ABSTRACT 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

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. SIMILAR CONTENT BEING VIEWED BY OTHERS BRICK STREX: A ROBUST DEVICE BUILT OF

LEGO BRICKS FOR MECHANICAL MANIPULATION OF CELLS Article Open access 16 September 2021 ARCHITECTURAL CONTROL OF METABOLIC PLASTICITY IN EPITHELIAL CANCER CELLS Article Open access 19 March

2021 GEOMETRICALLY DEFINED ENVIRONMENTS DIRECT CELL DIVISION RATE AND SUBCELLULAR YAP LOCALIZATION IN SINGLE MOUSE EMBRYONIC STEM CELLS Article Open access 29 April 2021 INTRODUCTION 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 changes1,2,3. Cells have mechanisms to

sense transient alterations in their morphology, such as the mechanosensitive calcium (Ca2+) channel PIEZO1. PIEZO1 is critical in various processes, including endothelial cells detecting

shear stress and regulation of vascular tone and blood pressure4,5. PIEZO1 appears to be important in the cell spreading of HEK293 cells on elongated micropatterned surfaces6 and the Ca2+

increases that occur in CHO-α4WT cells as they are physically confined7. When moving from primary tumor sites to metastatic sites, cancer cells must squeeze through blood vessels, and in

doing so, they change shape1,8. Alterations in cellular geometry can be a response to stimuli, such as inducers of epithelial to mesenchymal plasticity1,9, 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, respectively10. Similarly, in human mesenchymal stem cells, decreasing micropattern size causes the localization of YAP to change from predominantly nuclear to cytoplasmic11. Although

some transcription factors and coactivators, such as YAP/TAZ11 and MRTF12, are regulated by cellular geometry, there is a lack of knowledge on how cellular geometry influences more dynamic

cellular signaling pathways, such as Ca2+ influx. However, studies in cell migration (a process that generally relies on cellular geometric changes)13,14,15 implicate a potential

intersection between Ca2+ signaling and cellular geometry. Here, we investigated how cell shape may alter the “Ca2+ 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 Ca2+ 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. RESULTS CHANGES IN GENE EXPRESSION WHEN

MCF-7 CELLS ARE CONFINED TO ELONGATED TRIANGULAR MORPHOLOGY To investigate how cell shape may alter the “Ca2+ signaling toolkit”16,17 components and epithelial to mesenchymal

plasticity-related genes, we grew MCF-7 cells on unpatterned surfaces. Consistent with the epithelial-like features of this breast cancer cell line18, the cells exhibited an epithelial-like

polygonal morphology (Fig. 1a). Using commercially available surface micropatterning (refer to Methods), we then confined MCF-7 cells to various cellular geometry, and we found that the

elongated triangular MCF-7 cells (“L” micropattern; 1100 μm2) demonstrated the most pronounced gene expression changes (Supplementary Fig. 1). Figure 1b–d shows the comparison between

non-polarized rounded (“O” micropatterned) and elongated triangular (“L” micropatterned) geometries (Fig. 1b–d). Epithelial-mesenchymal (EPI-MES) markers, _VIM_ and _CDH1_, differed

significantly between rounded MCF-7 cells (“O” micropattern; 1100 μm2) and elongated triangular MCF-7 cells (“L” micropattern; 1100 μm2) (Fig. 1e, left panel). The more elongated triangular

MCF-7 morphology was also associated with pronounced upregulation and remodeling of a variety of Ca2+ signaling components (Fig. 1e, left panel). Upregulation of gene expression was only

observed on larger (1100 μm2), not smaller (700 μm2), micropattern surfaces (Fig. 1e, right panel). The mechanosensitive Ca2+ channel, PIEZO1, was one of the Ca2+ permeable ion channels

significantly upregulated with the elongated triangular geometry (Fig. 1e, left panel). SHAPE-INDUCED ALTERATIONS IN PIEZO1-MEDIATED CA2+ INFLUX Amongst the Ca2+ signaling components that

showed pronounced gene upregulation with cellular elongation (“L” micropattern; 1100 μm2), PIEZO1 is a bona fide mechanosensitive Ca2+ channel and has roles in the sensing of cellular

forces19,20. Hence, we next investigated if _PIEZO1_ upregulation also corresponded with changes in PIEZO1-mediated Ca2+ influx. We compared cytosolic free Ca2+ ([Ca2+]CYT) responses to the

pharmacological activator of PIEZO1, YODA 121, in rounded and elongated triangular MCF-7 cells (“O” vs “L” micropatterns; 1100 μm2, Fig. 2a, b). Assessment of MCF-7 cells expressing the

genetically encoded Ca2+ sensor, GCaMP6m, via automated epifluorescence microscopy showed that YODA 1 induced rapid, concentration-dependent increases in [Ca2+]CYT (Fig. 2c). Differences

between the two cellular geometries were most pronounced in the Ca2+ influx phase induced by YODA 1, where MCF-7 cells with elongated triangular morphology exhibited a more sustained

increase in [Ca2+]CYT than rounded MCF-7 cells (Fig. 2b–e). Interestingly, the maximum relative [Ca2+]CYT induced by YODA 1 was augmented only at submaximal concentrations in elongated

triangular cells (Fig. 2f). This shows that although PIEZO1-mediated Ca2+ influx sensitivity is remodeled in elongated MCF-7 breast cancer cells, it is the duration of increases [Ca2+]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 Ca2+ 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 Ca2+ influx in elongated triangular MCF-7 cells. We further quantified

the differences in decay times by fitting Ca2+ 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 Ca2+ 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 cohort22. Using an extensive list of EPI-MES marker genes23,24,25, _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 phenotypes26, 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:

high-mesenchymal (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 re-assessed 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 cells27,28; 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 Ca2+ influx-dependent in other cell types,

including breast cancer cells29. Thus we evaluated if augmented PIEZO1-induced Ca2+ 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 Ca2+ influx has been most directly

characterized29. YODA 1-mediated Ca2+ 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 Ca2+ levels and

its upregulation by YODA 1 was Ca2+ signal-dependent as demonstrated by the effects of intracellular Ca2+ 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 [Ca2+]CYT increases were abolished in the absence of PIEZO1, while ATP

and epidermal growth factor (EGF)-induced [Ca2+]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 Ca2+ 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 off-target 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 coactivator30. 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 cells31. 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 gene32,33. Expression

of _SERPINE1_ and _CTGF_ was additionally sensitive to silencing of _TEAD4_, a well-documented transcription factor that complexes with YAP134 (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 expected35; 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 Ca2+ signaling. We identified that _PIEZO1_, a force-activated Ca2+ channel, is upregulated with an

elongated triangular cellular morphology and this is associated with an augmentation of intracellular Ca2+ increases induced by the PIEZO1 activator, YODA 1. The most pronounced gene

expression changes were observed in the 1100 μm2 elongated triangular but not at 700 μm2, when compared to other shapes. The maximum distance between two points was 25% greater for 1100 μm2

surfaces than for 700 µm2 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 μm2 (from _n_ = 448 segmented MCF-7 cells on unpatterned surface), the 1100 μm2 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

Ca2+ channel, _PIEZO1_19,20. The augmentation of intracellular Ca2+ increases induced by the PIEZO1 activator, YODA 1, in 1100 μm2 “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 Ca2+ signaling pathways.

Indeed, Yang et al. found that the membrane curvature can regulate the spatial distribution of Piezo1 on the plasma membrane36. As previous studies have found that micropatterning can create

localized tension at specific subcellular regions37, 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 Ca2+ signaling. _PIEZO1_ is

associated with cellular organization and upregulation of _PIEZO1_ occurs in disorganized malignant T4-2 breast cells compared with non-malignant S1 cells that grow in organized acini38.

Mechanical stress (in the form of cardiac hypertrophy) similarly results in the induction of _PIEZO1_ expression and augments electrically evoked Ca2+ transients in mouse cardiomyocytes39,

and membrane curvature regulates the plasma membrane distribution of PIEZO136. Prior to the identification of PIEZO1, Lee et al. observed that fish epithelial keratocytes with innate

fibroblastic shape demonstrate more frequent Ca2+ transients than fan-shaped cells40. Our results show that in addition to being a force sensor19,20 and regulator of cellular morphology in

CHO-α4WT cells7 and muscle stem cells41, 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 Ca2+ signaling influences EPI-MES plasticity in breast cancer cells29,42. 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 osteoblasts43, 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 patients44,45, has pro-tumorigenic roles46, and is upregulated when

triple-negative breast cancer cells transition from epithelial to a mesenchymal state47. 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 apoptosis48. One feature of EPI-MES plasticity is the loss or decrease of junctional protein

E-cadherin1. 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 PECAM149, and Piezo1-induced remodeling of junctional proteins in endothelial cells and lymphatic endothelial cells50,51. Future studies could

further evaluate the intersection of PIEZO1 and junctional proteins in the context of cancer progression pathways. Ca2+ signaling plays a critical role in normal cellular processes16,17,52

and in many disease processes4,5,53,54. Cancer cells change morphology while metastasizing to sites distant from the primary tumor and Ca2+ signaling is critical in processes important in

cancer progression, such as proliferation and cell migration54. The results presented here demonstrate a clear intersection between cellular geometry, Ca2+ signaling, the PIEZO1 force

channel, and EPI-MES plasticity in breast cancer cells. Our identification that some Ca2+ 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 Ca2+ 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% CO2. 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 [Ca2+]CYT studies, GCaMP6m-MCF-7

cells were detached using Accumax and plated on 1100 μm2 “O” micropatterned (CYTOOplate 96 RW DC-M-A, CYTOO) and 1100 μm2 “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% CO2. 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 plugin55. 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. qRT-PCR was performed using TaqMan Gene expression assays (Applied Biosystems) with TaqMan® Fast Universal PCR Master Mix (2×), no AmpErase® UNG (Life Technologies) in a StepOne

Plus Real-Time PCR System (Applied Biosystems). Gene expression changes induced by micropatterning were normalized to the endogenous control _18S_ rRNA. Unless otherwise indicated, other

target gene expression were normalized to _PUM1_. Quantitation was performed using the comparative Ct (threshold cycle) method56. Unless specified, statistical analyses were performed on

log2 transformed relative fold change (relative mRNA, -ΔΔCt). TaqMan gene expression assays used were _18S_ 4319413E, _ACTA2_ Hs00426835_g1, _AREG_ Hs00950669_m1, _CAV1_ Hs00971716_m1,

_CCND1_ Hs00765553_m1, _CLDN4_ Hs00976831_s1, _CDH1_ Hs00170423_m1, _CTGF_ Hs00170014_m1, _FOS_ Hs00170630_m1, _HIF1A_ Hs00153153_m1, _HSP90AA1_ Hs00743767_sH, _HSPB1_ Hs03044127_g1, _HSPA9_

Hs00269818_m1, _HSPD1_ Hs01036753_g1, _IGF1R_ Hs00609566_m1, _ITPR1_ Hs00181881_m1, _ITPR2_ Hs00181916_m1, _ITPR3_ Hs01573555_m1, _MKL1_ Hs01090249_g1, _MKL2_ Hs00401867_m1, _MYC_

Hs00153408_m1, _OCLN_ Hs00170162_m1, _ORAI1_ Hs03046013_m1, _PIEZO1_ Hs00207230_m1, _PKD2_ Hs00960946_m1, _PUM1_ Hs00472881_m1, _SERPINE1_ Hs01126606_m1, _SNAI1_ Hs00195591_m1, _SRF_

Hs00182371_m1, _STIM1_ Hs00162394_m1, _TRPC1_ Hs00608195_m1, _TRPM7_ Hs00292383_m1, _TRPV1_ Hs00218912_m1, _TRPV4_ Hs01099348_m1, _VIM_ Hs00185584_m1, _WWTR1_ Hs00210007_m1, and _YAP1_

Hs00902712_g1. LENTIVIRAL VECTORS, LENTIVIRUS PRODUCTION AND INFECTION _GCaMP6m_ was amplified from _pGP-CMV-GCaMP6m_ (a gift from Dr. Douglas Kim, Addgene plasmid #40754) and cloned into

_pCDH-EF1-FHC_ lentiviral vector (a gift from Dr. Richard Wood, Addgene plasmid #64874) as previously described57. CRISPR/Cas9 plasmids were constructed from lentiCRISPRv2 hygro (a gift from

Dr. Brett Stringer, Addgene plasmid #98291). Short guide sequences (sgPIEZO1#1: ACAGGAAGTAGTCCCCGGAG, sgPIEZO1#2: AGGCTGTTCCTGAAGACCCG, scrambled#1: GCACTACCAGAGCTAACTCA and scrambled#2:

CCTAAGGTTAAGTCGCCCTCG) were cloned between the BsmBI restriction sites using a protocol deposited by the Zhang Lab on Addgene58. All CRISPR/Cas9 plasmids were sequenced with Sanger

sequencing using forward primer for human U6 promoter. Lentiviral particles were produced by transfection using Lipofectamine 2000 (Invitrogen) on HEK293T cells, as previously described59.

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-468-scrambled 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 [Ca2+]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). TRANSIENT GENE SILENCING MDA-MB-468 cells were seeded into 96‐well plates (6000 cells per well) for 24 h before siRNA transfection. Cells were then incubated in 8%

v/v FBS transfection media containing DharmaFECT4 (0.1 µL per well, Dharmacon) and 100 nM of siRNA for 24 h. The following SMARTpool ON-TARGETplus siRNAs (Dharmacon) were used: Non-Targeting

Pool (D-001810-10), _MKL1_ (57591) siRNA (L-015434-00), _MKL2_ (57496) siRNA (L-019279-00), _PIEZO1_ (9780) siRNA (L-020870-03), _SRF_ (6722) siRNA (L-009800-00), _TEAD4_ (7004) siRNA

(L-019570-00), _WWTR1_ (25937) siRNA (L-016083-00), and _YAP1_ (10413) siRNA (L-012200-00). The following siGENOME SMARTpool siRNAs (Dharmacon) were used: Non-Targeting Pool #2

(D-001206-14-05) and _YAP1_ (10413) siRNA (M-012200-00). The transfection media was removed and changed to serum-reduced media for 48 h before experiments. Gene silencing was confirmed using

qRT-PCR. Statistical analysis was performed on relative mRNA (-ΔΔCt). The % mRNA remaining was calculated as relative fold change (2-ΔΔCt) × 100%. HIGH-CONTENT IMAGING OF INTRACELLULAR CA2+

FLUORESCENCE USING AUTOMATED EPIFLUORESCENCE MICROSCOPY An ImageXpress Micro automated epifluorescence microscope was used to assess [Ca2+]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 [Ca2+]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

Hoechst-tracked 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 μm2 (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 time-lapse experiment). [CA2+]CYT IMAGING USING FLUOROMETRIC IMAGING PLATE READER (FLIPR) [Ca2+]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 FLIPRTETRA (Molecular Devices) using the PBX no-wash Ca2+ Assay Kit (BD Biosciences), as previously described29 in

serum-reduced FluoroBrite DMEM or physiological salt solution (PSS; 10 mM HEPES, 5.9 mM KCl, 1.4 mM MgCl2, 1.2 mM NaH2PO4, 5 mM NaHCO3, 140 mM NaCl, 11.5 mM glucose) with 1.8 mM CaCl2

(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. FLIPRTETRA was programmed to

automatically add 50 μL to the cell-containing sample plates to obtain the final concentrations as stated in the figures and Ca2+ signaling changes were continuously assessed before,

during, and after reagent addition. PROTEIN ISOLATION AND IMMUNOBLOT Cells were lysed using protein lysis buffer containing PhosSTOP (Sigma Aldrich) and cOmplete™ Mini Protease Inhibitor

Cocktail (Sigma Aldrich). Gel electrophoresis was performed using 4-15% Mini-PROTEAN TGX Stain-Free Protein Gel (Bio-Rad) and transferred to polyvinylidene difluoride membranes (Trans-Blot

Turbo Mini 0.2 µm PVDF Transfer Packs, Bio-Rad). The membrane was blocked for 1 h in 5% w/v skim milk powder in PBS containing 0.1% v/v Tween-20 (Aldrich Chemical Company) before treating

with primary antibodies overnight at 4 °C. Membrane was then treated with horseradish peroxidase-conjugated secondary antibodies for 1 h at room temperature before being imaged using

SuperSignal West Dura Extended Duration Substrate (Thermo Scientific) and ChemiDoc Imaging System (Bio-Rad). Each band was quantified using Image Lab Software (version 5.2.1, Bio-Rad) or

ImageJ55. Densitometry was performed relative to the β-actin loading control. The antibodies used were anti-PIEZO1 antibody (1:1000 in 5% w/v milk PBST, NBP275617, Novus Biologicals),

anti-vimentin antibody (1:1,000 in 5% w/v milk PBST, V6389, Sigma), anti-E-cadherin antibody (1:1,000 in 5% w/v milk PBST, 14472, Cell Signaling Technology), anti-β-actin antibodies

(1:10,000 in 5% w/v milk PBST, A5441, Sigma-Aldrich) and horseradish peroxidase-conjugated secondary goat-anti-mouse antibodies (1:10,000 in 5% w/v milk PBST, 170-6516, Bio-Rad).

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. BREAST TUMOR CORRELATION ANALYSIS Genes used to explore the

epithelial or mesenchymal state of breast tumors were sourced from ref 23,24,25. Epithelial genes were: _CDH1, CLDN3, CLDN4, CLDN7, CRB3, DSP, EHF, EpCAM, EPN3, GRHL2, IRF6, KRT5, KRT5,

KRT8, KRT14, KRT18, KRT19, LLGL2, MARVELD3, MYO5B, OVOL1, PRSS8, RAB25, S100A14, ST14_ and _TJP3_. Mesenchymal genes were: _AP1M1, BICD2, CCDC88A, CDH2, CMTM3, EMP3, FN1, GNB4, QKI,

SERPINE1, SNAI1, SNAI2, VIM, ZEB1_ and _ZEB2_. Additionally, markers of breast cancer molecular subtypes were also included: _AR, AURKA, EGFR, ERBB2, ESR1, FOXA1, FOXM1, MKI67_, and _PGR_.

Expression values (RSEM) were obtained from the TCGA22 online data portal, cBioPortal61,62, and log2 transformed for analysis. Pearson correlation analysis was done using the rcorr function

in the corrplot package63 of R v4.1.2. Hierarchical clustering was achieved via average-linkage of the Manhattan distance; rectangles were assigned based on the results of the hierarchical

clustering, seven for all tumors in Fig. 3a and six for each of the MES/EPI groups in Supplementary Fig. 3c. To establish refined signatures for MES and EPI genes, the Z-scores of all genes

from both lists were correlated together across all breast tumors, those genes displaying a Pearson correlation coefficient > 0.5 to the average Z-score of all MES or EPI genes were used

to make the final signatures: MES (_CCDC88A, CMTM3, FN1, QKI, SNAI2, VIM, ZEB1_ and _ZEB2_) and EPI (_CLDN4, CRB3, KRT8, KRT18, PRSS8_ and _RAB25_). Finally, the MES Z-score of each tumor

was subtracted from the EPI Z-score to then give a relative EPI-MES score, where negative values indicate a tumor with a higher level of MES gene expression and positive scores a higher EPI

(Supplementary Fig. 3a). PRINCIPAL COMPONENT ANALYSIS OF TRANSIENT CALCIUM RESPONSE TO YODA 1 AGONIST The fluorescence data for each cell \(i\) are scalar time series

\({{{{{{\boldsymbol{y}}}}}}}_{i}=\{{y}_{n}\}_{n=0}^{N}\), where \({y}_{n}\) is the detrended and normalized fluorescence value at the \({n}^{{{\mbox{th}}}}\) 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 \({{{{{{\boldsymbol{y}}}}}}}_{i}\) as a single vectorial observation with \(N\) dimensions and applied principal component analysis (PCA).

Components were computed by using Scikit-learn64, 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 Statsmodels65 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-learn64. 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

\({{{{{{\boldsymbol{y}}}}}}}_{i}\) (Fig. 2j). NONLINEAR MODEL FITTING Data were fitted using nonlinear least squares optimization with a Trust Region Reflective algorithm66, as implemented

in the SciPy function _optimize.curve_fit_65. We modelled transient calcium responses as an exponential rise and decay process given by: $$f\left(t\right)=-a{e}^{-{{{{{{\rm{\tau

}}}}}}}_{{{\mbox{rise}}}}t}+b{e}^{-{{{{{{\rm{\tau }}}}}}}_{{{\mbox{decay}}}}t}+c,$$ (1) where \(f\left(t\right)\) is the detrended and normalized fluorescence time series, \(t\) is time,

\({{{{{{\rm{\tau }}}}}}}_{{{\mbox{rise}}}}\) and \(a\) are constants controlling the rate and magnitude of exponential rise, respectively, \({{{{{{\rm{\tau }}}}}}}_{{{\mbox{decay}}}}\) 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 \({{{{{{\rm{\tau }}}}}}}_{{{\mbox{decay}}}} < {{{{{{\rm{\tau

}}}}}}}_{{{\mbox{rise}}}}\). To achieve this we defined: $${{{{{{\rm{\tau }}}}}}}_{{{\mbox{rise}}}}\triangleq {{{{{{\rm{\tau }}}}}}}_{{{\mbox{decay}}}}+{{{{{{\rm{\tau }}}}}}}_{\Delta },$$

(2) where \({{{{{{\rm{\tau }}}}}}}_{\Delta }\ge 0\) and replaces \({{{{{{\rm{\tau }}}}}}}_{{{\mbox{rise}}}}\) as a model parameter, and rewrote the model as:

$$f\left(t\right)=-a{e}^{-\left({\tau }_{{{\mbox{decay}}}}+{\tau }_{\Delta }\right)t}+b{e}^{-{\tau }_{{{\mbox{decay}}}}t}+c.$$ (3) To force the model to start with zero fluorescence at the

time that the transient began (i.e., \(f\left(0\right)=0\)) we further constrained the model by: $$a=b+c,$$ (4) and rewrote the final model with four parameters as:

$$f\left(t\right)=-\left(b+c\right){e}^{-\left({{{{{{\rm{\tau }}}}}}}_{{{\mbox{decay}}}}+{{{{{{\rm{\tau }}}}}}}_{\Delta }\right)t}+b{e}^{-{{{{{{\rm{\tau }}}}}}}_{{{\mbox{decay}}}}t}+c.$$ (5)

We used nonlinear least squares optimization with a Trust Region Reflective algorithm66 as implemented in the SciPy function _curve_fit_67 to fit the model in Eq. 5. Data were fitted to

each time series \({{{{{{\boldsymbol{y}}}}}}}_{i}^{{\prime} }=\{{y}_{n}\}_{n=8}^{N}-{\bar{y}}_{{{\mbox{baseline}}}}\), where \({\bar{y}}_{{{\mbox{baseline}}}}\) is the mean of

\(\{{y}_{n}\}_{n=0}^{7}\) and \(n=8\) 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 \({{{{{{\rm{\tau }}}}}}}_{{{\mbox{decay}}}}\ge 0\), \({{{{{{\rm{\tau }}}}}}}_{\Delta }\ge

0\), and \(b\ge 0\). 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

\({{{{{{\boldsymbol{y}}}}}}}_{i}^{{\prime} }\)). Hence, \(0\le c\le \max {{{{{{\boldsymbol{y}}}}}}}_{i}^{{\prime} }\). It follows that \(a\ge b\), 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

\({{{{{{\boldsymbol{y}}}}}}}_{i}^{{\prime} }\), 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 τdecay, such that \(\frac{1}{{{{{{{\rm{\tau }}}}}}}_{{{\mbox{decay}}}}}\) ranged from \(15\) to \(1500\)

seconds, six logarithmically spaced values of τΔ from \({10}^{-6}\) to \({10}^{-1}\), and five logarithmically spaced values of \(b\) from \(0.1\) to \(1000\). We only attempted to fit the

model to the data for the \(i\) th cell if \({{{{{{\boldsymbol{y}}}}}}}_{i}^{{\prime} }\) met three specified criteria. Firstly, the median of \({{{{{{\boldsymbol{y}}}}}}}_{i}^{{\prime} }\)

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 \(\{{y}_{n}\}_{n=8}^{N}\) (i.e.,

the transient response) had to have higher fluorescence values on average than those for \(\{{y}_{n}\}_{n=0}^{7}\) (i.e., prior to the transient response), as determined by a one-sided

Wilcoxon rank-sum test with significance level \({{{{{\rm{\alpha }}}}}}=0.005\), otherwise we deemed the cell to be non-responsive. Thirdly, the maximum of

\({{{{{{\boldsymbol{y}}}}}}}_{i}^{{\prime} }\) 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 \({{{{{{\rm{\tau }}}}}}}_{{{\mbox{decay}}}}\) 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). GENOTYPING MDA-MB-468-PIEZO1 KO AND MDA-MB-468-SCRAMBLED CELLS Knockdown of _PIEZO1_ was confirmed by genotyping (Supplementary

Table 1). The genomic DNA of two passages of MDA-MB-468-_PIEZO1_ KO and MDA-MB-468-scrambled cells (passage 6 and 9) were extracted using a GeneJET Genomic DNA Purification Kit (Thermo

Scientific) and amplified using a Phusion High-Fidelity PCR Kit (Thermo Scientific) with forward primer 5’-CCACCTCCCAGGTTCAAAGG-3’ and reverse primer 5’- CAGATCCAGATCCCTGCTCTG-3’. Amplicons

were purified using agarose gel electrophoresis and the GeneJET Gel Extraction Kit (Thermo Scientific). Purified amplicons were sequenced with Sanger sequencing (Australian Genome Research

Facility, Australia). Deconvolution analysis was performed using ICE Synthego software. STATISTICS AND REPRODUCIBILITY PCA and nonlinear model fitting analyses68, were performed with Python

in Jupyter Lab using NumPy69, SciPy67, Scikit-learn64, and Statsmodels65. Unless otherwise indicated, data were visualized and analyzed using R60 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. DATA AVAILABILITY Uncropped and unedited blot images are in Supplementary Fig. 10. All data supporting

the findings of this study are available within the paper as figures and source data are available within Supplementary Data 1–5. All other data are available from the corresponding author

upon reasonable request. CODE AVAILABILITY The custom code used for PCA and nonlinear model fitting analyses is available through GitHub (https://github.com/mhmcc/calcium-PIEZO1) and

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was partly supported by the National Health and Medical Research Council of Australia (1181922 and 1196855). We thank Mr. Stéphane Guillou for assistance with the R codes used for data

analysis. We thank Dr. Blake Chapman for the manuscript writing feedback. AUTHOR INFORMATION Author notes * Choon Leng So Present address: Department of Biochemistry and Molecular Biology,

Johns Hopkins Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD, 21205, USA * Michael H. McCullough Present address: Eccles Institute of Neuroscience, John Curtin

School of Medical Research, and School of Computing, ANU College of Engineering and Computer Science, The Australian National University, Canberra, ACT, 2600, Australia * Geoffrey J.

Goodhill Present address: Departments of Developmental Biology and Neuroscience, Washington University School of Medicine, St. Louis, MO, 63110, USA AUTHORS AND AFFILIATIONS * School of

Pharmacy, The University of Queensland, Woolloongabba, QLD, 4102, Australia Choon Leng So, Mélanie Robitaille, Francisco Sadras, Sarah J. Roberts-Thomson & Gregory R. Monteith *

Queensland Brain Institute and School of Mathematics and Physics, The University of Queensland, Brisbane, QLD, 4072, Australia Michael H. McCullough & Geoffrey J. Goodhill * ACRF Cancer

Biology and Stem Cells Division, The Walter and Eliza Hall Institute of Medical Research, Melbourne, VIC, 3052, Australia Michael J. G. Milevskiy * Department of Medical Biology, The

University of Melbourne, Parkville, VIC, 2010, Australia Michael J. G. Milevskiy Authors * Choon Leng So View author publications You can also search for this author inPubMed Google Scholar

* Mélanie Robitaille View author publications You can also search for this author inPubMed Google Scholar * Francisco Sadras View author publications You can also search for this author

inPubMed Google Scholar * Michael H. McCullough View author publications You can also search for this author inPubMed Google Scholar * Michael J. G. Milevskiy View author publications You

can also search for this author inPubMed Google Scholar * Geoffrey J. Goodhill View author publications You can also search for this author inPubMed Google Scholar * Sarah J. Roberts-Thomson

View author publications You can also search for this author inPubMed Google Scholar * Gregory R. Monteith View author publications You can also search for this author inPubMed Google

Scholar CONTRIBUTIONS C.L.S., S.J.R-T, and G.R.M. conceived the study and designed the research. C.L.S. and M.R. performed the experiments. C.L.S., F.S., and M.H.M. analyzed the Ca2+

signaling data for micropatterned cells. M.J.G.M. performed bioinformatics analyses. C.L.S. performed all other data analyses. G.J.G., S.J.R-T. and G.R.M. provided supervision and assisted

with data interpretation. C.L.S. and G.R.M. wrote the manuscript with input from all authors. CORRESPONDING AUTHOR Correspondence to Gregory R. Monteith. ETHICS DECLARATIONS COMPETING

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_et al._ Cellular geometry and epithelial-mesenchymal plasticity intersect with PIEZO1 in breast cancer cells. _Commun Biol_ 7, 467 (2024). https://doi.org/10.1038/s42003-024-06163-z

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