Numb prevents a complete epithelial–mesenchymal transition by modulating Notch signalling

Epithelial–mesenchymal transition (EMT) plays key roles during embryonic development, wound healing and cancer metastasis. Cells in a partial EMT or hybrid epithelial/mesenchymal (E/M) phenotype exhibit collective cell migration, forming clusters of circulating tumour cells—the primary drivers of metastasis. Activation of cell–cell signalling pathways such as Notch fosters a partial or complete EMT, yet the mechanisms enabling cluster formation remain poorly understood. Using an integrated computational–experimental approach, we examine the role of Numb—an inhibitor of Notch intercellular signalling—in mediating EMT and clusters formation. We show via an mathematical model that Numb inhibits a full EMT by stabilizing a hybrid E/M phenotype. Consistent with this observation, knockdown of Numb in stable hybrid E/M cells H1975 results in a full EMT, thereby showing that Numb acts as a brake for a full EMT and thus behaves as a ‘phenotypic stability factor' by modulating Notch-driven EMT. By generalizing the mathematical model to a multi-cell level, Numb is predicted to alter the balance of hybrid E/M versus mesenchymal cells in clusters, potentially resulting in a higher tumour-initiation ability. Finally, Numb correlates with a worse survival in multiple independent lung and ovarian cancer datasets, hence confirming its relationship with increased cancer aggressiveness.


Introduction
Epithelial -mesenchymal transition (EMT) and its reverse mesenchymalepithelial transition (MET) play crucial roles during embryonic development, wound healing and tumour progression [1]. Typically, cells that undergo EMT lose cell -cell adhesion and gain migration and invasion. These bidirectional transitions are rarely 'all-or-none'. Instead, cells can display one or more hybrid phenotype(s) that possess a mix of epithelial and mesenchymal traits, thereby biasing them to undergo collective cell migration, instead of individual migration enabled by a complete EMT [1]. Collective migration, where cells maintain physical contact with their neighbours, has been considered to be a hallmark of multiple developmental processes such as neural crest migration, branching morphogenesis and wound healing [1]. Recent studies have emphasized that collective cell migration can be a predominant path for cancer metastasis [2]. Collective cell migration can enable the formation of clusters of circulating tumour cells (CTCs) [3]. When compared with individually disseminating CTCs, these clusters are highly resistant to cell death in circulation, possess high tumour-initiation ability, and correlate with a worse clinical outcome across different cancer types [4]. Therefore, deciphering the intracellular and intercellular mechanisms that enable CTC clusters is essential to curb metastatic load.
The formation of clusters of CTC typically requires two conditions. First, individual cells can display a phenotype capable of both adhesion and migration, as is usually found in a hybrid epithelial/mesenchymal (E/M) phenotype [5][6][7][8]. Second, such cells must be spatially co-located. It is possible that cells first become hybrid E/M in a random spatial pattern and then dynamically find each other, but this mechanism is much more complex and hence less likely. Thus, we focus our attention to chemical and/or mechanical cell-cell communication mechanisms that can foster the direct formation of clusters via spatial organization; such mechanisms remain relatively less studied.
Previously, we reported that Notch-Jagged signalling may increase the frequency of cells in a hybrid E/M phenotype and their spatial proximity to form clusters of CTCs [9]. Notch signalling is an evolutionarily conserved cell-cell communication signalling pathway comprising a transmembrane receptor, Notch, and two transmembrane ligands, Delta and Jagged. When Notch binds to Delta or Jagged of a neighbouring cell, Notch is cleaved to release Notch intra-cellular domain (NICD) that enters the nucleus, activates the Notch pathway and regulates its target genes [10]. NICD activates the transcription of Notch and Jagged, but represses that of Delta [11]. Thus, Notch-Jagged signalling between two neighbouring cells leads to convergent cell fates (lateral induction) [12,13], whereas Notch-Delta signalling to divergent cell fates (lateral inhibition) [11]. Consequently, neighbouring hybrid E/M can reinforce the stability of hybrid E/M phenotype and lead to the formation of clusters of hybrid E/M cells via Notch-Jagged signalling [9].
Based on this proposed role of Notch -Jagged signalling in inducing and maintaining a hybrid E/M phenotype, we hypothesized that the proteins affecting Notch signalling may modulate the stability of a hybrid E/M phenotype. Here, we focused on Numb and its homologue Numb-like (Numbl) that can inhibit Notch signalling through multiple mechanisms [10,14,15]. Also, activated Notch signalling can inhibit Numb and Numb-like, generating a mutually inhibitory feedback loop between Numb/Numb-like and Notch [10]. Identified as a cell-fate determinant in Drosophila development, Numb has been since implicated in multiple aspects of cellular homeostasis and tumour progression such as proliferation, apoptosis and stem cell maintenance. Numb-like is much less studied comparatively, and may have partially distinct functions when compared with Numb [16]. However, their effect on Notch has been largely reported to be similar [10].
Here, through a mathematical model for

Analysis of clinical data
For all the examined datasets, the pool of patients was divided into two groups according to their expression of Numb being below or above median, and the overall survival and relapsefree survival of the two groups were plotted separately and compared. All survival analysis plots were generated using ProgGeneV2 [17], (http://watson.compbio.iupui.edu/chirayu/ proggene/database/?url=proggene).

Numerical calculation and plotting
The single-cell and the multi-cell systems are implemented and solved numerically using the python numerical library PyDsTool [18]. All plots are realized with the plotting library Matplotlib [19]. All source code is freely available on GitHub (https:// github.com/federicobocci91/Numb_project).

Numb inhibits a complete epithelialmesenchymal transition at a single-cell level
As a first step to investigate the effect of Numb on the dynamics of epithelial-hybrid-mesenchymal transitions, we extend our previously defined mathematical model [9] to include the regulation of Notch by Numb. Both Numb and Numbl form a mutually inhibitory feedback loop with Notch [10] (figure 1a), thus, for modelling purposes in the context of this study, we consider Numb and Numbl to be equivalent and group them into one variable-Numb. As mentioned earlier, Notch signalling takes place when Notch (transmembrane receptor) of one cell binds to Delta or Jagged (transmembrane ligands) of the neighbouring cell(s). Signalling through different ligands, Delta or Jagged, leads to a different phenotypic patterning at a multi-cellular level. Notch-Delta signalling between two cells creates divergent cell fates-one cell behaves as a receiver (high receptor, i.e. Notch, low ligand, i.e. Delta) and the other behaves as a sender (low receptor, i.e. Notch, high ligand, i.e. Delta). Conversely, Notch-Jagged signalling leads to convergent cell fates-both cells behave as hybrid sender/receiver (high receptor, i.e. Notch, high ligand, i.e. Jagged) [11,12] (figure 1b). This trait of the Notch-Jagged signalling can contribute to the formation of clusters of hybrid E/M cells by 'lateral induction' of a hybrid E/M phenotype [9], due to the coupling between Notch and EMT circuits (figure 1a), where Notch activates Snail, an EMT-inducing transcription factor, and miR-34 and miR-200 families-guardians of an epithelial phenotype [1]-inhibit Notch, Delta and Jagged [9].
First, we compared the intracellular dynamics of coupled Notch -EMT and Notch -EMT-Numb circuits as a function of fixed levels of external ligands, J ext and D ext , that represent the average concentration of Delta and Jagged available at the surface of the neighbouring cells. Previous work has shown that activation of Notch signalling by either Delta or Jagged can induce a partial or complete EMT in epithelial cells [9,20,21]. Consistently, we observed cells attaining a partial or complete EMT in both cases, i.e. with and without Numb (figure 1c-f ).
In the absence of Numb, at a low external concentration of either ligand, a cell maintains its epithelial phenotype and can behave as either a sender or a receiver-(E), (S) or (E), (R). At higher ligand concentrations, the cell transits to a hybrid E/M state and can act both as sender and receiver-(E/M), (S/R). Eventually, at an even higher concentration of ligands, the cell undergoes a complete EMT-(M), (S/R) (figure 1c,e). A similar trend is observed in the presence of Numb, but the range of existence of these different states is altered. Numb enlarges the range of J ext and D ext values for which the (E), To probe the robustness of these results, we conducted a sensitivity analysis by assessing the change in the interval of stability of the hybrid E/M phenotype resulting from a small variation of the model's parameters. Our results are robust upon parameter variation, albeit a higher sensitivity was observed for some parameters of the original EMT circuit (electronic supplementary material, figures S5 and S6).
Overall, our results suggest that Numb or Numbl can act as a PSF that can stabilize a hybrid E/M phenotype at a single-cell level.

Numb knockdown drives hybrid epithelial/ mesenchymal cells to a completely mesenchymal phenotype
To test the prediction of the single-cell model on the action of Numb as PSF for the hybrid E/M phenotype, we knocked down either Numb or Numb-like (Numbl) in non-small cell lung cancer (NSCLC) H1975 cells that display a stable hybrid E/M phenotype over many passages in vitro.
Knockdown of Numb or Numbl changed the morphology of H1975 cells to being more spindle-shaped (see cartoon in figure 1c,f and red arrows in figure 2a), and individual cells stained positive only for mesenchymal marker vimentin (VIM) but not for epithelial marker E-cadherin (CDH1), when compared with the control H1975 cells that co-express E-cadherin and vimentin stably over many passages [5] ( figure 2a,b). Moreover, in transwell migration assays, control H1975 cells exhibited collective cell migration, but Numb-or Numbl-knockdown H1975 cells displayed individual cell migration (figure 2c). These observations mimic earlier observations made in multiple contexts such as mammary gland development [14], MCF10A cells [22], MDCK cells [23] and oesophageal cancer cells [24]. Further, knockdown of Numb or Numbl leads to inhibition of cell proliferation, a trait also typically associated with EMT progression [25] (figure 2d). A similar effect on inhibited proliferation was also observed for knockdown of GRHL2-another proposed PSF-in lung [5] and ovarian [26] cancer cells.
Consistently, Numb-or Numbl-knockdown increased the mRNA and protein levels of (i) mesenchymal marker Vimentin, (ii) EMT-inducing transcription factor ZEB1, and (iii) Notch ligand JAG1. Conversely, mRNA and protein levels of E-cadherin were decreased (figure 2e,f; electronic supplementary material, S7). Put together, these observations indicate that knockdown of Numb or Numbl in stable hybrid E/M cells drives them towards a more mesenchymal phenotype, thereby validating our prediction that Numb or Numbl can stabilize a hybrid E/M phenotype and act as a brake on complete EMT progression.

Numb alters the composition of clusters of nonepithelial cells at a tissue level
After evaluating the effect of Numb on EMT at a single-cell level, we compared the dynamics of Notch-EMT and Notch -EMT-Numb circuits at a tissue level by simulating a two-dimensional lattice of 50 Â 50 cancer cells communicating with one another via Notch signalling. Specifically, we studied the relative abundance of epithelial (E), hybrid (E/M) and mesenchymal (M) cells and the spatial patterns that these subpopulations form in this lattice, at different production rates of Jagged (g J ) and Delta (g D ), starting from random initial conditions. We first compared the tissue-level dynamics of Notch-EMT and Notch -EMT-Numb circuits, when cells mainly interact via Notch -Jagged signalling (figure 3). It is worth noting that these results were not collected upon full equilibration of the system, but after a transient time of 5 days, a typical time-scale for EMT. After this time window, we believe that biophysical processes such as altered cell morphology during EMT and consequent cell migration would disrupt the phenotypic patterning that emerges from the model. Notch-Jagged signalling can promote the formation of clusters containing hybrid E/M and M cells [9]. At low levels of Jagged production (g J ¼ 45 molecules h 21 ), Notch -Jagged signalling is only weakly activated and thereby weakly induces EMT (see the activation of Snail by NICD in figure 1a). In this regime, additional inhibition on this signalling brought by Numb decreases the abundance of both hybrid E/M and mesenchymal cells (figure 3a, solid vertical black line), thus halting EMT progression. Consequently, Numb reduces the frequency of clusters containing hybrid E/M and M cells (compare figure 3c with figure 3b; electronic supplementary material, movies M1 and M2). To quantify the changes induced by Numb, we counted the fraction of epithelial, hybrid and mesenchymal cells over many different simulations (each simulation has slightly different initial conditions). For g J ¼ 45 molecules h 21 , Numb significantly reduces the number of cells in a partial or complete EMT state, and consequently increased those in an epithelial state ( figure 3d, left).   for the case of a large production rate of Jagged that can push approximately 75% cells in a complete EMT state (g J ¼ 80 molecules h 21 ). Finally, to quantify the spatial co-localization of hybrid E/M cells, we counted how many cells adjacent to a hybrid E/M cell exhibited the same, i.e. a hybrid E/M, phenotype (electronic supplementary material, figure S8). For the case of weakly activated Notch -Jagged signalling corresponding to lower g J ( figure 3b,c), the average number of hybrid E/M neighbours for a hybrid E/M cell decreased (compare electronic supplementary material, figure S8 middle panel with S8 left panel) due to a decreased total frequency of hybrid E/M cells. However, an increased production of Jagged (figure 3e,f ) can counteract this effect of Numb and consistent with previous reports [9], it can significantly increase the colocalization of hybrid E/M cells (electronic supplementary material, figure S8, right).
Similar to the Notch-Jagged case, we compared the tissue-level spatio-temporal dynamics for Notch-EMT and Notch-EMT-Numb circuits in a lattice of cells that communicate with one another predominantly via Notch-Delta (figure 4). The inhibition of Notch signalling by Numb reduces cellular NICD levels [10], thereby effectively relieving the inhibition of Delta by NICD. This effective increase in the levels of Delta can potentiate Notch signalling in neighbouring cells and thus promote EMT in those cells. As a result, in the case of Notch-EMT-Numb circuit and Delta-dominated signalling, lower basal production levels of Delta (g D ) can enable transitions into the hybrid E/M state, when compared with that required to observe these transitions in the absence of Numb (compare the solid yellow curve with dotted yellow curve in figure 4a). Therefore, at a fixed production rate of Delta (g D ), the Notch-EMT-Numb circuit can induce significantly more epithelial cells to attain a hybrid E/M phenotype when compared with that by Notch-EMT circuit (figure 4c). Contrary to the case of strong Notch-Jagged signalling, here the increase of the hybrid E/M cell population is mostly due to a decrease in the frequency of epithelial cells. Despite the effect of Numb in altering the ratio of cells in a hybrid E/M and epithelial phenotype, it did not alter the predominant 'salt-and-pepper' pattern of epithelial and hybrid E/M cells (figure 4b; electronic supplementary material, S9). Such pattern formation is a cornerstone of Notch-Delta signalling as observed in multiple biological contexts [11].  Collectively, these results suggest that irrespective of the ligand activating Notch signalling-Delta or Jagged-Numb can increase the number of cells in a hybrid E/M phenotype at both a single-cell and a tissue-level.
After investigating the effect of Numb on the Notch-EMT circuit, we explored the effect of Numb on modulating the paracrine version of Notch signalling, i.e. when cells are exposed to soluble Delta (sD ext ) or soluble Jagged (sJ ext ), in addition to membrane-bound ligands ( juxtacrine signalling) considered so far in our simulations. Consistent with our results, Numb reduced the frequency of cells in a mesenchymal phenotype in a cohort of cells that were exposed to either soluble ligand (figure 5a-d; electronic supplementary material, S10-S12). Similar to previous observations (figure 3), an increase in soluble Jagged concentration rescues the cluster frequency, but these clusters predominantly contain hybrid E/M cells and not mesenchymal cells (figure 5e,f; electronic supplementary material, S12). These effects of Numb on paracrine signalling are more prominent in case of Jagged-dominated juxtacrine signalling instead of Delta-dominated juxtacrine signalling (electronic supplementary material, figures S10 and S12).
In addition, the presence of soluble Jagged in the microenvironment has a crucial consequence on the dynamics of cell fractions in different phenotypes. It can increase the lifetime of transiently observed clusters of hybrid E/M and mesenchymal cells for both Delta-dominated and Jagged-dominated juxtacrine signalling. Without the presence of soluble Jagged, as the Notch-EMT system tends towards a stable equilibrium, hybrid E/M and epithelial cells arrange themselves in a 'saltand-pepper' pattern for Delta-dominated signalling. On the other hand, in the case of Jagged-dominated signalling, cells in hybrid E/M and M phenotypes tend to an epithelial switch (elctronic supplementary material, figure S13a,b). The presence of external soluble Jagged stabilizes the hybrid E/M phenotype, thereby further increasing the lifetime of the clusters in the Notch-Jagged signalling case (electronic supplementary material, figure S13c,d).This effect of soluble Jagged in the extracellular environment may help explain how soluble Jagged can drive the cells towards a cancer stem cell phenotype [27] which is often correlated with a hybrid E/M phenotype [1].
It should be noted that soluble Delta-or Jagged-driven signalling is fundamentally different from the formation of intercellular feedback loops between Notch-Delta or Notch-Jagged signalling that are responsible for different patterns formed in Delta-dominated and Jagged-dominated signalling. When soluble ligands-whether Jagged or Delta-activate Notch signalling, the cells only behave as 'receiver' or 'target' in case of either ligand, without any tangible feedback on the amount of these soluble ligands. Therefore, Numb similarly affects the dynamics of the system in case of soluble Delta-or soluble Jagged-driven signalling.

External epithelial -mesenchymal transition induction can overcome the inhibition of epithelial -mesenchymal transition by Numb
We next considered the effect of an external EMT inducer such as TGF-b (I ext ) that activates Snail. As shown in the case of Jagged-dominated Notch signalling, high levels of I ext significantly increase the number of cells in a fully mesenchymal phenotype (electronic supplementary material, figure S14a). Consistent with our single-cell results, Numb acts as a molecular brake on EMT (compare the dotted curves against solid curves in electronic supplementary material, figure S14a), and therefore a stronger induction of EMT is needed to increase the number of mesenchymal cells. Intriguingly, the frequency of cells in a hybrid E/M phenotype in this case is minimal (electronic supplementary material, figure S14b-d). These results may help explain why ectopic overexpression of ligand-of-Numb X (LNX)-an ubiquitin ligase that targets Numb for degradation-can enhance TGF-b induced EMT [28]. Conversely, when cells communicate predominantly via Notch-Delta signalling, Numb can mildly assist EMT induction and increase the fraction of mesenchymal cells in the population (electronic supplementary material, figure S15a-d). This differential effect of Numb in regulating Notch-Jagged and Notch-Delta signalling is further confirmed by assessing the temporal changes in fraction of epithelial, hybrid E/M and mesenchymal cells (electronic supplementary material, figure S13e,f).   figure S16).
Finally, we considered the effect of another recently reported feedback regulation in coupled EMT-Notch circuit-the relatively weak inhibition of Numb by miR-34 [29]. Owing to its weak strength, miR-34 only subtly alters the effect of Numb on EMT and Notch signalling (electronic supplementary material, figures S17-S21).

Higher Numb or Numbl levels predict poor patient survival
The ability of Numb to stabilize a hybrid E/M phenotype and increase the number of hybrid E/M cells in CTC clusters strongly suggested its potential role as a PSF. Given the association of other PSFs such as GRHL2 and DNp63a with poor patient survival [30,31], we next investigated the association of Numb or Numbl with patient survival.
High levels of Numb or Numbl were found to associate with poor overall survival (length of time after the start of treatment of a cancer that the patients are still alive, OS) and relapsefree survival (length of time after the primary treatment of a cancer ends that the patients do not show any symptoms of that cancer, RFS) in multiple independent lung cancer datasets (figure 6a-d) as well as in ovarian cancer datasets (figure 6e,f ): patients with higher relative levels of Numb or Numbl were observed to have shorter OS or RFS in these datasets. Our results are consistent with the reported association of high levels of Numb with poor overall survival and post-operative survival across multiple cancer types [32][33][34].
Low levels of Numb and/or Numbl, indicative of cells that have completely progressed to a mesenchymal phenotype, associate with a better survival, thereby reinforcing the emerging notion that a partial EMT, instead of a full EMT, may be a better marker for tumour aggressiveness [1]. These notions are supported by recent clinical evidence indicating that single-cell migration (a canonical readout of full EMT) happens extremely rarely, if any, in cancer dissemination [2].

Discussion
Notch signalling pathway is implicated in multiple hallmarks of cancer including metastasis and angiogenesis, and other  The effect of Numb/Numbl on tissue-level patterning is reminiscent of glycosyltransferase Fringe that can increase the binding affinity of Notch with Delta, but decrease the affinity with Jagged, thus affecting tissue patterning in a layer of cells [12]. Therefore, both Numb/Numbl and Fringe tend to antagonize Notch-Jagged signalling predominantly (electronic supplementary material, figures S22 and S23). This selective inhibition of Notch-Jagged signalling-an axis involved in drug resistance and colonization [9,38,39]-may help rationalize, at least in part, multiple experimental observations, such as (i) Numb and/or Fringe is/are often lost in many cancer types, including aggressive ones such as basallike breast cancer [40][41][42], (ii) Numbl knockdown increases chemoresistance and tumorigenic properties in cell lines of different origins-HeLa (cervix), T47D (breast) and AX (sarcoma) [43], (iii) lunatic fringe (Lfng) suppresses in vitro tumorsphere formation in prostate cancer DU145 cells [40] and (iv) Numbl knockdown inhibited the ability of lung cancer cells to form liver metastasis in vivo [34]. Importantly, Notch pathway need not be the sole pathway through which Numb modulates EMT. Numb can directly interact with E-cadherin and regulate its membrane localization, as well as control its endocytosis to retain apico-basal polarity in epithelial cells [44,45]. Knockdown of Numb alters E-cadherin localization and polarity complexes such as Par3, and as a result, decreases cell-cell adhesion and increase cell migration [44]. Besides, Numb, but not necessarily Numbl, can stabilize p53 [42] that can activate family members of miR-200 and miR-34 that can restrict EMT and even drive MET [1]. All these aspects of Numb and/or Numbl can be integrated with existing theoretical frameworks to better characterize how Numb affects EMT/MET as well as other traits associated with EMT/MET-immune evasion [46], tumour-initiation potential [1,36] and drug resistance [9,47].
Although we consider Numb and Numbl as equivalent here for mathematical modelling purposes, and observe that knockdown of either of them was sufficient to drive a full EMT in H1975 cells, they may have non-overlapping functions and expression patterns in tissues. For instance, Numb is often associated with asymmetric stem cell division both for developmental stem cell lineages [48] and cancer stem cells (CSCs) [29], but Numbl is symmetrically distributed in daughter cells [49]. Therefore, future modelling efforts will benefit from integrating the different signalling aspects of Numb and Numbl with population-level models of stem cell division. Similarly, consistent with our results, inhibition of either Numb or Numbl can induce Notch activity [43]. However, quantitative differences in effect of Numb versus Numbl, and that in individual versus combined inhibition remain elusive.
To conclude, we found that Numb or Numbl can help in maintaining hybrid E/M phenotype and prevent a full transition to a mesenchymal phenotype, and its knockdown can release the brake for full EMT. Our theoretical framework offers a platform to assess the role of many players that can regulate cellular plasticity in both cell-autonomous and non-cell-autonomous manner, and proposes another target that may potentially break the clusters of tumour cells in a hybrid E/M phenotype-the key drivers of cancer metastasis [1,4].
Data accessibility. The codes developed for the numerical simulation of the mathematical model are freely available on the github page of FB (federicobocci91). To access experimental data, please contact Prof. Samir Hanash (shanash@mdansderon.org).