Pressure drives rapid burst-like collective migration from 3D cancer aggregates

Collective migration of cells is a key behaviour observed during morphogenesis, wound healing and cancer cell invasion. Hence, understanding the different aspects of collective migration is at the core of further progress in describing and treating cancer and other pathological defects. The standard dogma in cell migration is that cells exert forces on the environment to move and cell-cell adhesion-based forces provide the coordination for collective migration. Here, we report a new collective migration mechanism that is independent of pulling forces on the extra-cellular matrix (ECM), as it is driven by the pressure difference generated inside model tumours. We observe a striking collective migration phenotype, where a rapid burst-like stream of HeLa cervical cancer cells emerges from the 3D aggregate embedded in matrices with low collagen concentration (0.5 mg ml−1). This invasion-like behaviour is recorded within 8 hours post embedding (hpe), and is characterised by high cell velocity and super-diffusive collective motion. We show that cellular swelling, triggered by the soft matrix, leads to a rise in intrinsic pressure, which eventually drives an invasion-like phenotype of HeLa cancer aggregates. These dynamic observations provide new evidence that pressure-driven effects need to be considered for a complete description of the mechanical forces involved in collective migration and invasion.

liferation, migration and protein expression [10][11][12][13][14][15][16] . Summarising, these findings show that pressure is not only a consequence of cell proliferation in confined geometries, but may also play a pivotal role in cellular functions and tumour progression. Although it may seem intuitive that pressure relaxation could lead to collective cell migration, this has not been addressed so far as a realistic mechanism.
One reason this has not yet been investigated might be that in experimentally attractive in vitro systems of cancer spheroids embedded in ECM matrices, cells actively pull on the ECM, which can result in a release of pressure within the aggregate. In fact, cells at the periphery of in vitro spheroids, sense and respond to ECM via integrins, inducing changes in their morphology, polarity, and contractile forces by which they pull on the ECM [17][18][19] . For example, collective cell-generated forces have produced matrix contractile pressures of up to ≈700 Pa, showing that, collectively, cells can strongly affect their environment 20 .
Here, we demonstrate that pressure-induced invasion is a collective migration mechanism that is fundamentally different from previously described adhesion-based strategies. Using a simple model system of HeLa cervical cancer aggregates embedded in 0.5 mg ml −1 collagen, cell swelling leads to a pressure increase that climaxes in a burst-like invasion as result of a series of mechanical events. After an initial contractile phase, where the cells potentially probe the mechanical environment of the soft ECM, cells undergo a volume increase that, consequently, raises the internal pressure. Then, rapid collective outbursts occur as the high pressures relax into regions with the least mechanical resistance. Using a computer simulation based on the initial experimental 3 conditions, we can fully recapitulate the experimental result, further supporting the finding that pressure-driven collective invasion is a novel mechanical phenotype of cell motility.

Rapid collective outbursts triggered by low density collagen microenvironment
To investigate pressure-driven collective migration we use cancer cell aggregates as standard model systems to study the interaction between 3D simple tissues and well controlled ECM microenvironments 17 (Figure 1a). Exploiting light sheet-based 3D microscopy we followed the motion of individual HeLa cells within aggregates by tracking the fluorescently marked nuclei via histone H2B-mCherry or H2B-RFP. HeLa tumour models embedded in 2.5 mg ml −1 collagen I (higher concentration collagen, HCC) did not show any shape changes but simply grew due to proliferation ( Figure 1b). However, by merely reducing the collagen concentration to 0.5 mg ml −1 (lower collagen concentration, LCC) without any other changes to the cell culture or sample preparation, we observed a drastic migration phenotype marked by rapid cell outbursts starting between [6][7][8] hpe, in which a large amount of cells were expelled into the surrounding ECM (Figure 1b Quantitative analysis of the cell tracks revealed that, while during the first hour after embedding the overall velocity of the cell motion within the spheroid was similar in the different collagen concentrations, we find a drastic increase of mean absolute cell velocity within aggregates embedded in the LCC matrices when compared to the HCC (Figure 1c). Additionally, the visually obtained phenotype suggested a more directional motion during the bursts. Indeed, detailed analysis of the mean squared displacement (MSD) demonstrates that both conditions followed a power law x(τ ) 2 = 6 D τ α , where D is the diffusion constant and τ the lag-time. However, while cells in the HCC behave diffusive, as quantified by an exponent of α HCC = 1.03, in the burst phase we saw super-diffusive motion where α LCC = 1.55, suggesting a ballistic behaviour (Figure 1d, g).
To understand if the LCC condition had an immediate or rather delayed effect on this directional movement, we created a time-resolved MSD by a 2.5 h sliding window (Figure 1f, Supplementary   Figure 1). Both the time evolution of the diffusion coefficient and the power law exponent showed time dependence, with a peak at 7-8 hpe, which is consistent with the observed morphological change. Surprisingly, the power law exponent showed a complex switching behaviour. After an initial slight super-diffusive behaviour (α LCC,0 = 1.2) it first tended briefly towards normal diffusion, before drastically increasing to its peak value and finally decreasing again, ending close to the initial value. This suggests that the coordination of the cell movement changes several times within a rather short time span of only 12 h. To further confirm this, we checked the correlation length of the velocity correlation function (Figure 1g, h), which quantifies collective migration. Indeed, the correlation length λ showed a similar behaviour as the power law exponent, with an initial decrease that was followed by a monotonic increase up to a peak value of about 120 µm at 8 hpe, before it again decayed ( Figure 1i). These rapid and fundamental changes in migration behaviour are intriguing, as they are typically associated with differential gene expression, for example, in the context of epithelial-mesenchymal transition 21 .
As the observed switching back and forth between random and collective migration seems at odds with biology, we considered a rather physical explanation. Therefore, we checked the forces exerted by the cells on the collagen matrix, however, they were not significantly changing over time, 5 but confirmed the expected increase for HCC (Figure 1j). This finding is puzzling, as it shows that rapid and collective cell migration is not accompanied by a significant increase in traction forces applied on the ECM. To understand what factors are driving the outbursts, we checked the volume of the cells in the spheroid based on a Voronoi tessellation that uses the nucleus as a proxy for the cell position. As presented in Figure 1k, we saw an impressive and rapid increase in cell volume within aggregates in the LCC condition, whereas in HCC, the volume remained unchanged over the same time span. Changes in migration modes are accompanied by aggregate shape changes and a volume increase To further understand both the changes in the motility characteristics and the volume change we developed a second approach to quantify the aggregate shape and volume by using a mathematical decomposition into spherical harmonics (SHs). SHs allow to develop any radial surface function into a series of shapes with increasing complexity, where the relative contribution of each shape is quantified by a single parameter (Figure 2a, b). As expected, the aggregate volume obtained from the SHs closely followed the time evolution that was observed for the Voronoi tessellation ( Figure   2c). However, a close inspection of the different degrees and their relative contributions gave an additional surprise. While in the first two hours, the actual shape of the aggregate resembled an oblate, as quantified by the second mode of the SHs, we saw a rapid decrease of this mode within 5 hours, followed by a drastic increase of the higher modes marking the burst phase (Figure 2a, b) starting at 7 hpe. Hence, up until 4 hpe the aggregates changed their initial oblate shape towards a sphere without any volume change. Then, a massive volume increase sets in, which we hypothesize effectively pushed cells outwards in the observed bursts. This is consistent with the observed superdiffusive motion and higher collectivity, as the cells moved in a coordinated way. To test whether individual cells embedded in the LCC condition would also show the observed volume increase, we dispersed isolated HeLa cells in the LCC condition and measured the change in volume. Consistent with the aggregate, we found a drastic increase in volume immediately after seeding ( Figure 2d).
Interestingly, the volume increase in the aggregate started later, which suggests that in the tumour model embedded in LCC condition, the contact with other cells partially stabilises the cell volume.

Rise in internal aggregate pressure before burst phase
The observed lack of correlation between the ECM pulling forces and the outbursts suggests that the cells did not migrate out in a classical collective migration mechanism, but that the observed bursts were a collective effect due to the cell volume increase. Such a swelling may lead to a pressure increase inside the aggregate, similar to previous observations in mouse embryos and epithelial monolayers 5,6 . To confirm such a volume-increase based pressure-rise hypothesis, we Indeed, we found that the internal forces acting on the pressure sensors increased monotonically and showed a significant peak at 6-7 hpe, correlating with the onset of the outbursts (Figure 2f, g).
After verifying that the pressure inside the aggregate was increasing, we wondered whether this could also exert a consequential pushing force on the environment, which would directly prove that the cells may be pushed out. To test this, we devised a modified 2.5D traction force microscopy approach 22, 23 , where the aggregate was confined in a sandwich-like fashion between a bottom polyacrylamide (PAA) gel of Young's modulus E ≈1800 Pa and a top layer of collagen I-coated glass (Figure 2h), without compressing the aggregate. When the aggregates were surrounded by LCC, we could see a significant increase in pushing forces, marked by z-traction stress at 2-6 hpe of up to ≈200 Pa, thereby deforming the bottom gel (Figure 2i, j). As the stiffness of the LCC was only about 10 Pa (confirmed by rheometry and from previous work) 24 , we did not expect that the aggregate would generate larger forces, as most cells started to move laterally in this situation (Supplementary Video 4). Nevertheless, these experiments confirmed that the pressure inside the aggregate rose in the LCC condition, and that this rise resulted in the cells generating a pushing force on the environment. This further supports the hypothesis that during the outbursts the cells are pushed by the pressure within aggregates, which is induced by the cell swelling.
To further test this hypothesis, we decided to increase the pressure acting on the aggregate 25  Collective pressure-driven invasion is independent of cell proliferation and correlates with cell death Although the pressure-driven effect provides an excellent explanation for the observed collective cell bursts, it does not illuminate the underlying mechanism. As proliferation might explain the volume increase, we arrested cells in S-phase of the cell cycle, by adding (5 µg ml −1 ) aphidicolin.
However, this did not reduce the burst phenotypes (Figure 3c), suggesting that proliferation is not required for the collective bursts. Another mechanism could be that in soft environments, like the LCC condition, cell death occurs via failed mechanotransduction 27,28 . To test whether the cells 14 within the aggregates underwent massive cell death we used the membrane-permeable dead cell stain DRAQ-7, which marks nuclei in the case of plasma membrane rupture. Indeed, we found that one day post embedding, a high number of cell nuclei stained positive for DRAQ-7 ( Figure   3b), demonstrating increased cell death. Furthermore, cell death increased in the regions of the outbursts, suggesting a relation between bursts and reduced cell survival. Since DRAQ-7 is a classical necrosis marker, we further wanted to confirm whether apoptosis possibly preceded the cell death, as reported previously 29 . Staining against the apoptosis marker Caspase-3 was highest at 4 hpe as compared to mixed lineage kinase domain-like pseudokinase (MLKL, for necrosis) which drastically increased between 6-24 hpe (Figure 3d). Thus, these markers establish the series of events leading to cell death during the burst phase. Interestingly, when inspecting the live aggregates 4 days after bursts, the DRAQ-7 staining was largely absent, indicating that the overall cell viability had recovered, even though the environment remained the same. As the current picture of collective migration is rooted in force transmission between cells by pulling forces, which is the opposite of the pushing force (pressure) we identified here, we wondered whether we would still observe the outbursts if we blocked cell-cell adhesion by a commonly used cadherin antibody (Supplementary Figure 2). Indeed, we observed that the bursts were even more pronounced when reducing the cell-cell adhesion, suggesting that the pressure-based collective migration mechanism is fundamentally different from classical collective migration schemes.

Outburst regions are controlled by a limited mechanical resistance due to collagen in-homogeneities
We demonstrated that the bursts are pressure-driven, independent of cell proliferation or cell-cell adhesion, and generated by cell swelling that is triggered by the LCC. However, the reason for depicts collagen density (in-homogeneity in LCC)).

Conclusion
Here, we report a new, pressure-driven collective migration mechanism that is initiated by a contraction of cells in a low collagen concentration environment (Figure 4b). The contraction explains the observed initial collective and super-diffusive motion while the aggregate changed from an oblate to a more spherical shape. In this process, we suspect that the integrins failed to mechanically engage because of the LCC condition's low mechanical resistance. Similar to anoikis 30 , such a failed engagement leads to massive cell death that is accompanied by cell swelling, which autonomously starts to increase the pressure inside the aggregate and pushes the cells into the environment in the direction of the least mechanical resistance. This model can explain all the observations and suggests a new mechanism of collective migration that is driven by pressure and, hence, is independent of cell-cell adhesion. In fact, this mechanism contradicts the standard paradigm for collective migration, but it is nonetheless a simple and almost intuitive outcome of pressure release. Although here we report a special situation in low collagen concentration matrices, the general pressure-driven burst mechanism might be highly relevant in the context of cancer cell invasion. Primary tumours are often encapsulated by a basement membrane that constraints the growing tumour. Upon increased proliferation, the pressure inside the tumour is known to increase. The basement membrane may rupture either by simple mechanical tension or due to active degradation by the cancer cells. In this situation the pressure might push the cells out in a similar way as demonstrated here, via cell outbursts, potentially producing drastic consequences while promoting metastasis.
Cancer aggregates were prepared in a 48-well plate (Greiner Bio-one) as previously described 17 .
Plates coated with 150 µl of 1% ultra-pure agarose (Invitrogen) in each well were cooled for 30 min prior to adding 1 ml of cell suspension containing 2000-2500 cells. The aggregates were collected between days 2-4 and imaged.
Collagen polymerisation. Collagen concentrations of either 0.5 mg ml −1 or 2.5 mg ml −1 were prepared using a mixture of 10x phosphate-buffered saline (PBS, Sigma-Aldrich) (diluted to 1x in the final volume prepared), rat tail collagen I (Corning, stock: 3.77 mg ml −1 ), and cell culture medium. The polymerisation was activated by adding 1 M NaOH to attain a pH of 7.5. All solutions used were stored in 4°C before, and kept on ice under sterile conditions while preparing the polymerisation mix. CO 2 independent medium supplemented with 10% (v/v) fetal bovine serum (FBS, Sigma-Aldrich) and 1% (v/v) penicillin-streptomycin solution (Gibco) was used instead of DMEM for experiments performed with either light sheet or spinning disk confocal microscopes.
In order to mark the collagen fibres, a collagen-binding adhesion protein 35-Oregon Green 488 (CNA35-OG488, stock: 8.2 mg ml −1 , a kind gift from Gijsje Koenderink) was used at 1:20 of the final collagen concentration for either 0.5 or 2.5 mg ml −1 as required.
Aggregate sample preparation and multi-view imaging. To image the aggregate at sub-cellular resolution we used a dual illumination light sheet microscope (Zeiss Z.1, 20x objective, N.A. Single cells sample preparation and imaging. The preparation was done immediately after passaging HeLa cells (stably expressing H2B-mCherry and LifeAct-GFP) using culture media. Cell pellets were re-suspended in 1 ml CO 2 independent medium. LCC polymerisation mixture volume of 100 µl consisting of 80,000 cells was prepared by adjusting the volume of the medium (for collagen) with respect to the volume of cells added in the mixture. The sample mix was not vortexed to prevent any damage to cells. Once the pH was adjusted to 7.5, the sample mix was pulled into the FEP capillary and rotated until the collagen polymerised (similar to aggregate preparation) and imaged with the light sheet microscope.
Cell detection and tracking in aggregates. Nuclei marked for H2B-mCherry or H2B-RFP were tracked via 'Autoregressive Motion' algorithm in Imaris 9.3.0 through the 'Spot detection and tracking' method. XY diameters were estimated from the 'Slice' view and thresholds were set for the minimum intensity and quality of detection in order to filter for noise spots detected. All further analyses of tracks were done using MATLAB R2016a. Nuclei that were unable to be segmented since their intensities did not match the threshold criteria, were omitted, and track positions were interpolated for missed links (typically 1-2).
Track analysis. Absolute velocity: The absolute velocity V i for every particle i in 3D (x, y, z) C ij (t) was binned over the distances between particles i, j (bin size = 20 µm) and the averages per bin were acquired for each time point. Next, C ij (t) up to a binned distance of 150 µm was fit by an exponential function f(x) = a e −b x , where the correlation length is defined as λ = 1 b .
Spherical harmonics for shape change and aggregate volume. Spherical harmonics are a complete set of orthogonal functions defined on the unit sphere and are extracted using the Python toolbox shtools 35 . To determine the shape and volume changes of the aggregates over time, their surfaces were described using the expansion where r denotes the distance of a point on the surface from the center of mass of the aggregate, θ and φ are the spherical coordinate angles, c lm the spherical harmonic coefficients, Y lm the spherical harmonics, l and m their degree and order, respectively, and l max the maximum degree of the expansion.
The enclosed volumes of these surfaces were determined by the integral dr r(θ, φ) 2 sin θ .
The higher the limit of the sum l max , the finer the details of a surface that can be described by the spherical harmonics. Due to this reason, on the raw data, a variable expansion degree was used as the shape of the aggregates evolved, starting with typically l max = 4 for the oblate shape at earlier time points and reaching up to l max = 15 for the intricate shapes occurring at later time points as a consequence of the bursts.
We observed that such a variation in the spherical harmonic expansion degrees on raw data over time gave rise to offsets/artefacts in the volume detection, that had to be corrected. Assuming that drastic changes in volume do not occur at short time scales, and understanding the error source due to the expansion degree changes, we readjusted the volume by adding the difference caused threshold was applied to segregate pixel intensities to background or foreground. This was followed by a standard 'Watershed' algorithm and segmented objects were measured for shape volume. Exported measurements were extracted and represented using MATLAB R2016a.
Elastic beads as pressure sensors. A custom made 37 water-in-oil emulsion was used to prepare the inert PAA beads of Young's modulus E = 3.9 ± 0.9 kPa, by injecting the water-based bead mix in oil dissolved in n-Hexane (Supelco). The PAA beads were fluorescently labelled (Atto 488 NHS-Ester, Atto-Tec) several times until sufficient fluorescent signal was achieved. HeLa H2B-mCherry aggregates were prepared (Methods) such that each well of the 48-well plate comprised ≈30 PAA beads. Aggregates with randomly incorporated elastic beads were imaged in the same way as mentioned before (Methods).
To calculate the pressure applied on the elastic beads by the cells within aggregates, we retrieved first the main force dipole deforming the bead surfaces using spherical harmonics expansions. For this, it is sufficient to use the spherical harmonic components Y 00 and Y 20 as where the first term corresponds to the radius of the beads by r 0 = c 00 √ 4π and the second term describes the major uni-axial deformation of a sphere. The surfaces of the beads were expanded in the 0 th and 2 nd degrees of the spherical harmonics using the above function, and the surfaces were rotated in such a way that the c 20 coefficient was minimized, aligning then the main axis of compression with the z-axis. Using this expression as an ansatz to tackle the elastic problem on a sphere as expressed in the Navier-Cauchy equation, we arrived at the force dipole acting on the bead and N θ (ν) = 1 2 − 1 4−6ν , and ν and G being Poisson ratio and shear modulus of the PAA beads, respectively.
The pressure was then estimated from the relation P = F A with F = F and A is taken as the surface of the bead, Measuring the internal pressure by confining aggregates. HeLa H2B-mCherry day 2 aggregates were equilibrated for 1 h in CO 2 independent medium containing 10%  Chemical reagents to inhibit aggregate bursts. Aphidicolin (Sigma-Aldrich, A4487) and Ecadherin Antibody (G-10, SCBT) were used at working concentrations of 5 µg ml −1 and 10 µg ml −1 , respectively. Aggregates to be treated with aphidicolin were pre-incubated with the drug along with culture media for 1 h at 37°C in a humidified atmosphere with 5% CO 2 . After an hour, aphidicolin pre-incubated aggregates and E-cadherin untreated aggregates were embedded in FEP capillaries containing LCC along with the respective drug/chemical (N = 10 each). Sample capillaries were immersed in 1 ml culture medium (with or without drug/chemical (control)) and stored at 37°C in a humidified atmosphere with 5% CO 2 overnight. After 24 h, samples were slid out of the capillaries carefully into a Petri dish and bright-field images were taken using an inverted microscope (Vert.A1 Zeiss, Axio).
Quantifying cell survival. FEP capillaries consisting of HeLa (stably expressing H2B-mCherry, or H2B-mCherry and LifeAct-GFP) aggregates that had undergone a burst-like invasion within 8 h of sample preparation (Methods), were continued to be stored at 37°C in a humidified atmosphere with 5% CO 2 from days 1-4 (N = 10, for each day). After each day, the capillaries were removed and samples were pushed out carefully into a Petri dish (60/15 mm, Greiner Bio-one), after which 100 µl of culture medium was added on top of each of the aggregates (still in LCC) to prevent drying out. From here on the samples were protected from light, and DRAQ-7 (Thermofisher) was administered at 1:100 ratio to every sample droplet and the Petri dish was stored at room temperature for 10 min. Spinning disk confocal images of the nuclei with lasers 561 nm and 647 nm (DRAQ-7) were acquired with the Slidebook 6 software (3i) using an inverted microscope (Nikon Eclipse Ti-E) equipped with a CSU-W1 spinning disk head (Yokogawa) and a scientific CMOS camera (Prime BSI, Photometrics).
Nuclei were detected using Laplacian of Gaussian detection algorithm from Trackmate 38 . The number of dead cells was subtracted from the total number of cells detected, to retrieve the % live cells.
Cryosectioning and immunostaining aggregates. Capillaries consisting of HeLa H2B-mCherry day 3 aggregates in 0.5 mg ml −1 collagen were removed from the medium at 4, 6 and 24 h and immersed in 1x PBS (3 times) to wash. The capillaries were dipped into 4% Paraformaldehyde 1 ml for 30 min. Next, capillaries were washed again 3 times with 1x PBS. To preserve the structure of the bursts in collagen, the capillaries were subjected to 500 µl optimal cutting temperature mounting medium (Sakura) for 1 h. They were then partially snap-frozen with liquid nitrogen vapour. After 30 s at room temperature, the frozen samples were pushed out of the capillaries into a block of liquid optimal cutting temperature mounting medium and centred before it was snap-frozen completely. Samples were stored at -80°C until further processing.
Samples were finally washed with PBS three times and confocal images were acquired with Slidebook 6 software (3i) using an inverted microscope (Nikon Eclipse Ti-E) equipped with a CSU-W1 spinning disk head (Yokogawa) and a scientific CMOS camera (Prime BSI, Photometrics).
Statistics. Data noise emerging as part of the image acquisition over a 12 h time series was reduced by applying a median smoothing (median of every 5 consecutive time points). The application of this smoothing function is mentioned in each figure legend. All error shades (s.e.m.) in plots were generated using an adapted function (shaded area error bar plot, https://www.mathworks.com/matlabcentral/fileexchange/58262-shaded-area-error-bar-plot, MAT-
Data availability. All relevant data supporting the findings of this study are available from the corresponding author upon reasonable request.
Code availability. The codes that were used to analyse the data or to perform the simulations are available from the corresponding author upon reasonable request.