# Extracellular fluid viscosity enhances cell migration and most cancers dissemination | Aici

### Experimental strategies

Human MDA-MB-231 adenocarcinoma (ATCC), MDA-MB-231 BrM218 (MDA-MB-231 cells remoted from mind metastasis have been a present from J. Massagué), HOS (ATCC), U87 (ATCC) and HEK293 (ATCC) cells and dermal fibroblasts (Coriell Institute) have been grown in DMEM (Life Applied sciences/Gibco) supplemented with 10% heat-inactivated FBS (Gibco) and 1% penicillin–streptomycin (10,000 U ml−1; Gibco). hAOSMCs (PromoCell) have been grown in clean muscle cell progress medium (PromoCell). SUM159 cells have been obtained from D. Wirtz (Johns Hopkins College) and have been grown in Ham’s F-12 medium (Gibco) containing 5% FBS, 1% penicillin–streptomycin (10,000 U ml−1; Gibco), 1 μg ml−1 hydrocortisone (Sigma-Aldrich) and 5 μg ml−1 insulin (Sigma-Aldrich). Cells have been maintained in an incubator at 37 °C and 5% CO2 and passaged at 60–90% confluency each 3 to five days. Cells have been recurrently checked for mycoplasma contamination by PCR utilizing the next primer pairs: ahead, 5′-GGGAGCAAACAGGATTAGATACCCT-3′; reverse, 5′-TGCACCATCTGTCACTCTGTTAACCTC-3′.

In choose experiments, cells have been handled with the next pharmacological brokers (bought from Sigma-Aldrich except in any other case acknowledged) and corresponding car controls: 2-APB (Calbiochem, 100 μM), CK666 (100 µM), latrunculin A (2 µM), NSC 668394 (Calbiochem, 10 μM), Y-27632 (10 µM), blebbistatin (50 µM), BAPTA (50 µM), GSK2193874 (15 µM), GSK1016790A (1 or 15 µM), BAPTA AM (Invitrogen, 25 µM), EIPA (40 µM), HC-067047 (1 μM) and verteporfin (0.1 µM).

#### Preparation and characterization of media of various viscosities

Methylcellulose inventory resolution (3%) in IMDM was bought from R&D Methods, and media of desired viscosities have been ready by diluting the inventory resolution with acceptable quantities of IMDM (Life Applied sciences/Gibco) containing 10% heat-inactivated FBS (Gibco) and 1% penicillin–streptomycin (10,000 U ml−1; Gibco). Instead means of accelerating viscosity, Dextran 500 kDa (Spectrum Chemical) and PVP (Okay-90; Sigma Aldrich; molecular mass, 360 kDa) have been used as suspension in acceptable basal medium. In choose experiments, Detran 6 kDa (Alfa Aesar) was used as a management to Dextran 500 kDa, as low-molecular-mass (6 kDa) dextran on the identical molarity doesn’t change viscosity appreciably2. Cannon–Fenske capillary viscometers have been used to measure the viscosity of the ensuing medium at 37 °C. Osmolarity was measured utilizing freezing-point melancholy with a 3205 Single-Pattern Osmometer (Superior Devices). To make sure the profitable entry of the viscous medium into the microchannels, crimson fluorescent beads of 0.5 μm diameter (FluoSpheres) have been dispersed uniformly within the medium, and their circulation by way of the units was imaged by epifluorescence microscopy.

Throughout medium preparation, as much as 0.6% or 92 µM of 65 kDa methylcellulose was used. Thus, osmolarity variations as a result of addition of methylcellulose may be solely as much as 100 μOsm, which is insignificant relative to the osmolarity vary of basal media that’s 3,000× larger (~300 mOsm).

#### 2D assays

In wound-healing assay, cells have been allowed to develop to confluence on collagen-I-coated (20 µg ml−1; collagen I rat tail; Thermo Fisher Scientific) tissue tradition plastic plates (Falcon). After reaching confluency, a scratch within the cell monolayer was created utilizing a 200 µl pipette tip with a plastic ruler as a information. In 2D single-cell motility assays, cells have been plated at 5–8% confluency on collagen-I-coated (20 µg ml−1) tissue tradition plastic plates (Falcon). After cell spreading or after wound creation, the tradition medium was changed with that of the suitable viscosity, and the acquisition of time-lapse photographs began 30 min after medium change. In choose 2D assays involving high-resolution imaging, cells have been plated on collagen-I-coated (20 μg ml−1) dishes (Cellvis or IBIDI).

#### Microfluidics machine fabrication and cell seeding

PDMS-based microfluidics units containing an array of parallel microchannels of particular dimensions (200 µm in size, 10 μm in peak, and three.5 μm or 10 μm in width) have been fabricated as described beforehand20,46. A laser profilometer was used to confirm the peak and width of microchannels. Microchannels have been coated with collagen I (20 µg ml−1) earlier than medium loading and cell seeding. All cell sorts apart from hAOSMCs and human dermal fibroblasts have been examined inside slim (3.5 × 10 µm2) channels. hAOSMCs and human dermal fibroblasts have been examined inside 10 × 10 µm2 channels.

Microfluidics units have been loaded with medium of acceptable viscosities by filling the inlet wells with 100 μl of medium 15 min earlier than including cells. Cells have been indifferent from tradition flasks or plates utilizing 0.05% trypsin-EDTA (Gibco), adopted by centrifugation at 300g for five min and resuspension in medium of the required viscosity at a focus of 5 × 106 cells per ml. After eradicating the medium from the inlets and shops of the machine, 20 μl of cell suspension was added into the cell-seeding inlet to create a stress pushed circulation of cells into the cell-seeding channel. Cells have been allowed to stick and unfold exterior the microchannel entrances for no less than 20 min earlier than filling all inlet wells to 100 μl with medium on the acceptable viscosities. Units have been incubated at 37 °C and 5% CO2 earlier than imaging. Cells weren’t subjected to any chemotactic stimulus or medium circulation in the course of the migration assay. In experiments with pharmacological brokers, the medium within the units was changed with that containing the drug of consideration or its respective car management as soon as cells had totally entered the microchannels. By imaging the circulation of fluorescent beads dispersed in 8 cP medium, we confirmed their profitable entry into the microchannels (Supplementary Video 5).

#### Cell migration monitoring and evaluation

Cells have been imaged each 2 to twenty min for 12 to twenty h on an inverted Nikon Eclipse Ti microscope (Nikon) with automated controls (NIS-Components; Nikon) and a ×10/0.45 NA ph1 goal utilizing time-lapse microscopy. In choose experiments, cells have been imaged utilizing fluorescein isothiocyanate filters. For experiments with NHE1-GFP-transfected cells, a Nikon A1 confocal microscope (Nikon) with ×20 or ×60 goal was used. In the course of the course of the experiments, cells have been maintained on a stage-top incubator (Tokai Hit) at 37 °C and 5% CO2. The A1 confocal system additionally had a temperature-controlled cage.

Reside-cell movies have been exported to ImageJ (Nationwide Institutes of Well being), and the MTrackJ plugin47 was used for cell motility monitoring. In single-cell 2D migration assays, cells that weren’t in touch with any neighbours have been chosen and manually tracked. Cell monitoring was carried out till the tip of the video except a neighbouring cell touched the tracked cell, through which case monitoring was stopped. In microfluidics experiments, cell paths have been recorded from the time of full entry into the microchannel till contact was made with the tip of the microchannel. A customized MATLAB (MathWorks) script was used to analyse cell migration velocity and velocity from the cell paths. Cell entry time was calculated by manually evaluating the time elapsed between main and trailing edge entry right into a microchannel. Dividing or apoptotic cells have been excluded from evaluation in each 2D and microchannel migration. Wound-healing assays have been analysed utilizing ImageJ by drawing a line indicating the migrating fronts on two sides of the scratch wound. Wound closure was recorded when each apposing fronts touched one another.

For cell migration phenotype classification, dwell cells expressing Lifeact–GFP or fastened cells stained with Alexa Fluor 488 phalloidin (1:100; Invitrogen) and Hoechst (1:2,000; Invitrogen) have been noticed utilizing an inverted Nikon Eclipse Ti microscope (Nikon) utilizing a ×40 air goal 4 to eight h after channel entry. Cell phenotype below confinement was tabulated manually, as reported beforehand47.

#### Spheroid assays

Spheroids with MDA-MB-231 cells have been generated as described beforehand48. In short, growth-factor-reduced Matrigel (Corning) was diluted 1:3 with chilly DMEM supplemented with 10% heat-inactivated FBS and 1% penicillin–streptomycin. Then, 50 µl of the diluted Matrigel was transferred to every effectively of a 96-well plate (Falcon) and allowed to polymerize at 37 °C and 5% CO2 for 1 h. Cells have been collected from tradition flasks, resuspended in diluted Matrigel and have been gently disbursed (2,000 cells per 50 µl) on prime of the beforehand polymerized Matrigel in every effectively. After incubation at 37 °C and 5% CO2 for 1.5 h, 100 µl of DMEM with 10% heat-inactivated FBS and 1% penicillin–streptomycin was added into every effectively. The medium was changed each 2 days till spheroids have been collected for experiments (usually ~10–15 days later). Spheroids have been collected after dissolving the Matrigel in chilly DMEM and centrifuged at 2,655g for five min. After eradicating the supernatant, the spheroids have been resuspended in both 0.77 or 8 cP medium and plated onto collagen-I-coated (20 μg ml−1) 24-well plates. After 60 min, the spheroids have been imaged each 20 min for no less than 20 h on an inverted Nikon Eclipse Ti microscope with automated controls (NIS-Components; Nikon) with a ×10/0.45 NA ph1 goal utilizing time-lapse microscopy. In the course of the course of the experiments, the spheroids have been maintained on a stage-top incubator at 37 °C and 5% CO2. First-cell dissociation occasions have been acquired utilizing the NIS Component Software program (Nikon) by manually recording the time required for the primary cell to totally detach from every intact spheroid.

#### Cloning, lentivirus preparation, transduction and transfection

To generate MDA-MB-231 cells with steady knockdown of ARP3 and/or ARPC4, or TRPV4, the pLKO.1 puro (plasmid 8453; Addgene; a present from B. Weinberg) spine was used. The next sequences have been subcloned into the pLKO.1 puro spine: Non-targeting scramble sequence: 5′-GCACTACCAGAGCTAACTCAGATAGTACT-3′; shARP3 sequence 1: 5′-GTAACACCAAACATGATTATA-3′; shARPC4 sequence 1: 5′-GCTGAAGAGTTCCTTAAGAAT-3′; shITGB1 sequence 1: 5′-TGCCTACTTCTGCACGATGT-3′; shTRPV4 sequence 1: 5′-TCTTGGTAACAAACTTGGT-3′; and shTRPV4 sequence 2: 5′-TGCTCCTATGGAGTCACATAA-3′.

Whereas shTRPV4 sequence-1 was utilized in Prolonged Knowledge Fig. 6, in the remainder of the manuscript, sequence-2 was used. For AQP5 knockdown, the next focusing on sequence was subcloned into the pLVTHM (plasmid 12247; Addgene; a present from D. Trono) spine: shAQP5 sequence 1: 5′-ACGCGCTCAACAACAACACAA-3′.

For NHE1 depletion, the next sequences have been subcloned into each the pLKO.1 puro and pLVTHM backbones and used with SC sequences subcloned into the respective backbones: shNHE1 sequence 1: 5′-GACAAGCTCAACCGGTTTAAT-3′; and shNHE1 sequence 2: 5′-CCAATCTTAGTTTCTAACCAA-3′.

Whereas the shNHE1 sequences have been used individually in Prolonged Knowledge Fig. 5, each sequence-1 and sequence-2 have been utilized in mixture in all the different experiments. MDA-MB-231 cells stably transduced with shMIIA and shMIIB3 have been used for migration assays. For actin retrograde circulation evaluation, the shMIIA sequence was cloned into the pLKO.1 puro spine. After each cloning, sequence integrity and orientation have been verified by Sanger Sequencing on the JHU Genetic Assets Core Facility.

For lentivirus manufacturing, HEK293T/17 cells have been co-transfected with psPAX2, pMD2.G and the lentiviral plasmid of curiosity. Then, 48 h after transfection, the lentivirus was collected and concentrated utilizing centrifugation. Wild-type MDA-MB-231 cells at 60–80% confluency have been incubated for twenty-four h with 100× virus suspension and eight µg ml−1 of Polybrene transfection reagent (Millipore Sigma). To keep up steady knockdown, cells transduced with the pLKO.1 puro spine have been cultured in medium containing 0.5 µg ml−1 puromycin (Gibco).

#### Reside-cell reporters

The pGP-CMV-GCaMP6s (40753; a present from D. Kim and the GENIE Undertaking), FUGW-pHRed (65742; a present from M. Tantama), pLentiRhoA2G (40179; a present from O. Pertz), pLenti.PGK.LifeAct-GFP.W and pLenti.PGK.LifeAct-Ruby2.W (51010 and 51009 respectively; presents from R. Lansford) plasmids have been bought from Addgene and used for lentiviral cell transduction. The GFP-AHD plasmid was provided by M. A. Glotzer49, and was cloned into the lentiviral spine modified from pLV-EF1a-IRES-Puro (plasmid 85132; Addgene; a present from T. Meyer) utilizing BamHI and NotI. The next sequences have been used to amplify GCaMP6s: 5′-CAAATGTGGTATGGCTGATTATG-3′ and 5′-GTACGCGTCACCATGGGTTCTCATCATC-3′. The PCR product was subsequently inserted into pLV-EF1a-IRES-Puro utilizing MluI and NotI. pEYFP-C1 (Clontech)2 was cloned into pLV-EF1a-IRES-Purousing the next sequences and NotI and HpaI restriction websites: 5′-GTGCGGCCGCGTCGCCACCATGGTGAGC-3′ and 5′-CTGTTAACTCACTTGTACAGCTCGTCCATGC-3′. The aforementioned plasmids have been used to organize lentiviral particles for steady cell transduction.

Arp3-pmCherryC1 (27682; a present from C. Merrifield) and β-actin-mRFP-PAGFP (62382; a present from G. Charras and T. Mitchison) have been bought from Addgene. The NHE1-GFP plasmid was a present from J. Orlowski. The above-mentioned plasmids have been used for transient transfections. About 60–80% confluent MDA-MB-231 cells have been transfected utilizing Lipofectamine 3000 reagent in line with the producer’s suggestions. To counterpoint the inhabitants of cells expressing Arp3-pmCherryC1, β-actin-mRFP-PAGFP or NHE1-GFP, cells have been chosen with 0.5 mg ml−1 G418 (Corning) and sorted. Cells expressing Myosin IIA-GFP have been generated as beforehand described3.

#### Lamellipodial actin staining and imaging

To stain for F-actin, a beforehand described protocol50 was used for cells plated on collagen-I-coated glass backside dishes (Cellvis). In short, when cells reached about 20% confluency, their medium was changed with that of the specified viscosity and so they have been incubated for two–6 h at 37 °C. Cells have been then washed as soon as with PBS containing Ca2+/Mg2+ (Gibco), fastened and extracted for 1 min utilizing 0.25% glutaraldehyde and 0.5% Triton X-100 in cytoskeleton buffer (150 mM NaCl, 10 mM MES buffer, 5 mM EGTA, 5 mM glucose, 5 mM MgCl2 in water; pH 6.8) after which fastened for five min in 2% glutaraldehyde in cytoskeleton buffer. The samples have been both processed instantly or saved with 2% glutaraldehyde in cytoskeleton buffer at 4 °C till subsequent staining. The background autofluorescence from glutaraldehyde was quenched with 1% NaBH4 for 15 min earlier than blocking with 5% bovine serum albumin (BSA) for 1 h. Cells have been stained with rhodamine or Alexa Fluor 488 phalloidin (1:100; Invitrogen) and Hoechst (1:2,000; Invitrogen). Excessive-resolution photographs have been acquired utilizing the Zeiss LSM800 Confocal with AiryScan super-resolution module with an x,y decision of 120 nm and a z-resolution of 350 nm.

#### STORM pattern preparation, imaging and evaluation

Samples have been ready, fastened and extracted as described within the ‘Lamellipodial actin staining and imaging’ part. Subsequent, fastened samples have been handled with 0.2% NaBH4 for 7 min, and thrice with 0.5% glycine in PBS for 10 min, earlier than blocking with 5% BSA resolution containing 0.1% Triton X-100 (Sigma-Aldrich) for 1 h. The samples have been subsequently stained in a single day at 4 °C with Alexa Fluor Plus 647 Phalloidin (1:400; Invitrogen). On the day of imaging, the next options have been ready: buffer A (10 mM Tris at pH 8.0 containing 50 mM NaCl), buffer B (50 mM Tris at pH 8.0 containing 10 mM NaCl and 10% glucose) and GLOX (14 mg glucose oxidase (Millipore Sigma) and 0.85 mg catalase (Millipore Sigma) dissolved in 200 µl buffer A and 50 µl distilled H2O). The samples have been washed 5 occasions with PBS containing 0.05% Triton X-100 for five min. Instantly earlier than imaging, recent STORM imaging buffer (7 µl GLOX resolution, 7 µl 2-mercaptoethanol and 690 µl buffer B) was ready and added to the dishes. A glass coverslip was gently positioned on prime to seal off the samples from atmospheric oxygen, and the dishes have been mounted on the scope.

Photographs have been acquired on a Nikon Eclipse Ti-E (Nikon) microscope geared up with a ×100/1.49 NA Plan-Apo goal, 647 nm fibre laser operated at 500 mW and Evolve 512 EMCCD digicam (Photometrics). A complete of fifty,000 cropped photographs (128 × 128 px2) have been captured in NIS-Components (Nikon) at 120 fps. TIRF was used to restrict fluorescence to a skinny area of the pattern and the Nikon Good Focus System was used to cut back z-drifts. STORM photographs have been reconstructed and visualized utilizing Picasso software program51. Localizations have been filtered by the purpose unfold perform width (sx = 2) and peak (sy = 2) and localization precision in x (lpx = 2) and y (lpy = 2) in digicam pixels. For analysing actin density, the reconstructed photographs have been exported to ImageJ and the fibres have been reworked into binary masks utilizing the Auto Native Threshold perform of ImageJ, utilizing the Phansalkar algorithm. The sting of the cells was manually traced and the proportion of ON pixels over complete pixels was calculated inside 1.5 µm from the cell edge.

#### Cell quantity and lamella space measurements

Cell quantity measurements have been carried out as described beforehand20. Cells stably expressing Lifeact–GFP have been imaged utilizing a Nikon A1 confocal microscope with a ×60 oil-immersion goal inside 2–6 h after the substitute of the medium with that of the specified viscosity. Photographs have been acquired at 1,024 × 1,024 px decision, and confocal slices have been spaced at 0.5 µm aside. A 488 nm laser was used to picture the cells and procure their boundaries from the Lifeact–GFP sign. All through the course of the experiments, cells have been maintained at 37 °C and 5% CO2 inside a stage-top incubator and cage (Tokai Hit).

Cell quantity was measured from z-stacks utilizing a customized MATLAB script described beforehand20. Out-of-focus z-planes have been eliminated. Photographs from every analysed focal airplane have been processed utilizing the binary thresholding perform in MATLAB to take away noise. The cell boundary was detected in every picture utilizing the Canny Edge Detector operator. The sting was dilated and refilled as to acquire the cross-sectional space of the cell from every slice. The amount was calculated by multiplying the z-slice interval by the common space from two adjoining slices and integrating all the values. In choose experiments, cell quantity was analysed utilizing quantity measurement wizards of NIS-Components v.5.02.01 (Nikon) and Imaris v.9.7.0 (Bitplane).

Along with measuring the projected space of the whole cell, we assessed the realm of the a part of the cell above a vital peak from the substrate. A vital peak of two µm was chosen after making an allowance for the usually reported lamella thickness of 1 µm. Notably, this threshold eradicated attainable z-aberrations from confocal imaging. The projected lamella space was calculated by subtracting the projected space of the cell above the vital peak from the general projected cell space. To normalize the measurements with respect to the cell measurement, information have been reported as projected space of lamella over projected space of the whole cell.

#### Lamella progress imaging and evaluation

Cells stably expressing Lifeact–GFP or Lifeact–Ruby have been plated on collagen-I-coated glass-bottom dishes (Cellvis) at about 20% confluency. After treating the cells with medium of the specified viscosities for two–6 h, time-lapse photographs have been acquired each 5 s for 110 s or 2 min with a Nikon A1 confocal microscope geared up with a ×60 oil-immersion goal. Cells have been maintained at 37 °C and 5% CO2 inside a stage-top incubator and cage.

Time-lapse photographs have been imported into ImageJ and the rising entrance of the cells was manually extracted. Subsequently, a customized macro was used to establish the instantaneous cell space and edge size (or perimeter). The lamella progress at each occasion (i), was calculated by utilizing the ratio of space change over the past perimeter, utilizing the components:

$${rm{Development}}(i)=frac{{rm{Space}}left(iright)-{rm{Space}}(i-1)}{{rm{Perimeter}}(i-1)}$$

A warmth map summarizing instantaneous modern lamella progress was ready by combining all the cases from cells at a selected viscosity.

#### Actin retrograde circulation imaging and evaluation

For measuring actin retrograde circulation, MDA-MB-231 cells stably expressing β-actin-mRFP-PAGFP have been plated on collagen-I-coated glass-bottom dishes (Cellvis). Cells have been imaged utilizing the FRAP capabilities of a Nikon A1 confocal microscope (Nikon) with a ×60 oil-immersion goal. The course of cell motility was manually recognized by visible inspection over 3 min, after which an oblong area of curiosity (ROI; 60.75 × 7.25 µm2) was drawn with its size aligned perpendicular to the cell vanguard. A degree within the cytoplasm was uncovered to ultraviolet mild (405 nm) at 20% depth for 500 ms, after which imaged at GFP and RFP channels, each 100 ms or 400 ms for 30 s after ultraviolet illumination.

For evaluation of retrograde circulation, the time-lapse movies have been imported into ImageJ. RFP and GFP channels have been individually extracted, transformed to binary and smoothed twice. Subsequent, a kymograph was drawn perpendicular to the vanguard for the picture with GFP sign, and the angle subtended by the retrograde circulation of the photo-converted PAGFP molecule was used to estimate the circulation fee with respect to the laboratory body. The uninterrupted vanguard progress fee was quantified by measuring the slope generated by the cell vanguard within the kymograph earlier than a retraction occasion occurred. The picture from the RFP channel was used to find the cell edge earlier than photoactivation.

#### Measurement of epifluorescent FRET-based RHOA exercise

Cells expressing the RhoA2G biosensor have been plated onto collagen-I-coated glass-bottom dishes. Inside 2–6 h of exposing cells to medium of the specified viscosity, photographs at CFP (excitation: 430/24, emission: 470/24), YFP (excitation: 500/20, emission: 535/30) and FRET (excitation: 430/24, emission: 535/30) settings have been acquired. For RHOA-activity quantification, the imply pixel ratio of FRET over CFP was measured after subtraction of the background sign from the corresponding channels20,52. The picture within the YFP channel was used for tracing the cell boundary. Imaging and quantification have been carried out utilizing Nikon Components. For management experiments with FBS (10%) activation, cells have been serum-starved for twenty-four h earlier than including medium containing 10% FBS, and the pictures have been acquired inside 0.5–2 h.

#### FLIM evaluation of membrane rigidity and RHOA exercise

For membrane-tension measurements, cells, plated on collagen-I-coated glass-bottom dishes and incubated for 3–4 h in media of the particular viscosities within the absence or presence of the indicated medication, have been stained with the live-cell membrane rigidity probe Flipper-TR (Spirochrome, 0.5 mM) and imaged instantly thereafter. Confocal fluorescence lifetime imaging microscopy (FLIM) evaluation of dwell cells stained with Flipper-TR or stably expressing the RhoA2G sensor was carried out as described beforehand20,47 utilizing a Zeiss LSM 780 microscope and a PicoQuant system consisting of a PicoHarp 300 time-correlated single-photon counting (TCSPC) module, two-hybrid PMA-04 detectors and a Sepia II laser management module. For Flipper-TR imaging, a 485 nm laser line was used for excitation with 600/50 band-pass detector unit. Cells have been maintained at 37 °C and 5% CO2 throughout imaging inside a PeCon surroundings chamber and stage.

#### FLIM reconvolution, picture segmentation and segmentation quantification

The FLIM information have been processed as described beforehand20,47 utilizing SymPhoTime 64 (PicoQuant) software program. In short, a custom-made script was used for the calculation of the interior response perform from 100 information factors with no smoothing. After binning the information to make sure no less than 500 photons per binned pixel, a cell-specific threshold was utilized to get rid of out-of-cell fluorescence. The fluorescence decays have been match into each binned pixel utilizing the three-exponential reconvolution. For Flipper-TR quantification, the longest lifetime (τ1) with the upper match amplitude was recorded for every cell in line with the producer’s suggestions. For RHOA-FLIM segmentation quantification, the intensity-weighted fluorescence lifetime averages (τAI) have been measured utilizing SymPhoTime 64 in numerous areas of the cells. Knowledge from the nuclear area have been excluded throughout FLIM segmentation utilizing a free-form ROI as a result of the RHOA FRET sensor was excluded from the nucleus, leading to low and variable photon counts within the centre of the cells. The whole cell with out the nucleus is outlined as ‘entire’, whereas the lamella area at cell edge is recognized from DIC photographs (Prolonged Knowledge Fig. 8d). The ‘physique’ of the cell includes of the rest of the cell with out the lamella and the nucleus.

#### Calcium dynamics imaging and quantification

Cells transiently or stably expressing GCaMP6s have been plated on collagen-I-coated glass coverslips with PDMS partitions3 and have been grown to 60–80% confluency. Inside 5 min of the addition of the indicated stimulus, cells have been imaged each minute for 80–120 min with a ×20 goal on a Nikon A1 confocal microscope utilizing the 488 laser and the GFP filter settings. The GFP sign of consultant cells was manually traced in ImageJ over time by measuring the imply depth of a round ROI contained in the cell. Calcium spikes have been recognized as cases with better than 2× depth over the baseline ranges.

#### Osmotic shock experiments

For utility of osmotic shocks, hypotonic media have been ready and their osmolarity was measured as described beforehand20. Medium options have been ready by diluting basal IMDM medium (292 mOsm) twofold (2×, leading to 141 mOsm) or four-fold (4×, 71 mOsm) with ultrapure water. For FLIM measurements, cells have been serum-starved for twenty-four h earlier than measuring RHOA exercise inside 5–30 min after utility of the osmotic shock. Cell quantity measurements have been additionally accomplished inside 50 min after shock.

#### Immunofluorescence and picture evaluation

For pMLC, Ki-67 and YAP1 staining, cells have been fastened with 4% paraformaldehyde (Thermo Fisher Scientific), permeabilized in 0.1% Triton X-100 and blocked for 1 h at room temperature with 5% BSA resolution containing 2% (for YAP1) or 5% regular goat serum (Cell Signaling) and 0.1% Triton X-100. Subsequent, cells have been incubated at 4 °C with an anti-pMLC (Ser19) antibody (raised in rabbit; Cell Signaling; 3671; 1:100), anti-YAP antibody (raised in mouse; clone 63.7; Santa Cruz Biotechnology; sc-101199; 1:50) or anti-Ki-67 antibody (raised in mouse; 8D5; Cell Signaling, 9449; 1:800) in a single day. For NHE1 and ezrin staining, cells have been fastened with 4% paraformaldehyde, permeabilized in 0.1% Triton X-100 and blocked for 1 h at room temperature with 1% BSA containing 0.1% Triton X-100. Subsequently, cells have been incubated at 4 °C with an anti-NHE1 antibody (raised in mouse; 54; Santa Cruz Biotechnology; sc-136239; 1:50) or anti-ezrin antibody (raised in rabbit; Cell Signaling; 3145S; 1:200) in a single day. After washing thrice with PBS, samples have been incubated for 1 h at room temperature with Alexa Fluor 488 goat anti-rabbit immunoglobulin G (IgG) H+L (Invitrogen; A11034; 1:200), Alexa Fluor 488 goat anti-mouse immunoglobulin G (IgG) H+L (Invitrogen; A11029; 1:200) or Alexa Fluor Plus 647 goat anti-mouse immunoglobulin G (IgG) H+L (Invitrogen; A32728; 1:100). All antibodies have been ready within the respective blocking buffer. Nuclei and actin have been additionally stained with Hoechst 33342 (Invitrogen; 1:2,000) and rhodamine phalloidin (Invitrogen; 1:200), respectively. Samples have been imaged utilizing a ×60 oil-immersion goal on a Nikon A1 confocal system. Samples stained with solely secondary antibodies have been used as unfavourable controls.

The spatial distribution of pMLC and ARP3 was evaluated by drawing a rectangle alongside the whole size of the cell and recording the common depth throughout the rectangle’s width utilizing the Plot Profile perform in ImageJ. Uncooked depth information from every cell have been compiled in Excel, and the transferring common was calculated after normalizing the depth with respect to the bottom sign for the cell. For quantification of NHE1 and ezrin polarization, free-form areas on the entrance and rear edges of the cells have been manually drawn, and their imply depth values have been recorded. The front-to-rear ratio was calculated from the imply depth values for every cell. For analysis of the proportion of Ki-67-positive cells, 2,396 × 1,917 µm2 photographs have been exported to ImageJ, and the entire variety of nuclei recognized by DAPI in addition to the variety of Ki-67-positive cells have been enumerated utilizing the Discover Maxima perform on the respective fluorescent channels. To quantify the nuclear-to-cytoplasmic ratio of YAP1, the imply fluorescence depth of YAP1 inside a manually drawn ROI contained in the nucleus was divided by the imply depth of the identical ROI positioned exterior the nucleus.

#### qPCR evaluation

Scramble management, shTRPV4 or shAQP5 cells have been grown to 95% confluency and their complete RNA was remoted utilizing Direct-zol RNA isolation package (Zymo Analysis) in line with producer’s suggestions. Reverse transcription and qPCR have been carried out utilizing normal strategies described beforehand19 utilizing the next primer units: TRPV4: F, 5′-CCCGTGAGAACACCAAGTTT-3′ and R, 5′-GTGTCCTCATCCGTCACCTC-3′; AQP5: F, 5′-CAGCTGGCACTCTGCATCTT-3′ and R, 5′-TGAACCGATTCATGACCACC-3′; MIIA: F, 5′-ATCCTGGAGGACCAGAACTGCA-3′ and R, 5′-GGCGAGGCTCTTAGATTTCTCC-3′; MIIB: F, 5′-GCTGATGGCAACTCTCCGAAAC-3′) and R, 5′-CTTCCAGGACACCATTACAGCG-3′); MIIC: F, 5′-CAGCCGTCAAATGCAAACCGAG-3′ and R, 5′-TTGCCTCTGTCGTCACCTTCTC; 18S: F, 5′-CAGCCACCCGAGATTGAGCA-3′ and R, 5′-TAGTAGCGACGGGCGGTGTG-3′.

#### Western blotting

Western blots have been carried out as described beforehand19,20,47 utilizing NuPage 4–12% gels and the next antibodies. Uncropped, unique blots are supplied in Supplementary Fig. 1.

The next main antibodies have been used: anti-TRPV4 antibody (raised in mouse; 1B2.6; Millipore Sigma; MABS466; 1:1,000), anti-ARP3 (mouse; FMS338; Abcam; ab49671; 1:5,000), anti-ARPC4 (rabbit; Abcam; ab217065; 1:2,000), anti-integrin β1 antibody (rabbit; Cell Signaling; 4706S; 1:1,000) and anti-NHE1 (raised in mouse; 54; Santa Cruz Biotechnology; sc-136239; 1:200). GAPDH was used as a loading management (rabbit; 14C10; Cell Signaling; 2118S; 1:5,000).

The next secondary antibodies have been used: anti-mouse IgG, HRP-linked antibody (Cell Signaling; 7076S; 1:1,000) and anti-rabbit IgG, HRP-linked antibody (Cell Signaling, 7074S; 1:1,000).

#### Electrophysiological recording

Ionic currents have been recorded within the whole-cell patch-clamp mode32. Patch pipettes have been crammed with an answer containing 140 mM N-methyl-d-glucamine chloride, 1 mM MgCl2, 5 mM EGTA, 10 mM HEPES, 4 mM ATP and 0.1 mM GTP (300 mOsm l−1, pH 7.3). The tub resolution contained 125 mM NaCl, 1.5 mM MgCl2, 1 mM EGTA, 10 mM HEPES and adjusted to 305 mOsm l−1 (with d-mannitol) and pH 7.36. Cells have been held at 0 mV and ramps from −100 mV to +100 mV (400 ms) have been utilized at a frequency of 0.2 Hz. Ramp information have been acquired at 10 kHz and have been low-pass filtered at 1 kHz utilizing Axon p-Clamp software program. Experiments have been carried out at room temperature.

#### NHE1 exercise measurement

To measure NHE1 exercise, two totally different probes and strategies have been used. A technique described in ref. 53 was used, which quantifies the speed of pH restoration in cells stably expressing the ratiometric pH sensor pHRed28 after intracellular acidosis as a result of transient publicity to NH4Cl. The second methodology used was the quantification of intracellular pH in SC and shNHE1 cells loaded with the pHrodo red-AM (Molecular Probes; P35372) in addition to the measurements of modifications in pHrodo sign in cells uncovered to the NHE1 inhibitor EIPA. MDA-MB-231 cells expressing pHRed have been excited at 561 nm and 405 nm laser traces, and emission was collected utilizing a 600/50 detector. Intracellular pH is inversely proportional to the ratio of intensities at 561 nm over 405 nm (I561/I405).

Cells expressing pHRed have been plated on collagen-I-coated glass-bottom dishes (Cellvis) at 20% confluency. After 2–6 h publicity to media of desired viscosities, cells have been incubated with DMEM supplemented with 10% heat-inactivated FBS and 1% penicillin–streptomycin for 10 min. Subsequent, cells have been imaged each 30 s for two min on a Nikon A1 confocal microscope with a Plan Apo ×60 goal. Thereafter, the medium was gently aspirated and changed with DMEM containing 10% heat-inactivated FBS, 1% penicillin–streptomycin and 15 mM NH4Cl. Cells have been then imaged each 30 s for 4 min earlier than changing NH4Cl-containing medium with DMEM supplemented with 10% heat-inactivated FBS and 1% penicillin–streptomycin. Imaging was continued each 30 s for an additional 5 min. For evaluation, the boundary round every cell was robotically traced at each time level utilizing the ROI detection perform in NIS Component (Nikon), and the ratiometric depth values over time have been exported. GraphPad Prism (GraphPad) was used to plot the time-dependent variation in intracellular pH and linear curves have been match to the pH restoration section of every cell. The slope from the fitted line was used to quantify the speed of proton efflux or NHE1 exercise the place the fee of pH restoration is -dR/dt.

Intracellular pH was measured utilizing pHrodo Purple AM in line with the producer’s directions. In short, cells grown on 13 mm coverslips have been uncovered to 1 ml of bathing resolution containing a dilution of 1 µl of 5 mM pHrodo Purple AM in 10 µl of PowerLoad 100× focus at 37 °C for 30 min. Cells have been washed twice with isotonic resolution and allowed to accept 5 min at room temperature in a home made perfusion chamber. Video microscopic measurements of pHrodo Purple AM fluorescence have been obtained utilizing an Olympus IX70 inverted microscope with a ×20 goal (Olympus). ROIs of GFP-positive cells have been chosen earlier than operating the experiment utilizing a 488 nm excitation filter. To watch pHrodo Purple sign, cells have been excited at 572 nm utilizing a xenon arc lamp coupled to computer-controlled filter wheel (Lambda Collection, Sutter Instrument). Fluorescence photographs have been collected by an ORCA Flash4plus digicam (Hamamatsu Photonics) after being handed by way of eGFP/mCherry dual-emission filter (Chroma Know-how) utilizing the HCI software program (Hamamatsu Photonics). Photographs have been acquired each 5 s after 65 ms publicity time. Basal fluorescence ranges have been recorded for two min in isotonic resolution and the medium was then exchanged to isotonic medium containing 10 µM EIPA for 10 min. Subsequent intraexperimental calibration of the probe was carried out utilizing a commercially accessible intracellular pH calibration buffer package (Molecular Probes; P35379) in line with the producer’s directions. In short, after every experiment, 2–3 ml of seven.5, 6.5, 5.5 and 4.5 pH calibration requirements containing 10 µM valinomycin and 10 μM of nigericin have been gently perfused for 3–5 min. A median of the final ten information factors of every normal measurement have been plotted and fitted to an ordinary linear curve. A linear pattern equation was used to extrapolate the experimental pH values.

#### Cell publicity to medium of various viscosities

In some experiments, cells have been plated in tissue tradition flasks/plates in medium of varied viscosities. The medium was changed each alternate day, and cells have been handed to a recent flask/plate after reaching 90% confluency. Cells have been maintained in medium of the specified viscosity for six days earlier than being examined in in vitro and in vivo assays.

#### RNA-seq and evaluation

Complete RNA was extracted and purified utilizing the Zymo Analysis Fast-DNA/RNA MiniPrep Plus Package (Zymogen) in line with the producer’s suggestions. Strand-specific mRNA libraries have been generated utilizing the NEBNext Extremely II Directional RNA library prep Package for Illumina (New England BioLabs, E7760), and mRNA was remoted utilizing the poly(A) mRNA magnetic isolation module (New England BioLabs, E7490). Preparation of libraries was carried out in line with the producer’s protocol (New England BioLabs, 2.2 05/19). Enter was 1 µg and the samples have been fragmented for 15 min for an RNA insert measurement of ~200 bp. The next PCR biking situations have been used: 98 °C for 30 s; adopted by 8 cycles of 98 °C for 10 s and 65 °C for 75 s; and a ultimate extension of 65 °C for five min. Stranded mRNA libraries have been sequenced on an Illumina NovaSeq instrument, SP flowcell utilizing 100 bp paired-end dual-indexed reads and 1% PhiX management. The entire samples had over 39 million reads.

We mapped the reads to the human GRCh38.p13 genome (hg38) utilizing the HISAT2 package deal54, annotated every gene utilizing Ensemble104 and totalled the variety of exon reads for every pair utilizing the HTSEQ package deal. The human GRCh38.p13 genome (hg38) was obtained from Ensembl. The DESeq2.r package deal was used (in R, v.4.0) to normalize and examine the reads for every gene between the samples of curiosity, with respective P values for every gene per comparability and PCA rating for every pattern (Prolonged Knowledge Fig. 11a). We chosen differentially expressed genes with P ≤ 0.05 between SC samples at 0.77 cP versus 8 cP and between SC versus shTRPV4 at 8 cP. These information have been introduced in volcano plots (Prolonged Knowledge Fig. 11b) and used for pathway evaluation utilizing ingenuity pathway evaluation (Qiagen) (Prolonged Knowledge Fig. 11c). The P values for the differentially expressed genes have been generated by the DESeq2.r package deal (assuming a unfavourable binomial mannequin and corrected for FDR). Fisher’s actual technique was used to calculate the importance of pathway enrichment from ingenuity pathway evaluation with a threshold of P ≤ 0.05. Pattern preparation and RNA-seq evaluation have been carried out in a blinded method.

#### Zebrafish husbandry

Animal research have been performed in Okay. Tanner’s laboratory below protocols permitted by the Nationwide Most cancers Institute and the Nationwide Institutes of Well being Animal Care and Use Committee. Sexually mature zebrafish used for breeding have been maintained at 28.5 °C below a 14 h–10 h mild–darkish cycle. Transgenic Tg(mpx:eGFP/flk:mCherry) zebrafish55,56 have been obtained from pure spawning, saved at 28.5 °C till the time of cell injection, and maintained in fish water (60 mg On the spot Ocean sea salt (On the spot Ocean) per litre of deionized water). To inhibit melanin formation and preserve optical transparency, embryos have been transferred to fish water supplemented with N-phenylthiourea (PTU; Millipore Sigma) between 18–22 h after fertilization. PTU water was ready by dissolving 16 µl of PTU inventory (7.5% w/v in DMSO) per 40 ml of fish water. Water was changed each day. Injected fish have been maintained at 33 °C after injection and through intravital imaging.

#### Zebrafish circulatory injections

Earlier than injection, cells have been washed thrice with PBS and incubated for 20 min at 37 °C at a focus of two × 106 cells per ml in PBS containing 1 µM CellTracker Deep Purple (Thermo Fisher Scientific). Stained cells have been then washed with PBS and resuspended to a focus of 1 × 106 cells per 20 µl in PBS for injection.

For injection to the circulation, 3 days post-fertilization zebrafish have been anaesthetized in 0.4% Tris-buffered tricaine and oriented in a lateral orientation on an agarose mattress. Then, 2–5 nl of cell suspension was injected utilizing a pulled-glass micropipette within the circulation and directed in direction of the tail by way of the dorsal aorta. Fish from a given clutch have been randomly divided into experimental teams earlier than injection, and experiments have been blocked in order that handled and management cells have been injected into larvae from the identical clutch for 3 unbiased clutches. Injected fish have been screened between 1–4 h after injection to test for profitable dissemination of cells by way of the circulatory system, and have been then imaged as described beneath. Fish missing cells within the circulation have been euthanized. Gonad differentiation to find out intercourse had not been accomplished by the point factors utilized in these experiments.

#### Intravital microscopy of cell trafficking

Zebrafish larvae have been anaesthetized and immobilized in a lateral orientation in 1% (w/v) low-gelling-temperature agarose (Millipore Sigma) dissolved in fish water roughly 4 h after cell injection. To allow high-resolution confocal imaging, fish have been laterally oriented in coverglass-bottom chamber slides (Nunc Lab-Tek Chambered #1.0 Borosilicate Coverglass slides, Thermo Fisher Scientific). PTU water supplemented with 0.4% buffered tricaine was then added to the imaging chamber to maintain the larvae anaesthetized over the course of the experiment.

One-photon, confocal 2D photographs have been acquired at a decision of 512 × 512 pixels, which have been stacked to amass 3D photographs. Photographs have been obtained on the Zeiss 780 or 880 confocal microscope. For every larva, 1–2 confocal z-stacks centred on the intersegmental vessels have been acquired each 10 min for ~50 frames at 2 µm axial steps to picture a complete depth of ~100 µm. Photographs have been acquired with a Zeiss ×20 EC Plan-Apochromat, 0.8 NA goal. The samples have been concurrently excited with 488 nm mild from an argon laser, 561 nm mild from a solid-state laser and 633 nm mild from a HeNe633 solid-state laser. The zebrafish larva was maintained at 33 °C for the course of imaging on a stage prime incubator.

#### Intravital most cancers cell monitoring

Time-lapse microscopy photographs have been exported to ImageJ for evaluation. Photographs have been analysed provided that blood circulation was visually confirmed all through the larvae. To regulate for fish progress throughout imaging, photographs have been first registered by phase-correlation-based translational registration utilizing the Appropriate 3D Drift plugin57, with the vasculature of the fish used as a topographical reference. The multi-time scale computation, subpixel drift correction and edge enhancement choices have been enabled throughout registration. Most cancers cells have been tracked in 3D in registered photographs for as much as 12 h from the registered picture stacks utilizing the TrackMate plugin for ImageJ58. Tracks have been visually inspected for accuracy over the whole acquisition interval and have been manually edited to make sure that point-to-point tracks have been generated for the whole time {that a} cell moved by way of the intersegmental vessels.

Cell tracks (x,y,t,z) have been exported to MATLAB for evaluation. For every cell, the frame-to-frame velocity was calculated by dividing the displacement of the cell by the point interval between frames. A median velocity for that cell over the course of imaging was then calculated by averaging these frame-to-frame speeds. The persistence of migration was calculated by dividing the online displacement of a given cell over the course of monitoring by the entire point-to-point distance travelled. Velocity and persistence values have been calculated just for cells remaining within the intersegmental vessels for no less than 4 frames, and values have been calculated over a most of 71 frames. The common velocity of cell motion by way of the intersegmental vessels for a given larva was calculated from imply cell speeds.

#### Ex ovo chick embryo most cancers cell extravasation mannequin

Fertilized white leghorn rooster eggs have been acquired from the College of Alberta Poultry Analysis Centre and maintained at 38 °C. Embryos have been remoted from their shells after 4 days of incubation and maintained below shell-less situations in a lined dish positioned in an air incubator at 38 °C and 60% humidity2. A protocol described beforehand59 was adopted to picture and quantify tumour cell extravasation in chick embryos, which have been randomly divided into experimental teams earlier than injection. In short, 25–50 × 103 YFP-tagged MDA-MB-231 cells, preconditioned for six days at both 3 cP or 0.77 cP (naive cells), have been suspended in ice-cold PBS and injected intravenously into the CAM vasculature. Tumour cell extravasation was assessed by intravital confocal imaging 5 h after cell injection. Then, 15 min earlier than intravital imaging, lectin-649 was injected into the CAM vasculature for visualization of blood vessels. At the least 16 animals have been used for every situation for 3 unbiased experiments. The entire procedures have been permitted by College of Alberta Institutional Animal Care and Use Committee (IACUC).

#### Tail-vein injection into mice

The protocol adopted for intravenous injection of MDA-MB-231 cells was beforehand described45. In short, feminine NOD-SCID Gamma (NSG) mice (aged 5 to 7 weeks) have been obtained from the Johns Hopkins animal core facility, and have been distributed into teams to acquire a random weight distribution throughout situations. Injections have been carried out in a blinded method, with out information of cell pretreatment situations or identification of shRNA-mediated modifications. Earlier than injection, the mice have been warmed for five–10 min with an overhead warmth lamp to dilate the tail veins. MDA-MB-231 cells (5 × 105) suspended in 200 µl of regular saline have been injected. To evaluate the extent of micro- and macro-metastasis within the lungs, mice have been euthanized 48 h or 3 weeks after inoculation, respectively. Lungs have been inflated with optimum chopping temperature (OCT) compound (Fisher Healthcare) and excised for each picture and qPCR evaluation. Animal research have been performed with all related moral laws outlined in protocols permitted by the Johns Hopkins College Animal Care and Use Committee. For the three week lung colonization experiments, mice have been noticed for any potential humane experimental end-point indicators, together with respiratory misery, hunched posture, poor grooming and lack of weight in line with IACUC permitted protocols. No humane end-point indicators have been noticed throughout any experiment. Animal rooms have been maintained at 30–70% relative humidity and a temperature of 18–26 °C with a minimal of 10 room air modifications per hour. Cages have been modified as soon as per week. Mice have been fed a eating regimen containing low fibre (5%), protein (20%) and fats (5–10%).

#### Metastatic burden evaluation by imaging

Excised lungs inflated with OCT have been formalin-fixed, saturated in 30% sucrose at 4 °C in a single day, embedded in OCT compound, flash-frozen in liquid nitrogen and sectioned (15 µm thick) utilizing a cryotome CM1100 (Leica). The sections have been mounted onto Superfrost Plus Microscope Slides (Thermo Fisher Scientific), permeabilized with 1% Triton X-100 for 10 min and blocked with 2% BSA for 30 min. The sections have been stained for human vimentin (raised in mouse; O91D3; BioLegend; Alexa Fluor 647 conjugated; 677807; 1:200 dilution) for 1.5 h adopted by DAPI (1:1,000) incubation for 15 min and mounted for imaging with anti-fade resolution (90% glycerol, 20 mM Tris, pH 8.0, and 0.5% N-prolyl gallate). Background fluorescence was lowered with 0.1% Sudan Black therapy for 25 min.

Tissue-mounted slides have been imaged utilizing a Nikon A1 confocal microscope with a ×10/0.45 NA air goal. 5 or ten areas of 1,272 × 1,272 μm2 every have been randomly chosen for samples collected 48 h or 3 weeks after injection, respectively. Photographs have been exported to ImageJ and vimentin-bearing metastatic websites have been annotated for handbook counting. Micrometastases after 48 h have been enumerated as any vimentin-positive single cell, whereas macrometastases after 3 weeks have been outlined as vimentin-positive clusters containing >5 nuclei.

#### Lung colonization evaluation by qPCR

qPCR evaluation of hLINE19,60 was carried out in triplicate and the common worth per mouse was reported. In short, two small lobes of the excised lungs have been lower and flash-frozen in liquid nitrogen. For DNA extraction, the lung tissue was lysed in lysis buffer (1 M Tris, pH 8.0, 5 M NaCl, 0.5 M EDTA, 10% Tween-20, 10% NP-40 and 40 µg of proteinase Okay), homogenized and incubated at 55 °C. After 2 h, proteinase Okay was deactivated at 95 °C for two min. DNA was then extracted by phenol–chloroform, precipitated with 2.5 mM NaCl and 100% ethanol (prechilled at −20 °C), and washed with 70% ethanol. DNA samples have been resuspended in pure water after air drying. qPCR was carried out utilizing the primer pair for hLINE: ahead, 5′-TCACTCAAAGCCGCTCAACTAC-3′; reverse, 5′-TCTGCCTTCATTTCGTTATGTACC-3′. A primer pair detecting each mouse and human beta actin sequences within the DNA samples (ahead, 5′-ACGAGGCCCAGAGCAAGAGA-3′; reverse, 5′-GCCACACGCAGCTCATTGTAG-3′) was used as baseline to normalize the expression stage of human DNA (measured by hLINE) over the entire quantity of DNA enter (measured by mouse and human actin).

#### Statistics and reproducibility

Knowledge characterize the imply ± s.d. of ≥3 experiments (reflecting unbiased organic replicas) with ≥30 cells analysed per situation per experiment, and information factors denote values from every cell, except in any other case specified. Shapiro–Wilk assessments have been used for normality testing in instances through which the variety of information factors was between 3 and eight. For samples with >8 information factors, the D’Agostino–Pearson omnibus normality check was used to find out whether or not information have been usually distributed. Datasets with Gaussian distributions have been in contrast utilizing two-tailed Scholar’s t-tests and one-way ANOVA adopted by Tukey’s put up hoc check. For log regular distribution, statistical comparability was made after logarithmic transformation of the information adopted by unpaired two-tailed Scholar’s t-tests or one-way ANOVA adopted by Tukey’s put up hoc check. For non-Gaussian distributions, nonparametricMann–Whitney U-tests have been used evaluating two situations, and comparisons for greater than two teams have been carried out utilizing Kruskal–Wallis assessments adopted by Dunn’s multiple-comparison check. Choose experiments have been analysed utilizing two-way ANOVA adopted by Šidák’s or Tukey’s multiple-comparisons check. Evaluation was carried out utilizing GraphPad Prism 7, 8 or 9 (GraphPad Software program). P < 0.05 was thought of to be statistically vital; *P < 0.05, **P < 0.01, ***P < 0.001, ****P < 0.0001. The precise pattern measurement, variety of replicates, P values and statistical assessments carried out are supplied in Supplementary Data 5–19.

In Fig. 1, photographs are consultant of three (Fig. 1d,h,l) or 2 (Fig. 1f,i) unbiased organic replicas. In Fig. 2, photographs are consultant of three (Fig. 2b,g) or 2 (Fig. 2o) unbiased organic replicas. In Fig. 3, photographs are consultant of ≥3 (Fig. 3a,d) or 2 (Fig. 3g) unbiased experiments. In Fig. 4, photographs are consultant of three (Fig. 4e) or 2 (Fig. 4i) unbiased experiments.

### Theoretical strategies

#### Stochastic mannequin of actin community

A stochastic 2D mannequin of actin-based lamellipodia protrusion was constructed in Python v.3.8 utilizing frameworks and public code established in ref. 23. As actin filaments on the cell vanguard endure elongation, branching and capping occasions on the barbed ends following a Poisson course of, the actin community grows in opposition to the plasma membrane rigidity, and exerts a pressure that determines the protrusion velocity of the community vanguard. The mannequin used beforehand decided pressure–velocity relationships recapitulating not solely the Brownian ratchet mannequin of polymerization but in addition different fashions such because the tethered ratchet or end-tracking motors. Whereas the revealed mannequin examined the consequences of transient modifications in membrane rigidity on vanguard community group, we included dynamic forces appearing on the actin community as a result of extracellular fluid of an outlined viscosity into the present mannequin. We launched viscous resistive pressure into the mannequin utilizing a linear-viscous dashpot61 the place viscous loading forces on the vanguard scaled linearly with extracellular viscosity. The whole pressure per unit width at the vanguard may be described as

$$F={F}_{0}+{F}_{eta },$$

(1)

the place, F0 and Fη are forces as a result of membrane rigidity and the viscous exterior fluid, respectively. The viscous pressure at each iteration (i) may be written as

$${F}_{eta }=ktimes eta occasions {v}_{i-1},$$

(2)

the place, ok(=100,000) is a dimensionless scaling fixed, η is the extracellular viscosity and vi − 1 is the sting velocity from the final iteration.

Utilizing viscosity values examined experimentally, the consequences of viscous loading in actin community formation was modelled.

### Two-phase mannequin for confined cell migration

#### Mannequin description

A two-phase, actin–water-osmosis-coupled cell migration mannequin26,62 was used to elucidate the cell behaviour noticed experimentally at totally different extracellular viscosities. The 2 phases confer with the F-actin community and the cytosol. G-actin is within the cytosol section. The mannequin additionally contains ion diffusion and flux. Energetic ion fluxes come up from ion pumps on the cell membrane. With out lack of generality, we assume that the ions are electroneutral. The steady-state mannequin is briefly described beneath.

To mannequin cell migration in confined channels, we use a 1D coordinate system to characterize the cell. For a cell of size L, we let x (0,L) characterize the cell area, which is hooked up to the transferring cell. The cytosol section, with stress p and velocity vc, may be thought of to be an incompressible fluid and the stress gradient ought to be balanced by the friction between the cytosol and the actin community. These two situations may be written as

$$-frac{{rm{d}}p}{{rm{d}}x}-eta {theta }_{n}left({v}_{c}-{v}_{n}proper)=0,,frac{{rm{d}}{v}_{c}}{{rm{d}}x}=0,$$

(3)

the place η is the coefficient of interfacial friction between the 2 phases; θn and vn are the focus and velocity of the actin community section, respectively. On the cell boundary, water flows throughout the cell membrane because of the chemical potential distinction of water between the within and outdoors of the cell7. If we assume the water flux, Jwater, to be optimistic within the inward course, then the boundary situation for the cytosol section is

$${v}_{c}-{v}_{0}=-{J}_{{rm{w}}{rm{a}}{rm{t}}{rm{e}}{rm{r}}}^{{rm{f}}},{rm{a}}{rm{t}},x=L,;,{v}_{c}-{v}_{0}={J}_{{rm{w}}{rm{a}}{rm{t}}{rm{e}}{rm{r}}}^{{rm{b}}},{rm{a}}{rm{t}},x=0,$$

(4)

the place v0 is the steady-state velocity of the cell. The superscript notes f and b point out portions related to the entrance and rear (or again) of the cell, respectively. The water flux is calculated from

$${J}_{{rm{water}}}^{{rm{f}}left({rm{b}}proper)}=-{alpha }^{{rm{f}}left({rm{b}}proper)}(({p}^{{rm{f}}left({rm{b}}proper)}-{p}_{* }^{{rm{f}}left({rm{b}}proper)})-RT({c}^{{rm{f}}left({rm{b}}proper)}-{c}_{0}^{{rm{f}}left({rm{b}}proper)})),$$

(5)

the place α is the permeability coefficient of water, c is the focus of ion, and RT is the perfect fuel fixed multiplied by absolutely the temperature. The subscript 0 signifies the extracellular surroundings. p* is the hydraulic stress skilled by the cell, which is totally different from the hydraulic stress on the finish of the channel, p0, owing to hydraulic resistance developed within the channel. From the evaluation of a generic pipe circulation, the stress skilled by the cell may be expressed as

$${p}_{ast }^{{rm{f}}}={p}_{0}^{{rm{f}}}+{d}_{g}^{{rm{f}}}({v}_{0}-{J}_{{rm{w}}{rm{a}}{rm{t}}{rm{e}}{rm{r}}}^{{rm{f}}}),,{p}_{ast }^{{rm{b}}}={p}_{0}^{{rm{b}}}-{d}_{g}^{{rm{b}}}({v}_{0}+{J}_{{rm{w}}{rm{a}}{rm{t}}{rm{e}}{rm{r}}}^{{rm{b}}}),$$

(6)

the place dg is the coefficient of exterior hydraulic resistance, which depends upon the geometry of the channel and viscosity of the extracellular medium.

The actin community section additionally has a stress, σn, arising from actin swelling. With out lack of generality, we are able to assume that the passive swelling stress is proportional to the focus of the actin community, that’s, ({sigma }_{n}={ok}_{{sigma }_{n}}{theta }_{n}), the place ({ok}_{{sigma }_{n}}) is a continuing. The pressure from focal adhesions supplies an efficient physique pressure on the actin community. The pressure steadiness on the actin community is

$$-frac{{rm{d}}{sigma }_{n}}{{rm{d}}x}+eta {theta }_{n}left({v}_{c}-{v}_{n}proper)-{eta }_{{rm{st}}}{theta }_{n}{v}_{n}=0,$$

(7)

the place ηst is the power of focal adhesions. Actin polymerization usually happens on the entrance of the cell, whereas actin depolymerization happens inside the cytoplasm. We assume that γ is a continuing fee of actin depolymerization. As F-actin and G-actin convert interchangeably, the mass conservations of the 2 actin species are described by

$$frac{{rm{d}}}{{rm{d}}x}left({v}_{n}{theta }_{n}proper)=-gamma {theta }_{n},frac{{rm{d}}}{{rm{d}}x}left({v}_{c}{theta }_{c}proper)={D}_{{theta }_{c}}frac{{{rm{d}}}^{2}{theta }_{c}}{{rm{d}}{x}^{2}}+gamma {theta }_{n},$$

(8)

the place θc and ({D}_{{theta }_{c}}) are the focus and diffusion coefficient of G-actin, respectively. On the entrance finish of the cell, the flux boundary situation for F-actin and G-actin are associated to the speed of actin polymerization, Jactin, and the boundary situation for F-actin and G-actin is

$${theta }_{n}({v}_{0}-{v}_{n})={J}_{{rm{a}}{rm{c}}{rm{t}}{rm{i}}{rm{n}}},{theta }_{c}({v}_{0}-{v}_{c})=-{J}_{{rm{a}}{rm{c}}{rm{t}}{rm{i}}{rm{n}}},textual content{at},x=L,$$

(9)

the place ({J}_{{rm{actin}}}={J}_{{rm{actin}}}^{{rm{f}}}{theta }_{c}/({theta }_{c,c}+{theta }_{c})) and ({J}_{{rm{actin}}}^{{rm{f}}}) and θc,c are constants. As actin depolymerization happens all through the cytoplasm, the flux boundary situations for F-actin and G-actin are zero on the rear of the cell. On the time scale we’re curious about, the entire quantity of F-actin and G-actin stay a continuing in order that ({int }_{0}^{L}left({theta }_{n}+{theta }_{c}proper){rm{d}}x=L{theta }_{* }), the place θ* is the common focus of actin.

The diffusion–convection equation for ions is

$$frac{{rm{d}}}{{rm{d}}x}left({v}_{c}cright)={D}_{c}frac{{{rm{d}}}^{2}c}{{rm{d}}{x}^{2}},$$

(10)

the place Dc is the diffusion coefficient of ions. The flux on the boundary is a mix of passive, Jc,p, and energetic, Jc,energetic, fluxes. The passive flux follows the focus distinction of the ion, that’s, ({J}_{c,{rm{p}}}^{{rm{f}}left({rm{b}}proper)}=-{ok}_{{rm{sol}}}^{{rm{f}}left({rm{b}}proper)}({c}^{{rm{f}}left({rm{b}}proper)}-{c}_{0}^{{rm{f}}left({rm{b}}proper)})), the place oksol is the permeability of the passive ion flux. The unfavourable signal arises from the mannequin conference that every one inward fluxes are thought of optimistic. The energetic ion flux is prescribed within the mannequin.

Frictional forces exist between the cell’s lateral membrane and the channel wall. The magnitude of the frictional pressure may be expressed as Ff = ξv0, the place ξ is a friction coefficient. This pressure is in the other way of cell migration. By contemplating all of the exterior forces appearing on the cell, the pressure steadiness on the mobile stage is

$$-left({p}_{0}^{{rm{f}}}-{p}_{0}^{{rm{b}}}proper)-left({d}_{g}^{{rm{f}}}+{d}_{g}^{{rm{b}}}proper)left({v}_{0}-{J}_{{rm{water}}}^{{rm{f}}}proper)-{eta }_{{rm{st}}}{int }_{0}^{L}{theta }_{n}{v}_{n}{rm{d}}x-{F}_{f}=0.$$

(11)

The system is solved by contemplating all the equations collectively.

#### Mannequin specs and parameters

From experiments, we noticed a polarized distribution of focal adhesions, myosin II exercise (pMLC) and NHE1 at elevated viscosities. The distributions of focal adhesions and pMLC are extremely correlated (Prolonged Knowledge Figs. 4i and 8j), which is according to the concept myosin II exercise facilitates the maturation of focal adhesions63,64. We due to this fact assume that the distribution of focal adhesions happens on account of the distribution of myosin II, which isn’t explicitly included within the mannequin. The polarized distribution of NHE1 (Fig. 2c) can be part of the mannequin enter.

The experimental information recommend that the distribution of focal adhesions is non-uniform throughout the cell size (Prolonged Knowledge Fig. 4i). For cells at 0.77 cP medium (low viscosity (LV)), the distribution of focal adhesions is excessive at each ends and low in the midst of the cell. We use a quadratic perform

$${bar{eta }}_{st,{rm{LV}}}=4left(1-{b}_{{rm{LV}}}proper){left(bar{x}-1/2right)}^{2}+{b}_{{rm{LV}}}$$

(12)

to explain the normalized distribution of focal adhesions in low viscosity medium (Prolonged Knowledge Fig. 5e), the place (bar{x}) is the normalized coordinate of the cell size, and bLV (0,1) is the minimal worth of the profile at (bar{x}=1/2). For cells in 8 cP medium (excessive viscosity (HV)), the distribution of focal adhesions is excessive at the vanguard and low on the trailing fringe of the cell. Subsequently, we use a special perform

$${bar{eta }}_{st,{rm{HV}}}=left(1-{b}_{{rm{HV}}}proper){bar{x}}^{4}+{b}_{{rm{HV}}}$$

(13)

to explain the normalized distribution of focal adhesion for prime viscosity medium (Prolonged Knowledge Fig. 5e), the place the minimal worth bHV happens at (bar{x}=0). Experimental information recommend that bLV = 0.3 at 0.77 cP and bHV = 0.25 at 8 cP (Prolonged Knowledge Fig. 4i).

The non-normalized native power of focal adhesions is expressed as ({eta }_{st,i}={eta }_{st,i}^{0}{bar{eta }}_{st,i}) the place i {LV,HV} and ({eta }_{st,i}^{0}) is the coefficient of focal adhesions, which varies with the extracellular viscosity. To approximate the power of focal adhesions, we mixed the distribution of focal adhesion measurement and quantity for all cells in every group (Prolonged Knowledge Fig. 4j) and divided them by the corresponding variety of cells to acquire a normalized focal adhesion power map alongside the cell size. From experimental information (Prolonged Knowledge Fig. 4j), the utmost native focal adhesion space at 8 cP is about 8× bigger than that at 0.77 cP. We due to this fact assume ({eta }_{st,{rm{HV}}}^{0}=8{eta }_{st,{rm{LV}}}^{0}). The worth of ({eta }_{st,{rm{LV}}}^{0}) is estimated from literature62,65 with the consideration that cells below confinement expertise a comparatively low density of focal adhesions in contrast with cells in 2D66,67.

For confined cell migration in a 1D channel, the coefficient of hydraulic resistance is estimated from a pipe circulation68 as dg = 12 μl0/w2, the place μ is the viscosity of the extracellular medium, l0 is the efficient channel size and w is the smallest dimension of the cross-sectional geometry, which is 3.5 μm on this work. Whereas the size of cells varies with viscosity by advantage of their quantity alteration, the channel size (L0 = 200 μm) and cross-sectional space (35 μm2) are constants throughout each viscosities. For this maths mannequin, we assume that the cell occupies the whole cross part of the channel and due to this fact the cell lengths may be calculated from the measure of common cell quantity in confinement (Fig. 2a): for 0.77 cP, the cell size is L = 85 μm, and for 8 cP, the cell size is L = 125 μm. The efficient channel size is calculated by l0 = L0 − L. On the premise of those parameters, we are able to then calculate the coefficient of hydraulic resistance for every given viscosity μ. The viscosity of the medium not solely will increase the hydraulic resistance skilled by a cell, but in addition will increase the friction between the cell and channel. Thus, we use a better frictional coefficient for 8 cP medium (ξHV = 900 Pa s μm−1) than 0.77 cP (ξLV = 180 Pa s μm−1).

The polarized ion fluxes are decided by the distribution of membrane ion channels. We use ({J}_{c,{rm{energetic}}}^{{rm{b}}}) and ({J}_{c,{rm{energetic}}}^{{rm{f}}}) to characterize energetic ion fluxes on the again (trailing edge) and entrance (vanguard) of a cell, respectively. For polarized cells, (left|,{J}_{c,{rm{energetic}}}^{{rm{f}}}proper|{ne {rm }J}_{c,{rm{energetic}}}^{{rm{b}}},{rm }) and we let the ratio (gamma ={rm }{J}_{c,{rm{energetic}}}^{{rm{f}}}{/J}_{c,{rm{energetic}}}^{{rm{b}}}{rm }) be the identical because the polarization ratio of NHE1. Thus, for 0.77 cP medium, γLV = 1.67, and for 8 cP medium, γHV = 2.84 (Fig. 2c). Within the mannequin, we repair ({J}_{c,{rm{energetic}}}^{{rm{b}}}) and let ({J}_{c,{rm{energetic}}}^{f}=-gamma {J}_{c,{rm{energetic}}}^{{rm{b}}}). When NHE1 is inhibited, ({J}_{c,{rm{energetic}}}^{f}={J}_{c,{rm{energetic}}}^{{rm{b}}}=0).

The remaining parameters are equivalent at each viscosities and are listed in Supplementary Data 4.

### Reporting abstract

Additional info on analysis design is offered within the Nature Analysis Reporting Abstract linked to this text.