Numb prevents a complete EMT 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 tend to 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 of hybrid E/M cells. 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. Consistent with this observation, we show via a mathematical model that Numb inhibits a full EMT by stabilizing a hybrid E/M phenotype. Thus, Numb can behave 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 poor survival in multiple independent lung and ovarian cancer datasets, hence confirming its relationship with increased cancer aggressiveness. Major Findings: we adopt an integrative computational-experimental approach to identify that Numb, an inhibitor of Notch signalling, can stabilize a hybrid epithelial/mesenchymal (E/M) phenotype. We show that knockdown of Numb in H1975 cells that display a stable hybrid E/M state is sufficient to destabilize a hybrid E/M state and push them to a full EMT phenotype. Next, we develop a mechanism-based mathematical model that recapitulates this ability of Numb in maintaining a hybrid E/M state, and predicts that Numb can alter the relative frequency of hybrid E/M and mesenchymal cells at a tissue level or in clusters of circulating tumor cells (CTCs) – the primary drivers of metastasis. Finally, we show that across cancer types, Numb correlates with worse patient survival, thus reinforcing the emerging notion that a hybrid E/M, but not necessarily a completely mesenchymal, phenotype associates with elevated tumour progression.


Quick guide to equations and assumptions
The level of a generic protein, mRNA or micro-RNA (miR) X is described via a chemical rate equation that assumes the generic form: In (eq. 1), the first term on the right-hand side represents the production of X while the second term accounts for the degradation of X. Specifically, 0 and 0 are basal production and degradation rates, while the functions P represents possible transcriptional/translational/posttranslational regulations in the production rate of X and can be a function of any protein/mRNA/micro-RNA in the system.
Specifically, if the production rate of any chemical species X is increased/decreased in presence of an activator/inhibitor A, the overall production rate = 0 takes the form: where is the shifted Hill function 12 , defined as: ( , , , ) = + ( ) In (eq. 3), A is the level of activator/inhibitor expressed in number of molecules, is a threshold level, is the Hill coefficient and represents the fold change in the production rate of X due to A. If A is an activator of X, then λ A >1 and the production rate is increased.
Conversely, if A is an inhibitor of X, λ A <1 and the production rate is decreased.

Introduction
Epithelial-Mesenchymal Transition (EMT) and its reverse Mesenchymal-Epithelial Transition Cells (CTCs) 2 . As compared to 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 3 . Therefore, deciphering the intracellular and intercellular mechanisms that enables 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. Further, such cells must be spatially co-located. It is theoretically possible that cells become hybrid in a random pattern and then dynamically find each other after the transition, but this is much more complex and hence less likely. Cellular mechanisms maintaining a hybrid E/M phenotype have received much attention [4][5][6][7] , particularly in a panel of non-small cell lung cancer (NSCLC) cell lines, but cell-cell communication in 6 chemical and/or mechanical ways that can foster the direct formation of clusters via spatial organization remain relatively less studied.
Previously, we reported that Notch-Jagged signalling may both increase the frequency of cells in a hybrid E/M phenotype and their spatial proximity to form clusters of CTCs 8

RT-PCR
Total RNA was isolated following manufacturer's instructions using RNAeasy kit (Qiagen).
cDNA was prepared using iScript gDNA clear cDNA synthesis kit (Bio-Rad

Western Blotting Analysis and Immunofluorescence
Cells were lysed in RIPA lysis assay buffer (Pierce) supplemented with protease and phosphatase inhibitor. The samples were separated on a 4-15% SDS-polyacrylamide gel

Kaplan-Meier plots
All survival analysis plots were generated using ProgGene 13 .

Mathematical model of the Notch-EMT-Numb axis
The In the single cell model (Fig. 2), the isolated cell is described by the levels of all proteins, transcription factors (TFs) and micro-RNAs (miRs) in the model, always expressed in number of molecules. Additionally, the cell can be exposed to an external level of Notch receptor and

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The multi-cell model ( Fig. 3-4-5) extends the single cell model to a two-dimensional layer of 50x50 cells arranged in a hexagonal lattice. In this model, each cell is still described by its own set of proteins, TFs and miRs. Additionally, the Notch receptors and ligands of every cell can bind with the receptors and ligands of any neighboring cell. Also, cells in the layer can be exposed to a constant level of soluble ligand ( , ) as in Fig. 5 or to an external EMTinducer .

Numerical calculation and plotting
The single cell and the multi-cell systems are implemented and solved numerically using the python numerical library PyDsTool 14 . All plots are realized with the plotting library Matplotlib 15 .

Numb knockdown drives hybrid E/M cells to a completely mesenchymal phenotype
As a first step to investigate the effect of Numb on EMT, we knocked down either Numb or its homolog 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 spindleshaped, and individual cells stained positive only for mesenchymal marker vimentin (VIM) but not for epithelial marker E-cadherin (CDH1), as compared to the control H1975 cells that coexpress E-cadherin and vimentin stably over many passages 4 (Fig. 1A, B). Moreover, in transwell migration assays, control H1975 cells exhibited collective cell migration, but Numb-or Numbl-knockdown H1975 cells displayed individual cell migration (Fig. 1C). These observations mimic earlier observations made in multiple contexts such as mammary gland development 16 , MCF10A cells 17 , MDCK cells 18 , and esophageal cancer cells 19 . Further, knockdown of Numb or Numbl lead to inhibition of cell proliferation, a trait also typically associated with EMT progression 20 (Fig. 1D). Similar effect on inhibited proliferation was also observed for knockdown of GRHL2another proposed PSFin lung 4  Altogether, these results indicate that Numb can restrict the progression of a complete EMT, and may stabilize both epithelial and hybrid E/M phenotypes at a single-cell level.
To probe the robustness of these results, we conducted a sensitivity analysis by assessing the change in the level of NICD resulting from a small variation of the model's parameters. Our results are robust upon parameter variation (Fig. S6), albeit a higher sensitivity was observed for the inhibition of Notch by Numb than vice-versa (Fig. S7).
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 alters the composition of clusters of non-epithelial 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 50x50 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.
When comparing Notch-EMT and Notch-EMT-Numb circuits for higher production rates of Jagged (g J =80 molecules/h), a different role of Numb is revealed. In this regime, a strong activation of Notch-Jagged signalling is capable of pushing most cells to either a partial or a complete EMT (Fig. 3A, dashed vertical black line). However, Numb inhibits the accumulation of cells in a complete EMT state while increases those in a hybrid E/M state (compare Fig. 4F with Fig. 3E). This behaviour of Numb as a PSF is reminiscent of its role seen both in H1975 cells ( Fig. 1) and in our single-cell simulations (Fig. 2). This effect of Numb has been quantified by measuring the change in the fraction of hybrid E/M versus mesenchymal cells in the absence or presence of Numb (Fig. 3D, right) for the case of a large production rate of Jagged that can push ~75% cells in a complete EMT state (g J =80 molecules/h).
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 (Fig. S8). For the case of weakly activated Notch-Jagged signalling corresponding to lower gJ ( Fig. 3B-C), the average number of hybrid E/M neighbours for a hybrid E/M cell decreased (compare Fig. S8 middle panel with S8 left panel) due to a decreased total frequency of hybrid E/M cells.
However, an increased production of Jagged ( Fig. 3E-F) can counteract this effect of Numb and consistent with previous reports 8 , it can significantly increase the co-localization of hybrid E/M cells (Fig. S8, right).
Similar to the Notch-Jagged case, we compared the tissue-level spatiotemporal dynamics for

Notch-EMT and Notch-EMT-Numb circuits in a lattice of cells that communicate with one
another predominantly via Notch-Delta, instead of Notch-Jagged (Fig. 4). Inhibition of Notch signalling by Numb reduces NICD levels 9 (Fig. 4B, S9). Such pattern formation is a cornerstone of Notch-Delta signalling as observed in multiple biological contexts 10 .
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 Notch-EMT circuit, both for Jagged-dominated and Delta-dominated scenarios, 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 ( Fig. 5A-D, S10-12).
Similar to previous observations (Fig. 3), an increase in soluble Jagged concentration rescues the cluster frequency, but these clusters predominantly contain hybrid E/M cells and not mesenchymal cells (Fig. 5E-F, S12). These effects of Numb on paracrine signalling are more prominent in case of Jagged-dominated juxtacrine signalling instead of Delta-dominated juxtacrine signalling (Fig. S10, S12).
In addition, the presence of soluble Jagged in the microenvironment has a crucial consequence  (Fig. 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 (Fig. 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 24 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 ligandswhether Jagged or Deltaactivate 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 EMT induction can overcome the inhibition of EMT by Numb
We next considered the effect of an external EMT inducer such as TGF-β (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 (Fig. S14A).
Consistent with our single-cell results, Numb acts as a molecular brake on EMT (compare the dotted curves against solid curves in Fig. S14A), and therefore 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 (Fig. S14B-D). These results may help explain why ectopic overexpression of ligand-of-Numb X (LNX)an ubiquitin ligase that targets Numb for degradationcan enhance TGF-β induced EMT 25 .
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 (Fig. S15 A-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 (Fig. S13 E-F), where Numb slows down the induction of EMT for Notch-Jagged signalling but enhances that for Notch-Delta signalling.
Finally, we considered the effect of another recently reported feedback regulation in coupled EMT-Notch circuitthe relatively weak inhibition of Numb by miR-34 26 . Owing to its weak strength, miR-34 only subtly alters the effect of Numb on EMT and Notch signalling (Fig. 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. These observations are conceptually similar to previous computational and experimental attempts in identifying PSFs such as OVOL2, GRHL2, and ∆Np63α that can induce and/or maintain a hybrid E/M phenotype, as observed in breast cancer and NSCLC cells 4,27,28,7,29 . Intriguingly, high levels of such PSFs have been proposed to predict poor survival, for instance, GRHL2 is associated with poor survival across different breast cancer subtypes 30 , and high ∆Np63α correlate with poor survival in ER -/HER2patients 27 . Thus, 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 (OS) and relapse-free survival (RFS) in multiple independent lung cancer datasets (Fig. 6, top and middle rows) as well as in ovarian cancer datasets (Fig. 6, bottom row). Our results are consistent with the reported association of high levels of Numb with poor survival in hepatocellular carcinoma 31 , with tumour recurrence and poor overall post-operative survival in esophageal squamous cell carcinoma 32 , and that of with poor overall survival in NSCLC patients 33 . Also, siRNA against Numbl inhibited the ability of lung cancer cells to form liver metastasis 33 , thus reinforcing a role of Numb and/or Numbl in driving tumor aggressiveness.
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 singlecell migration (a canonical readout of full EMT) happens extremely rarely, if any, in cancer dissemination 34 .

Discussion
Notch signalling pathway is implicated in multiple hallmarks of cancer including metastasis and angiogenesis, and other clinically insuperable aspects such as drug resistance 35  Knockdown of Numb can not only drive a complete EMT, but also stunt the ability of NSCLC cells to form liver metastases 33 . This effect of Numb corroborates its observed role in predicting poor survival across cancer types, and reinforces strongly the emerging notion that a hybrid E/M phenotype instead of a full EMT may be the hallmark of tumour aggressiveness 1,36,37 .
The effect of Numb on tissue-level patterning is reminiscent of glycosyltransferase Fringe that can alter the binding affinity of Notch with Delta and Jagged, thus affecting tissue patterning in a layer of cells 11 . Both Numb and Fringe tend to antagonize Notch-Jagged signalling predominantly ( Fig. S22-S23). This selective inhibition of Notch-Jagged signallingan axis 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  Numb has been specifically well-studied in the context of asymmetric stem cell division both for developmental stem cell lineages 48 and cancer stem cells (CSCs) 26 . Therefore, future modelling efforts will benefit from integrating the signalling aspects of Numb with population-level models of stem cell division. Such multi-scale spatial models can be critical in explaining the observed spatial patterns of different subpopulations of CSCs in breast cancer tissues 49 .
To conclude, we found that Numb 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 phenotypethe key drivers of cancer metastasis 1,3 .  Fig. S2-S5.