Mesenchymal to Epithelial Transition (MET) in Cancer Progression: Insights from logical modeling

Sophia Orozco-Ruiz^1,2,3,*, Marco Ruscone^1,2,3,4, Emmanuel Barillot^1,2,3, Olivier Destaing⁵, Laurence Calzone^1,2,3,*

1 Institut Curie, Université PSL, F-75005, Paris, France

4 Barcelona Supercomputing Center, Life Science Department, Barcelona, Spain

2 INSERM, U1331, F-75005, Paris, France

3 Mines ParisTech, Université PSL, F-75005, Paris, France

5 University Grenoble Alpes, INSERM 1209, CNRS UMR5309, Institute for Advanced Biosciences, Grenoble, France

* corresponding author: Laurence.calzone@curie.fr, sophia.orozco-ruiz@curie.fr

Abstract

The ability of carcinoma cells to transition along the epithelial-mesenchymal spectrum is crucial for metastasis. While the process of Epithelial to Mesenchymal Transition (EMT) has widely been studied, its reverse, Mesenchymal to Epithelial Transition (MET), has been less thoroughly explored.

Here, we first present a comprehensive overview of the known MET inducers in cancer, detailing the cellular contexts in which they play a role and their interactions with EMT drivers. Based on these observations, we constructed a minimal regulatory network centered on key signaling pathways, including Transforming Growth Factor β (TGFβ), Bone morphogenetic protein (BMP), and other growth factors. This network was then translated into a logical model to explore the dynamic interplay between EMT and MET programs.

Through in silico simulations, we demonstrate how perturbing this network can interfere with EMT programs to induce MET. Our findings highlight that the MET process is highly dependent on the mesenchymal context. We further demonstrate that persistence of EMT programs constrains how far along the epithelial–mesenchymal spectrum different MET inducers can reposition mesenchymal cells. Moreover, perturbing components of one EMT program can reinforce alternative EMT pathways, thereby preserving this balance and preventing a full reversion to epithelial states, highlighting a new function for cells with transitive states.

Introduction

Epithelial to Mesenchymal Transition (EMT) and its reversed process, Mesenchymal to Epithelial Transition (MET), are programs that occur in physiological contexts, such as development or tissue repair, and in pathological conditions, including cancer and fibrosis[1], [2], [3]. Carcinoma cells (i.e., cancerous cells derived from the epithelial tissue) rely on paracrine and autocrine signals to trigger their ability to move along the epithelial-to-mesenchymal spectrum. This adaptability, known as Epithelial-Mesenchymal Plasticity (EMP), enables cells to invade and colonize secondary tissues[4].

EMT causes tumor cells to lose epithelial traits (such as polarity and cell–cell junctions) and gain mesenchymal features (like motility and ECM degradation), enabling them to detach and enter blood or lymph vessels (intravasion). Circulating tumor cells then leave the circulatory system (extravasation) and arrive in a new microenvironment where they undergo MET, recovering their epithelial phenotype. They can proliferate and survive, forming micrometastasis that can potentially evolve into secondary tumors[4], [5], [6]. However, cancer cells rarely become fully mesenchymal; instead, they often adopt hybrid or partial EMT (pEM) states that combine both traits[7], [8], [9], [10], [11].

Multiple studies regarding EMT inducers and their underlying regulatory networks have shown that EMT is a context-dependent process, with no universal path or markers. Distinct EMT inducers, such as TGFβ, Tumor Necrosis Factor (TNF), and Epidermal Growth Factor (EGF), can generate EMT gene expression patterns and cellular phenotypes that are highly context-specific, dependent on the cell line and the inducer. Moreover, even with the same inducer but a different time regime, the underlying mechanism that maintains the mesenchymal phenotype has been shown to differ[12], [13].

In a physiological context, MET has been extensively studied in development, particularly during kidney organogenesis and somitogenesis, as well as in adult tissues to maintain the homeostasis and integrity of these functional units in multicellular organisms[1], [14]^,[15]. MET can occur in different contexts. Some studies have highlighted the importance of FGFR1-2 or 4, Wnt4-1-3a-7a or 7b, and BMP7 to induce MET[14]. The link between BMP7 and MET is reinforced by its ability to highly sustain the epithelization of renal tissues during development and fibrosis[16].

MET is less studied in cancer, although evidence from squamous cell carcinoma and breast cancer studies has shown that cancer cells must regain epithelial traits to form macrometastases[9], [17], [18]. However, the signals and mechanisms driving MET during metastasis remain unclear. While some MET drivers have been identified, their roles during tumor progression are not fully understood. Evidence suggests that, like EMT, MET is context-dependent. Since MET likely depends on overcoming the autocrine and paracrine signals that maintain EMT, these signaling agents may determine the cell’s response to MET inducers[19]. Moreover, short-term EMT can be reversed, but long-term reversibility is limited by chromatin-based memory[20], [21]. MET inducers do not always trigger the same transcriptional program to abolish EMT[22]^,[23]. In certain contexts, established inducers like BMP7 may promote migration, such as in chondrosarcoma[24]. Furthermore, understanding how MET inducers operate under different cellular contexts to produce pEM states is also crucial, as such cells often exhibit greater invasiveness and metastatic potential[7].

EMT and MET are determined by multiple regulatory interactions between ligands, receptors, and their downstream pathways, forming complex networks of intertwined signaling pathways. Due to this complexity, mathematical modeling is a useful tool to elucidate non-intuitive observations. Because they do not require quantitative parameters, Boolean models allow for a high number of variables and the study of more complex regulatory networks[25], [26], [27]^,[28], [29]. Despite the tight interplay between the two processes, both in development and tumor progression, these models do not consider the multiple extracellular and intracellular mechanisms that regulate MET.

In this article, we first report on the current knowledge on MET inducers in cancer cells, highlighting what is known about the cellular contexts that trigger the program. Based on this work, we then propose a regulatory network encompassing the most characterized pathways and genes known to induce MET. Finally, the network is translated into a dynamic Boolean model that integrates the reviewed knowledge and recapitulates some central aspects of EMT and the context specificity of MET. Our model shows how interference with EMT and MET drivers triggers cells to different places within the Epithelial-Mesenchymal spectrum according to the environment.

1 Results

1.1 MET, an opposing process of EMT in the context of cancer progression

Several reported observations have suggested that signaling cascades and/or microenvironmental factors lead to MET in cancer cells (Supplementary Table 1). Some but not all of these inducers are known to be needed for metastatic colonization. Others have only been shown to be able to abolish EMT in primary tumors and thus stop tumor metastasis.

In cancer, MET is often considered to occur by opposing and overcoming EMT signals. TGFβ is one of the main EMT drivers, responsible for the activation of diverse signaling cascades and the expression of EMT transcription factors (EMT-TFs) through a complex regulatory network. Pro-MET inducers such as versican and BMP7 do not activate a specific MET-signaling cascade but rather induce this process by perturbing TGFβ-mediated EMT activation and it downstream pro-EMT regulatory network [29], [30]. Lumican, another MET-inducer, can trigger this transition by perturbing the EGF pathway, another pro-EMT signal[22]. The existence of a specific MET signaling pathway is yet to be described, and MET has been seen as a passive system in cancer. However, some evidence highlights that MET signaling mechanisms can be independent of those regulating EMT signaling³⁹.

1.2 Assembling a regulatory network of epithelial/mesenchymal plasticity

The information about the main key genes and their interactions, dispersed in the literature, was recapitulated into a comprehensive network aiming to understand the triggering of both EMT and MET, to define the various contexts for this plasticity. We focused mainly on the role of BMP, TGFβ, and other growth factors (GF) such as EGF in triggering downstream events that, through a complex network, lead to MET and EMT (Figs. 1, 2). We selected GF and TGFβ as EMT triggering factors because the majority of MET inducers act by opposing their signal (lumican, versican, and BMP). We chose BMP from the list of MET signaling agents because the other inducers act through pathways for which we lack sufficient information[11], [31].

1.2.1 EMT-TFs

Several transcription factors have been identified by their ability to induce EMT and are hence given the name of EMT-TFs. Among them, we can cite SNAI1, SNAI2, ZEB1, ZEB2, and TWIST1. They contribute to crucial aspects of the EMT program, including changes in cellular morphology and activity of E-cadherin, β-catenin, and p120-catenin that drive epithelial states through the formation and maturation of cell-cell contacts[32]. ZEB1/2 and SNAI1/2 control E-cadherin expression by directly binding to the promoter region of CDH1 (E-cadherin gene) and TWIST1 through the upregulation of SNAI2[6], [33], [34]. N-cadherin (the cadherin associated with mesenchymal cells) is induced by ZEB1/2[34], and Claudin-1 (a component of Tight Junctions, which are crucial for epithelial polarity) is repressed by SNAI1/2[35]. ZEB2 induces the expression of vimentin, which contributes to migration[36]. In addition, cells going through EMT modify the extracellular matrix (ECM) to invade the surrounding tissue. Matrix metalloproteinases (MMPs), induced by EMT-TFs, are involved in the degradation of the ECM and play an important role in migration (e.g., ZEB1 and TWIST1 participate in MMP2 upregulation[37], [38]).

The EMT-TFs have specific targets highlighting their non-redundant nature and the need for cooperation. For example, SNAI1 participates in the upregulation of ZEB1 through indirect mechanisms[33], [39]. It has also been shown that EMT-TFs can negatively interact with each other and generate distinct EMT programs. It was found that SNAI1 and PRRX1, another EMT-TF, show mutually exclusive expression patterns during development and in cancer cell lines, involving microRNAs such as miR15[40]. On the contrary, PRRX1 expression correlates with that of TWIST1, whose transcript is downregulated by SNAI1[12], [40] (Fig. 1).

1.2.2 MET drivers

For EMT to occur, transcription factors and miRNAs responsible for maintaining the epithelial phenotype must be downregulated. Among them, GRHL2, ∆Np63, OVOL1, OVOL2, and miR200 stand out as members of a complex regulatory circuit with the EMT-TFs (Fig. 1). GRHL2 and ZEB1 have reciprocal inhibitory interactions at the transcriptional level[41], [42]. OVOL2 has also been shown to be a strong and direct repressor of ZEB1, TWIST1, and ZEB2, while ZEB1 overexpression leads to OVOL2 downregulation[43], [44], [45], [46]. OVOL2 family member OVOL1 is also capable of inducing MET by interfering with ZEB1[43]. ∆Np63, an isoform of the p63 gene, indirectly represses ZEB1 and ZEB2 by inducing the expression of miR205, a direct inhibitor of ZEB1 and ZEB2[47, p. 63]. Similarly, miR200 represses ZEB1/2 and SNAI2, while being inhibited by ZEB1/2 and SNAI1/2[48], [49], [50], [51]. SNAI1 is also an indirect inhibitor of ∆Np63 [52]. TWIST1 has been shown to bind to miR200 and miR205 promoters, and hence proposed as one of their repressors[53]. GRHL2 can further repress ZEB1 by inducing OVOL2 and miR200[54], [55]. Moreover, a positive feedback loop between GRHL2 and ∆Np63 has been proposed based on the reciprocal and positive influence of each other’s promoter activity, explained in part by the direct binding of GRHL2 to ∆Np63 promoter[56], [57], [58].

It is important to consider that some interactions may be context-specific. For example, in radioresistant populations of breast cancer, ZEB1 can repress miR205, but there is no downregulation of miR200[59]. Further, the direct repression of ZEB1 by GRHL2 is absent in a luminal breast cancer model[60]. As we aimed for our model to be generic, we do not consider these tissue-specific cases, but the network can be modified to explore these interactions in future work.

Fig. 1

Regulatory networks involved in epithelial/mesenchymal plasticity. Transcription factors and miRNAs involved in epithelial/mesenchymal plasticity. Figure made with GINsim[61].

1.2.3 TGFβ-EMT program

TGFβ signaling is at the crossroads of regulation and control of RTK/NRTKs signaling and upstream of numerous features of migratory and invasive mesenchymal functions. Its canonical pathway consists of the activation of the SMAD2/3-SMAD4 complex (referred to as SMAD2_3 in Fig. 2) following the phosphorylation of the TGFβ receptor. The SMAD2/3–4 complex translocates to the nucleus, where it can regulate the gene expression of EMT-MET genes[6], [62]. For instance, SMAD2/3–4 can induce SNAI1/2 by cooperating with MAPK-activated genes[63], [64], [65]. TGFβ can also induce PRRX1[40]. In addition, SMAD2/3–4 contributes to the downregulation of epithelial genes, as is the case for CEBPa (not included explicitly in the model), a transcription factor that is associated with the epithelial identity and that also activates ∆Np63[52], [66] (Supplementary Fig. 1A and Fig. 2). Apart from SMAD-mediated signaling, TGFβ contributes to EMT through other non-canonical pathways such as PI3K-AKT, JNK, NFkB, and MAPK-ERK. Through these pathways, other positive feedback loops are formed to maintain EMT [6], [32] (see Supplementary Text).

Autocrine TGFβ has been identified as essential to sustain tumoral EMT in some cases. For instance, silencing the TGFβ receptor can partially block the progression of EMT even in programs that were initially triggered by other EMT-inducers[67]. These inducers can also promote TGFβ1 transcript (TGFB1)[67]. Furthermore, chronic exposure of cancer cells to TGFβ has resulted in the maintenance of a mesenchymal phenotype in the absence of treatment with the ligand[13], [68]. Autocrine TGFβ signaling involves some of the EMT-associated proteins. For instance, AP1 can induce TGFB1 gene transcription[69], and MMPs and integrins (e.g., αV integrins) are required to liberate secreted TGFβ into its active form[70], [71]. Furthermore, ZEB2 has been proposed as a transcriptional regulator of αV integrin, whereas miR200 has been implicated in the interference of integrin cell surface expression and signaling[72], [73].

1.2.4 The complex link between BMP signaling and MET program

BMPs are members of the TGFβ superfamily. Similar to TGFβ, BMP ligand binds to the receptor complex formed by type I and type II BMP receptors, which, instead of activating SMAD2/3, activate SMAD1/5/8. SMAD1/5/8 (SMAD5 in Fig. 2) can then form a complex with SMAD4 and act as a transcriptional regulator[6] (Supplementary Fig. 1B). As TGFβ, BMPs have several isoforms that can interact with different BMP receptors to generate diverse responses in cancer cells[74].

Regarding Epithelial-Mesenchymal plasticity, BMPs can act both as promoters of EMT (e.g., BMP2 in breast cancer and BMP7 in chondrosarcoma)[24], [75], and inhibitors (e.g., BMP7)[30]. The BMP-SMAD1/5/8 − 4 signaling axis can activate ID1/2/3 and OVOL1[76] (Fig. 2). ID proteins do not have a DNA-binding site, but they function as repressors of bHLH proteins by hybridizing with them. Their targets include TWIST1/2, TCF3 (E47), and TCF4 (E2-2), which are also inducers of EMT[77]. Therefore, it has been suggested that BMPs can induce MET by opposing TWIST1. It has been shown that ID1 overexpression could counteract EMT induced by TWIST1 in HMLE cells but not EMT induced by SNAI1[78]. Notably, TGFβ is a repressor of ID proteins; however, in some cases, it can act as an inducer[76], [78]. Here, we will only consider its inhibitory role.

BMP signaling can promote MET genes and interact with TGFβ in several ways, though the mechanisms in cancer remain unclear[79]. In normal cells, TGFβ limits its own activity via SMAD7-mediated receptor degradation, but in cancer, this feedback is lost as miR182 inhibits SMAD7[80]. In breast cancer, OVOL1 restores SMAD7 expression and suppresses TGFβ signaling, while mesenchymal-like tumors show reduced BMP ligands and increased BMP antagonists[81]^,[19]. Finally, ∆Np63 enhances BMP7 expression but is downregulated during EMT, which could allow TGFβ dominance in breast cancer cell lines[82]. BMPs may support MET through context-dependent mechanisms that remain to be elucidated. In the context of our model, we will mostly consider BMP7 (Fig. 2, Supplementary Fig. 1B).

Fig. 2

Regulatory Network of Epithelial-Mesenchymal Plasticity. A schematic version of the network described and annotated in Supplementary Material 1. The network has inputs TGFB: TGFB ligand, GF: growth factors (to keep it general, it represents growth factors as PDGFRα or EGF that signal through RTKs) BMP: BMP ligand (representing BMP7). aTGFB: autocrine TGFB, TGFB1T: TGFβ1 transcript, Ecad: E-cadherin, Ncad: N-cadherin, AdhJunc: Adherens Junctions, TightJunc: Tight Junctions. Figure made with GINsim [61].

1.3 Insights from the modeling approach

1.3.1 Boolean model of Epithelial-Mesenchymal Plasticity

The interactions between the main contributors of EMT and MET form a very complex network, making it difficult to anticipate the cells’ behavior in particular contexts, including genetic and transcriptomic profiles of patients or cells. To cope with this issue, we integrated the knowledge reviewed above into a comprehensive network (Fig. 2). In this literature-based network, nodes are genes, proteins, signaling cascades, and processes; edges are positive or negative effects that one entity has over another. These influences can be a complexation, a phosphorylation, a transcription of a gene, etc. The network was translated into a Boolean model and simulated using a stochastic approach (see Methods).

1.3.2 The Boolean model can recapitulate the Epithelial-Mesenchymal Plasticity spectrum

The model has 25 solutions (referred to as stable states, see Methods), which correspond to all the possible long-term behaviors of the system no matter what the initial conditions are. They are classified as follows according to the epithelial and mesenchymal markers: 6 epithelial (E), 8 mesenchymal (M), 10 partial EMT (pEM), and one naive state (Fig. 3A). States corresponding to a mesenchymal phenotype can be divided into two groups: M1, characterized by the activation of PRRX1 and TWIST and not SNAI1, and M2, with an opposite pattern. Epithelial states show two possibilities: E1, encompassing the complete panel of MET drivers, and E2, which corresponds to an epithelial phenotype because of the lack of EMT drivers rather than the presence of other epithelial drivers, except for OVOL1. Thus, we consider E2 a quasi-epithelial state instead of an epithelial one. pEM states can similarly be subdivided into 3 groups: pEM1, with an epithelial-like phenotype except for the lack of AdhJunc; pEM2, with no activation of TighJunc, AdhJunc, ECAD, nor NCAD but with VIM present (this state is characterized by a mixture of EMT drivers SNAI2 and BCAT-TCF and all MET drivers but miR200); and pEM3, a mesenchymal-like state, except for active OVOL1. Noticeably, in pEM states, MMP2 and ZEB1 are not activated (unlike in the M states). In our model, the lack of AdhJunc and the presence of growth factors (GF) are consistent throughout the pEM spectrum. This is due to SRC activation by GF and how SRC disrupts AdhJunc. Another characteristic of pEM states is the presence of OVOL1 in all states. The steady states can be visualized as a PCA plot (Supplementary Fig. 2), and the complete table of fixed points can be found in Supplementary Fig. 3.

1.3.3 Input combinations shape the Epithelial-Mesenchymal Plasticity landscape

To validate that the model can reproduce EMT and MET, we first establish initial conditions that set the context for epithelial (EpiIC) and mesenchymal (MesIC) cells, respectively. In EpiIC, the MET drivers (GRHL2, P63, miR200, miR205, OVOL1, and OVOL2) have a high initial probability of being activated (0.8), whereas the probability for EMT drivers (TWIST, SNAI1, SNAI2, ZEB1, ZEB2, PRRX1, and BCAT-TCF) is low (0.2). The remaining internal nodes have a 0.5 value (cf. random). Conversely, in MesIC, MET drivers were set to 0.2 and EMT drivers to 0.8, while maintaining the rest of the internal nodes at 0.5. We then performed simulations under different environmental conditions by modifying the value of the inputs TGFβ ligand (TGFB_L), BMP, and growth factors (GF) (Fig. 3B,C).

In EpiIC, under all inputs off (TGFB_L = 0, BMP = 0, GF = 0), most cells are epithelial (40.6%) or naive (35,5%) and a small proportion mesenchymal (23.9%). When TGFB_L is activated (TGFB_L = 1), the majority of cells become mesenchymal with a high percentage of M1. With subsequent activation of GF (TGFB_L = 1, BMP = 0, GF = 1), most cells become mesenchymal (78.8% M1 and M2 combined) and pEM phenotypes appear (with predominant pEM1). The combination of all inputs yields only pEM cells. Noticeably, pEM3 is only possible when BMP is activated in combination with GF (Fig. 3B). When TGFB_L and BMP inputs are ON, all cells acquired an epithelial (E1) or a quasi-epithelial (E2) phenotype, showing complete blockage of the TGFβ-EMT program by BMP, although E2 greatly dominates over E1. All other input combinations are reported in Supplementary Fig. 4.

Fig. 3

Phenotypes along the epithelial-mesenchymal spectrum. a) Table of stable states, showing only EMT, MET drivers, and their markers, according to the different input combinations. b) Pie charts showing the final state probabilities of simulations of EpiIC under different input combinations. c) Pie charts showing the final state probabilities of simulations of MesIC under different input combinations.

The input combinations for MesIC were also tested (Fig. 3C, Supplementary Fig. 5). With all inputs OFF, cells were mainly mesenchymal (53.3% of M1 and M2 combined) or naive, as expected. Then, we investigated the role of BMP in inducing MET in MesIC cells. With inputs TGFB_L = 1, BMP = 1, and GF = 0, the mesenchymal phenotype was completely disrupted, and all cells acquired either an epithelial or a quasi-epithelial state (mainly the latter). The same is true for BMP ON alone (Supplementary Fig. 5). Similar to EpiIC, the combined presence of GF and BMP promotes pEM phenotypes, whereas the combined presence of GF and TGFB_L favours a mesenchymal state.

Because the epigenetic status of OVOL1 has been shown to be important in some mesenchymal cell lines[81], we simulated this effect by suppressing the BMP regulation and made OVOL1 solely determined by its initial condition (set to 0.2 in a MesIC context). Under MesIC, with TGFB_L = 1, BMP = 1, and GF = 0, 20% of the cells end in an epithelial phenotype, and 80% are mesenchymal (Supplementary Fig. 6), whereas all cells were epithelial with OVOL1 regulated by BMP (Fig. 3C). Moreover, MesIC cells with only BMP ON became either naive (most likely), M1/2, E1/2, instead of acquiring only E1 and E2 as in the original model (Supplementary Fig. 6). These results show the crucial role of the BMP and OVOL1 interaction in EMT-MET plasticity.

1.3.4 Autocrine TGFβ and RTK loops independently sustain mesenchymal states

Our previous results show that even without external signals (TGFB_L = BMP = GF = 0), the model predicts the existence of some mesenchymal states (23.9% Fig. 3B; 53.3% Fig. 3C). To understand the context for these states, we investigated how autocrine loops influence the emergence of mesenchymal states under epithelial conditions.

We first assessed the role of autocrine TGFβ signaling by simulating mutations (corresponding to experimental loss or gain-of-functions, see Methods) known to disrupt it: (1) activating mutation on miR200, (2) knockout of both ZEB1 and ZEB2, and (3) knockout of the TGFβ receptor, TGFB_R[68]. Consistent with published results, simulations of the mutations (1) and (2) fully abolished mesenchymal states, whereas the receptor (TGFB_R) knockout only reduced their probability, suggesting additional feedback mechanisms (Supplementary Notebook 2).

To remove the TGFβ loop, we constrained TGFB_R activation to depend solely on external TGFβ ligands (TGFB_L; model referred to as aRTK-only model). With this setting, mesenchymal states still appeared, albeit less frequently, and both miR200 forced activation and ZEB1/2 knockouts eliminated these states. The persistent presence of mesenchymal states suggested the existence of an additional loop.

Given TWIST’s role in activating RTK, we tested TWIST and RTK knockouts, both of which suppressed mesenchymal states, indicating that an autocrine RTK loop could sustain them in the absence of autocrine TGFβ. In the original model, where both autocrine loops were active, these knockouts only reduced, not abolished, mesenchymal states. Removing the RTK autocrine loop (aTGFB-only model) confirmed that TGFβ alone can sustain mesenchymal states.

We further performed activating and inactivating mutations across all nodes (except inputs) and visualized those abolishing mesenchymal states in each model (Fig. 4). In all cases, activation of MET drivers eliminated mesenchymal phenotypes, consistent with their antagonistic roles. BMP pathway elements also suppressed the M state. In the aRTK-only model, TWIST, RTK, or SNAI2 knockouts abolished mesenchymal states, while in the aTGFB-only model, knockouts disrupting the autocrine TGFβ loop (e.g., TGFB_T, SRC) could suppress these states. Activating ID, SNAI1, or SMAD2_3 also suppressed mesenchymal states in the aRTK-only setting.

Our results reveal that mesenchymal states are not solely dependent on the EMT inducers but are maintained by redundant autocrine feedback loops, involving TGFβ and RTKs, each capable, to a certain extent, of independently driving EMT-like phenotypes. (Fig. 4).

Fig. 4

Mutations capable of abolishing input-independent mesenchymal states. Activating and inactivating mutations that led the final state probability of a mesenchymal state to 0 in all three models described in the supplementary text. Simulations were made with random initial conditions on all nodes and with an input configuration of TGFB L = 0, BMP = 0, GF = 0.

1.3.5 Overexpression of MET drivers disrupts mesenchymal phenotypes

We investigated how activating known MET drivers influences mesenchymal cells under different signaling conditions. Overexpression of GRHL2, P63, miR200, miR205, OVOL1, and OVOL2, known MET inducers, was simulated in MesIC conditions, along with other literature-reported drivers considered here via their downstream targets (Table 1). Under TGFβ stimulation (MesIC, withTGFB_L = 1, GF = 0, BMP = 0; Fig. 5A), only GRHL2, P63, OVOL1, and CEBPa significantly increased epithelial states, with P63 and CEBPa achieving complete MET. Others, including miR200, miR205, OVOL2, EHF, Rap1, and miR30a, mainly led to pEM, while GATA3, CLDN7, FBXO22, and KLF4 showed little effect.

With all inputs OFF (MesIC with TGFB_L = GF = BMP = 0; Fig. 5B), most MET drivers reduced the mesenchymal phenotype, but only GRHL2, P63, miR200, miR205, OVOL1, OVOL2, and CEBPa increased the epithelial states’ probability. Notably, FBXO22 activation promoted mesenchymal states (simulated in the model by inhibiting SNAI1). Under combined GF and TGFβ (or GF alone), most drivers (GRHL2, P63, miR200/205, OVOL1/2, CEBPa, miR30a, EHF) completely suppressed M states, leading cells to pEM, while only Rap1, GATA3, and CLDN7 induced limited epithelial transitions through interference with AdhJunc, SRC, RTK, and ERK. (Supplementary Fig. 7). Noticeably, SCR KO was also able to abolish the autocrine TGFβ EMT program (Fig. 4).

To identify factors that could reverse mesenchymal states, we simulated knockouts of all internal nodes in MesIC cells under TGFB_L = 1 (Supplementary Fig. 8). Only KO of TGFB_R, miR128, SMAD2_3, or SNAI2 reduced the mesenchymal fraction but did not fully abolish it. SNAI2 KO yielded a pEM characterized by the presence of PRRX1 and TWIST, and the lack of SNAI1, which could no longer repress TightJunc (Supplementary Fig. 9). No knockout substantially increased epithelial cells (probability for reaching E phenotypes < 0.1; Supplementary Fig. 10).

Table 1

MET factors. Signaling agents identified as MET-promoting factors (column 1) through their downstream targets (column 2) according to the literature (column 4). Column 3 specifies how we simulated the effect of MET factors KI on the model.
MET factor	Downstream targets	Mutation in model	REF
Elf5	Represses SNAI2	SNAI2 KO	[83]
Klf4	Induces ECAD	ECAD KI	[84]
FBXO22	Represses SNAI1	SNAI1 KO	[85]
EHF	Represses ZEB1 and ZEB2	ZEB1 and ZEB2 KO	[86]
CKB	Represses AKT	PI3K_AKT KO	[87]
Claudin 7	Represses ERK and SRC through Rab25	ERK and SRC KO	[88]
C/EBPa	Induces P63 and represses ZEB1	P63 KI and ZEB1 KO	[52], [66]
GATA3	Induces miR-29b, which represses PDGF	RTK KO	[89]
miR30a	Represses SNAI1 and VIM	SNAI1 and VIM KO	[90], [91]
Rap1	Required for cadherin junctions (AdhJunc)	AdhJunc KI	[92]

Fig. 5

Activating mutations of MET drivers. Each row represents the proportion of the final state probabilities, according to the phenotype. Mutations of nodes not included in the network are indicated by *. Mutant simulations were performed in MesIC with inputs. a) TGFB_L = 1, BMP = 0, GF = 0, and b) TGFB_L = 0, BMP = 0, GF = 0.

2 Discussion

Epithelial–mesenchymal plasticity is a context-dependent process with high complexity and sometimes non-intuitive outcomes, and thus could highly benefit from a modeling study. While EMT has been extensively studied, the mechanisms driving MET remain less understood. Current knowledge on MET emphasizes the influence of cellular context and key regulators along the epithelial–mesenchymal spectrum. We then proposed a knowledge-based regulatory network and developed a logical model that appears robust since it can reproduce known features of the process. Especially, the model: (1) recapitulates distinct EMT programs, defined by the differential presence of EMT-TFs consistent with previous observations[12], [40]; (2) represents different states within the epithelial-mesenchymal spectrum; (3) reproduces self-sustained EMT by autocrine signals; and (4) reproduces MET induction by BMP and MET drivers overexpression. Using our model opens the possibility to fine-tune the interplay between these EMT-MET modulators.

Simulations of epithelial (EpIC) and mesenchymal (MesIC) cells under different input combinations revealed that BMP could promote MET to different degrees depending on the context. BMP was always able to abolish M states in TGFβ-driven EMT, producing mainly a quasi-epithelial (E2) state rather than a fully epithelial one. In our model, GF was needed to generate pEM states. This could provide insight into why growth factors such as EGF have been shown to induce EMT to a more modest degree[67]. Noticeably, BMP combined with GF favored the mesenchymal-like hybrid state (pEM). Perturbations of the RTK and TGFβ loops in the model allowed us to explore how autocrine signals are responsible for maintaining a robust mesenchymal phenotype. Mutations differentially disrupt the M states in the two programs (Fig. 4). Three notable examples are SRC, ID, and SNAI1. In agreement with other EMT models[26], we underscored the role of SRC in the M identity but in a context-dependent manner. Our model suggested that SRC inactivation may not only hinder TGFβ signal propagation (as reported previously[93]), but also its ability to establish an autocrine signal in the absence of an external input. In the case of autocrine RTK signals driven by TWIST, our simulations showed that overexpression of ID or SNAI1 was able to completely abolish the M state (as shown experimentally for ID[78]) (Fig. 4). The regulation between SNAI1 and TWIST reflects their respective roles within the TGFβ-induced EMT cascade. It was reported that cells treated with TGFβ ligand rapidly increased SNAI1 expression, which quickly decreased upon ligand removal at the same time that TWIST levels began to increase, which seems to be required to maintain it in the absence of TGFβ ligand[12]. The model reproduces the known dynamic between SNAI1 and TWIST, where SNAI1 initiates, and TWIST maintains EMT. The model fails to capture SNAI1’s requirement for EMT initiation, though, likely due to missing regulatory interactions or chromatin-level mechanisms beyond this model’s scope, suggesting that BMP can yield unexpected outcomes depending on signaling context. Moreover, our simulations show that OVOL1 (the only MET driver in pEM3) alone may not be sufficient to drive the cells to a fully epithelial state, but it is necessary for BMP-induced MET. We also found that combined activation of TGFβ and GF has a greater effect on the disruption of epithelial states than TGFβ alone.

Through model perturbations, we obtained a list of expected and unexpected nodes that lead to MET. For instance, all MET drivers included explicitly in the model abolished M states, although some to a greater degree than others. Particularly, the ability to induce an E state was exacerbated when EMT was maintained by autocrine signals (i.e., no inputs present) for some MET drivers, such as GRHL2, while others produced the same effect independently of the EMT signal (P63 and OVOL1). Noticeably, FBXO22 activation (simulated as SNAI1 KO) produced no effect in the proportion of M states in the presence of TGFβ ligand, but increased M state proportion in self-sustained EMT. As discussed before, SNAI1 can disrupt self-sustained EMT. The lack of SNAI1 could liberate the TWIST repression and favor the autocrine-RTK EMT program, leading to a higher proportion of M states. Rather than the vision of a specific genetic program, it appears that numerous and different autocrine loops lead to multiple possible paths explaining this context-specific EMT-MET plasticity

Finally, the model successfully reproduced partial EMT (pEM) states characterized by co-expression of epithelial and mesenchymal markers. In the future, the model will be extended to account for crosstalk with other pathways and to consider various mechanosensitive signals [94]¹⁰³. Moreover, if the current Boolean model framework effectively integrates multiple pathways, its discrete nature limits the full representation of all transient states, which should be explored using more continuous modeling approaches [95], [96].

Overall, our logical model captures key aspects of MET and provides a framework for exploring epithelial–mesenchymal plasticity. Importantly, it highlights non-intuitive behaviors that underscore the role of cellular context in the cellular outcomes. Future extensions could incorporate newly identified pro-MET pathways, tissue-specific interactions, paracrine and microenvironmental signals, and spatial–temporal dynamics to better reflect the complexity of metastatic progression[97], [98].

3 Methods

3.1 Construction of a regulatory network

The biological information described in the main text was recapitulated in the form of an activity flow network, constructed with the tool GINsim[61]. It is a signed and directed network[99], where nodes represent biological entities (genes, proteins, miRNAs, protein complexes, receptors) and edges positive or negative influences of one entity on the others. The initial network was inspired by published models of EMT [26], [28]. The network was then completed and modified incrementally by a thorough literature review, and by exploring pathway databases [100], [101]. It recapitulates current known interactions and remains simple and focused on the processes leading to the transitions. The network interactions are described in the main text (see Results) and annotated in Supplementary Material 1.

The model has three input nodes: TGFβ (TGFβ active ligand), GF (growth factors as EGF or PDGFRα), and BMP (BMP7). The combinatorial activations of these extracellular signals can be modulated and thus simulate different extracellular contexts. These inputs can also be activated through autocrine mechanisms as described in the previous section. This is explicitly defined for TGFβ and BMP as aTGFB and aBMP. For each variable, a logical rule is associated, defining the condition for this variable to be active. The rules and the rationale behind them can be found in Supplementary Material 1.

3.2 Logical formalism

The mathematical formalism used is based on a logical framework that considers that entities can take only two values, 0 or 1, corresponding to an inactive or active state. If the value is 1, the entity can be considered present or active, which may correspond to a phosphorylated or transcriptionally active state, depending on the entity. A change of state for an entity is determined by a logical rule that links the inputs of the entity by logical connectors AND, OR, and NOT. For nodes that are influenced by multiple input nodes, biological information was searched to find the appropriate rule. If no information was found, the default rule consists of having at least one activator ON and none of the inhibitors ON. For the interactions for which it is known that proteins act as a complex, the AND connector is used so that all complex members are required for the interaction. The logical rules and the rationale behind them can be found in Supplementary Material 1.

The solutions of a Boolean model are called attractors and can be either a stable state (a unique vector of node states that does not have a successor in the solution graph called the state transition graph, or limit cycles, which correspond to a succession of these model states with no outgoing edges. When the model converges to stable states, we try to associate these states to physiological behaviors (death, proliferation, differentiation, etc.). In this model, the long-term solutions are stable states, and are linked to epithelial and mesenchymal states.

3.3 Model Simulation using MaBoSS

The model was simulated using MaBoSS[102], a C + + software for simulating Boolean models using continuous-time Markov processes. Upon an initial condition (i.e., a vector with the node probabilities to be ON or OFF), MaBoSS computes stochastic trajectories by applying continuous-time Markov chains over the Boolean network, providing the time evolution of the probabilities for a chosen output set of nodes. When possible, the output can be interpreted as a cellular phenotype and each run of the simulation as the trajectory of a single cell; therefore, the phenotypic probabilities correspond to a population of independent cells. For each initial condition tested, 10000 runs were simulated until the system reached its asymptotic solution (200 max time). MaBoSS allows associating transition rates to each node, for both the activation and inactivation (i.e., the time it takes for a node to get activated or inactivated, respectively). Without any specific information, all transition rates are kept to their default value of 1.

Long-term or asymptotic solutions were estimated with MaBoSS, by simulating the time evolution of the system with random initial conditions (i.e., equal probability for each node to be ON or OFF) and retrieving the final states. Steady states were computed exactly with compatible tools from CoLoMoTo[103]. These solutions were associated with phenotypes. We established: (1) the epithelial phenotype (E) as the activation of the nodes TightJunc (tight junctions), AdhJunc (adherin junctions), and at least one MET driver GRHL2, P63, miR200, miR205, OVOL1, or OVOL2 (blue in Fig. 2). Further, the absence of N-cadherin (NCAD), Vimentin (VIM), and the EMT drivers TWIST, SNAI1, SNAI2, ZEB1, ZEB2, PRRX1, and BCAT-TCF (purple in Fig. 2) is also required. (2) The mesenchymal phenotype (M) corresponds to the contrary rule. It must have VIM and NCAD activated, TightJunc and AdhJunc inactivated, as well as at least one EMT-driver and no MET-driver. (3) In the case of a partial epithelial-mesenchymal state (pEM), genes from both phenotypic definitions can be activated concomitantly; thus, it is defined as a state where the conditions of epithelial and mesenchymal are not fulfilled (i.e., !E & !M). We also considered that in this state, at least one EMT or MET driver must be activated. (4) Finally, we defined a naive phenotype as one that does not belong to any previous classifications. The steady states were visualized using a principal component analysis plot, where the classification can be validated according to the formed clusters.

3. 4 Mutant Simulation using MaBoSS

In the Boolean framework, mutations are represented by forcing the levels of the chosen nodes to 1 in case of an activating (ON) mutation or to 0 in case of an inactivating (OFF or knockout (KO)) mutation. The effect of a mutation can modify the probabilities for reaching a phenotype. Its effect can be qualitatively assessed.

The code for all the simulations and figures in this work is available in a set of notebooks in Supplementary Notebook 1–2 and an R script in Supplementary Material 3. They can also be found at https://github.com/sophia-orozco/met-model.

Supplementary material

Supplementary Material 1

Supplementary Material 2

GitHub with Supplementary Notebooks, models, and code: https://github.com/sophia-orozco/met-model.

Acknowledgement

We would like to thank Vincent Noel for his useful comments on the model simulations, and Hava Gil Henn for fruitful discussions on MET.

Funding

declaration

SOR, LC, and MR were supported by the Certainty project, which is part of the European Union’s Horizon Europe research and innovation program under grant agreement n101136379.

Author Contribution

SOR developed the model, performed simulations, and wrote the manuscript. MR contributed to the development of the model. OD, EB, and LC conceived the project. LC supervised the work, contributed to the analysis, and wrote the manuscript. All co-authors read and corrected the manuscript.

Competing interests

The author(s) declare no competing interests.

Data Availability

All data generated or analyzed during this study are included in this published article.

Ethics declarations

No data were used in the study.

Electronic Supplementary Material

Below is the link to the electronic supplementary material

Supplementary Material 1

Supplementary Material 2

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Figure Legend

Figure 1. Regulatory networks involved in epithelial/mesenchymal plasticity. Transcription factors and miRNAs involved in epithelial/mesenchymal plasticity. Figure made with GINsim61.

Figure 2: Regulatory Network of Epithelial-Mesenchymal Plasticity. A schematic version of the network described and annotated in Supplementary Material 1. The network has inputs TGFB: TGFB ligand, GF: growth factors (to keep it general, it represents growth factors as PDGFRα or EGF that signal through RTKs) BMP: BMP ligand (representing BMP7). aTGFB: autocrine TGFB, TGFB1T: TGFβ1 transcript, Ecad: E-cadherin, Ncad: N-cadherin, AdhJunc: Adherens Junctions, TightJunc: Tight Junctions. Figure made with GINsim 61.

Figure 3: Phenotypes along the epithelial-mesenchymal spectrum. A) Table of stable states, showing only EMT, MET drivers, and their markers, according to the different input combinations. B) Pie charts showing the final state probabilities of simulations of EpiIC under different input combinations. C) Pie charts showing the final state probabilities of simulations of MesIC under different input combinations.

Figure 4. Mutations capable of abolishing input-independent mesenchymal states. Activating and inactivating mutations that led the final state probability of a mesenchymal state to 0 in all three models described in the supplementary text. Simulations were made with random initial conditions on all nodes and with an input configuration of TGFB L = 0, BMP = 0, GF = 0.

Figure 5: Activating mutations of MET drivers. Each row represents the proportion of the final state probabilities, according to the phenotype. Mutations of nodes not included in the network are indicated by *. Mutant simulations were performed in MesIC with inputs A) TGFB_L = 1, BMP = 0, GF = 0, and B) TGFB_L = 0, BMP = 0, GF = 0.

Table 1: MET factors. Signaling agents identified as MET-promoting factors (column 1) through their downstream targets (column 2) according to the literature (column 4). Column 3 specifies how we simulated the effect of MET factors KI on the model.

Yes