Cellular geometry and epithelial-mesenchymal plasticity intersect with PIEZO1 in breast cancer cells

Differences in shape can be a distinguishing feature between different cell types, but the shape of a cell can also be dynamic. Changes in cell shape are critical when cancer cells escape from the primary tumor and undergo major morphological changes that allow them to squeeze between endothelial cells, enter the vasculature, and metastasize to other areas of the body. A shift from rounded to spindly cellular geometry is a consequence of epithelial-mesenchymal plasticity, which is also associated with changes in gene expression, increased invasiveness, and therapeutic resistance. However, the consequences and functional impacts of cell shape changes and the mechanisms through which they occur are still poorly understood. Here, we demonstrate that altering the morphology of a cell produces a remodeling of calcium influx via the ion channel PIEZO1 and identify PIEZO1 as an inducer of features of epithelial-to-mesenchymal plasticity. Combining automated epifluorescence microscopy and a genetically encoded calcium indicator, we demonstrate that activation of the PIEZO1 force channel with the PIEZO1 agonist, YODA 1, induces features of epithelial-to-mesenchymal plasticity in breast cancer cells. These findings suggest that PIEZO1 is a critical point of convergence between shape-induced changes in cellular signaling and epithelial-mesenchymal plasticity in breast cancer cells.

As a fundamental part of all living things, cell shape is critical to functionality, from the biconcave shape of red blood cells to the long axonal processes of interconnected neurons.However, many cell types also need to remain plastic, able to drastically alter their shape to enable movement through the body and to enact other physiological changes [1][2][3] .Cells have mechanisms to sense transient alterations in their morphology, such as the mechanosensitive calcium (Ca 2+ ) channel PIEZO1.PIEZO1 is critical in various processes, including endothelial cells detecting shear stress and regulation of vascular tone and blood pressure 4,5 .PIEZO1 appears to be important in the cell spreading of HEK293 cells on elongated micropatterned surfaces 6 and the Ca 2+ increases that occur in CHO-α4WT cells as they are physically confined 7 .
When moving from primary tumor sites to metastatic sites, cancer cells must squeeze through blood vessels, and in doing so, they change shape 1,8 .Alterations in cellular geometry can be a response to stimuli, such as inducers of epithelial to mesenchymal plasticity 1,9 , but cell geometry can also causally contribute to phenotypic transformations.Confinement of NIH 3T3 fibroblasts to rectangular or circular geometries causes the upregulation of serum response factor and NF-κB target genes, respectively 10 .Similarly, in human mesenchymal stem cells, decreasing micropattern size causes the localization of YAP to change from predominantly nuclear to cytoplasmic 11 .
Although some transcription factors and coactivators, such as YAP/TAZ 11 and MRTF 12 , are regulated by cellular geometry, there is a lack of knowledge on how cellular geometry influences more dynamic cellular signaling pathways, such as Ca 2+ influx.However, studies in cell migration (a process that generally relies on cellular geometric changes) [13][14][15] implicate a potential intersection between Ca 2+ signaling and cellular geometry.Here, we investigated how cell shape may alter the "Ca 2+ signaling toolkit" 16,17 components and the potential intersection with the induction of epithelial to mesenchymal plasticity.We found that changes in cellular architecture resulted in an upregulation of PIEZO1 and consequently the augmentation of PIEZO1-mediated Ca 2+ influx.We further identified that PIEZO1 activation induces features of epithelial-to-mesenchymal plasticity in breast cancer cells.Collectively, our results suggest how shape-induced changes in cellular signaling and epithelial-mesenchymal plasticity intersect with the PIEZO1 force channel in breast cancer cells.
Shape-induced alterations in PIEZO1-mediated Ca 2+ influx Amongst the Ca 2+ signaling components that showed pronounced gene upregulation with cellular elongation ("L" micropattern; 1100 μm 2 ), PIEZO1 is a bona fide mechanosensitive Ca 2+ channel and has roles in the sensing of cellular forces 19,20 .Hence, we next investigated if PIEZO1 upregulation also corresponded with changes in PIEZO1-mediated Ca 2+ influx.We compared cytosolic free Ca 2+ ([Ca 2+ ] CYT ) responses to the pharmacological activator of PIEZO1, YODA 1 21 , in rounded and elongated triangular MCF-7 cells ("O" vs "L" micropatterns; 1100 μm 2 , Fig. 2a, b).Assessment of MCF-7 cells expressing the genetically encoded Ca 2+ sensor, GCaMP6m, via automated epifluorescence microscopy showed that YODA 1 induced rapid, concentration-dependent increases in [Ca 2+ ] CYT (Fig. 2c).Differences between the two cellular geometries were most pronounced in the Ca 2+ influx phase induced by YODA 1, where MCF-7 cells with elongated triangular morphology exhibited a more sustained increase in [Ca 2+ ] CYT than rounded MCF-7 cells (Fig. 2b-e).Interestingly, the maximum relative [Ca 2+ ] CYT induced by YODA 1 was augmented only at submaximal concentrations in elongated triangular cells (Fig. 2f).This shows that although PIEZO1-mediated Ca 2+ influx sensitivity is remodeled in elongated MCF-7 breast cancer cells, it is the duration of increases [Ca 2+ ] CYT induced by YODA 1 which is the most augmented and can be observed even at maximal concentrations of YODA 1.
We also investigated the underlying low dimensional structure in the time series trajectories by applying principal component analysis (PCA); this further supported augmented PIEZO1-mediated Ca 2+ influx in the elongated triangular morphologies of MCF-7 cells.More than 95% of the variance in the data can be explained by the top three principal components (PCs, Supplementary Fig. 2a).PC1 and PC2 corresponded to transient responses with relatively slower and faster decay times than the mean of the data, respectively (Fig. 2g).A scatter plot of PC1 and PC2 scores at 3 μM YODA 1 revealed separate clusters for rounded and elongated triangular MCF-7 cells (Fig. 2h).The two clusters were statistically distinct, as revealed by linear discriminant analysis (LDA) (Fig. 2i).On average, the "L" micropattern cluster was characterized by higher values for PC1 and lower values for PC2 relative to the "O" micropattern cluster, indicating slower decay in the elongated triangular cells.This was also evident from the reconstructed trajectories of the cluster means in PCA space (Fig. 2j) and was consistent with enhanced PIEZO1-mediated Ca 2+ influx in elongated triangular MCF-7 cells.
We further quantified the differences in decay times by fitting Ca 2+ transients with a nonlinear model (refer to Methods; Fig. 2k, left panel).Figure 2k (middle panel) shows a representative example of a model fit for cells on "O" and "L" micropatterns responding to YODA 1 (3 μM).For data that met the fitting criteria (refer to Methods; Supplementary Fig. 2b), the fitted decay time of the model was significantly longer for cells on "L" micropatterns compared to cells on "O" micropatterns for YODA 1 concentrations at 0.3-3 μM (Fig. 2k, right panel).At these concentrations, the model error was low and not significantly different between "O" and "L" micropatterns (Supplementary Fig. 2c).Collectively, the area under the curve (AUC), PCA, and nonlinear model fitting analyses demonstrated that elongated triangular MCF-7 cells had augmented YODA 1-induced Ca 2+ influx compared to rounded MCF-7 cells, as well as elevated PIEZO1 mRNA levels.

Association between PIEZO1 and EPI-MES markers in breast tumors
Given that selected EPI-MES marker genes were differentially expressed in elongated triangular MCF-7 cells, and that this coincided with a marked increase in PIEZO1, we explored these associations in breast tumor samples from the TCGA cohort 22 .Using an extensive list of EPI-MES marker genes [23][24][25] , PIEZO1 expression clustered with both mesenchymal (AP1M1, SNAI1) and epithelial (KRT5, KRT7, KRT14 and ST14) genes (Fig. 3a).Since tumor cells possess a spectrum of EPI-MES phenotypes 26 , we developed an EPI-MES signature (Methods; Supplementary Fig. 3a) and stratified all breast tumors from the TCGA breast tumor dataset into quintiles based on their EPI-MES score: highmesenchymal (H-MES), low-mesenchymal (L-MES), ambiguous (Ambig), low-epithelial (L-EPI) and high-epithelial (H-EPI) (Supplementary Fig. 3b, top panel).When the quintiles were assessed across the PAM50 molecular subtypes, >60% of basal-like breast tumors were assigned H/L-MES, whilst >50% of luminal B tumors were assigned H/L-EPI (Supplementary Fig. 3b, bottom panel).Given the ambiguity of PIEZO1 expression correlating to both MES and EPI markers, we reassessed correlations within the EPI-MES quintiles (Fig. 3b, Supplementary Fig. 3c).This revealed that both EPI (e.g.LLGL2, CLDN4, KRT7, ST14) and MES (e.g.SNAI1, VIM, AP1M1) genes positively correlated with PIEZO1 expression across all quintiles, whilst markers of luminal breast tumors (ESR1, FOXA1, PGR) negatively correlated in all instances.Of the four marker genes assessed in the morphological analysis, SERPINE1 displayed an increasing level of correlation as the EPI signature increased in the breast tumors (Fig. 3c).A similar pattern was observed for ZEB1 (and to a lesser extent ZEB2), genes commonly upregulated in mesenchymal cells 27,28 ; expression negatively correlated in MES tumors and increased as the EPI signature increased (Fig. 3b).These associations between both EPI and MES genes suggest that PIEZO1 might be associated with the transition state, rather than definitive epithelial or mesenchymal state.

PIEZO1 channel activation is associated with EPI-MES plasticity
The link between PIEZO1, cellular geometry, and EPI-MES markers could indicate a role for PIEZO1 in EPI-MES plasticity, which is Ca 2+ influx-dependent in other cell types, including breast cancer cells 29 .Thus we evaluated if augmented PIEZO1-induced Ca 2+ influx, such as those seen in elongated triangular MCF-7 cells, could induce changes in the expression of the EPI-MES plasticity markers.Our studies were first conducted in MDA-MB-468 breast cancer cells, where the link between EPI-MES plasticity and Ca 2+ influx has been most directly characterized 29 .YODA 1-mediated Ca 2+ influx (Supplementary Fig. 4a, b) induced a concentration-dependent decrease in the epithelial marker, E-cadherin, and a concentration-dependent increase in the mesenchymal marker, vimentin, in MDA-MB-468 breast cancer cells (Fig. 4a, b).YODA 1 also affected concentration-dependent changes in the expression of EPI-MES markers, with significant upregulation of CDH1, VIM, and CLDN4 in MDA-MB-468.However, the most pronounced increase was seen in the EPI-MES plasticity marker, SERPINE1 (Fig. 4c), where expression in the TCGA tumor samples additionally correlated with PIEZO1 in an EPI-MES score-dependent manner (Fig. 3c).SERPINE1 levels were particularly sensitive to intracellular Ca 2+ levels and its upregulation by YODA 1 was Ca 2+ signal-dependent as demonstrated by the effects of intracellular Ca 2+ chelation with BAPTA-AM (Supplementary Fig. 4c).YODA 1 induced increases in SERPINE1 were also observed in MCF-7 breast cancer cells (Supplementary Fig. 4d).
To further explore the association between PIEZO1 and EPI-MES markers, we generated a CRISPR/Cas9 PIEZO1 knockout (KO) in MDA-MB-468 cells with two independent guide RNAs (Fig. 4d, Supplementary Fig. 5a).YODA 1-dependent [Ca 2+ ] CYT increases were abolished in the absence of PIEZO1, while ATP and epidermal growth factor (EGF)-induced [Ca 2+ ] CYT increases were relatively unaffected (Fig. 4e, f, Supplementary Fig. 6a, b).Basal expression of EPI-MES markers was similar in both scrambled and PIEZO1-KO cells (Supplementary Fig. 5b), as was the induction of EPI-MES markers induced by EGF at the 6 h timepoint (Supplementary Fig. 6c); the latter of which is dependent on Ca 2+ influx and transient receptor potential-melastatin-like 7 (TRPM7) 29 .However, increases in EPI-MES markers induced by YODA 1, and in particular, SERPINE1, were clearly attenuated in the PIEZO1-KO cells and in cells with transient PIEZO1 silencing using siRNA (Fig. 4g, Supplementary Fig. 7).YODA 1-induced changes in vimentin and E-cadherin protein were moderately reversed in the PIEZO1-KO cells, suggesting some YODA 1 offtarget effects and highlighting the importance of our silencing studies (Supplementary Fig. 5c, d).Collectively, these studies link PIEZO1 activation to the process of EPI-MES plasticity via modulation of selected EPI-MES markers.
PIEZO1 activation induces the localization-reset of YAP1 and upregulates SERPINE1 via YAP1 PIEZO1 modulates the localization and activity of YAP1, a mechanosensitive transcriptional coactivator 30 .YODA 1 activation in MDA-MB-468 breast cancer cells induced a YAP1 localization reset phenomenon.This was characterized by initial depletion and subsequent accumulation of nuclear YAP1 (Fig. 5a, b), which is essential for YAP1 transcriptional activity in MCF10A breast cells 31 .Here, we also observed a decrease in nuclear YAP1 upon YODA1 treatment at 15 min, and a subsequent "reset" at 1 h time point (Fig. 5a, b).YODA 1-induced mRNA upregulation of the YAP1 target gene, CTGF, was sensitive to YAP1 silencing, as was SERPINE1 (Fig. 5c, Supplementary Fig. 8a, b), which is also a downstream YAP1 gene 32,33 .Expression of SERPINE1 and CTGF was additionally sensitive to silencing of TEAD4, a well-documented transcription factor that complexes with YAP1 34 (Fig. 5c).While the YAP1 paralog, TAZ (encoded by WWTR1), regulated the expression of CTGF, the expression of SERPINE1 was not TAZ-dependent in MDA-MB-468 cells (Fig. 5c).Silencing components of the mechanosensitive serum response factor (SRF) transcription pathway (MKL1, MKL2, and SRF) attenuated YODA 1-induced upregulation of CTGF, as expected 35 ; however, these components were also not involved in YODA 1-induced upregulation of SERPINE1 (Supplementary Fig. 8c-e).

Discussion
Using surface micropatterning to induce a change in cellular geometry, we showed alterations in gene transcription including genes that are key markers of EPI-MES and those involved in Ca 2+ signaling.We identified that PIEZO1, a force-activated Ca 2+ channel, is upregulated with an elongated triangular cellular morphology and this is associated with an augmentation of intracellular Ca 2+ increases induced by the PIEZO1 activator, YODA 1.The most pronounced gene expression changes were observed in the 1100 μm 2 elongated triangular but not at 700 μm 2 , when compared to other shapes.The maximum distance between two points was 25% greater for 1100 μm 2 surfaces than for 700 µm 2 micropattern surfaces: 37.4 μm compared to 29.9 μm ("O" micropattern) and 66.3 μm compared to 52.9 μm ("L" micropattern).Given that MCF-7 cells had a surface area of ~1017 μm 2 (from n = 448 segmented MCF-7 cells on unpatterned surface), the 1100 μm 2 provides the most suitable surface area for assessment.The elongated triangular cellular geometry creates a long single free-edge organization not seen in other micropatterns used in this study.These features could influence the expression and activity of the bona fide mechanosensitive Ca 2+ channel, PIEZO1 19,20 .
The augmentation of intracellular Ca 2+ increases induced by the PIEZO1 activator, YODA 1, in 1100 μm 2 "L" cells could be explained by the upregulation of PIEZO1 in these cells.Other potential mechanisms could include the sensitivity, kinetics, or spatial distribution of PIEZO1, or changes in other associated Ca 2+ signaling pathways.Indeed, Yang et al. found that the membrane curvature can regulate the spatial distribution of Piezo1 on the plasma membrane 36 .As previous studies have found that micropatterning can create localized tension at specific subcellular regions 37 , future studies could investigate PIEZO1 protein expression and the spatial distribution of PIEZO1 in cells adopting different cellular geometries and their correlation with local tensions at subcellular regions.Future work could also evaluate the relative contributions of changes in PIEZO1 levels and/or channel kinetics to the shape-dependent increases in calcium influx induced by YODA 1 that have been observed in our studies.
Various forms of mechanical stimuli can remodel Ca 2+ signaling.PIEZO1 is associated with cellular organization and upregulation of PIEZO1 occurs in disorganized malignant T4-2 breast cells compared with nonmalignant S1 cells that grow in organized acini 38 .Mechanical stress (in the form of cardiac hypertrophy) similarly results in the induction of PIEZO1 expression and augments electrically evoked Ca 2+ transients in mouse cardiomyocytes 39 , and membrane curvature regulates the plasma membrane distribution of PIEZO1 36 .Prior to the identification of PIEZO1, Lee et al. observed that fish epithelial keratocytes with innate fibroblastic shape demonstrate more frequent Ca 2+ transients than fan-shaped cells 40 .Our results show that in addition to being a force sensor 19,20 and regulator of cellular morphology in CHO-α4WT cells 7 and muscle stem cells 41 , PIEZO1 can be remodeled as a consequence of changes in cell shape, further exemplifying the interdependence and dynamic reciprocity of mechanical signaling.
We and others have shown that Ca 2+ signaling influences EPI-MES plasticity in breast cancer cells 29,42 .We now show that the activation of PIEZO1 caused pronounced induction of the EPI-MES marker SERPINE1 in breast cancer cells.This result along with a previous study in MC3T3-E1 osteoblasts 43 , suggests that SERPINE1 gene expression is very sensitive to PIEZO1 activation.SERPINE1 (which encodes for PAI1) is a prognostic marker of poor clinical outcomes in breast cancer patients 44,45 , has protumorigenic roles 46 , and is upregulated when triple-negative breast cancer cells transition from epithelial to a mesenchymal state 47 .We also showed that SERPINE1 induction by PIEZO1 activation was dependent on the transcriptional coactivator YAP1, which is a well-characterized influencer of cellular proliferation and apoptosis 48 .
One feature of EPI-MES plasticity is the loss or decrease of junctional protein E-cadherin 1 .In MDA-MB-468 breast cancer cells, YODA 1 activation resulted in an increase in vimentin and a decrease in E-cadherin.The association of PIEZO1 and junctional proteins is also seen through the interaction of Piezo1 with PECAM1 49 , and Piezo1-induced remodeling of junctional proteins in endothelial cells and lymphatic endothelial cells 50,51 .Future studies could further evaluate the intersection of PIEZO1 and junctional proteins in the context of cancer progression pathways.
Ca 2+ signaling plays a critical role in normal cellular processes 16,17,52 and in many disease processes 4,5,53,54 .Cancer cells change morphology while metastasizing to sites distant from the primary tumor and Ca 2+ signaling is critical in processes important in cancer progression, such as proliferation and cell migration 54 .The results presented here ] CYT changes in GCaMP6m-MCF-7 cells on "O" and "L" micropatterns with increasing YODA 1 concentrations.[Ca 2+ ] CYT changes in ten randomly selected representative cells on "O" (left) and "L" (middle) micropatterns and averages of all cells (right).d [Ca 2+ ] CYT area under the curve (AUC), e sustained [Ca 2+ ] CYT , last data point (ΔF/F 0 ) and f maximum relative [Ca 2+ ] CYT change (ΔF/F 0 ) for cells on "O" and "L" micropatterns induced by increasing concentrations of YODA 1 (0-3 μM).From 0-750 s (top panel) and 750 s -end (bottom panel).Data shown represent the mean ± S.E.M. g Top components from PCA captured differences between slow and fast decay.h Scatter plots of PC1 and PC2 scores of single cells activated by 3 μM YODA 1. i Means of "O" and "L" micropatterned cell clusters were significantly different at 3 μM YODA 1 (left).Linear discriminant analysis (LDA) shows that cluster means were best separated along a direction corresponding to the difference between fast and slow decay (right; i.e., positive LDA weight for PC1 and negative weight for PC2).j Reconstructed Ca 2+ transients for cluster means show that "L" micropatterned cells decayed more slowly than "O" micropatterned cells at 3 μM YODA 1. k Illustration of a nonlinear model for Ca 2+ transients incorporating an exponential rise, a slower exponential decay, and a steady-state constant (left).Representative model fits (median model error) for "O" and "L" micropatterned cells, respectively, at 3 μM YODA 1 (middle).Fitted decay time (1/τ decay ) was significantly longer for "L"-shaped cells at 0.3, 1, and 3 μM YODA 1 (right; Y-axis is truncated to 1/τ decay = 1000 s) (n = 4 biological replicates).Unmarked P ≥ 0.05, **P < 0.01, ***P < 0.001, ****P < 0.0001.demonstrate a clear intersection between cellular geometry, Ca 2+ signaling, the PIEZO1 force channel, and EPI-MES plasticity in breast cancer cells.Our identification that some Ca 2+ signaling pathways become more predominant with an elongated triangular morphological cellular state, will pave the way for the improved targeting of specific cellular processes important in different diseases.The high-throughput and automated approaches used to define cell morphology-dependent alterations in Ca 2+ signaling represent a powerful new approach to identifying agents and targets that could disrupt the interplay between cellular geometry, cell signaling pathways, and cellular plasticity.

Methods
Cell lines and cell culture MCF-7 and HEK293T cell lines were sourced from ATCC.The MDA-MB-468 cell line was from The Brisbane Breast Bank, UQCCR, Australia.All cell lines were cultured in DMEM (Sigma-Aldrich) supplemented with 10% v/v  FBS (Life Technologies) and 4 mM L-glutamine (Thermo Fisher Scientific) for less than 10 passages post-thaw in a humidified 37 °C incubator with 5% CO 2 .Unless otherwise indicated, experiments conducted in serum-reduced conditions were in FluoroBrite DMEM (Thermo Fisher Scientific) supplemented with 0.5% v/v FBS, 4 mM L-glutamine, and 25 mM HEPES buffer (Thermo Fisher Scientific).All cell lines were routinely tested for mycoplasma contamination.MCF-7 and MDA-MB-468 cell lines were routinely authenticated by short tandem repeat (STR) profiling.To assess YODA 1-induced mRNA expression changes, cells were serum-reduced for 24 h, detached using Accumax (Invitrogen), and seeded into 96-well plates (3000 cells per well for MCF-7 and 6000 cells per well for MDA-MB-468) in serum-reduced media for 48 h before being treated with YODA 1 (Tocris) for the duration stated in the figure legends.To assess YODA 1-induced protein expression changes, YODA 1-induced YAP1 translocation and hEGF (Sigma-Aldrich)-induced mRNA expression changes, MDA-MB-468 cells were seeded into 6-well plates (250,000 cells/well) or 96-well plates (6000 cells/well) for 24 h before being serum-reduced for 24 h.Cells were then treated with YODA 1 or hEGF for the duration stated in the figure legends.To assess the effect of BAPTA-AM on YODA 1-induced mRNA expression changes, MDA-MB-468 cells were seeded into 96-well plates (6000 cells/well) for 24 h before being serum-reduced for 48 h, Cells were then treated with 100 µM BAPTA-AM (B6769, Invitrogen) or DMSO for 1 h, before YODA 1 treatment.

Cell culture on micropatterned plates
CYTOOplates 96 Starter-A (CYTOO) were used for live-cell imaging and qRT-PCR studies.MCF-7 cells were serum-reduced for 48 h, detached using 0.2% w/v EDTA in pH 7.4 PBS/EDTA, resuspended and pelleted twice with media, and syringed slowly through a 23 G needle four times prior to plating at a density of 3,000 cells per well using serum-reduced media.Wells were washed twice 1 h after plating to remove unattached cells.Cells were allowed to attach for 24 h before performing experiments.For the [Ca 2+ ] CYT studies, GCaMP6m-MCF-7 cells were detached using Accumax and plated on 1100 μm 2 "O" micropatterned (CYTOOplate 96 RW DC-M-A, CYTOO) and 1100 μm 2 "L" micropatterned (CYTOOplate 96 RW L-M-A, CYTOO) plates using a similar protocol.Unless otherwise indicated, cells were allowed to attach for 16-24 h before performing experiments.

Brightfield imaging
Brightfield imaging was performed using the brightfield mode of a JuLi Stage microscope (NanoEntek) using a 4× objective kept in a humidified 37 °C incubator with 5% CO 2 .To determine the proportion of single-cells, images at the 24-h timepoint were exported into ImageJ, and cells were manually counted using the Cell Counter plugin 55 .

RNA preparation and qRT-PCR
RNA was isolated using an RNeasy Plus Micro Kit (Qiagen) or RNeasy Plus Mini Kit (Qiagen) according to the manufacturer's protocol.Multiple wells (four to six) were pooled together to provide sufficient mRNA yield for qRT-PCR of multiple targets.cDNA was synthesized using the Omniscript Reverse Transcription Kit (Qiagen) according to the manufacturer's protocol.RNase inhibitor (Promega) and random primers (Promega) were purchased separately.
Lentiviral particles were produced by transfection using Lipofectamine 2000 (Invitrogen) on HEK293T cells, as previously described 59 .To generate GCaMP6m-MCF-7 cells, MCF-7 cells were infected for 24 h in the presence of 8 μg/mL polybrene (Merck).Selection with 2 μg/mL puromycin (Sigma) was applied 48 h after infection.Mixed populations of GCaMP6m-MCF-7 cells were fluorescence-activated cell sorted (FACS) into single cells using Beckman Coulter MoFlo Astrios EQ (Translational Research Institute, Australia), and viable clones were then expanded and the expression of hormone receptors at mRNA level, expression of epithelial markers at protein level and STR profiling were used to validate the selected clone.
To generate MDA-MB-468-PIEZO1-KO and MDA-MB-468scrambled cells, MDA-MB-468 cells were transduced twice with viral media (equal volumes of sgPIEZO1#1 and sgPIEZO1#2 or equal volumes of scrambled#1 and scrambled#2, respectively) in the presence of 8 μg/mL polybrene (48 h per infection).Selection with 400 μg/mL hygromycin B (Gibco) was applied 48 h after the second infection.Selected cells were used immediately as a mixed population for less than 10 passages and were not cryopreserved.Functional knockdown of PIEZO1 was assessed with each experiment/passage using YODA 1-induced [Ca 2+ ] CYT increases in MDA-MB-468-PIEZO1-KO cells and MDA-MB-468-scrambled cells (Fig. 4e, f) and genotyping (Methods and Supplementary Table 1).
High-content imaging of intracellular Ca 2+ fluorescence using automated epifluorescence microscopy An ImageXpress Micro automated epifluorescence microscope was used to assess [Ca 2+ ] CYT in single GCaMP6m-MCF-7 cells on micropatterned plates (100 μL FluoroBrite DMEM, supplemented with 0.5% v/v FBS, 4 mM L-glutamine and 25 mM HEPES buffer).Images were acquired with a 10× objective an excitation filter of 472/30 nm and an emission filter of 520/ 35 nm with an exposure time of 40 ms for GCaMP6m every 30 s for 30 min (referred to as calcium images).YODA 1 solutions were prepared in FluoroBrite DMEM, supplemented with 0.5% v/v FBS, 4 mM L-glutamine, and 25 mM HEPES buffer to obtain the final concentrations as stated.At the tenth time point, 20 μL of the prepared YODA 1 was added to the micropatterned plates.Images were continually acquired before, during, and after YODA 1 addition.
At the end of the experiment, nuclei were counterstained with Hoechst 33342 dye, and images were acquired at two wavelengths: (1) 40 ms exposure with a 10× objective and an excitation filter of 472/30 nm and an emission filter of 520/35 nm for GCaMP6m, and (2) 5 ms exposure with a 10× objective and an excitation filter of 377/50 and emission filter of 447/ 60 nm for Hoechst 33342 dye (referred to as post-Hoechst images).Unless otherwise specified, all images were acquired with binning at 3 × 3 to improve the signal-to-noise ratio of each image.Experiments were performed across four independent cell passages, in duplicate wells per treatment across two independent ImageXpress time-lapse experiments (two independent cell passages each time-lapse experiment).
Image analysis was performed using MetaXpress High Content Image Acquisition and Analysis software using a custom-written analysis journal.Data from each part of the journal analysis (described below) were exported in CSV format as individual data files.All data files were subsequently combined and analyzed using R (refer to Supplementary Fig. 9 for a general overview).
The first image from the raw time-lapse calcium images was removed and not further analyzed.The remaining 60 images were auto-aligned using the first plane as the reference plane.From the aligned time-lapse calcium images, an image stack of the first image was segmented to identify regions containing GCaMP6m-MCF-7 cells.Image segmentation was performed using the auto-find object tracking algorithm with an adaptive threshold.The settings for minimum width, maximum width, and intensity above the local background were 10 pixels, 60 pixels, and 5 intensity values, respectively.Segmented objects were eroded by 3 pixels to account for any slight image drift between timepoints.This created a mask that could identify a single cell as a region and allowed for tracking of [Ca 2+ ] CYT changes (GCaMP6m emission intensity) for each single cell over time (referred to as calcium GCaMP6m object, Data file #1).
Post-Hoechst nuclei images were used to obtain single-cell information.The post-Hoechst nuclei image was duplicated to create an image stack, which was segmented to identify regions containing nuclei.Image segmentation was performed using the auto-find object tracking algorithm with an adaptive threshold.The settings for minimum width, maximum width, and intensity above the local background were 10 pixels, 20 pixels, and 800 intensity values, respectively.Segmented nuclei were binarized and dilated by 3 pixels.Objects touching the border were removed.The remaining objects were then eroded back by 3 pixels to create a new Hoechst mask.
Each Hoechst-tracked object on the new Hoechst mask was processed in two ways: a) associate each nucleus (from the Hoechst mask) to individual cells (GCaMP6m object), and b) identify regions that contained only a single cell.First, to associate each Hoechst object to each GCaMP6m object, the Hoechst mask was overlaid on the post-Hoechst GCaMP6m image to match each Hoechst-tracked object with post-Hoechst GCaMP6m object (Data file #2).Second, to identify regions that contained only single cells, the minimum distance of each Hoechst-tracked object to every other Hoechsttracked object was obtained; a close distance would indicate more than one cell (nuclei) per region.To do that, an Euclidean distance image for each Hoechst-tracked object was generated.Using the Euclidean distance image, the minimum distance of each Hoechst-tracked object to every other Hoechst-tracked object was identified and logged (Data file #3).Finally, for each cell, their post-Hoechst GCaMP6m object was associated with the corresponding calcium GCaMP6m object.This was achieved by aligning and matching the post-Hoechst GCaMP6m image and the first image from the time-lapse calcium images as part of the analysis journal (Data file #4).
Files were processed using R (version 3.5.1) 60.Briefly, the data files (#1 -4) from each well were combined and merged.Raw data were filtered so that only data from single cells that adopted the intended shapes were assessed.For the "O" shape, GCaMP6m objects with shape factors of ≥0.9 were included (a shape factor of 1 is a perfect circle).For the "L" shape, a GCaMP6m object with a shape factor of 0.5-0.85(inclusive) was included.As each micropattern was sometimes occupied by more than one cell, only micropatterned regions that contained a single nucleus (reflective of one cell attached to a region) were included in the analysis.Data from regions with only one cell were identified, by identifying nuclei (Hoechst-tracked object) that were at least 20 pixels away from other nuclei.Large nuclei could also indicate more than one nucleus per region.Therefore, only nuclei that were less than 300 μm 2 (the size of the largest single nuclei based on manual sampling) were included in the data analysis.To ensure that the GCaMP6m objects (calcium GCaMP6m object and post-Hoechst GCaMP6m object) and the Hoechst-tracked object were matched correctly, the centroid locations from all files were compared.Data were excluded if the differences of any two sets of centroids were > 30 μm-the approximate width of one cell.Data that fulfilled the above criteria were analyzed.Unless otherwise stated, for pooled quantitative data, data points are the mean of duplicate wells across four independent cell passages assessed as two time-lapse ImageXpress experiments (two independent cell passages each timelapse experiment).
[Ca 2+ ] CYT imaging using fluorometric imaging plate reader (FLIPR) [Ca 2+ ] CYT changes in MDA-MB-468 cells in response to YODA 1, ATP (Sigma-Aldrich) and hEGF were assessed using a fluorometric imaging plate reader FLIPR TETRA (Molecular Devices) using the PBX no-wash Ca 2+ Assay Kit (BD Biosciences), as previously described 29 in serum-reduced FluoroBrite DMEM or physiological salt solution (PSS; 10 mM HEPES, 5.9 mM KCl, 1.4 mM MgCl 2 , 1.2 mM NaH 2 PO 4 , 5 mM NaHCO 3 , 140 mM NaCl, 11.5 mM glucose) with 1.8 mM CaCl 2 (Sigma-Aldrich) or 100 μM BAPTA tetrasodium salt, cell impermeant (Invitrogen).Unless otherwise stated, YODA 1, ATP, and hEGF were prepared on a compound plate.FLIPR TETRA was programmed to automatically add 50 μL to the cellcontaining sample plates to obtain the final concentrations as stated in the figures and Ca 2+ signaling changes were continuously assessed before, during, and after reagent addition.

Immunofluorescence
Cells were fixed with formaldehyde solution, methanol free (4% w/v, Thermo Scientific) for 30 min, permeabilized and blocked using PBS containing 10% v/v goat serum (Sigma Aldrich), 0.3 M glycine (Sigma Aldrich), 1% w/v bovine serum albumin (Sigma Aldrich) and 0.1% v/v Triton X-100 (Sigma Aldrich) for 1 h before treating with anti-YAP1 antibody (63.7) (1:200 in blocking buffer, SC-101199, Santa Cruz) overnight at 4 °C.Cells were then treated with goat-anti-mouse Alexa 488 antibody (1:200 in blocking buffer, #4408 S, Cell Signaling) for 1 h at room temperature.Nuclear staining was performed using DAPI (1 μg/mL, Invitrogen) incubated at room temperature for 10 min before imaging using ImageXpress Micro at: (1) 100 ms exposure with an excitation filter of 472/30 nm and an emission filter of 520/35 nm for GFP, and (2) 2 ms exposure with an excitation filter of 377/50 and an emission filter of 447/60 nm for DAPI, with a 20× objective and binning at 2 × 2. Analysis of nuclear YAP1 was performed using the Standard Translocation application in MetaXpress High Content Image Acquisition and Analysis software.The settings for minimum width and intensity above the local background were 10 pixels and 50 intensity values, respectively.

Principal component analysis of transient calcium response to YODA 1 agonist
The fluorescence data for each cell i are scalar time series y i ¼ fy n g N n¼0 , where y n is the detrended and normalized fluorescence value at the n th time point for a total of N observations.Data were recorded with a consistent sampling rate and were time-aligned with respect to the addition of the YODA 1 agonist.Therefore, to investigate patterns in the shape of the transient calcium responses, we treated each y i as a single vectorial observation with N dimensions and applied principal component analysis (PCA).Components were computed by using Scikit-learn 64 , with a full singular value decomposition solver for the complete data pooled over "O" and "L" cell shapes, and for all tested concentrations of the agonist.We reduced the dimensionality of the data by retaining the three components that explained the most variance.We refer to the projection onto these three components as PC space (Fig. 2g and h, and Supplementary Fig. 2a).
We applied a MANOVA to observations in PC space using Statsmodels 65 to determine if the means of the clusters corresponding to each cell shape were different (Fig. 2i).The test was applied to the data for each agonist concentration level separately and p-values were adjusted for multiple comparisons by Bonferroni correction.To understand the nature of the identified differences between the calcium responses for different cell shapes, we applied linear discriminant analysis (LDA) to the same observations in PC space using Scikit-learn 64 .The weights of the linear projection learned by LDA were used to interpret shape-related differences.We visualized the estimated average calcium responses corresponding to the means of the respective clusters for each cell shape in PC space by projecting the cluster centroids back into the full N-dimensional space of y i (Fig. 2j).
Nonlinear model fitting Data were fitted using nonlinear least squares optimization with a Trust Region Reflective algorithm 66 , as implemented in the SciPy function optimize.curve_fit 65.
We modelled transient calcium responses as an exponential rise and decay process given by: where f t ð Þ is the detrended and normalized fluorescence time series, t is time, τ rise and a are constants controlling the rate and magnitude of exponential rise, respectively, τ decay and b are constants controlling the rate and magnitude of exponential decay, respectively, and c is the constant corresponding to the steady state of the system (Fig. 2k, left panel).To ensure that the model conformed to a rise followed by a decay (not a decay followed by a rise), we constrained τ decay <τ rise .To achieve this we defined: where τ Δ ≥ 0 and replaces τ rise as a model parameter, and rewrote the model as: To force the model to start with zero fluorescence at the time that the transient began (i.e., f 0 ð Þ ¼ 0) we further constrained the model by: and rewrote the final model with four parameters as: We used nonlinear least squares optimization with a Trust Region Reflective algorithm 66 as implemented in the SciPy function curve_fit 67 to fit the model in Eq. 5. Data were fitted to each time series y 0 i ¼ fy n g N n¼8 À y baseline , where y baseline is the mean of fy n g 7 n¼0 and n ¼ 8 is the time point corresponding to the start of the calcium transient.We specified additional bounds on the parameters during fitting.Firstly, to ensure that the fit conformed to the desired shape of a rise followed by a decay, we constrained τ decay ≥ 0, τ Δ ≥ 0, and b ≥ 0. Secondly, we assumed that the steady state must be greater than or equal to zero and less than the maximum fluorescence value observed (after the baseline adjustment in y 0 i ).Hence, 0 ≤ c ≤ max y 0 i .It follows that a ≥ b, which is also necessary to maintain the desired model behavior.
Model parameters must be initialized when fitting using the Trust Region Reflective algorithm.We initialized the steady-state constant c with the median of y 0 i , which was typically a good approximation of this parameter for our data.Using the median was more effective than the mean because the data were positively skewed due to the asymmetrical nature of the calcium transient.For the other parameters, τ decay , τ Δ and b, we ran the model fit many times for a range of initializations and selected the fit with the lowest r 2 error (sum of squared residuals).This was to avoid local minima in the solution space.Specifically, we used a 3-dimensional grid search for the best nonlinear fit over ten logarithmically spaced values of τ decay , such that 1 We only attempted to fit the model to the data for the i th cell if y 0 i met three specified criteria.Firstly, the median of y 0 i had to be greater than or equal to zero, or else c would be initialized outside of the parameter bounds.Secondly, the distribution of the observations fy n g N n¼8 (i.e., the transient response) had to have higher fluorescence values on average than those for fy n g 7 n¼0 (i.e., prior to the transient response), as determined by a one-sided Wilcoxon rank-sum test with significance level α ¼ 0:005, otherwise we deemed the cell to be non-responsive.Thirdly, the maximum of y 0 i had to occur in the first half of the time series.If this condition was not met, and given that the model specifies that transients must decay more slowly than they rise, then the fit of τ decay might not be reliable because the modelled transient would not be able to converge to the steady state value over the observed period (Supplementary Fig. 2b).

Statistics and reproducibility
PCA and nonlinear model fitting analyses 68 , were performed with Python in Jupyter Lab using NumPy 69 , SciPy 67 , Scikit-learn 64 , and Statsmodels 65 .Unless otherwise indicated, data were visualized and analyzed using R 60 or GraphPad Prism (version 7.01 or 9.0 for Windows).Unless otherwise indicated, statistical analysis was performed using a two-tailed paired t-test or two-way ANOVA with Šídák's multiple comparisons test with the matched pairing of each cell passage/ experiment.For Fig. 2i (left panel), statistical analysis was performed using MANOVA (Wilk's lambda (F statistic) with 3 degrees of freedom; Bonferroni corrected for multiple comparisons with respect to different YODA 1 concentrations).For Fig. 2k (right panel) and Supplementary Fig. 2c, statistical analysis was performed using two-sided Wilcoxon rank-sum tests (Fig. 2k, right panel was Bonferroni corrected for multiple comparisons with respect to different YODA 1 concentrations).For Figs. 4a-c, 5b (bottom panel), and Supplementary Fig. 5c, statistical analysis was performed using two-way ANOVA with Dunnett's multiple comparisons test with the matched pairing of each cell passage/experiment.Experiments on micropatterned plates were from four independent cell passages on two independent cell platings for qRT-PCR or two independent time-lapse ImageXpress experiments.Other data were from at least three independent experiments.Unless otherwise indicated, where appropriate, n indicates the number of independent experiments.

Reporting summary
Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Fig. 3 |
Fig. 3 | PIEZO1 expression correlates with specific EPI-MES markers in breast tumours.a Correlation matrix for mRNA expression of PIEZO1 and the EPI, MES, and breast cancer marker genes in the TCGA breast tumour dataset.The inset shows genes grouped with PIEZO1 by hierarchical clustering.b Correlation of PIEZO1 expression with EPI, MES, and breast cancer marker genes in each EPI-MES quintile: high-mesenchymal (H-MES), low-mesenchymal (L-MES), ambiguous (Ambig), low-epithelial (L-EPI) and high-epithelial (H-EPI).c Correlation of PIEZO1 with CDH1, VIM, CLDN4 and SERPINE1 in each EPI-MES quintile.The left Y-axis is the Pearson correlation coefficient of each gene with PIEZO1.The right Y-axis is the correlation P-value.The horizontal dotted line represents P = 0.05.

τ decay ranged from 15
to 1500 seconds, six logarithmically spaced values of τ Δ from 10 À6 to 10 À1 , and five logarithmically spaced values of b from 0:1 to 1000.