states, and is reminiscent of the free energy measured in glassy materials and disordered solids. Our work not only elucidates the nature of hybrid mesenchymal/epithelial states but also provides a general strategy to construct a topographic representation of phenotypic plasticity from gene expression data using statistical physics methods.

Keywords: Boolean networks; epigenetic landscape; epithelial–mesenchymal transition.

Fig. 1.

The topography of E/M states displays a hierarchical complex structure. (A) Illustration of the Boolean update rule. The state of a node $s_i$ depends on the state of its promoters ($J_{ij}=+1$, $\to$) and inhibitors ($J_{ij}=-1$, ). (B) PCA projection of $10^6$ steady states. Color corresponds to the ratio of steady states that express E-cadherin. The panel shows intricate patterns of transition between areas of high/low Ecadherin expression probability, colored in green/violet shades. (C) A 3D reconstruction of topography of EMT. The $xy$ projection reproduces the data in B. The $z$ axis corresponds to the value of $H$, showing that high-$H$ states (colored in darker blue shades) coincide with the central transition area in B. (D) Distribution of steady-state abundances, computed from $10^7$ steady states of the EMT model (blue symbols). The relative abundance $a$ of a steady state is the fraction of times it is found, starting from random initial conditions. The black line of slope −2 is shown only as a guide to the eye. The Inset shows the number of distinct steady states $U_{ss}$ as a function of the total number of steady states $N_{ss}$ found in the simulations. (E) Clustering of steady states, computed using 500 steady states of the model. The heat map shows the correlation between steady states. Colors adjacent to the dendogram mark the expression of E-cadherin (green) or lack of expression (violet). States expressing E-cadherin cluster together but display additional hierarchical organization. (F) Overlap distribution over the 20% of steady states with lowest $H$. A two-peak distribution marks the presence of two symmetric sets as in disordered magnets. (G) The broad overlap distribution over all steady states resembles the one observed in spin glasses.

Fig. 2.

EMT/MET occurs with different probabilities through multiple paths. The model shows many forms of EMT/MET, and these occur with different probabilities. (A and B) One-dimensional PCA projection of the $H$ landscape where (A) OE or (B) KD of SNAI1 tilts the landscape toward the M or E regions, respectively. (C) Transition map under SNAI1 OE. The model displays different forms of SNAI1-induced EMT. (D) The distribution of gene expression avalanches after individual KD/OE is a power law with exponent $\tau \simeq 1.5$. (E) The cutoff of the distribution depends on $H$, quantified here by quartiles, with high-$H$ states producing larger avalanches. (F) EMT/MET probabilities under KD/OE conditions. The model lays out a nondeterministic picture of EMT/MET, where well-known factors such as SNAI1 (EMT) or KLF4 (MET) induce phenotypic transitions with higher probability (see Materials and Methods and SI Appendix, Fig. S2 for further details).

Fig. 3.

Multitissue gene expression data display statistical features in agreement with simulations. (A) Illustration of the binarization process (see Materials and Methods for details). Gene-level expression data are casted into node-level binary data using binarization thresholds, computed using two reference samples (orange and black coloring). (B) Skin (orange) and fibroblast (black) samples from the GTEx project projected in PCA space. The E-cadherin expression probability in the model is shown with green (100%) to violet (0%) shades. Fibroblast samples tend to be in areas of very low E-cadherin expression probability. (C) Same as B but coloring the model steady states by average $H$. (D) Distribution of abundances, computed using all GTEx binarized samples and the 14 most relevant nodes (see SI Appendix and SI Appendix, Fig. S3 for details). (E) Clustering of 500 GTEx samples (all tissues), displaying a hierarchical structure qualitatively similar to that of the model (compare with Fig. 1E). (F) Overlap distribution over skin and fibroblast samples from the GTEx project (compare with Fig. 1F). (G) Overlap distribution over all GTEx samples (compare with Fig. 1G).

Fig. 4.

Single cells and bulk transcriptomic data yield trajectories through the E/M map with putative hybrid states lying on high-$H$ regions. (A) Data from TGF-$\beta$–treated lung adenocarcinoma cell lines [GSE17708 (42)] yield a trajectory moving from the E to the M region. (B) Data from Dox-induced somatic cell reprogramming [GSE21757 (30)] display a reverse trajectory from M to E. Experimental data are shown as colored symbols with time course marked with arrows. The colored background depends on the ratio of steady states of the model that express E-cadherin at a given location in PCA coordinates, ranging from 100% (green) to 0% (violet). (C) Experimental data from single-cell embryonic-to-endoderm differentiation [GSE75748 (43)] move across the map as cells undergo EMT. The background color indicates the ratio of steady states that express E-cadherin or KLF4 (see SI Appendix, Fig. S7 for more markers). (D) Localization of single-cell gene expression data from tumor cells obtained from head and neck squamous cell carcinoma patients (45). All tumor cells correctly lie in the E region of the map, with high pEMT-scored cells located toward high-$H$ areas. (E) The pEMT score correlates with $H$. Each gray dot represents a single cell. $R$ and $p$ denote the Pearson correlation coefficient and its associated P value (Student’s $t$ test, two-tailed). The red line shows the average $H$.