Alicia M Salvi

Jennifer L Bays

Samantha R Mackin

René-Marc Mege

Kris A Demali
email: kris-demali@uiowa.edu

Ankyrin G Organizes Membrane Components to Promote Coupling of Cell Mechanics and Glucose Uptake

The response of cells to forces is critical for their function and occurs via rearrangement of the actin cytoskeleton 1 . Cytoskeletal remodeling is energetically costly 2, 3 , yet how cells signal for nutrient uptake remains undefined. In this study, we present evidence that force signals for increased glucose uptake by stimulating glucose transporter 1 (GLUT1). GLUT1 recruitment to and retention at sites of force transmission requires non-muscle myosin IIA-mediated contractility and ankyrin G. Ankyrin G forms a bridge between the force transducing receptors and GLUT1. This bridge is critical for allowing cells under tension to tune glucose uptake to support remodeling of the actin cytoskeleton and forming an epithelial barrier. Collectively, these data reveal an unexpected mechanism for how cells under tension take up nutrients and provide insight into how defects in glucose transport and mechanics might be linked.

Results:

).

To more rigorously test the requirement for GLUT1, GLUT1 expression was stably inhibited using two different shRNAs in the MDCKII and MCF-10A cells. A scramble sequence

(scrGLUT1) was included as a control. Using this approach, GLUT1 expression was inhibited by 43% with one of the shRNAs (shGLUT1.1) and 53% by the second shRNA (shGLUT1.2) in MDCKII cells (Figure 1c). A 40% and 56% inhibition of GLUT1 were achieved in MCF-10A cells expressing shGLUT1.1 and shGLUT1.2, respectively (Figure 1d). An examination of glucose uptake in these cells revealed that shear stimulated glucose uptake in the parental and scramble-expressing MDCKII (Figure 1e) and MCF-10A cells (Figure 1f). This effect was abrogated in the MDCKII and MCF-10A cells expressing the shRNAs against GLUT1 (Figure 1e andf). Stable inhibition of another glucose transporter, GLUT3, had no effect on force stimulated glucose uptake (Extended Data Figure 1a andb).

To ensure the increased glucose uptake was not dependent on shear, an alternative form of force was employed. For this, cells were incubated with magnetic beads coated with E-cadherin extracellular domains (or IgG as a control), and tensile forces were applied as previously described [START_REF] Guilluy | The Rho GEFs LARG and GEF-H1 regulate the mechanical response to force on integrins[END_REF][START_REF] Marjoram | Using magnets and magnetic beads to dissect signaling pathways activated by mechanical tension applied to cells[END_REF][START_REF] Barry | alpha-catenin cytomechanics--role in cadherin-dependent adhesion and mechanotransduction[END_REF][START_REF] Collins | Localized tensional forces on PECAM-1 elicit a global mechanotransduction response via the integrin-RhoA pathway[END_REF][START_REF] Kim | Dynamic visualization of alpha-catenin reveals rapid, reversible conformation switching between tension states[END_REF][START_REF] Bays | Linking E-cadherin mechanotransduction to cell metabolism through force-mediated activation of AMPK[END_REF][START_REF] Bays | Vinculin phosphorylation differentially regulates mechanotransduction at cell-cell and cell-matrix adhesions[END_REF][START_REF] Tzima | A mechanosensory complex that mediates the endothelial cell response to fluid shear stress[END_REF] . Application of tensile forces stimulated an increase in glucose uptake in the MDCKII (Figure 1g) and MCF-10A cells (Figure 1h and Extended Data Figure 1c). Importantly, glucose uptake was GLUT1-dependent (Figure 1g-h and Extended Data Figure 1c). GLUT4 was not involved (Figure 1g and Extended Data Figure 1c).

To ensure that the glucose uptake stimulated by force was not a consequence of culturing cells on stiff substrates, glucose uptake in cells plated on soft elastic collagen matrices (storage modulus (G') = 16.1 Pa, loss modulus (G'') = 2.7 Pa) was examined [START_REF] Park | Mechanical regulation of glycolysis via cytoskeleton architecture[END_REF] . A similar magnitude of glucose uptake was observed on soft substrates (Extended Data Figure 1d) and in cells plated on stiff tissue culture substrates (Figure 1a). Taken together, these data demonstrate that GLUT1 specifically increases glucose uptake in cells exposed to force.

To define how GLUT1 changes in response to force, its localization in cells exposed to force was examined. For this, MDCKII cells were subjected to shear, and GLUT1 localization was examined. In the absence of shear stress, there was some GLUT1 in the cytoplasm and some co-localization was observed between GLUT1 and β-catenin, a marker of cell-cell junctions (Figure 2a). Application of shear stress stimulated a 2.5±0.2-fold enrichment of β-catenin (Figure 2b) and a 5.5±2.0 fold increase in GLUT1 (Figure 2c) in the cell-cell junctions in parental cells (Figure 2a-c). The scramble expressing cells showed a similar effect (Extended Data Figure 1e-g). This observation agrees with published findings showing junctional GLUT1 localization in tissues [START_REF] Camps | High and polarized expression of GLUT1 glucose transporters in epithelial cells from mammary gland: acute down-regulation of GLUT1 carriers by weaning[END_REF][START_REF] Yang | PRKAA1/AMPKalpha1-driven glycolysis in endothelial cells exposed to disturbed flow protects against atherosclerosis[END_REF][START_REF] Farrell | GLUT-1 glucose transporter is present within apical and basolateral membranes of brain epithelial interfaces and in microvascular endothelia with and without tight junctions[END_REF] . Orthogonal sections revealed co-localization of GLUT1 with β-catenin in cell-cell junctions was increased when cells were exposed to force (Extended Data Figure 1h). In contrast, in cells with depressed levels of GLUT1, little GLUT1 was observed in cell-cell junctions (Figure 2a andc). To examine whether surface expression of GLUT1 was altered by shear, surface proteins were biotinylated and examined by immunoblotting. In the absence of shear, little GLUT1 appeared in the biotin labeled fraction. Shear induced a small, but significant 1.9±0.3-fold increase in surface levels of GLUT1 (Figure 2d). The enrichment of GLUT1 in cell-cell junctions was not the consequence of an increase in GLUT1 expression (Extended Data Figure 1i). Taken together with the immunofluorescence data, these experiments reveal that there is a small increase in total surface levels of GLUT1 in response to shear, but the amount of GLUT1 in the cell-cell junctions increases dramatically.

To determine if E-cadherin was required for GLUT1 enrichment in cell-cell junctions, we examined GLUT1 localization in published cell lines lacking E-cadherin (shEcad) [START_REF] Capaldo | Depletion of E-cadherin disrupts establishment but not maintenance of cell junctions in Madin-Darby canine kidney epithelial cells[END_REF] . Consistent with published findings, cells formed β-catenin containing cell-cell junctions in the absence of shear stress (Figure 2a-b) [START_REF] Capaldo | Depletion of E-cadherin disrupts establishment but not maintenance of cell junctions in Madin-Darby canine kidney epithelial cells[END_REF] . These junctions also contained GLUT1 (Figure 2a), and the amount of GLUT1 in cell-cell junctions did not statistically change when force was applied (Figure 2a and2c). Thus, E-cadherin is required for force stimulated enrichment of GLUT1 in cell-cell junctions.

To test if GLUT1 co-localization to cell-cell junctions was limited to cells in 2D cultures, MDCKII cells were embedded in a 3D extracellular matrix of Matrigel. Consistent with published reports, MDCKII cells formed a spherical cyst with a hollow lumen surrounded by a monolayer of polarized cells that resemble that of epithelia in vivo (Figure 2e) [START_REF] O'brien | Building epithelial architecture: insights from three-dimensional culture models[END_REF][START_REF] Yu | Formation of cysts by alveolar type II cells in three-dimensional culture reveals a novel mechanism for epithelial morphogenesis[END_REF][START_REF] Zegers | Epithelial polarity and tubulogenesis in vitro[END_REF] . Under these conditions, strong GLUT1 co-localization with E-cadherin was observed in the cells on the cyst exterior and with the basolateral surface of the cells on the cyst interior (Figure 2e). Interestingly, strong GLUT1 staining was also observed on the apical surface of the cyst lumen. Thus, GLUT1 co-localization with E-cadherin occurs in 3D (Figure 2e).

The requirement for E-cadherin for GLUT1 enrichment in cell-cell junctions (Figure 2a) suggested that GLUT1 might be integrating into the cadherin adhesion complex. To test this possibility directly, E-cadherin was immunoprecipitated in the presence or absence of shear, and GLUT1 association was examined by immunoblotting. In the absence of shear, some GLUT1 co-immunoprecipitated with E-cadherin in the control cells (Figure 2f). The amount of GLUT1 that co-immunoprecipitated increased significantly upon exposure to shear. In contrast, in the cells with depressed levels of GLUT1, there was little GLUT1 bound to E cadherin and the amount did not change when shear was applied (Figure 2f). To determine if force transmission was required, the cells were pre-incubated with blebbistatin. Under these conditions, GLUT1 co-immunoprecipitation with E-cadherin was blocked (Figure 2f). Taken together, these data suggest that GLUT1 is recruited to and integrates in cadherin-containing cell-cell junctions in response to shear.

Glucose enters cells in response to force and is metabolized into ATP, which in turn provides the energy necessary to support the growth of the cadherin adhesion complex and reinforcement of the actin cytoskeleton in order for the cell to resist force [START_REF] Bays | Linking E-cadherin mechanotransduction to cell metabolism through force-mediated activation of AMPK[END_REF] . This process is known as cell stiffening. To begin to determine the role of GLUT1 in this process, the time course of reinforcement was examined. For this, MDCKII cells were subjected to shear stress for 2 hours, and the cells were stained with antibodies against E-cadherin or phalloidin. Both E-cadherin (Extended Data Figure 2a-b) and F-actin (Extended Data Figure 2a andc-f) were enriched in cell-cell junctions immediately after application of shear (0 minutes) and 30 minutes of recovery from shear, suggesting that reinforcement was occurring. F-actin enrichment in cell-cell junctions was significantly decreased 1 hour after shear (Extended Data Figure 2a and2c). In contrast, E-cadherin enrichment persisted for 4 hours (Extended Data Figure 2a andb). By 6 hours of recovery, both E-cadherin and F-actin had returned to prestress levels (Extended Data Figure 2a-c). Based on these observations, actin and E-cadherin were examined immediately after application of shear in all subsequent studies.

To investigate whether GLUT1 is required for cell stiffening, the effect that loss of GLUT1 has E-cadherin and actin reinforcement was examined. Shear stress increased both E-cadherin (Figure 3 a, Extended Data Figure 3a-b) and F-actin (Figure 3a-b, Extended Data Figure 3a) enrichment in cell-cell junctions by 3-fold in parental cells or in cells expressing a scrambled shRNA (Extended Data 2d-f) [START_REF] Bays | Linking E-cadherin mechanotransduction to cell metabolism through force-mediated activation of AMPK[END_REF] . The magnitude of the reinforcement was independent of plating the cells on stiff (Figure 3a) or soft matrices (Extended Data Figure 3c-e). Furthermore, inhibition of GLUT1 prevented E-cadherin and F-actin enriched in cell-cell junctions (Figure 3a-b, Extended Data 3a-b).

To ensure the that inhibition of GLUT1 was specific for the actin cytoskeletal rearrangements and not simply altering ATP dependent processes, the activity of two protein kinases involved in cell stiffening were examined [START_REF] Bays | Linking E-cadherin mechanotransduction to cell metabolism through force-mediated activation of AMPK[END_REF][START_REF] Bays | Vinculin phosphorylation differentially regulates mechanotransduction at cell-cell and cell-matrix adhesions[END_REF] . Both AMPK (Extended Data Figure 3f) and Abelson tyrosine kinase (Abl) (Extended Data Figure 3g) were unaltered by GLUT1 inhibition.

Finally, to determine if reinforcement required glucose to be metabolized, cells were preincubated with 3PO, a phosphofructokinase-2 inhibitor. 3PO blocked force-stimulated enrichment of F-actin (Figure 3c-d) and E-cadherin (Figure 3c, Extended Data Figure 3h). This observation is further supported by our published data demonstrating that incubation of cells in low glucose containing media or inhibition of ATP synthesis prevents cell stiffening in response to shear stress [START_REF] Bays | Linking E-cadherin mechanotransduction to cell metabolism through force-mediated activation of AMPK[END_REF] . Taken together, these data demonstrate that GLUT1 recruitment to cell-cell junctions allows for glucose uptake-an event that is essential for reinforcement of the cytoskeleton.

The images in Figure 3 a suggested that the actomyosin structure induced by force is very similar in appearance to the junctional localized non-muscle myosin IIA stress fibers previously described by the Mege group [START_REF] Heuze | Myosin II isoforms play distinct roles in adherens junction biogenesis[END_REF] . To determine if non-muscle myosin IIA is required for reinforcement of the actin cytoskeleton in response to force, the cells employed in the Mege studies [START_REF] Heuze | Myosin II isoforms play distinct roles in adherens junction biogenesis[END_REF] were obtained, and their ability to reinforce the actin cytoskeleton in response to shear was examined. These MDCK cells express GFP-E-cadherin with non muscle myosin IIA (shNMIIA) or IIB (shNMIIB) inhibited. A control cell line (shCtrl) was also examined. When shear was applied to the control cells or cells lacking non muscle myosin IIB, E-cadherin (Figure 3e, Extended Data figure 3i) and F-actin (Figure 3e-f) enrichment in cell-cell junctions were increased. In contrast, in the cells with non muscle myosin IIA inhibited, neither E-cadherin nor F-actin was enriched (Figure 3e-f and Extended Data Figure 3i). Thus, reinforcement requires non-muscle myosin IIA.

Given the roles of GLUT1 (Figure 3a) and non-muscle myosin IIA (Figure 3e-f) in reinforcement of the actin cytoskeleton, we examined their interdependency. For this, force stimulated glucose uptake (Figure 3g) and GLUT1 localization to cell-cell junctions (Figures 3h) were monitored in the cells lacking non-muscle myosin II isoforms. The control and shNMIIB cell lines took up glucose in response to shear (Figure 3g). In contrast, glucose uptake was not increased in shNMIIA cells (Figure 3g). Similarly, in the absence of shear, there was little GLUT1 co-localization with E-cadherin (Figure 3h-j). Upon exposure to shear, robust enrichment of GLUT1 (Figure 3h-i) and E-cadherin (Figure 3h,j) were observed in the control cells and the cells lacking non-muscle myosin IIB. There was not a significant increase in enrichment of E-cadherin or GLUT1 in the cells with suppressed levels of non-muscle myosin IIA (Figure 3h-j). Thus, GLUT1 recruitment, glucose uptake, and reinforcement of the actin cytoskeleton are non-muscle myosin IIA-dependent.

Figure 2 indicates that GLUT1 is retained in cell-cell junctions in response to shear. How might GLUT1 be retained at the plasma membrane in response to tension? Ankyrin G emerged as a good candidate [START_REF] Bennett | Membrane domains based on ankyrin and spectrin associated with cell-cell interactions[END_REF][START_REF] Nelson | Identification of a membrane-cytoskeletal complex containing the cell adhesion molecule uvomorulin (E-cadherin), ankyrin, and fodrin in Madin-Darby canine kidney epithelial cells[END_REF] because it binds E-cadherin [START_REF] Kizhatil | Ankyrin-G is a molecular partner of E-cadherin in epithelial cells and early embryos[END_REF][START_REF] Jenkins | E-cadherin polarity is determined by a multifunction motif mediating lateral membrane retention through ankyrin-G and apical-lateral transcytosis through clathrin[END_REF][START_REF] Cadwell | Ankyrin-G Inhibits Endocytosis of Cadherin Dimers[END_REF] , and it and its family members mediate the retention of many surface proteins at the plasma membrane via its linkages to the spectrin-actin cytoskeleton [START_REF] Kizhatil | Ankyrin-G is a molecular partner of E-cadherin in epithelial cells and early embryos[END_REF][START_REF] Yang | Ankyrin-G mediates targeting of both Na(+) and KATP channels to the rat cardiac intercalated disc[END_REF][START_REF] Zhou | AnkyrinG is required for clustering of voltage-gated Na channels at axon initial segments and for normal action potential firing[END_REF][START_REF] Lowe | Voltage-gated Nav channel targeting in the heart requires an ankyrin-G dependent cellular pathway[END_REF][START_REF]Baines AJThe spectrin-ankyrin-4.1-adducin membrane skeleton: adapting eukaryotic cells to the demands of animal life[END_REF][START_REF] Bennett | The molecular basis for membrane -cytoskeleton association in human erythrocytes[END_REF][START_REF] Drenckhahn | Colocalization of band 3 with ankyrin and spectrin at the basal membrane of intercalated cells in the rat kidney[END_REF][START_REF] Drenckhahn | Polarized distribution of Mr 210,000 and 190,000 analogs of erythrocyte ankyrin along the plasma membrane of transporting epithelia, neurons and photoreceptors[END_REF] . To test whether ankyrin G was required for GLUT1 retention at cell-cell contacts, its sensitivity to force was examined. For this, epithelial cells were exposed to shear and localization of ankyrin G to cell-cell junctions was examined. In the absence of shear, low levels of ankyrin G were observed (Figure 4a and 4b) [START_REF] Jenkins | E-cadherin polarity is determined by a multifunction motif mediating lateral membrane retention through ankyrin-G and apical-lateral transcytosis through clathrin[END_REF][START_REF] Cadwell | Ankyrin-G Inhibits Endocytosis of Cadherin Dimers[END_REF] Upon application of shear, there was a 16±0.2 fold enrichment of β-catenin and 2.8±0.4-fold enrichment in ankyrin staining in cell-cell junctions (Figure 4a and4b. This enrichment required E-cadherin expression (Figure 4a-b). In further support of a sensitivity to force, co-immunoprecipitation of ankyrin G with E-cadherin increased in response to shear (Figure 4c). Thus, ankyrin G recruitment to E-cadherin containing cell-cell junctions requires force.

To test if ankyrin G was required for GLUT1 recruitment to cell-cell contacts, cells with ankyrin G silenced (shANKG) or expressing a scrambled sequence (scrANKG) were generated. Using this approach, a 50% reduction in ankyrin G levels was achieved (Figure 4d). Co-localization of GLUT1 with β-catenin in cell-cell junctions was examined using immunofluorescence. In these studies, GLUT1 was observed in cell-cell junctions in the absence of shear (Figure 4e andf). Application of shear induced a robust recruitment of GLUT1 to cell-cell contacts, and this effect was completely blocked in cells lacking ankyrin G (Figure 4e andf).

To determine if ankyrin G was required for GLUT1 functions identified in Figures 1 and2, we examined if glucose uptake and cell stiffening required ankyrin G. Control scrANKG-expressing cells exhibited an increase in glucose uptake (Figure 4g), whereas shear stimulated glucose uptake was blocked in the shANKG expressing cells (Figure 4g). Additionally, the control cells expressing the scramble sequence reinforced their actin cytoskeletons and cell-cell junctions in response to shear, whereas the cells lacking ankyrin G did not (Extended Data Figure 4a-c). These observations suggest that ankyrin G is sensitive to force and is required for cells to recruit GLUT1 to cell-cell junctions and shear stress stimulated glucose uptake.

To understand how ankyrin G recruits GLUT1 to cell-cell junctions, co-immunoprecipitation of GLUT1 and ankyrin G with E-cadherin was examined. In control cells expressing a scramble sequence (scrANKG), both ankyrin G and GLUT1 co-precipitated with E-cadherin. Upon exposure to shear stress, the amount of ankyrin G and GLUT1 co precipitating with E-cadherin increased significantly (Figure 4h). This finding is not simply the result of an increase in ankyrin G expression as the amount of ankyrin G does not change in either the soluble or insoluble fraction in response to shear (Extended Data Figure 4d). Strikingly, inhibition of ankyrin G completely blocked the force stimulated co-precipitation of GLUT1 with E-cadherin (Figure 4h). This data suggests a force-induced complex of E-cadherin, ankyrin G, and GLUT1 forms. How ankyrin G binds GLUT1 is not completely understood. Both proteins bind to the spectrin cytoskeleton [START_REF]Baines AJThe spectrin-ankyrin-4.1-adducin membrane skeleton: adapting eukaryotic cells to the demands of animal life[END_REF][START_REF] Khan | Dematin and adducin provide a novel link between the spectrin cytoskeleton and human erythrocyte membrane by directly interacting with glucose transporter-1[END_REF][START_REF] Jiang | Interaction of glucose transporter 1 with anion exchanger 1 in vitro[END_REF] and spectrin was enriched in cell-cell junctions in response to force (Extended Data Figure 4e). Taken together these data suggest that ankyrin G tethers GLUT1 to the cadherin adhesion complex.

Global inhibition of ankyrin G could have many effects [START_REF] Kizhatil | Ankyrin-G is a molecular partner of E-cadherin in epithelial cells and early embryos[END_REF][START_REF] Jenkins | E-cadherin polarity is determined by a multifunction motif mediating lateral membrane retention through ankyrin-G and apical-lateral transcytosis through clathrin[END_REF] . To specifically probe its function, mutant E-cadherins unable to bind ankyrin G were generated. For this, we employed a previously described E-cadherin PolyA mutant protein in which seven residues between amino acids 738-758 of human E-cadherin juxtamembrane region were mutated to alanine residues to prevent ankyrin G binding [START_REF] Jenkins | E-cadherin polarity is determined by a multifunction motif mediating lateral membrane retention through ankyrin-G and apical-lateral transcytosis through clathrin[END_REF] . The PolyA E-cadherin mutant or a wildtype (WT) control E-cadherin protein were expressed to similar extents in cells lacking E cadherin (Extended Data Figure 5a). The PolyA mutation prevented co-immunoprecipitation of E-cadherin and ankyrin G (Extended Data Figure 5b andc). Thus, the PolyA mutant is behaving as previously reported [START_REF] Jenkins | E-cadherin polarity is determined by a multifunction motif mediating lateral membrane retention through ankyrin-G and apical-lateral transcytosis through clathrin[END_REF] To identify the effects that this mutant has on GLUT1, the E-cadherin proteins were immunoprecipitated and co-precipitation of GLUT1 was monitored using immunoblotting. In contrast to the wildtype protein, which bound GLUT1 when shear was applied, the PolyA mutant did not bind GLUT1 (Figure 5a). An examination of these cells using immunofluorescence revealed similar findings (Figure 5b). Both the wildtype and PolyA mutant localized to cell-cell junctions to a similar extent in the absence of shear. When shear was applied, the levels of GFP-E-cadherin were enriched while the PolyA mutant remained at pre-shear levels. GLUT1 was highly enriched and co-localized with wildtype, GFP-E-cadherin in cell-cell junctions in response to shear, whereas GLUT1 did not localize to cell-cell junctions in cells expressing the PolyA mutant (Figure 5b-c). Taken together, these data suggest that ankyrin G binding to E-cadherin is required for GLUT1 enrichment at cell-cell junctions in response to force.

Estimates suggest that 50% of ATP within a cell is used to support the actin cytoskeleton [START_REF] Bernstein | Actin-ATP hydrolysis is a major energy drain for neurons[END_REF][START_REF] Daniel | Nucleotide exchange between cytosolic ATP and F-actin-bound ADP may be a major energy-utilizing process in unstimulated platelets[END_REF] . During highly dynamic actin cytoskeletal events, cells increase their energy production [START_REF] Zhang | Energetic regulation of coordinated leader-follower dynamics during collective invasion of breast cancer cells[END_REF][START_REF] Decamp | Epithelial layer unjamming shifts energy metabolism toward glycolysis[END_REF][START_REF] Zanotelli | Energetic costs regulated by cell mechanics and confinement are predictive of migration path during decision-making[END_REF] . To determine if ankyrin G is also required for GLUT1 function, the ability of the PolyA mutant to support force stimulated glucose uptake and ATP production were examined. Cells expressing wildtype E-cadherin protein showed a 2.8-fold increase in glucose uptake and a 1.8-fold increase in the amount of relative intracellular ATP when exposed to shear stress (Figure 5d ande). In contrast, cells expressing the PolyA mutant E-cadherin were defective in taking up glucose and elevating intracellular ATP levels in response to shear (Figure 5d ande). Similarly, to determine if ankyrin G binding to E-cadherin is required for reinforcement of the actin cytoskeleton in response to application of shear stress, F-actin enrichment was monitored using immunofluorescence. Cells expressing the wildtype E-cadherin exhibit robust enrichment of actin cytoskeleton in response to shear (Figure 5f-h). In contrast, cells expressing the PolyA mutant E-cadherin had the same amount of F-actin in their cell-cell junctions in the presence and absence of force. Similarly, spectrin was not reinforced in response to shear in cells expressing the PolyA mutant (Extended Data 5d-e). Taken together, these data indicate a requirement for ankyrin G binding to E-cadherin for reinforcement of the actin and spectrin cytoskeleton (Figure 5f-h).

To assess the physiological significance of ankyrin G recruitment of GLUT1, the formation of an epithelial barrier was monitored in MDCKII cells after a calcium switch-this is an event highly dependent upon increased contractility [START_REF] Bays | Linking E-cadherin mechanotransduction to cell metabolism through force-mediated activation of AMPK[END_REF][START_REF] Kannan | Synaptopodin couples epithelial contractility to alpha-actinin-4-dependent junction maturation[END_REF][START_REF] Maiers | ZO-1 recruitment to alpha-catenin--a novel mechanism for coupling the assembly of tight junctions to adherens junctions[END_REF][START_REF] Tang | Paracellular ion channel at the tight junction[END_REF] . After re-addition of calcium, cells expressing the wildtype E-cadherin gradually formed an epithelial barrier over the first ten hours (Figure 5i) [START_REF] Bays | Linking E-cadherin mechanotransduction to cell metabolism through force-mediated activation of AMPK[END_REF][START_REF] Kannan | Synaptopodin couples epithelial contractility to alpha-actinin-4-dependent junction maturation[END_REF][START_REF] Tang | Paracellular ion channel at the tight junction[END_REF] . By twenty-four hours, the barrier had remodeled, and a strong barrier with a resistance value similar to what has been reported was achieved [START_REF] Bays | Linking E-cadherin mechanotransduction to cell metabolism through force-mediated activation of AMPK[END_REF][START_REF] Kannan | Synaptopodin couples epithelial contractility to alpha-actinin-4-dependent junction maturation[END_REF][START_REF] Tang | Paracellular ion channel at the tight junction[END_REF] . In contrast, both the initial formation and the final resistance of the epithelial barrier were significantly impaired in the cells expressing the PolyA E-cadherin (Figure 5i). Taken together, these data indicate GLUT1 recruitment to cell-cell junctions is required for efficient formation of an epithelial barrier.

The data presented herein establishes a mechanism for how force stimulates the uptake of metabolites from the environment in order to fuel the cell's efforts to resist the strain. Our data identifies GLUT1 as critical for the uptake of glucose in response to force and demonstrates a requirement for ankyrin G to retain GLUT1 at sites of E-cadherin force transmission. It is important to note that since the PolyA mutant did not localize to cell-cell junctions in response to shear as well as the wildtype protein, there is the possibility that another E-cadherin function is required. Nonetheless, as a result, glucose can be taken up and converted to ATP that is used to fuel non-muscle myosin IIA-dependent reinforcement of the actin cytoskeleton. This information provides a key missing link in understanding how mechanotransduction derives fuel sources. Importantly, this new insight could explain the defects that might arise in disease and highlight improvements that can be made to prevent metabolic disturbances.

Material/Methods:

Cells Lines MCF-10A human breast epithelial cells and MDCKII canine kidney epithelial cells were purchased from ATCC and were maintained as previously described [START_REF] Bays | Linking E-cadherin mechanotransduction to cell metabolism through force-mediated activation of AMPK[END_REF][START_REF] Bays | Vinculin phosphorylation differentially regulates mechanotransduction at cell-cell and cell-matrix adhesions[END_REF][START_REF] Maiers | ZO-1 recruitment to alpha-catenin--a novel mechanism for coupling the assembly of tight junctions to adherens junctions[END_REF] . All cell lines and their derivatives were used for no more than 12 passages and periodically checked for mycoplasma contamination. shGLUT1-1, shGLUT1-2, scrGLUT1, shGLUT3-1, shGLUT3-2, scrGLUT3 and scrANKG expressing cells were selected and maintained in puromycin (2μg/mL). shANKG cells were selected and cultured in G418. shEcad/WT and shEcad/PolyA were selected and maintained in blasticidin (3μg/mL) [START_REF] Jenkins | E-cadherin polarity is determined by a multifunction motif mediating lateral membrane retention through ankyrin-G and apical-lateral transcytosis through clathrin[END_REF] . shCtrl, shNMIIA and shNMIIB expressing cells were maintained in media containing geneticin (5 μg/mL) and puromycin (2.5 μg/mL). The 293GPG and 293FT (Invitrogen) cells are virus-producing cell lines that are a derivative of 293T cells. The 293 GPG were maintained as described previously [START_REF] Barry | alpha-catenin cytomechanics--role in cadherin-dependent adhesion and mechanotransduction[END_REF] and the 293FT were maintained in DMEM supplemented with 10% heat inactivated FBS, 0.1mM MEM Non-essential Amino Acids (NEAA), 6mM L-glutamine, 1mM MEM Sodium Pyruvate, 1% Pen-Strep. MDCKII cell lines expressing shEcad were previously described [START_REF] Capaldo | Depletion of E-cadherin disrupts establishment but not maintenance of cell junctions in Madin-Darby canine kidney epithelial cells[END_REF] .

Constructs

To inhibit expression of proteins using RNA interference, two distinct sequences targeting the exon portion of each gene of interest were individually inserted into pSUPER-retro-puro (Oligoengine), the sequences targeted were, shGLUT1.1: 5'-GATCCCCCACTGGAGTCATCAATGCCTTCAAGAGAGGCATTGATGACTCCAGTGT TTTTA-3'; shGLUT1.2: 5'-GATCCCCTGCTGATGATGAACCTGCTTTCAAGAGAAGCAGGUUCAUCAUCAGCAT TTTTA-3'; scrGLUT1: 5'-GATCCCCTTCTCCGAACGTGTCACGTTTCAAGAGAACGTGACACGTTCGGAGAAT TTTTA-3'; shGLUT3.1: 5' -GATCCCCCTTGGTCTTTGTAGCCTTCTTTTCAAGAGAAAGAAGGCTACAAAGACC AAGTTTTTA-3; shGLUT3.2: 5'-GATCCCCAGTAGCTAAGTCGGTTGAAATTTCAAGAGAATTTCAACCGACTTAGCTA CTTTTTTA-3 ' ; scrGLUT3.: 5'-GATCCCCGGCTTATTGTTCGCTTCTTCTTTCAAGAGAAGAAGAAGCGAACAATAA GCCTTTTTA-3'; scrANKG: 5'-GATCCCCAGCGTCGACGTTATCATAATCTTCAAGAGAGATTATGATAACGTCGACG CTTTTTTC-3'. cDNAs containing GFP-tagged wild-type E-cadherin or Poly A E-cadherin containing 7 amino acid changes in the ankyrin G binding site were previously described and the generous gift of Dr. Paul Jenkins [START_REF] Jenkins | E-cadherin polarity is determined by a multifunction motif mediating lateral membrane retention through ankyrin-G and apical-lateral transcytosis through clathrin[END_REF] . Specifically, the amino acid sequence corresponding with human CDH1 (738-758) was mutated from: KEPLLPPEDDTRDNVYYYDEE to AEPLLPPAAATRANVYYADEA.

Virus Production and infection

Retroviruses were produced as previously described [START_REF] Bays | Vinculin phosphorylation differentially regulates mechanotransduction at cell-cell and cell-matrix adhesions[END_REF] . To produce lentivirus, 293FT cells were transfected and viruses were produced according to the manufacturer's instructions (Invitrogen, R70007). Prior to infection, MCF-10A or MDCKII cells were grown to 75% confluency. On day of infection, cells were washed 2x with serum-free DMEM, incubated in OPTIMEM (GibcoBRL) plus 4 μg/mL of polybrene, and concentrated viral particles were added to the cultures for 4 hrs at 37 °C. Growth media was then added to the cultures, and 12-16 h later, the cells were placed in growth media plus drug.

Magnetic Bead Assay

The application of tensile force to E-cadherin using magnetic beads was performed as previously described [START_REF] Barry | alpha-catenin cytomechanics--role in cadherin-dependent adhesion and mechanotransduction[END_REF] . Briefly, for E-cadherin and IgG beads, 1.5 μg of paramagnetic Dynabeads Protein A (Invitrogen) were coated with 10μg of E-cadherin or IgG for 12 hours at 4 °C7, 11 . The beads were washed in phosphate buffered saline (PBS) and blocked in 5% bovine serum albumin (Sigma) in PBS. Coated beads were incubated with 90% confluent cells for 1 hour at 37 °C. Tensile force was applied for 10 minutes, by placing the cells 0.6 cm from a permanent ceramic magnet at room temperature. The cells were transferred to ice, washed, and lysed.

Orbital Shear Stress

Dishes of 90-95% confluent cells with growth media were rotated on a New Brunswick orbital shaker at 200 rpm for 2 h at 37 °C. The cells were transferred to ice and immediately lysed or fixed in paraformaldehyde.

Inhibitors and Functioning Blocking Antibodies

Inhibitors were incubated with the cells immediately before shear and during the experiment. For tensile force studies, inhibitors were pre-incubated with cells for 2 h prior to application of tensile force. GLUT1 was inhibited using 30 WZB117 (Tocris Biosciences). Myosin II was inhibited using 50μM blebbistatin (Sigma). E-cadherin was inhibited using a function blocking antibody, HECD-1 (Invitrogen) at 200 μg/mL, and PFK2 was inhibited by at 50 μM of 3PO (Millipore)..

Surface Biotinylation

Surface proteins were labelled with EZ-Link™ NHS-LC-Biotin (Thermo Scientific; 21335) as previously described [START_REF] Peng | Vinculin regulates cell-surface E-cadherin expression by binding to beta-catenin[END_REF] . Dynabeads™ M-280 Streptavidin (Invitrogen; 11205D) were used to recover biotinylated proteins. Surface and total cellular levels of GLUT1 were examined by immunoblotting.

3D Culture of Cysts

Matrigel cultures were generated by placing Matrigel (BD; 356231) into the wells of a 8-well chamber slide (LabTek II; 154534). The chamber slide was incubated at room temperature for 15 min. 2,500 cells in a 2% Matrigel and 98% growth medium solution were seeded into each well. The chamber slide was incubated at room temperature for 30 min and then growth media was added. Cells were incubated for 8-10 days or until acini formed. Growth medium was changed every 3 days [START_REF] O'brien | Building epithelial architecture: insights from three-dimensional culture models[END_REF] .

Stiff/Soft Substrate Culture

Stiff substrates were generated by coating glass cover slips with bovine collagen type I (PureCol, 2.5 mg/mL, Advanced BioMatrix). Collagen was diluted to 50 μg/mL in PBS and incubated on cover slips for 1 h at 37 °C. 5 ×10 5 were plated [START_REF] Park | Mechanical regulation of glycolysis via cytoskeleton architecture[END_REF] . Soft substrates were generated by polymerizing a bovine collagen type I gel (PureCol, 2.5 mg/mL; Advanced BioMatrix) on glass cover slips. A 2 mg/mL collagen gel solution was made by mixing 8 parts of chilled bovine collagen type I (PureCol, 2.5 mg/mL, Advanced BioMatrix) with 1 part of 10x PBS and 1 part of NaOH (0.1 N). The mixture was added to the cover slips and incubated for 1 h at 37 °C. Cells were then seeded at 5 ×10 5 cells in 500 μL of culture medium on top of the gels [START_REF] Park | Mechanical regulation of glycolysis via cytoskeleton architecture[END_REF] . For both soft and stiff matrices, cell culture growth medium was changed every two days and cells were grown to confluence.

Glucose Uptake

Glucose uptake was measured using a kit from Cayman Chemicals (600470) and used as previously described [START_REF] Bays | Linking E-cadherin mechanotransduction to cell metabolism through force-mediated activation of AMPK[END_REF] . For all lysates, 100 μL were loaded in triplicate onto a 96-well plate and a fluorescence reading of 485/535 was taken (Biotek Synergy Neo model NEOALHPA B, Gen 5 software). The concentration of glucose was determined using a standard curve and results are reported as micrograms per milliliter per 10 5 cells.

ATP Assays

Intracellular ATP was measured using a Fluorometric ATP assay kit from Abcam (ab83355) and used as previously described [START_REF] Bays | Linking E-cadherin mechanotransduction to cell metabolism through force-mediated activation of AMPK[END_REF] . 5 μL of de-proteinated sample was diluted with 45 μL of ATP assay buffer and added to ATP reaction mix in 96-well plates and fluorescence reading at 535/587nm was made.

Immunoprecipitation and immunoblotting

For immunoprecipitation of E-cadherin or ankyrin G, cells were lysed with EB lysis buffer (1 mM Tris-HCl, pH 7.6, 50 mM NaCl, 1% Triton X-100, 5 mM EDTA, 50 mM NaF, 20 μg/mL aprotinin, 2 mM Na 3 VO 4 , and 1 mM PMSF). The lysates were centrifuged at 12,000 xg and the supernatant was collected. A 1:100 dilution of E-cadherin antibodies, HECD1 (Invitrogen) or rr1 (DSHB), or an ankyrin G antibody (h-4; Santa Cruz,) was incubated with the supernatant. The complexes were recovered using protein G beads, washed 3 times, and resuspended in 2x sample buffer (200 mM Tris, pH 6.8, 20% glycerol, 5% BME (B-mercaptoethanol), 4% SDS, 15 mg Bromophenol Blue, brought up to 50 mLs with ddH 2 0) and resolved using SDS-PAGE, and transferred to PVDF (Immobilon). Samples blotted for GLUT1 were not boiled rather they were gently heated at 56 °C. The membranes were blocked in 5% BSA for pCRKL, pAMPK, AMPK, 1% BSA for GLUT1, GLUT3, GLUT4, ankyrin G), or 5% milk for E-cadherin, Vinculin, CRKL, B-actin. The membranes were incubated with the following antibodies O/N at 4 °C. Primary antibodies used for immunoblotting were polyclonal GLUT1 at 1:500 (abcam;15309), monoclonal E-cadherin at 1:1000 (BD; 610181), monoclonal vinculin at 1:1000 (Sigma; hVin1), monoclonal GLUT3 at 1:500 (Santa Cruz; 74399), monoclonal ankyrin G at 1:500 (Santa Cruz; H-4), at 1:1000, polyclonal phospho-CRKL at 1:1000 (Cell Signaling; 3181), monoclonal CRKL at 1:250 (Santa Cruz; C-20), polyclonal pAMPK at 1:1000 (Cell Signaling; 2535), polyclonal AMPK (Cell Signaling, 2532), and β-actin at 1:1000 (Cell Signaling, 3700). The membranes were washed 3x in TBST and incubated with 1:1000 concentration of anti-mouse HRP (Jackson Labs) or anti-rabbit HRP (Jackson Labs) The membranes were washed 3x in TBST and visualized by using chemiluminescence detection reagents (Pierce), and the signal was detected on a GE Image Quant LAS 400 Imager or an Odyssey Fc Imager (Li-Cor Biosciences). For analysis, the integrated density of each band was corrected for background. Ratios of phosphorylated compared to total proteins were quantified by stripping and re-probing membranes. Quantification of each assay represents a minimum of three experiments ± SEM. Quantification was done using either Image J (Version 2.0.1/1.53c) or Image studio lite (Version 5.2.5). Statistical analysis was conducted using two-tailed, unpaired Student's t-tests.

Immunofluorescence of 2D Cell Culture

Coverslips were coated with human fibronectin (10 μg/mL), and cells were plated and grown to confluency. Cells were fixed with 4% paraformaldehyde, permeabilized with 0.5% triton and washed with either universal buffer (UB; 150 mM NaCl, 50 mM Tris, pH 7.6, and 0.01% NaN3) or PBS. Cells were blocked with either 10% bovine serum albumin (Sigma) in UB or 5% BSA and 1% goat serum in PBS depending on primary antibody. Antibodies used: GLUT1 monoclonal antibody at 1:200 (Abcam), polyclonal β-catenin antibody at 1:500 (Sigma), monoclonal E-cadherin antibodies, HECD1 at 1:200 (Invitrogen) and rr1 at 1:50 (DSHB), monoclonal ankyrin G antibody at 1:200 (Santa Cruz), monoclonal β-spectrin antibody at 1:300 (BD Transduction, 612563), DAPI Solution at 1:5,000 (BD Pharmigen, 564907) and F-actin was stained using phalloidin conjugated with alexa-594 (1:300). Secondary antibodies used were anti-mouse alexa-488, anti-rabbit alexa-594, anti mouse alexa-594 or anti-mouse alexa-647, 1:400 in blocking solution.

Immunofluorescence of 3D Cell Culture

Matrigel embedded cells were fixed in 4% PFA in 1x PBS permeabilized using 0.2% Triton X-100 in PBS, and washed 3x with PBS +100 mM glycine. Cells were blocked for 90 minutes at room temperature in blocking buffer (7.7 mM NaN 3 , 0.1 % BSA, 0.2 % Triton X-100, 0.05% Tween-20, 10% goat serum in 1x PBS). Primary antibodies were diluted in the blocking solution incubated with the cells O/N at 4°C. Cells were washed 3x with washing buffer (blocking buffer minus the goat serum). Secondary antibodies were diluted in the blocking solution and incubated with the cells for 1 hours at RT. Cells were then washed 2x with washing buffer (blocking buffer minus goat serum), 1x with PBS + DAPI , and then 1x with PBS. E-cadherin was stained using a monoclonal antibody, rr1 at 1:50 (DSHB). GLUT1 was stained using a polyclonal antibody at 1:300 (Abcam, 15309). Secondary antibodies used were anti-mouse alexa-647 (Invitrogen, A-21235), and anti-rabbit alexa-488 (Invitrogen, A-11008) in blocking solution.

Quantification of Immunofluorescence Images

Fluorescence images were captured at room temperature with a confocal microscope (model LSM 710; Carl Zeiss Micro Imaging, Inc.). A 40× oil objective (Carl Zeiss Micro Imaging, Inc.) with a numerical aperture of 1.3 was used. Images were obtained using the Zen2009 software (Carl Zeiss Micro Imaging, Inc.). Laser settings were kept identical for all conditions for each individual experiment. Quantifications of images were made using ImageJ. Indicated number of junctions were chosen at random over at least five fields of view. Individual junctions were outlined creating unique regions of interest (ROI). The integrated density was measured for each ROI and across corresponding channels captured. Non-junctional staining was measured by shifting ROI to the cytoplasmic region. Graphs report the corrected fluorescence intensity of the ROI, the corrected fluorescence intensity = (integrated density of junction area -integrated density of non-junction area). Data represented as a box and whisker plots with 90-10 percentile shown. Pearson correlation coefficient was calculated by comparing two arrays of corrected fluorescence intensities for indicated number ofjunctions using the following equation: r = ∑ x -x y -y ∑ x -x 2 ∑ y -y 2

Transepithelial Resistance Assay

Cells were plated at a density of 5 ×10 4 cells per well of a Costar® 0.4 μm Polycarbonate membrane Transwell® 24-well plate and grown to confluence. The cells were then incubated in calcium free DMEM overnight. Growth media was added back to the cultures for the indicated times and transepithelial electrical resistance was measured in triplicate using a Millipore Voltmeter (MERS 000 01). Results are in Ω*cm 2 .

Statistics and Reproducibility

Statistical differences between groups of data were analyzed using a series of two-tailed unpaired Student t-tests. All statistical analysis and data graphing was done on Prism (Version 9.0.1). All quantified experiments represent at least three biologically independent samples with the exception of immunofluorescence data. All immunofluorescence experiments were repeated independently three times with similar results. 2) or a scramble sequence (scrGLUT1). GLUT1 expression was examined by immunoblotting whole cell lysates with an antibody against GLUT1 or vinculin as a loading control. The graphs beneath the blots depict the average amount of GLUT1 in the cells expressed as function of total GLUT1 levels in the parental cells ± SEM, n =3 biologically independent samples (e-h) Inhibition of GLUT1 using RNA interference or pharmacological inhibitor prevented glucose uptake in response to application of shear stress to MDCKII (e) or MCF-10A (f) or application of tensile forces to MDCKII (g) or MCF-10A cells (h). Shear stress was applied as described in (a) or tensile forces were applied to magnetic beads coated with E-cadherin extracellular domains (E-cadherin) or IgG as a control. A 10 pN tensile force was applied for 10 minutes. Glucose uptake was monitored as described above. The graphs represent average glucose taken up into the cells ± SEM. (g) n=5 (MDCKII), n=4 (GLUT4 inhibitor), n=3 (GLUT1 inhibitor), n=4 (Blebbistatin). (h) n=3. For all experiments, significance was calculated using a two-tailed unpaired Student t-test. GLUT1 recovery was examined by immunoblotting. The graphs beneath each immunoblot image show the average amount of GLUT1 recovered and normalized for E-cadherin levels ± SEM, n=3 biologically independent samples. For all experiments, significance was calculated using a two-tailed unpaired Student t-test. Cells were fixed and stained with an antibody against GLUT1. The graphs represent the average corrected fluorescence intensity of junctional GLUT1 (i) or GFP-E-cadherin (j). n=50 junctions over 5 fields of view. An average Pearson correlation coefficient ± SEM is reported beneath the images. All immunofluorescence data in this figure are represented as a box and whisker plot with median, 10th, 25th, 75th, and 90th percentiles shown. Scale bars=10 μM. For all experiments, significance was calculated using a two-tailed unpaired Student t-test. GLUTl/E-cad: n=3 (scrANKG/shANKG). ANKG/E-cad: n=4 (scrANKG), n= 3 (shANKG).

All immunofluorescence data are represented as a box and whisker plot with median, 10th, 25th, 75th, and 90th percentiles shown. Scale bars=10 μM. For all experiments, significance was calculated using a two-tailed unpaired Student t-test.

Figure 1 :

 1 Figure 1: GLUT1 mediates force-induced glucose uptake. (a and b) Pre-incubation of cells with GLUT1 inhibitors prevented glucose uptake. MDCKII (a) or MCF-10A (b) cells were incubated with the indicated inhibitors and the cells were left resting (no shear) or subjected to orbital shear stress for 2 hours (shear stress). Cells were lysed and the amount of a fluorescently labelled glucose analog, 2-deoxyglucose, taken up into the cells was monitored using a fluorimeter. The graphs represent the average glucose taken up into the cells ± SEM, n=3 biologically independent samples. (c and d), GLUT1 was stably inhibited using RNAi. MDCKII (c) or MCF-10A (d) cells were infected

Figure 2 :

 2 Figure 2: Force stimulates GLUT1 enrichment in cell-cell junctions.(a-c) GLUT1 is localized to cell-cell contacts in response to application of shear stress. MDCKII or MDCKII cells with GLUT1 (shGLUT1.1 or shGLUT1.2) or E-cadherin (shEcad) stably inhibited were left resting (no shear) or exposed to shear stress for 2 h. The cells were fixed and stained with antibodies against GLUT1 or β-catenin (a marker of cell-cell junctions) and examined by confocal microscopy using identical laser settings. Representative images are shown, and an average Pearson correlation coefficient ± SEM is reported beneath the images. Scale bars=10 μM. The graphs represent the average corrected

Figure 3 :

 3 Figure 3: GLUT1 is required for non-muscle myosin IIA-dependent reinforcement of the actin cytoskeleton. (a-d) Inhibition of GLUT1 or glycolysis prevents reinforcement of the actin cytoskeleton. MDCKII or MDCKII cells with GLUT1 stably inhibited (shGLUT1.1) were left resting (no shear) or exposed to shear stress. The cells were stained with phalloidin or antibodies against E-cadherin. Representative images are shown in a and c. Where indicated, the cells were pretreated with inhibitors against myosin II (Blebbistatin), GLUT1 (WZB117), or phosphofructokinase-2 (3PO). The graphs in b and d represent the average corrected fluorescence intensity of F-actin in junctions for the images in a and c, respectively. n=30-50 junctions over 5 fields of view. (e and f) Non-muscle myosin IIA is required for reinforcement of the actin cytoskeleton in response to shear. MDCKII cells expressing GFP-E-cadherin were treated with either a control (shCtrl) or shRNA targeted against non-muscle myosin IIA (shNMIIA) or non-muscle myosin IIB (shNMIIB). Cells were left resting (no shear) or exposed to shear. The cells were fixed and stained with phalloidin. Representative images are shown in e. Graph f represents the average corrected fluorescence intensity of junctional F-actin. n=50 junctions over 5 fields of view. (g) Non-muscle myosin IIA, but not IIB, is required for force stimulated glucose uptake. Cells were lysed, and the amount of a fluorescently labelled glucose analog, 2-deoxyglucose, taken up into the cells was monitored using a fluorimeter. The graphs represent the average glucose taken

Figure 4 :

 4 Figure 4: GLUT1 recruitment to cell-cell junctions requires ankyrin G (a-c) Ankyrin G is recruited to cell-cell junctions and binds E-cadherin. MDCKII or MDCKII cells lacking E-cadherin (shEcad) were left resting (no shear) or exposed to shear. (a) Representative images of cells, stained with antibodies against ankyrin G or P-catenin, are shown. The graph in b shows the average corrected fluorescence intensity of junctional F-actin and an average Pearson correlation coefficient ± SEM is reported beneath the images. n=50 junctions over 5 fields of view. (c) Ankyrin G was immunoprecipitated and co-precipitation of E-cadherin was examined using immunoblotting. The graph beneath

Figure 5 :

 5 Figure 5: Ankyrin G binding to E-cadherin is required for force-stimulated glucose uptake, reinforcement of the actin cytoskeleton, and formation of an epithelial barrier. MDCKII cells with depressed levels of E-cadherin were rescued with GFP tagged versions of wild-type E-cadherin (shEcad/WT) or a PolyA mutant E-cadherin unable to bind ankyrin G (shEcad/PolyA). (a-c) GLUT1 does not bind E-cadherin or localize to cell-cell junctions in cells expressing the PolyA mutant. (a) GFP-E-cadherin was immunoprecipitated and the co-precipitating levels of GLUT1 were examined. The graph beneath the immunoblot shows the average GLUT1 binding as a function of GFP-E-cadherin levels ± SEM, n=3 biologically independent samples. (b-c) Cells were stained with antibodies against GLUT1,

Nat Cell Biol. Author manuscript; available in PMC 2021 September 09.

Acknowledgements:

We thank Peter Rubenstein and Gillian DeWane for comments. This work is supported by National Institutes of Health Grants #R35GM136291 to KAD and P30CA086862 to the Holden Comprehensive Cancer Center. RMM was supported by Agence Nationale de la Recherche "POLCAM" (ANR-17-CE13-0013), "CODECIDE" (ANR-17-CE-13-0022) Ligue Contre le Cancer (Equipe labellisée 2019). National Institutes of Health predoctoral fellowships #T32 GM067795 and #1F31GM135962-01 supported AMS. American Heart Association Grant #16PRE26701111 supported JLB.

Data Availability

All data supporting the findings of this study are available from the corresponding author upon reasonable request.

Code Availability

No collection software was used in this study. Source data are provided with this paper.


Garcia Arellano

De Aquino

Laliotis A †1
email: laliotis@univ-paris13.fr

High resolution molecular spectroscopy in micrometric thin cells

Shrinking the size of atomic and molecular cells is a fascinating prospect with applications in quantum sensing and fundamental physics. Miniature atomic cells were proposed for example as portable atomic clocks 1 and hollow core fibers were filled with molecular gases for applications in frequency referencing 2 . Although compact, the above devices remain mesoscopic (confinement larger than the excitation wavelength). Atomic thin cells have been used to probe atoms under sub-wavelength confinement conditions allowing fundamental studies of the Dicke effect 3 and applications in quantum technologies 4 . High resolution probing of sub-wavelength confined molecules is more challenging, due to the small probabilities of molecular transitions, and was so far demonstrated only on a macroscopic cell via selective reflection spectroscopy 5 . Here we extend thin cell platforms to high-resolution molecular spectroscopy. We probe the ν1+ν3 line of acetylene at telecommunication wavelengths (1.53µm) and SF6 as well as NH3 rovibrations at mid-infrared wavelengths (10.6µm). The thin cell was fabricated in our laboratory using ZnSe windows that are transparent through the near and mid infrared spectrum (Fig. 1a). The thin cell thickness, measured by Fabry-Perot interferometry, is 5.35µm with small variations of about 0.1µm. This cell thickness corresponds to λ/2 for the SF6 et NH3 rovibrations and to 7λ/2 for the combination line of acetylene, conditions for which a Dicke-type narrowing is expected 3 . In our experiments we detect the low power thin-cell optical transmission using a frequency modulation. A number of techniques were developed to increase the signal to noise ratio and remove the parasitic background from our signals 5 .

Fig1.b shows our experimental thin-cell transmission spectra for different cell thicknesses (the acetylene pressure is 2 Torr in all cases). Solid lines represent the theoretical prediction of a model that includes the transient effects of the interaction of molecules with the laser light as they travel between the cell walls, the Fabry-Perot cavity effects as well as frequency modulation and laser linewidth effects 6 . The model considers a Maxwell-Boltzmann distribution of molecular velocities and assumes that the collisions with the hard cell walls completely interrupt the interaction with the laser field. The theoretical curves were fit to the experiment to extract the collisional linewidth (16MHz). The excellent agreement between theory and experiments suggests that thin cell platforms are very well adapted for compact frequency referencing at telecommunication wavelengths and fundamental physics measurements.

Our experiments are a first important step towards the fabrication of compact and simple frequency references at telecommunication wavelengths without resorting to nonlinear spectroscopic techniques like saturated absorption. We are currently working towards fabricating a new generation of thin cells of nanometric thickness suited for studies of the fundamental molecule-surface Casimir-Polder interaction.

Figure 1 :

 1 Figure 1: (a) thin cell photograph (b) transmission of an acetylene filled thin cell (2 Torr) at different thicknesses. Theoretical predictions are shown as solid lines. The pressure broadening is 16MHz.


S Bhatnagar

Jie Yuan
email: jie.yuan@imperial.ac.uk

Alfredo Fantetti

Enora Denimal

Loic Salles

Quantification of uncertainties in nonlinear vibrations of turbine blades with underplatform dampers

come   L'archive ouverte pluridisciplinaire

Introduction

The aerospace industry demands lighter and more efficient propulsion systems, thus driving the design of many components to their structural limits. During operation, a turbine blade experiences a combination of static and dynamic stresses [START_REF] Krack | Vibration prediction of bladed disks coupled by friction joints[END_REF]. The static stresses originate from thermal gradients, centrifugal loads and fluid pressure variation. On the other hand, dynamic stresses originate from mechanical and aero-dynamic vibration and have a negative impact on the high cycle fatigue (HCF) life [START_REF] Yuan | Efficient computational techniques for mistuning analysis of bladed discs: a review[END_REF]. Excessive stresses caused by significant vibrations can be dealt with by either moving the resonant frequency out of the operating range or by reducing the amplitude of vibration [START_REF] Griffin | A review of friction damping of turbine blade vibration[END_REF]. Whilst the former is theoretically achievable, it is not practically viable to avoid all resonant modes due to the wide distribution of such frequencies and hence the latter method is preferred. Reduced vibration amplitudes are achieved by removing energy from the system by using friction dampers [START_REF] Gaul | The role of friction in mechanical joints[END_REF][START_REF] Feeny | A historical review on dry friction and stick-slip phenomena[END_REF][START_REF] Fantetti | Modelling and testing flexible friction dampers : challenges and peculiarities[END_REF]. These dampers work by exploiting the relative motion between them and the vibrating blades [START_REF] Sanliturk | Friction damper optimisation: simulation of rainbow tests[END_REF] leading to a local contact transition between stick and slip. In the slip condition, energy is dissipated at the contact surface, primarily as heat [START_REF] Sanliturk | Underplatform dampers for turbine blades: theoretical modeling, analysis, and comparison with experimental data[END_REF]. Optimizing the design of such dampers requires an accurate modelling approach to simulate the vibration amplitude response to a harmonic excitation. This also needs to be backed with experimental validation. Unfortunately, advances in validation methods of the numerical models have not kept up with the advances in the numerical models [START_REF] Pesaresi | Modelling the nonlinear behaviour of an underplatform damper test rig for turbine applications[END_REF].

To obtain a better understanding of how to model friction dampers, and in particular underplatform dampers, a variety of studies have been conducted [START_REF] Csaba | Forced response analysis in time and frequency domains of a tuned bladed disk with friction dampers[END_REF][START_REF] Yang | Characterization of contact kinematics and application to the design of wedge dampers in turbomachinery blading: Part i-stick-slip contact kinematics[END_REF]. Initially, simple models using single [START_REF] Cameron | An integrated approach for friction damper design[END_REF] and two degree of freedom [START_REF] Yeh | Forced vibrations of a two-degree-of-freedom system with combined coulomb and viscous damping[END_REF] oscillators coupled with a type of Coulomb friction element (Jenkins Element [START_REF] Gaul | The role of friction in mechanical joints[END_REF]) were generated to investigate the dynamic response yielding partially analytic solutions. These systems were extended further by using complete FE models of the damper and bladed disks [START_REF] Sanliturk | Underplatform dampers for turbine blades: theoretical modeling, analysis, and comparison with experimental data[END_REF][START_REF] Csaba | Forced response analysis in time and frequency domains of a tuned bladed disk with friction dampers[END_REF][START_REF] Yang | Characterization of contact kinematics and application to the design of wedge dampers in turbomachinery blading: Part i-stick-slip contact kinematics[END_REF]. Underlying assumptions of the relative motion between the blades and damper proved difficult to validate suggesting the assumptions themselves were incorrect [START_REF] Sanliturk | Underplatform dampers for turbine blades: theoretical modeling, analysis, and comparison with experimental data[END_REF]. In order to remove these assumptions, models that calculated the damper motion directly were created [START_REF] Zucca | Modeling underplatform dampers for turbine blades: a refined approach in the frequency domain[END_REF][START_REF] Petrov | Advanced modeling of underplatform friction dampers for analysis of bladed disk vibration[END_REF][START_REF] Gastaldi | Forced response prediction of turbine blades with flexible dampers: The impact of engineering modelling choices[END_REF]. Calculating damper motion required advanced 3D friction elements to model the in-plane tangential motion, normal load based separation and nonlinear contact forces between the damper and blade. These advanced models are more accurate by better representing the damperblade contact domain. The underplatform damper model developed by [START_REF] Pesaresi | Modelling the nonlinear behaviour of an underplatform damper test rig for turbine applications[END_REF] can be classified as one of these advanced models. . The primary purpose of their study was to produce an accurate and replicable underplatform damper model [START_REF] Pesaresi | Modelling the nonlinear behaviour of an underplatform damper test rig for turbine applications[END_REF]. The input contact parameters were assumed to be deterministic based on experimental testing. A deterministic variable is one which has the exact same, pre-determined value and presents no degree of uncertainty in its realization [START_REF] Roncen | Non-linear vibrations of a beam with non-ideal boundary conditions and uncertainties-modeling, numerical simulations and experiments[END_REF]. Unfortunately, the underplatform damper contact domain is highly dynamic due to variations in contact parameters over time caused by fretting wear [START_REF] Sanliturk | Underplatform dampers for turbine blades: theoretical modeling, analysis, and comparison with experimental data[END_REF]. As such, uncertainties are present in the amplitude response and frequency when this deterministic approach is utilised.

The aim of this investigation is to quantify the uncertainties in the output response of an underplatform damper model by taking the input parameters to be stochastic. The purpose of this procedure is to account for variations in the input parameters to better understand the design considerations needed for friction dampers. A further goal is to implement Polynomial Chaos Expansion (PCE), a surrogate modelling technique, to improve the computational efficiency of the numerical approach. The underplatform damper model presented by [START_REF] Pesaresi | Modelling the nonlinear behaviour of an underplatform damper test rig for turbine applications[END_REF] is used as the test case. Hence, this paper first presents a background into the modelling approach techniques. It is followed by the presentation of techniques to quantify the uncertainty in the system output are formalised. Finally, the results are presented and some trends are highlighted.

Reference model

A 3D nonlinear model with an explicit FE damper design is used as in this UQ study and is better descrobed in [START_REF] Pesaresi | Modelling the nonlinear behaviour of an underplatform damper test rig for turbine applications[END_REF]. The FE models generated for the blades and damper consisted of quadratic hexahedral elements, made of steel. Each blade consists of 27486 elements and the damper consists of 3620 elements. As shown in 3 Modeling approach A general nonlinear system of equations can be represented as follows:

Mẍ(t) + C ẋ(t) + Kx(t) + F nl ( ẋ(t), x(t)) = F ex (t) (1)
Where M, C, K are the mass, damping and stiffness matrices. F ex is vector of external excitation forces and F nl is the vector of nonlinear contact forces.

Time integration is the most rigorous approach to solve these set of equations [START_REF] Park | An improved stiffly stable method for direct integration of nonlinear structural dynamic equations[END_REF]. However, it is computationally expensive and excessive when the steady-state response to harmonic excitation is the only study of interest. Consequently, the multi harmonic balance method (MHBM) [START_REF] Krack | Vibration prediction of bladed disks coupled by friction joints[END_REF][START_REF] Petrov | Analytical formulation of friction interface elements for analysis of nonlinear multi-harmonic vibrations of bladed disks[END_REF][START_REF] Petrov | A high-accuracy model reduction for analysis of nonlinear vibrations in structures with contact interfaces[END_REF] has been the most common approach to solve the nonlinear vibration system due to it being by far the most computationally efficient method [START_REF] Cameron | An alternating frequency/time domain method for calculating the steadystate response of nonlinear dynamic systems[END_REF]. MHBM solves the problem in the frequency domain due to the differential equations being represented as linear functions, making the system easier to solve. According to the MHBM, for each DOF in the system, the response can be expressed as a Fourier series truncated at the n th harmonic, which generates a system of equations in the frequency domain.

A Newton-Raphson iterative solver is used to calculate the harmonic coefficients while the FRF matrix is obtained by calculating its exact value at a particular frequency point. A more detailed outline of the solving method can be found here [START_REF] Pesaresi | Modelling the nonlinear behaviour of an underplatform damper test rig for turbine applications[END_REF]. The exact implementation of the nonlinear solver depends on the contact model used to describe the friction damping between the underplatform damper and blade root. The contact model used for the UPD rig is a 3D Jenkins element [START_REF] Petrov | Analytical formulation of friction interface elements for analysis of nonlinear multi-harmonic vibrations of bladed disks[END_REF]. It is composed of two Jenkins element together with a normal spring. This allows both in-plane frictional forces and normal load based variations to be captured. The definition of each element is made through several contact parameters: the friction coefficient µ between the two surfaces, the contact tangential stiffness k t and the normal stiffness k n and a normal load N 0 representing the pre-load. The contact surface is discretised into several contact elements, and each element has its own contact parameters. This contact model allows for three different contact conditions: stick, slip and separation.

The primary source of uncertainty is in dynamics simulations of blades with dampers is the variability observed in experimentally measured contact parameters [START_REF] Fantetti | Effect of friction on the structural dynamics of built-ip structures: An experimental study[END_REF][START_REF] Fantetti | impact of fretting wear on structural dynamics: Experiment and simulation[END_REF][START_REF] Pesaresi | On the use of ultrasound waves to monitor the local dynamics of friction joints[END_REF][START_REF] Fantetti | Comparison of contact parameters measured with two different friction rigs for nonlinear dynamic analysis[END_REF]. During slip, the two rubbing surfaces undergo solid to solid contact which causes the surface roughness and stiffness to change. In addition, the change in damper geometry could lead to variations in blade coupling, resulting in the natural frequency to change. All of these factors lead to random variations in the values of the input parameters causing the amplitude response as well as the resonant frequency to become uncertain. It is important to quantify these uncertainties in order to account for these variations in the design of friction dampers [START_REF] Gastaldi | The effect of surface finish on the proper functioning of underplatform dampers[END_REF]. Experimental testing has to be performed to estimate the variation of both the tangential contact stiffness k t and the friction coefficient µ. In this study, k t and µ were expressed as normally distributed parameters from experimental data presented in [START_REF] Fantetti | impact of fretting wear on structural dynamics: Experiment and simulation[END_REF]:

• µ~N(0.9,0.05 2 )

• k t ~N(60e6, 3e6 2 )

Uncertainty propagation

Different strategies exist to propagate uncertainty in numerical models. Monte Carlo Simulations (MCS) remains the most robust method to do so [START_REF] Yuan | Probabilistic dynamics of mistuned bladed disc systems using subset simulation[END_REF], however convergence is slow and requires a large number of simulations making the approach unusable in practical applications. To cope with this issue, Polynomial Chaos Expansion (PCE) can be used to surrogate the dynamic behaviour of the structure. Once built, PCE models have negligible numerical cost and so can be exploited to perform different types of analysis as variance based sensitivity analysis [START_REF] Iooss | A review on global sensitivity analysis methods[END_REF][START_REF] Sudret | Global sensitivity analysis using polynomial chaos expansions[END_REF].

PCE model

The basis of PCE is outlined here, but detailed literature can be found here [START_REF] Sudret | Global sensitivity analysis using polynomial chaos expansions[END_REF][START_REF] Crestaux | Polynomial chaos expansion for sensitivity analysis[END_REF][START_REF] Michaël Baudin | Openturns -an industrial software for uncertainty quantification in simulation[END_REF]. The principal concept of PCE is the ability to decompose a random process into independent deterministic and stochastic components. Generally, for a random process A, that is a function of a random variable ξ and deterministic coefficients x:

A(x, ξ) = P i=0 A i (x)Ψ i (ξ) (2)
Where A i (x) is the vector of deterministic coefficients and Ψ i is the orthogonal polynomial basis mapping the coefficients to the random process. The choice of the polynomial basis is determined by the distribution of the random variable ξ and can be found directly from literature. For computational efficiency, the theoretically infinite sum of deterministic coefficients is truncated to P terms. The only unknown in Equation eqn:PCEmain is A i (x). Both intrusive [START_REF] Didier | Nonlinear vibrations of a mechanical system with non-regular nonlinearities and uncertainties[END_REF][START_REF] Sinou | Stochastic non-linear response of a flexible rotor with local non-linearities[END_REF] and non-intrusive (NIPCE) methods [START_REF] Roncen | Non-linear vibrations of a beam with non-ideal boundary conditions and uncertainties-modeling, numerical simulations and experiments[END_REF][START_REF] Sarrouy | Phase driven study for stochastic linear multi-dofs dynamic response[END_REF] exist to solve for these coefficients but non-intrusive methods achieve this without the modification of the deterministic code that solves the nonlinear dynamic system. Hence, the non-intrusive regression method is employed here [START_REF] Sudret | Global sensitivity analysis using polynomial chaos expansions[END_REF].

From a set of N evaluations of the system, a least-squares problem is solved to get the coefficients A i (x).

In the present study, a Latin Hypercube Sampling strategy is employed to generate the N input points. The construction of the PCE models are done with OpenTurns [START_REF] Michaël Baudin | Openturns -an industrial software for uncertainty quantification in simulation[END_REF].

Variance based sensitivity analysis

Sobol analysis ranks the importance of the input parameters to the output response by measuring the change in the output's variance caused by a change in the input. The basis of the analysis is the ability to decompose the output variance into a sum of variances [START_REF] Iooss | A review on global sensitivity analysis methods[END_REF][START_REF] Xie | Probabilistic reliability analysis of carbon/carbon composite nozzle cones with uncertain parameters[END_REF] by creating linked sets of the input parameters.

V (output) = n i=1 V i + n i≤j<n V ij + ... + n i≤n V i...n (3)
In Equation eqn:sobol, V (output) is the total variance of the output, V i is the first order contribution of the i th stochastic parameter, V ij is the second order contribution of interaction effects of the i th and j th parameter and n is the number of stochastic parameters. The first order sensitivity index for the i th parameter is calculated from Equation eqn:sobolindex:

S 1,i = V i V (output) (4)
The variance decomposition from Equation eqn:sobol can be directly related to the PCE decomposition eqn:PCEmain [START_REF] Sudret | Global sensitivity analysis using polynomial chaos expansions[END_REF], and so the Sobol indices can be directly determined from the PCE coefficients without any additional simulation [START_REF] Michaël Baudin | Openturns -an industrial software for uncertainty quantification in simulation[END_REF].

6 Results

Nonlinear Vibration response

As explained previously, the first two bending modes of the structure are considered, which are the in-phase (mode 1) and out-of-phase (mode 2) motion of the two blades.

Uncertainty Quantification

In this section, the uncertainty associated to the contact parameters is propagated using the PCE method explained previously. The set of input points used to construct the PCE is generated with a LHS of 100 combinations of contact parameter values. For each of those combinations, the FRFs for both in-phase and out-of-phase modes were computed at different excitation amplitudes. Results for the 17N excitation loading are presented in Figure fig:rawData.

Since the FRFs are strongly non linear, the PCE meta-model cannot be constructed as a function of the frequency (in fact, for some frequency values there are more receptance solutions). To avoid this problem, the deterministic parameter used is the phase [START_REF] Sarrouy | Phase driven study for stochastic linear multi-dofs dynamic response[END_REF]. Once each FRF is decomposed into a phase frequency response and a phase amplitude response, two PCE meta-models are built for each mode and each phase value: one for the amplitude and one for the frequency.

Such PCE meta-modes can be exploited with an almost null numerical cost to generate the statistical distribution of the system response. Uncertainty bands obtained from those meta-models are shown in For the accelerance, it is evident that when the system has no slip, k t fully determines the system response as the first order Soblol index of k t is equal to 1, while µ has no impact. This can be seen in Figures fig:PCE s obol a mp1andf ig : P CE s obol a mp2.However, uponanypercentageof slip, thispatternf lipsandµ solely determines the system response as its first order Sobol index becomes equal to 1. This pattern is expected as during slip, the amplitude response is determined by the amount of damping and the amount of damping is determined by friction. In the stick case, there is no sliding and so µ is not relevant in determining the output response.

On the contrary, the Sobol indices for the frequency do not have such a clear pattern, as shown by Figures fig:PCE s obol f req1andf ig : P CE s obol f req2.Ingeneral, f orbothmodes, thetangentialstif f nessprimarilydetermin Around the ends of each plot, k t determines the output completely. This is expected with the system being in the stick condition as confirmed by the stick percentage. For the second mode, from a phase of -1 to 1 radians, the contact conditions do not vary significantly indicating the Sobol indices should follow a similar pattern. Rather surprisingly, there is a local minimum in the µ index and a local maximum in the k t index for both and a varying µ (here not shown). The simulations showed that for the 0.2 radians case, the frequency remains constant and only the amplitude varies as µ was changed, which explains these results.

Combining the Sobol analysis with the uncertainty bands, it is evident that uncertainty in accelerance is present only in the slip region and as the output in this region is determined by variations in µ only, it can be concluded that variations in µ determine the uncertainty in accelerance. For the frequency, uncertainties are present throughout. k t primarily determines the amount of uncertainty but local peaks in slip increase the contribution of µ. The uncertainty in resonant frequency is solely determined by variations in k t with µ altering the resonance amplitude only.

Conclusion

A method to quantify the uncertainties in the nonlinear response of an underplatform damper model has been successfully developed. The method is based on the generation of PCE meta-models, which make it possible to have a large sample size thus improving statistical accuracy as well as offering a significant reduction in computation time.

Uncertainty bands in the frequency response functions (FRFs) were obtained from these meta-models. Also a Sobol analysis was performed to rank the sensitivity of the FRFs on the different contact parameteres. From this analysis it was found that, for the accelerance, uncertainties only exist while the system is slipping. In this region, the extent of uncertainty is determined by variations in µ. Under the stick condition, µ has no impact and k t should control the accelerance amplitude. On the contrary, in the case of frequency, uncertainties are determined mainly by variations in k t , although trends are not directly related to the slipping conditions.

With regards to optimisation of damper design, the proposed uncertainty quantification method is useful since it provides bands in the output responses. With this information, damper design criteria can be updated to better inform the design decisions. In addition, the Sobol analysis allows the prioritisation of design decisions based on their impact on the output. Finally, the implementation of the PCE model makes the process computationally very efficient allowing wider underplatform damper studies to be performed with fewer computational resources. In order to have complete confidence in the statistical bands generated, an experimental validation of the approach will be performed with future work.

Figure 1 :

 1 Figure 1: Underplatform Damper Rig Set-up [9]

Figure 2 :

 2 Figure 2: (a) In-phase mode of the blades and (b) out-of-phase mode[9]

  Figure fig:amp c onditions(a, b)showsreceptancesf ordif f f ).Itcanbeseenthatf orlowshakerf orceamplitudes, bothmodesaresticking, resultinginlowdamping.Increasingt

  Figures fig:freqMap and fig:phaseMap show how the frequency is mapped to the phase. It should be noted that the phase decreases cyclically for each mode.

6 . 3

 63 Figure fig:UQ b andsf orthetwomodeswithanexcitationamplitudeof 17 N.F orthereceptance, theuncertaintyisnegligib -π/2 radians). The uncertainty in the frequency vector is also negligible at the extreme phase values, while it increases around resonance, as shown in Figure fig:UQ b ands(b).T hesametrendsarepresentf orthesecondmode, shown Sobol indices First order Sobol indices were also calculated directly from the PCE model to get insights into the influence of each contact parameter on the system dynamics. The contact conditions for the damper-blade nodes (as a percentage) were used in combination with Sobol indices to help explain the behaviour. Results are displayed in Figure fig:Solbol.

2 Figure 3 :

 23 Figure 3: Forced response and contact conditions for shaker force amplitude sensitivity analysis

Figure 4 :

 4 Figure 4: 100 LHS simulations run through FORSE, µ~N(0.6,0.05 2 ) and k t ~N(60e6, 3e6 2 )

Figure 5 :Figure 6 :

 56 Figure 5: Frequency and phase equivalency

Figure 7 :

 7 Figure 7: Sobol indices for accelerance, frequency with contact conditions superimposed

Acknowledgements

The authors would like to acknowledge the support of Rolls-Royce plc through the Vibration University Technology Centre (UTC) at Imperial College London, UK