Extracellular matrix in multicellular aggregates acts as a pressure sensor controlling cell proliferation and motility.

Imposed deformations play an important role in morphogenesis and tissue homeostasis, both in normal and pathological conditions. To perceive mechanical perturbations of different types and magnitudes, tissues need appropriate detectors, with a compliance that matches the perturbation amplitude. By comparing results of selective osmotic compressions of CT26 mouse cells within multicellular aggregates and global aggregate compressions, we show that global compressions have a strong impact on the aggregates growth and internal cell motility, while selective compressions of same magnitude have almost no effect. Both compressions alter the volume of individual cells in the same way over a shor-timescale, but, by draining the water out of the extracellular matrix, the global one imposes a residual compressive mechanical stress on the cells over a long-timescale, while the selective one does not. We conclude that the extracellular matrix is as a sensor that mechanically regulates cell proliferation and migration in a 3D environment.

Introduction

Aside from biochemical signaling, cellular function and fate also depend on the mechanical state of the surrounding extracellular matrix (ECM) (Humphrey et al., 2014). The ECM is a non-cellular component of tissues providing a scaffold for cellular adhesion and triggering numerous mechanotransduction pathways, involved in morphogenesis and homeostasis (Vogel, 2018). An increasing number of studies in vivo and in vitro shows that changing the mechanical properties of the ECM by re-implanting tissues or changing the stiffness of the adherent substrate is sufficient to reverse aging (Segel et al., 2019), accelerate developmental processes (Barriga et al., 2018) or modulate tumor malignancy (Paszek et al., 2005; Tanner et al., 2012).

The importance of the mechanical context in cancer has been highlighted for a long time by experiments altering the composition and stiffness of the ECM (Levental et al., 2009). It has also been shown that the tumor growth is modulated by the mechanical compression caused by the tumor itself, as it expands in a confined environment (Fernandez-Sanchez et al., 2010; Nia et al., 2017). Such patho-physiological growth under pressure has also been studied in vitro. When multicellular aggregates are confined by soft gels (Helmlinger et al., 1997; Alessandri et al., 2013; Taubenberger et al., 2019) or submitted to a gentle osmotic compression (Montel et al., 2011; Dolega et al., 2017), their growth is substantially reduced. It has been demonstrated that the cell cytoskeleton is involved in the response to compression and can trigger the growth impediment through a cell-cycle inhibition (Taubenberger et al., 2019; Delarue et al., 2014). In addition, the cellular volume has been recently proposed to be a key parameter in the mechanosensitive pathway (Delarue et al., 2014; Han et al., 2020). Nevertheless, it is not known how such mild global compression is transduced to the individual cells of the aggregate to alter their proliferation.

Here, we posit that cells mainly respond to the mechanical stress transmitted by the ECM, when the aggregate is under compression. This hypothesis is motivated by two evidences. First, an aggregate is a composite material made of cells, extracellular matrix and interstitial fluid. The presence of hydrated extracellular matrix is evidenced by the abundance of fibronectin in the interstitial space (Figure 1a and Appendix 8). As the ECM is 100- to 1000-fold more compressible than the cells, it absorbs most of the deformation, but still transmits the mechanical stress to the cells. Second, whereas an osmotic pressure of a few kPa strongly reduces the cell proliferation within multicellular aggregates, an identical pressure has no effect on individual cells cultured on a Petri dish, in the absence of ECM (Montel et al., 2011). In addition, the use of drugs affecting the cytoskeleton organization has a negligible effect on the effective compressibility of multicellular aggregates (Appendix 12). This indicates that the volume loss under compression is mainly due to ECM dehydration (Dolega et al., 2021).

Figure 1.

Selective compression method.

(a) Immunofluorescent staining of fibronectin in the interstitial space of a multicellular spheroid made of CT26 cells (b) Schematic view of a cell (gray) embedded in extracellular matrix (filaments), permeated by interstitial fluid (light pink). (c) Big osmolytes (green) do not penetrate through the ECM and induce a global compression. Being much more compressible than the cells, the extracellular matrix absorbs most of the deformation and exert a positive stress on the cell. (d) Small osmolytes (blue) enter the ECM without exerting any osmotic pressure on it. Conversely, they compress the cell which, in turn, exerts a tension on the ECM.

To test the hypothesis that cells respond to the ECM deformation, we introduce an experimental method that uncouples the cell volume change from the mechanical stress transmitted to the cells through the ECM. We apply this method for both multicellular aggregates and individual cells embedded in a gelified ECM. In parallel, we present a theoretical framework to estimate both the displacement and the stress at the ECM/cell interface in response to an osmotic compression, and verify experimentally its qualitative prediction. At a longer timescale, we probe the effect of the ECM compression on the cellular response. In particular, we demonstrate that, even in the absence of cell deformation, the ECM alone regulates cell proliferation and motility.

Results

Selective-compression method

We developed a simple method to either selectively compress cells embedded in ECM or the whole aggregate composed of ECM and cells. This method is based on the use of osmolytes of different sizes. When big enough, the osmolytes do not infiltrate the ECM and thus compress the whole aggregate by dehydrating the ECM, which in turn mechanically compresses the cells (Monnier et al., 2016). When smaller than the exclusion size of the ECM, the osmolytes percolate through the ECM meshwork and compress the cells which can then pull on the ECM (see schematic in Figure 1b–d and Appendix 7). We already proved (Montel et al., 2012) that a gentle osmotic pressure exerted using large dextran molecules considerably reduces the proliferation of cells inside multicellular spheroids. The effect was visible starting from and saturated at . Unless explicitly stated, the experiments described in this article were performed at , a value that minimizes the pressure, but exacerbates the biological effects.

We validated our approach by compressing ECM, cells and multicellular spheroids (MCS) using osmolytes with gyration radii respectively larger and smaller that the ECM pore sizes (Figure 2). As osmolytes, we used dextran molecules ranging from 10 to 2000 kDa. As a proxy of ECM, we used Matrigel (MG), a commercially available matrix secreted by cancer cells (Kleinman and Martin, 2005). To visualize the effect of the compression on the ECM, we prepared microbeads composed of matrigel, with a diameter of 100 μm (Figure 2a ). As shown in Figure 2a (top panel), fluorescent dextran molecules with a gyration radius below 5 nm (MW <70 kDa, hereafter called 'Small’; Granath, 1958) equally color the MG beads and the surrounding solution (left). Conversely, dextran molecules larger than 15 nm (MW >500 kDa, Big’) do not penetrate inside the MG beads, which appear darker than the surroundings (right). By following the evolution of the bead diameter subjected to (measurements taken before the compression and 45 min after the compression), we observed that small dextran molecules compress the matrigel beads by 2.5 ± 0.7% of their initial volume (Figure 2a, middle and bottom panels). Conversely, the same pressure caused by big dextran molecules occasions a much larger compression of 63 ± 5% (Figure 2b). The relatively minor compression occasioned by small dextran can be explained by thermodynamic theories involving chemical interaction between the matrix and the permeating polymer (Brochard, 1981; Bastide et al., 1981), an aspect that we neglect in this article.

Figure 2.

Cell and matrigel compression.

(a) Fluorescently labeled dextran molecules only permeate the beads (top-left panel) if their gyration radius is smaller than 5 nm. Otherwise (top-right panel) they are larger than the exclusion size of the matrigel network and are excluded from the bead. Compression of MG beads, occasioned by dextran molecules of two different sizes (Small: 70 kDa; Big: 500 kDa). Phase contrast images taken before and after the addition of pressure. (b) Beads lose 63 ± 5% of their initial volume when compressed using big dextran, and 2.5 ± 0.7% with small Dextran. N = 10. (c) Compression of individual cells using dextran of different sizes, with 15 kPa. At 5 kPa the compressibility of individual cells is not measurable. Cell compressibility is thus negligible in comparison to that of Matrigel. (d) MCS compression under 5 kPa, exerted using small (blue) and big (green) dextran molecules. In control experiments (0 kPa), the culture medium is replaced by fresh medium without dextran. (box : ±SEOM; error bars: ± SD • : single realizations).

Analogous experiments were performed using individual CT26 cells (murine colon carcinoma cells) and multicellular spheroids made with the same cell line. As the volume loss of individual cells is not measurable at kPa (Monnier et al., 2016), individual CT26 cells are submitted to kPa. At this pressure, we measured a relative compression (Figure 2c) , where is the cell volume and the volume loss upon the application of . This compression indicates that CT26 cells have an effective osmotic modulus 400 ± 100 kPa. In contrast to single cells, MCS are much more compressible, as they lose up to 15% of their volume under an omostic pressure with big dextran of kPa (Figure 2d; See also Dolega et al., 2021 for a detailed mechanical analysis). Furthermore, these measurements indicate that MCS have a typical effective osmotic modulus of 30 kPa, 15-folds smaller than that of individual cells (Dolega et al., 2021). In contrast, small dextran molecules have no measurable effect on the volume of MCS, for moderate osmotic pressures (up to kPa). However, larger pressures with these small osmolytes can lead to a cell compression within the MCS associated with a swelling of the interstitial space as we show in Section 'Selective compression of ECM in multicellular spheroids'.

These results confirm the ability of our method to discriminate between the effects occasioned by the compression of the whole MCS, and those due to the compression of the cells alone within the aggregate.

Theory: the effect of a selective compression applied to a cell nested in extracellular matrix

For simplicity, we consider the case of a single cell nested in a large -compared to the cell size- ball of ECM and subjected to the osmotic pressure obtained by supplementing the culture medium with either small or big dextran. We assume that the small dextran can freely permeate in the ECM meshwork while the big one is excluded. Our aim is to compute the displacement of the cell boundary as well as the stress applied on the cell upon application of in both conditions. Our model, detailed in Appendix 6.5, essentially couples a classical active pump-and-leak model (Hoppensteadt and Peskin, 2012) for the cell volume regulation through ion pumping and the constitutive behaviour of the ECM, which is assumed to be poro-elastic at a short timescale where remodeling is negligible. The cell cortex mechanics plays a negligible role in setting the cell volume since it involves stresses that are small compared to the osmotic forces. For simplicity, we neglect the mechano-sensitive nature of ion channels.

We show in Appendix A.5 that, for realistic estimates of the model parameters, the application of with both small or big dextran leads to the same cell volume loss which does not involve the mechanical properties of the ECM but only the cell volume regulation system:where is the osmotic pressure of ions in the culture medium and is a non-dimensional parameter representing the active pumping of ions (see Appendix A.4). The relation (Equation 1) shows that the reduction of the cell volume under compression is mainly resisted by the active osmotic equilibration of ions through the cell membrane. For relatively low pressures ( kPa), the relative change of volume is negligible. More quantitatively, formula (Equation 1) provides the estimate of the osmotic modulus of a cell kPa which is in agreement with the value measured for CT26 cells.

However, the mechanical stress applied by the ECM to the cell is qualitatively and quantitatively different in the two situations. For big dextran, this stress is compressive as the dominating effect of the dextran is to compress the ECM which in turn compresses the cells. Within some realistic approximations the amount of this compressive stress (the traction force applied by the matrix on the cell) can be approximated as the applied osmotic pressure:

In sharp contrast with the previous situation, for small dextran, the stress applied by the ECM on the cell is tensile. In fact, the dominating effect is that small dextran compresses the cells but not the ECM. Thus, cell compression is balanced by a tensile force in the ECM. This tension is given bywhere is the ECM shear modulus. Formulas (Equations 1, 2 and 3) hold in the ideal case, where osmolytes do not interact with the matrix and the axisymmetric system has stress free boundaries at infinity (the ECM ball radius is much larger than the cell radius).

In practice, for a moderate osmotic shock kPa, the dextran concentration is much smaller than the characteristic ion concentration of the external medium (few hundreds millimolars) and the tension can be considered negligible: because the ECM is soft. Therefore, in this condition, the presence of ECM makes the cell mechanically sensitive to a moderate osmotic compression using big dextran molecules, but not when using small dextran molecules. In both cases the cell volume is affected in the same negligible way, but the mechanical stress applied by small dextran on the cell is negligible compared to that exerted by big dextran.

If the osmotic pressure is further increased, the compression with small or big dextran can induce a measurable effect on the cell volume. However, the mechanical stress applied by the ECM to the cell remains fundamentally different in both situations: tensile for the small dextran and compressive for the big one.

Selective compression of ECM in multicellular spheroids

To test our theoretical predictions that the interstitial space is compressed under dextran pressure, we injected individual MCS (4–5 days old) into a 2D confiner microsystem and let them relax for few hours (Figure 3a). The MCS were thus immobilized and partially flattened inside the 2D confiner. In order to follow the evolution of the interstitial space under an osmotic compression, the culture medium was supplemented with a fluorescent tracer. The interstitial fluorescence was measured using two-photon microscopy (Figure 3b). The images of the confined multicellular aggregates were normalized to the fluorescence of the external medium and segmented with a thresholding procedure, and the signal exceeding the threshold value was integrated over the whole aggregate to quantify the total fluorescence of the interstitial space (Figure 3c). Due to optical limitations, we emphasized the effect by increasing the applied osmotic pressure to 40 kPa for small dextran and to 15 kPa for the big ones.

Figure 3.

Effect of small versus big dextran on tissue intercellular space.

(a) Schematic of the 2D confiner micro-device. The tissue is confined between the glass coverslip and the PDMS and does not move during medium exchange. (b) Two-photon images of the tissue before and after (20 min) osmotic shocks for dextran chains of 6 kDa (small) and 2MDa (big), for a given mass concentration of 100 g/L. Images were taken in the equatorial plane of the tissue, meaning 35 μm above the glass slide. Scale Bar: 50 μm (c) Mean fluorescence of the intercellular space averaged over the whole aggregate shown in panel b. (d) volume loss of spheroids submitted to = 40 kPa (small dextran) and = 15 kPa (big dextran).

In accordance with our theoretical predictions, we obtained two opposite behaviors, depending on the dextran size. Small dextran molecules induced a ∼35 ± 10% increase in the fluorescence intensity in the interstitial space (Figure 2c) while the total volume of the aggregate was reduced by ∼10% (Figure 2d). Simultaneously, the cell volume decreased (Appendix 9), thus stretching the ECM into occupying more interstitial space. In contrast, for big dextran we measured a loss of half the fluorescence, meaning that a large amount of interstitial liquid had left the intercellular space of the aggregate. The extracellular matrix was thus compressed as predicted by Equation (2) and the overall MCS volume of the whole aggregate was reduced by ∼17% (Figure 2d). We argued in Dolega et al., 2021 that the total volume reduction of the aggregate obtained with big dextran could be due mostly to the compressibility of the ECM, while the cells are quasi-incompressible. The volume reduction of the aggregate induced by a 15 kPa pressure did not differ much from the one obtained with a kPa compression, as the ECM was already fully squeezed at 5 kPa.

These results are consistent with our theoretical prediction that big and small dextran have an opposite effect on the matrix. The first puts the ECM under compression, while the latter puts the ECM under tension. Remarkably, in both cases, the cells within the aggregate undergo almost the same deformation.

ECM compression controls cell proliferation and motility

To understand the role of the ECM on the cell fate at longer timescale, we assessed the proliferation and the motility of cells within MCS cultured in the presence of small and big dextran. Figure 4a represents the equatorial cryosections of spheroids in the three mechanical states ( = 0 kPa, = 5 kPa small dextran, and = 5 kPa big dextran). Proliferating cells were immuno-stained for Ki-67, a nuclear antigen present during the cell cycle, but absent in G0 phase (Gerdes et al., 1984). Whereas cells in control MCS ( Pa) present a rather uniform proliferation pattern, a global compression of MCS (big Dextran) stops cell division in the core and alters the overall MCS growth, as previously reported (Helmlinger et al., 1997; Alessandri et al., 2013; Montel et al., 2011). The density of Ki67-positive cells is reported in panel Figure 4b, as a function of the distance from the spheroid center and for the three conditions represented in panel Figure 4a. Remarkably, under pressure the density of Ki67-positive cells uniformly decreases across the MCS. Consequently, the ratio between the proliferating cells in the periphery of the MCS and those in its core increases under pressure: 2 without pressure, 2.5 under 5 kPa exerted by small dextran and 5 when the same pressure is exerted by big dextran. To quantify the change of cell division rate, we monitored the volumetric growth of the spheroid for three conditions (control, small and big dextran) and for several days (Figure 4c–d). In all cases, the spheroids initially grew exponentially (continuous lines). However, the MCS growth rate (time to double its volume) almost doubled under the big dextran compression, increasing from 36 ± 1 hr for the control and small dextran conditions (gray circles and blue squares, respectively) to 68 ± 4 hr for the compression with big dextran (green triangles).

Figure 4.

Growth of spheroids under pressure.

(a) Proliferating cells inside MCS revealed by immunostaining of KI67 with no pressure, under global compression of kPa (big dextran) and under selective compression of the cells by the same amount (small dextran). Scale bar: 100 (b) Density of Ki67-positive cells with respect to the distance from the center of the aggregate. Three conditions: No pressure (9 MCS), kPa with small dextran (26 MCS) and kPa with big dextran (19 MCS). Error bars = standard error of the mean. (c) Time evolution of the spheroid sizes (Full images are 700 × 700 μm) and (d) quantification of the volume increase, in the three reference conditions. (e) Cell migration speed within MCS also significantly depends on ECM compression. N = 5 independent experiments per condition. Error bars represent ± SEM. Experiments were repeated at least on three independent samples. (f) Division time of CT26 cells in 2D (Petri dish), respectively with no pressure (11.4 ± 0.5 hr), with kPa/small dextran (11.0 ± 0.3 hr) and with kPa/big dextran (10.9 ± 0.4 hr). (g) Mean velocity of individual cells on a Petri dish, before (N = 9) and after compression (N = 7).

Because experiments with MCS are typically performed in solution, where a metastatic behavior is not possible, we evaluated the cell motility within the aggregate, using the Dynamic Light Scattering technique introduced by Brunel et al., 2020 (see details in Appendix 11). The mean migration velocity of cells was reduced by 50% at = 5 kPa with big dextran, as compared to the unstressed case (Figure 4e). Strikingly, both proliferation and motility remained almost unaltered when the MCS were exposed to an equivalent pressure ( kPa) applied by small dextran to selectively compress the cells while leaving the native ECM unstrained (small Dextran, blue).

To verify that neither proliferation nor motility are directly modified by the direct action of dextran in contact with the cells, we measured the proliferation and the velocity of individual cells plated in a Petri dish. Measurements were performed at low density to permit cell proliferation and migration. The results (Figure 4f-g) show that both proliferation and motility remained similar, before and after the addition of dextran at a final pressure 5 kPa.

Since the interstitial space is dehydrated under osmotic compression, cells may get in contact with each other, occasioning contact inhibition of proliferation and locomotion. However, it is also possible that cells sense and react to the stress in the ECM. To discriminate between these two hypotheses, we embeded individual cells in a MG matrix, before compressing the whole system with an osmotic pressure kPa using either small or big dextran. After a few days, we observed two clearly different phenotypes. Cells grown without pressure or in the presence of small dextran were sparse in the MG (Figure 5a, left panel). Conversely, cells cultured with big dextran proliferated locally (Figure 5a, right panel). Therefore, MG compression appears to inhibit cell motility and to promote the formation of mini-spheroids, which suggests that ECM compression has a direct effect on the cell-ECM biophysical signaling. The different cell morphology is particularly clear in the organization of the actin cytoskeleton. Cytoplasmic actin labeling revealed the presence of numerous protrusions, associated with high cell anisotropy, in cells cultured in a relaxed MG matrix (Figure 5b, left and middle panels), whereas cells appeared smooth and formed round structures, when the MG was compressed (Figure 5b, right panel). Of note, cells at the MG surface often extended outside the MG. Those cells not fully embedded in MG were excluded from our analysis.

Figure 5.

Individual cells in Matrigel.

(a) Hoechst-labeled cell nuclei superimposed to phase image. Images are taken after 2 days of proliferation in MG, either with small (left panel) or big (right panel) dextran molecules. Maximal projection from epifluorescence stacks. (b) Cell morphology and anisotropy revealed by labeling of cytoplasmic actin. Maximal projection of 50 μ m confocal Z-stack. In relaxed MG, the cells appear more elongated and with long protrusions. (c) Cell motility in MG under different compression states. Starting points of trajectories are translated to the origin, to highlight the typical distance over which cells move in the three compressive states. (d) Quantification of in-plane velocity extracted from mean square displacements, under different compression conditions. With no pressure or with small dextran (5 kPa), the average velocities are respectively 5.8 ± 0.8 / hr and 5.2 ± 0.5 / hr. Under 5 kPa exerted by big dextran, the cells are immobile (v = 0.5 ± 0.4 ), where the error is due to tracking uncertainties. (e) Temporal evolution of nuclear fluorescence intergrated over the whole sample. No pressure (ο), 5 kPa with small dextran () and 5 kPa with big dextran (). (f) Cell proliferation rate in the three conditions. n = 15, from eight independent experiments. (g) Cell proliferation rate at different initial matrigel concentration, with no pressure. Boxes represent the mean values ± SEM, error bars correspond to the standard deviation, small markers are individual experiments and large markers the median.

These different morphologies also correlates with different motilities. Cells embedded in a compressed MG were nearly immobile, while they migrated through relaxed MG with a velocity comparable to that measured on flat surfaces. The results are summarized in Figure 5c, where we report trajectories per condition. To highlight differences and similarities between the three compression conditions, the starting points of all trajectories are translated to the origin and, although isotropic, they are divided in three quadrants. Quantification is reported in Figure 5d. From this experiment we conclude that whereas no appreciable differences are observable between control and the small dextran condition, the cell motility dramatically drops under MG compression with big dextran.

To quantify the effect of ECM compression on proliferation, we prepared several samples with the same number of hoechst-stained cells embedded in the MG and measured the overall fluorescence over time. Figure 5e shows the typical time evolution of the Hoechst signal for the three conditions: proliferation rate drops considerably when the MG is compressed (Big Dextran, ), compared to the case without pressure (ο), but also compared to the case where the pressure is selectively exerted on the cells with no MG compression (Small Dextran, ). Figure 5f quantifies the mean growth rate, measured on at least 15 samples for each condition, collected on eight independent experiments (different days and cell passages). Under pressure, the matrigel get dehydrated and compacted, which may directly influence cell proliferation. On the one hand a denser matrigel is less compressible and, thus, less favorable to cell proliferation (Baker et al., 2015). On the other hand, matrigel compression concentrates matrix-bound growth factors, which may promote cell division. To determine which effect dominates, we measured the proliferation rate at different initial MG concentrations, between 2 g/l and 8 g/l (experiments reported in panels a-f were performed with MG at 4.5 g/l). Our experiments show that within this range, the matrigel density has little to no effect on cell proliferation (see Figure 5g). These experiments confirmed that it is the compressive stress transmitted to the cells by the surrounding ECM, rather than a direct osmotic pressure on the cells, that strongly impacts cell motility and proliferation.

Discussion and conclusion

Large osmotic and mechanical pressures (of the order of 100 kPa) can cause a decrease in cell volume and consequently a deformation of the cell nucleus (Zhou et al., 2009; Kim et al., 2015) which may ultimately feedback on the cell proliferation. It has been recently proposed that the volume of the cell or its nucleus can be key to crucial processes such as proliferation, invasion, and differentiation Guo et al., 2017; Han et al., 2020. However the weak osmotic pressures (of the order of 1 kPa) that we apply have no measurable effect on the cell volume. In addition, it is well-known from a biological standpoint that such small volume perturbations are buffered by active regulatory processes in the cell (Hoffmann et al., 2009; Cadart et al., 2019). Yet, both cell proliferation and motility decrease in MCS submitted to weak osmotic compression. Our results show that, for such weak compressions, the cell volume is unchanged while the ECM located in between the cells is directly impacted. This mechano-sensitive role of the ECM could explain the reported evidences that osmotic pressures applied by big dextran and mechanical pressures similarly affect the growth of MCS. (Helmlinger et al., 1997; Alessandri et al., 2013; Montel et al., 2011). Indeed, in this case the osmotic pressure induces a mechanical one applied on the cells through the ECM drainage. Thanks to its bulk modulus 1 kPa, the ECM behaves as a pressure sensor for the cell in the kPa range. Of note, stress relaxation in the ECM could occur through cleavage and remodeling of its components and such active processes should be quantified in the future.

Several mechanisms may explain how the dehydration of the extracellular matrix can result in an inhibition of proliferation and motility. First, the reduction of the interstitial space promotes interactions between neighbouring cells, which may activate contact inhibition signals of both proliferation and locomotion (Roycroft and Mayor, 2016). Second, the ECM porosity and tortuosity change within a compressed MCS, such that its effective permeability to oxygen, nutrients, growth factors and cytokines is reduced and might activate inhibition signals without cell-cell contact. However, both options are incompatible with the results we obtained with single cells embedded in MG (Figure 5). During the first 2–3 days after seeding, cells are either isolated or grouped in aggregates of two to four cells with limited cell-cell contacts. Additionally, a key factor limiting the diffusion of oxygen and nutrients in MCS is the tortuosity of the interstitial space (Bläßle et al., 2018). This constraint is simply absent in experiments with single cells embedded in MG, suggesting that the cell proliferation inhibition is most probably not related to hypoxia and starvation.

The present work therefore points at a direct mechanosensitive response of cells to the ECM deformation. The microscopic structure of the ECM is modified under compression (e.g. density increase and reduction of porosity), with consequences on the ECM rheology. Compression of the ECM is clearly accompanied by an increase in its bulk modulus and, due to its fibrillar structure, to a non-trivial and non-linear evolution of its stiffness (Sopher et al., 2018; Kurniawan et al., 2016). For example, the rheological properties of synthetic ECM have been shown to affect growth of aggregates and single cells through the regulation of streched-activated channels (Nam et al., 2019). As integrin-dependent signals and focal adhesion assembly are regulated by the stress and strain between the cell and the ECM, the osmotic compression may steer the fate of cells in terms of morphology, migration, and differentiation (Pelham and Wang, 1997; Choquet et al., 1997; Sunyer et al., 2016; Isenberg et al., 2009; Butcher et al., 2009; Engler et al., 2006; Staunton et al., 2019; Panzetta et al., 2019). This aspect is also relevant from an oncological point of view. Indeed the ECM is strongly modified in tumour tissues and the solid stress within tumors can reach several kPa, which is in accordance with the pressure applied here (Nia et al., 2017). For example, in tumors, there is a decrease in the ratio collagen/hyaluronan (Voutouri et al., 2016). The latter, more hydrophilic than the first one, tends to swell and stiffen the ECM. Whether a corrupted matrix is a contributing cause or the consequence of the neoplasia remains an open question, but the correlation between matrix mechanics and uncontrolled proliferation is more and more widely accepted (Bissell et al., 2002; Lelièvre and Bissell, 2006; Broders-Bondon et al., 2018).

In future experiments it will be crucial to identify whether the ECM compression and the associated changes in stiffness play a dominant role, or if – as we suggest – the mechanical stress applied on the cell through the ECM is the key ingredient directly triggering the cell biological adaptation in term of proliferation and motility.

Materials and methods

Cell culture, MCSs formation, and growth under mechanical stress

CT26 (mouse colon adenocarcinoma cells, ATCC CRL-2638); American Type Culture Collection were cultured under 37°C, 5% CO2 in DMEM supplemented with 10% calf serum and 1% antibiotic/antimycotic (culture medium). Cells are texted every month for mycoplasma. None of the experiments was made using cells with mycoplasma. Spheroid were prepared on agarose cushion in 96 well plates at the concentration of 500 cell/well and centrifuged initially for 5 min at 800 rpm to accelerate aggregation. After 2 days, Dextran (molecular mass 1, 10, 40, 70, 100, 200, 500, and 2000 kDa; Sigma-Aldrich, St. Louis, MO) was added to the culture medium to exert mechanical stress, as previously described (Monnier et al., 2016). To follow spheroid growth over the time, phase contrast images were taken daily. Spheroid were kept under constant pressure over observation period. Images were analysed manually using Imagej. Each experiment was repeated three times, with 32 individual spheroids per condition.

Measurement of MCSs volume

The area of the MCS equatorial section was measured before and after addition of dextran, then converted to volume assuming that the MCS is spherical. To induce compression, half of the culture medium was removed and replaced with fresh medium containing dextran 2X (two-fold the target concentration). The error affecting this measurement mainly comes from the fact that spheroids rotate during buffer exchange. As they are not perfectly spherical, the area of the equatorial section may change by up to few percent. To homogenize the experiments, control spheroids (no pressure) were also measured before and after buffer exchange. In the latter case, 50% of the culture medium was simply aspirated and replaced by fresh medium not supplemented with dextran.

Fabrication of Matrigel beads

Matrigel beads (Matrigel Corning, Ref: 354234) were prepared using vortex method (Dolega et al., 2017). Oil phase of HFE-7500/PFPE-PEG (1.5% w/v) was cooled down to 4°C. For 400 μL of oil, 100 μL of Matrigel were added. Solution was vortexed at full speed for 20 s and subsequently kept at 37°C for 20 min for polymerization. Beads were eventually transferred to PBS phase by washing out the surfactant phase.

Fluorescence eXclusion method (single-cell volume measurements)

Cell volume was obtained using Fluorescence Exclusion microscopy (Cadart et al., 2017; Zlotek-Zlotkiewicz et al., 2015). Briefly, cells were incubated in PDMS chips, with medium supplemented with a fluorescent dye that does not enter the cells. Cells thus excluded fluorescence, and one extracted cellular volume by integrating the fluorescence intensity over the whole cell . Chips for volume measurements of single cells were made by pouring a mixture (1:10) of PMDS elastomer and curing agent (Sylgard 184) onto a brass master and cured at 80 °C for at least of 2 hr. Inlet and outlets were punched with a 3 mm biopsy puncher. Chips were prepared few days before, bounded with oxygen plasma for 30 s, warmed up at 80°C for 3 min then incubated with Poly-l-lysine (sigma) for 30 min to 1 hr, washed with PBS, then washed with dH2O, dried and stored sealed with a paraffin film. The chambers were washed with PBS before cell injection. Imaging started within 10 min after cell injection in order to prevent adhesion and thus cells response to the shear stress generated by the medium exchange. Acquisition was performed at 37°C in CO2 independent medium (Life Technologies) supplemented with 1 g/L FITC dextran (10 kDa, from Sigma Aldrich) on an epifluorescence microscope (Leica DMi8) with a 10x objective (NA. 0.3 from LEICA). Master molds were fabricated on a brass substrate with a micromilling machine (MiniMill/3; Minitech) using a 100-μm-diameter milling cutter (Minitech). Height profiles and surface roughness were measured with a vertical scanning interferometric profilometer (Brucker). 3D mold design and tool paths were generated using Autodesk Inventor Professional software (Autodesk). Molds for spheroid confinement were made with classical soft lithography techniques.

Tissue compression experiments

Spheroids were harvested 4 or 5 days after cell seeding and injected in the 2D confiner microsystem (Figure 3a) using a MFCS pressure controller (Fluigent). Spheroid were partially flattened between two parallel surfaces, perpendicular to the optical axis of the microscope, and rested for two to 5 hr to relax in the microsystem at 37°C in CO2 independent medium. Before acquisition, medium supplemented with 2 g/L FITC-dextran (10 kDa from Sigma Aldrich) was injected to label the intercellular space. Medium exchange was performed manually using large inlets (<1 mm) during two-photon acquisition. Acquisitions were performed at 37°C on a Nikon C1 two-photon microscope coupled with a femtosecond laser at 780 nm with a 40x water-immersion (NA. 1.10) objective (Nikon). The 2D confiner chip was made by pouring PDMS elastomere and curing agent (1:10) into the mold and cured for at least 2 hr. The chips were bounded to glass coverslips with 30 s oxygen plasma, immediately after bounding. A solution of PLL-g-PEG (Surface Solutions) at 1 g/l was injected and incubated for 30 min in humid atmosphere to prevent cell surface adhesion during the experiment. The chips were washed with and dried and sealed with a paraffin film. Fluorescence of the Intercellular space (ICS) was measured using MatLab software. As control and dextran solutions have different levels of fluorescence, the fluorescence in the ICS was normalized by the one outside the ICS in order to compensate these variations. Then, first the tissue (cells and ICS) was segmented with a thresholding procedure. The threshold was determined in order to obtained accurate segmentation of the ICS before application of the osmotic stress. The surface of the ICS was computed as the ratio of pixels in the ICS to the number of pixels of the tissue. For each spheroid, 50 planes - 13 µm above and below the equatorial plane - were taken into account to compute the change of the ICS surface.

Cell culture in Matrigel

Experiments have been conceived to start the culture from individual cells embedded in Matrigel. At day 1, the cells were resuspended, then dispersed in a solution containing matrigel at the final concentration of 4.5 g/l. The cells were diluted to 10,000–50,000 cells/ml, a concentration at which the average distance between neighboring cells is about 250–400 μm. We therefore consider them as isolated entities. The MG/cell ensemble was gelified in 200 μl wells, at 37°C, for 30 min. To avoid cell sedimentation, we gently flipped the sample over, every two minutes. The samples were then redeposited in the incubator under three pressure conditions: no pressure and 5 kPa exerted by small and 5 kPa exerted big dextran.

Cells migration in Matrigel

To quantify cell migration in Matrigel, individual cells were observed by phase contrast microscopy. Z-stacks were collected every 20 min and for several days, with slices spaced by 50 μm. Then the full stack was projected to one single layer (maximum intensity projection). Cells were tracked manually in the 2D plane, using the ImageJ MTrackJ plugin (https://imagescience.org/meijering/software/mtrackj/).

Cryosectioning and immunostaining

Spheroids were fixed with 5% formalin (Sigma Aldrich, HT501128) in PBS for 30 min and washed once with PBS. For cryopreservation spheroids were exposed to sucrose at 10% (w/v) for 1 hr, 20% (w/v) for 1 hr and 30% (w/v) overnight at 4°C. Subsequently spheroids were transferred to a plastic reservoir and covered with Tisse TEK OCT (Sakura) in an isopropanol/dry ice bath. Solidified samples were brought to the cryotome (Leica CM3000) and sectioned into 15 μm slices. Cut layers were deposited onto poly-L-lysine coated glass slides (Sigma) and the region of interest was delineated with DAKO pen. Samples were stored at −20°C prior immunolabelling. For fibronectin and Ki67 staining samples were permeabilized with Triton X 0.5% in TBS (Sigma T8787) for 15 min at RT. Nonspecific sites were blocked with 3% BSA (Bovine serum Albumin) for 1 hr. Then, samples were incubated with first antibody (Fibronectin, Sigma F7387, 1/200 and Ki67; Millipore ab9260, 1/500) overnight at 4°C. Subsequently samples were thoroughly washed with TBS three times, for 15 min each. A second fluorescent antibody (goat anti-mouse Cy3, Invitrogen; 1/1000) was incubated for 40 min along with phalloidin (1/500, Alexa Fluor 488, Thermo Fisher Scientific). After extensive washing with TBS (four washes of 15 min) glass cover slides were mounted on the glass slides with a Progold mounting medium overnight (Life Technologies P36965) and stored at 4°C before imaging.

Statistical analysis

Student’s t-test (unpaired, two tailed, equal variances) was used to calculate statistical significance as appropriate by using the ttest2() function of Matlab (MathWorks). Statistical significance is given by *p<0.05; **p<0.01; ***p<0.001; ****p<0.0001.

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Acceptance summary:

This paper provides an elegant approach using crowding agents to study how distinct types of external mechanical perturbations influence the behavior of multicellular aggregates. The central finding is that cell proliferation and motility are significantly affected by solid stresses mediated by the extracellular matrix, whereas osmotic stresses of a similar magnitude have little effect. This finding highlights a mechano-sensory function of the extracellular matrix to regulate cell behavior in 3D environments.

Decision letter after peer review:

Thank you for submitting your article "Extra-cellular Matrix in cell aggregates is a proxy to mechanically control cell proliferation and motility" for consideration by eLife. Your article has been reviewed by three peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Aleksandra Walczak as the Senior Editor. The reviewers have opted to remain anonymous.

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

As the editors have judged that your manuscript is of interest, but as described below that additional experiments are required before it is published, we would like to draw your attention to changes in our revision policy that we have made in response to COVID-19 (https://elifesciences.org/articles/57162). First, because many researchers have temporarily lost access to the labs, we will give authors as much time as they need to submit revised manuscripts. We are also offering, if you choose, to post the manuscript to bioRxiv (if it is not already there) along with this decision letter and a formal designation that the manuscript is "in revision at eLife". Please let us know if you would like to pursue this option. (If your work is more suitable for medRxiv, you will need to post the preprint yourself, as the mechanisms for us to do so are still in development.)

Summary:

Dolega et al. investigate how proliferation and motility of cells inside multicellular aggregates are affected by different types of compression such as an osmotic pressure or a solid stress mediated by an extracellular matrix. They develop a selective compression method using crowding agents like dextran of different sizes: by using dextran that is small enough to penetrate the matrix, they impose an osmotic stress on the cells, while larger non-penetrating dextran instead results in a solid stress exerted by the matrix. The central find of this work is that cell proliferation and motility are significantly affects by solid stresses mediated by the extracellular matrix, whereas osmotic stresses of a similar magnitude have little effect.

Essential revisions:

The reviewers indicate that this is an interesting study and express enthusiasm about the ideas proposed in this study. However, several concerns are raised about the experimental evidence to support the main claims. Among other things, reviewer #2 points out that a better characterization of the ECM and the compressive deformations that are induced by the selective compression method is needed, as well as the induced compression of the cells. reviewer #3, raises similar issues, and suggest approaches to determine the stresses induced by the various types of dextran. While reviewer #1 seems quite positive overall, they also make the point that the precise mechanical role of the ECM in the observed behavior is not pinned down, and suggest that experiments that would clarify this would be a great addition. Together, the reports indicate the main claims of the manuscript would need to be more strongly supported by showing experimentally that the ECM is really produced by the cells and that there is ECM between the cells in the multicellular spheroids. In addition, the reviewers point out that direct evidence for induced stresses or deformations in the ECM is currently lacking. Finally, several comments from all reviewers raise issues about the statistical characterization of the data and possibly missing controls.

Reviewer #1:

This is an excellent study, which clearly demonstrates that the osmotic compression of the extracellular matrix (ECM) with large osmolytes reduces the growth rate of cells and their migration speed. In contrast, the same concentration of small osmolytes, which can infiltrate inside the ECM, results in a small tension of the ECM, while the growth rate of cells and their migration speed remain unaffected.

As the authors mention in the last paragraph of the Discussion, it remains unclear whether the observed behavior is due to the transmitted stress from the compressed ECM to the cells or due to the increased density of the compressed ECM. The authors mention that this could be resolved in the future by performing additional control experiments by varying the ECM density without any imposed osmotic pressure. Can the authors comment on how easy or hard it is to control the ECM density either in the matrigel or in the multicellular spheroids? If such experiments are straightforward, they would be a great addition to this paper.

Reviewer #2:

The manuscript provides an interesting work studying the effect of ECM transmitted compression on cancer cell proliferation and mobility. The main claim is that the ECM signals if cells are under global or local compression, thus resulting in different cell behavior. Although I really like the ideas proposed, I fear that the current data does not sufficiently support the claims. Overall the interpretation of the experimental data is largely exceeding what was actually shown. A simple example is that the authors constantly talk about ECM between cells in the MCS, however they never demonstrate that this ECM is indeed there. Unfortunately, there are a number of similar problems that largely reduce the quality of the work, making it currently unsuitable for publication in eLife.

1) My biggest concern is that the main claim of the work is not supported by direct measurements. It is claimed that the reduction in proliferation and motility is because of the compression transmitted by the ECM. However, the ECM and its deformation is not measured in the MCS experiments. It is simply assumed that it is there, and that it has the same properties as a individually polymerized Matrigel (MG). It is well established that the ECM organization by cells is different from repolymerized gels. The authors argue with previous studies, however, as this is the main point of the paper it is important to directly demonstrate the presence and the effect of the force transmission of the ECM in situ.

A possible experiment would be to prevent the ECM from forming in the spheroids, or to degrade it previous to the experiment. Alternatively the authors could try to use an inert hydrogel.

The very simple alternative to the ECM transmitted forces is that the cell directly push on each other, hence the ECM becomes irrelevant, as discussed by the authors. The authors try to convince the reader by the experiments of single cells in MG (Figure 5). However a simple explanation could be that due to pressure the density of the MG is beyond the point that motility is possible, hence the cells start clustering, and a local decrease of nutrients may explain the reduced proliferation.

Unfortunately, the data presented does not sufficiently demonstrate the claims.

2) It is quite irritating to be confronted with different pressures, and subsequent comparisons. Why not show the effect of 0,5,10 and 15 kPa pressure in all plots? Also the authors should provide statistical tests in all presented plots.

3) Simple controls are missing. What is the speed and proliferation of these cells in a 2D surface without dextran, and with the different dextran types and concentrations (to exclude effects of Dextran itself)?

4) The argument that commercially ECM is the same as cancer cells generate is not sufficiently backed regarding the importance of this point for the paper. You have to check if this is the case for the used cells, and if this is also happening in the spheroids.

5) A main claim at the end of the subsection “Selective-compression method” is that the single cell compression can be used as proxy for the individual cell compression in the spheroids. I fear given the importance of this point for the main message it is necessary to measure the compression of the individual cells in the spheroid. This should be possible looking at the data presented in Figure 3 (i.e. using cell profiler).

6) I am puzzled by the strong signal of KI67 in MCS without pressure. This suggests that almost all cells in the outer region are dividing, but the division time is 36 h. Since the mitosis needs about 1h, only 3% of the cells should be in mitosis. Here the thresholding is quite important and can lead to a wrong impression. Typically there should be no expression of KI67 during the time in between division (hence in more than 30h).

7) I think an important check for the overall hypothesis can be done with the cell confiner. Polymerizing single cells in Matrigel without the dextran, and then confining it with the instrument should give the same phenotype as the big dextran. I suggest to do this experiment.

Reviewer #3:

In this manuscript, Dolega and colleagues examine the impact of osmotic pressure versus solid stress (or "global compression" as the authors describe) on proliferation and motility in cell aggregates cultured in 3D gels. They develop a clever method of using dextrans that are small, so they can penetrate the gel, or are large, so that they are excluded from the gel, to exert increased osmotic pressure or solid stress, respectively. They find that solid stress impacts cell proliferation and migration within clusters, whereas increased osmotic pressure has a limited impact.

The question of how solid stress impacts cells is an important question, which is particularly relevant to the context of tumor growth. Approaches to test the impact of uniform solid stress on cells are limited. It is often assumed that modulating osmotic pressure can simulate solid stress. However, the authors show here that this assumption is incorrect. Thus, the approach the authors develop to modulating solid stress, and the finding that solid stress has a different impact than increased osmotic pressure, is important and a nice advance for the field, which is in principle suitable for eLife. This approach could serve as a powerful tool for the community. However, the method and biological results need to be better characterized in order for this manuscript to be suitable for publication in eLife. Additional no mechanistic insights are provided; some mechanistic insight would make the manuscript more impactful.

1) Characterization of method: How do the authors determine the solid stress for the large dextran used? Is it just assumed that whatever osmotic pressure is applied will translate to that amount of solid stress? While this might be the case, these gels are complex, some direct experimental measurement of this would build more confidence (e.g. by using a rheometer to measure negative normal stress of the gels or polyacrlymide hydrogel "reporter" beads). In addition, showing how solid stress varies as a function of big dextran density, and demonstrating the applicability of this idea in another common 3D culture gel system (e.g. collagen, PEG, agarose, or alginate) would facilitate the broader adoption and use of this technique.

2) Some of the experiments need more detail and statistical analysis:

Figure 2B, C and D – statistical analysis are needed.

Figure 4A: pattern and/or levels of proliferation should be quantified. Single representative images are not sufficient: quantitative data supported by statistically significant differences are required to make conclusions.

Figure 4B: are differences statistically significant? Statistical analyses should be included. Also, representative time series of images could be included.

Figure 4C: timelapse studies should be conducted, and timelapse images included, to better display the motion that is described.

Figure 5: statistical analysis should be included for D and F.

Figures 4 and 5: multiple levels of solid stress would be ideal to show the trend.

Figure 5: do cells extend beyond the periphery of the Matrigel beads?

3) Mechanistic insights – there are really no mechanistic insights provided as to how increased solid stress might lead to some of the behaviors observed. This is unusual for eLife papers. Even a screen of implicated small molecule inhibitors (e.g. actin, myosin, Rho,.…) could be valuable in generating some general idea into mechanism.

Reviewer #1:

This is an excellent study, which clearly demonstrates that the osmotic compression of the extracellular matrix (ECM) with large osmolytes reduces the growth rate of cells and their migration speed. In contrast, the same concentration of small osmolytes, which can infiltrate inside the ECM, results in a small tension of the ECM, while the growth rate of cells and their migration speed remain unaffected.

As the authors mention in the last paragraph of the Discussion, it remains unclear whether the observed behavior is due to the transmitted stress from the compressed ECM to the cells or due to the increased density of the compressed ECM. The authors mention that this could be resolved in the future by performing additional control experiments by varying the ECM density without any imposed osmotic pressure. Can the authors comment on how easy or hard it is to control the ECM density either in the matrigel or in the multicellular spheroids? If such experiments are straightforward, they would be a great addition to this paper.

We agree with the reviewer that this point is crucial. A partial answer to the question comes from the experiments added in Figure 5G of the revised version. We measured the proliferation of individual cells seeded in matrigel of increasing densities, but with no pressure. In the range 2-to-8 g/l, the MG density has a non-measurable effect. However, this measurement is not fully satisfying, as we should be able to vary the bulk modulus, the shear modulus and the biochemistry of the matrix independently. Unfortunately, this is long-term project, as the chemistry of the extracellular matrix is poorly known and its rheology depends in a non-trivial manner on the chemical composition. For instance, we have been surprised to measure that the Young modulus of MG decreases at high concentration (Atomic force microscopy experiments). This is probably because the thinning agent (Dulbecco medium), modifies the pH and the ionic strength of the solution and, thus, the MG polymerization.

Reviewer #2:

The manuscript provides an interesting work studying the effect of ECM transmitted compression on cancer cell proliferation and mobility. The main claim is that the ECM signals if cells are under global or local compression, thus resulting in different cell behavior. Although I really like the ideas proposed, I fear that the current data does not sufficiently support the claims. Overall the interpretation of the experimental data is largely exceeding what was actually shown. A simple example is that the authors constantly talk about ECM between cells in the MCS, however they never demonstrate that this ECM is indeed there. Unfortunately, there are a number of similar problems that largely reduce the quality of the work, making it currently unsuitable for publication in eLife.

1) My biggest concern is that the main claim of the work is not supported by direct measurements. It is claimed that the reduction in proliferation and motility is because of the compression transmitted by the ECM.

We agree that this is the crucial point of our article. Thus, we will try to convince the reviewer by giving a point to point answer.

However, the ECM and its deformation is not measured in the MCS experiments. It is simply assumed that it is there, and that it has the same properties as a individually polymerized Matrigel (MG).

A possible experiment would be to prevent the ECM from forming in the spheroids, or to degrade it previous to the experiment.

We can provide two evidences that the ECM is present in multicellular spheroids made of CT26 cells: first, CT26 spheroids disassemble when the ECM is degraded using collagenase. Collagen seems to be essential to maintain spheroid cohesion. Second, immunostaining indicates the presence of fibronectin in the interstitial space. An image showing the localization of fibronectin was added in the revised manuscript (Figure 1A).

It is well established that the ECM organization by cells is different from repolymerized gels. The authors argue with previous studies, however, as this is the main point of the paper it is important to directly demonstrate the presence and the effect of the force transmission of the ECM in situ.

In the manuscript, we do not need to assume that MG has the same properties as ECM. We show that it is not even necessary to use the native ECM, but a non-specific and commonly used matrix (matrigel) is sufficient to reproduce the phenotype observed in MCS under compression (results on cells isolated in matrigel).

We also added a section in Appendix, with the confocal images used to estimate the porosity of the interstitial space. These results indicate that the ECM pore-size has the same magnitude as that of matrigel, i.e. ~10 nm.

Alternatively the authors could try to use an inert hydrogel.

An inert hydrogel is even further from ECM as compared to MG.

The very simple alternative to the ECM transmitted forces is that the cell directly push on each other, hence the ECM becomes irrelevant, as discussed by the authors. The authors try to convince the reader by the experiments of single cells in MG (Figure 5.). However a simple explanation could be that due to pressure the density of the MG is beyond the point that motility is possible, hence the cells start clustering, and a local decrease of nutrients may explain the reduced proliferation.

We disagree with this interpretation. The proliferation of individual cells in MG is followed for few days. We observe a clear effect of pressure already at day 3, when the cells have divided twice. At this timepoint, the spherical structures are made of at most 4 cells. Thus, they have full access to oxygen and nutrients present in the surrounding medium. We also now show on Figure 5G that increasing the density of MG has almost no effect on the proliferation rate.

2) It is quite irritating to be confronted with different pressures, and subsequent comparisons. Why not show the effect of 0,5,10 and 15 kPa pressure in all plots?

All the biological experiments (Figure 4 and 5) have been done at 5 kPa.

This choice was motivated by our previously published experiments (Montel et al., 2012; Brunel et al., 2020) and reported in Author response image 1. Such experiments showed that 5 kPa is the value at which the effect of osmotic pressure on proliferation saturates. At lower pressure proliferation and motility inhibition is less clear. Larger pressures do not exacerbate the effect, but approach the regime of high osmotic pressures, where other cell responses are involved.

Author response image 1.

Only in Figures 2 and 3, we present experiments at 15 kPa and 70 kPa. This has been done to validate the method, as 5 kPa did not give a measurable effect on the compression of individual cells or on the compression/swelling of the interstitial space.

We added an inset to Figure 3A, to show the volume loss of submitted to Π = 15 kPa (big dextran) and Π = 70 kPa (small dextran), to allow the reader to compare with the methodological experiments cited above.

To better explain these points, we have modified the text in the revised version.

Also the authors should provide statistical tests in all presented plots.

We apologize for this omission. Statistical tests have been added to all plots.

3) Simple controls are missing. What is the speed and proliferation of these cells in a 2D surface without dextran, and with the different dextran types and concentrations (to exclude effects of Dextran itself)?

We have measured that the proliferation and the velocity of cells seeded on a Petri Dish are not affected by the presence of dextran at 5 kPa. Results have been added in the new Figure 4F and G.

4) The argument that commercially ECM is the same as cancer cells generate is not sufficiently backed regarding the importance of this point for the paper. You have to check if this is the case for the used cells, and if this is also happening in the spheroids.

As explained above, we disagree with this comment. The ECM varies from cell type to cell type even in vivo. Our argument is not that MG resembles to the native ECM of CT26, but that a generic matrix allows us to reproduce the phenotype observed in MCS.

5) A main claim at the end of the subsection “Selective-compression method” is that the single cell compression can be used as proxy for the individual cell compression in the spheroids. I fear given the importance of this point for the main message it is necessary to measure the compression of the individual cells in the spheroid. This should be possible looking at the data presented in Figure 3 (i.e. using cell profiler).

We thank the reviewer for this suggestion. Cell profiler did not work well in our case, thus cells have been segmented manually from images with labelled intercellular space. Unfortunately, this method is very inaccurate, and would require the generation of fluorescent cell lines with membrane markers rather than staining the intercellular space to deliminate the cell contours. Direct measurement of volume of cells with non-regular shapes is a tricky problem even for single cells in 2D, so for cell aggregate it represents a real challenge. Nevertheless, our rough approach shows that cells are qualitatively compressed in both cases, with big and small dextran.

The results have been added the Appendix in the revised version.

6) I am puzzled by the strong signal of KI67 in MCS without pressure. This suggests that almost all cells in the outer region are dividing, but the division time is 36 h. Since the mitosis needs about 1h, only 3% of the cells should be in mitosis. Here the thresholding is quite important and can lead to a wrong impression. Typically there should be no expression of KI67 during the time in between division (hence in more than 30h).

We respectfully disagree. According to the seminal articles by Gerdes et al., 1984, Ki67 is present through the whole cycle (not only in itosis), but absent in G0. We added to the revised version this reference, together with a short description of Ki67. The reviewer probably refers to Edu, which is incorporated during the S-phase.

7) I think an important check for the overall hypothesis can be done with the cell confiner. Polymerizing single cells in Matrigel without the dextran, and then confining it with the instrument should give the same phenotype as the big dextran. I suggest to do this experiment.

We disagree because a “hydrostatic” and “uniaxial” loading are different. A “hydrostatic” stress field correspond to a homothetic loading in all spatial directions as investigated in the article. Instead, the reviewer suggests to apply a uniaxial compression, which will deform the cell by activating a shear mode rather than compress it. Whereas this is certainly a very interesting experiment (that is currently under investigation in M. Piel’s team (Institut Curie)), it would neither confirm nor refute the experiments performed under Dextran pressure.

Instead, we have embedded polyacrylamide beads in MG droplets. Polyacrylamide (PA) beads are compressible with a bulk modulus KPA~15 kPa, which is considerably higher than that of MG KMG<1 kPa. When big dextran molecules surround the MG droplet, the embedded PA beads get compressed, even though they never get in contact with the osmolyte. This experiment, which shows that the matrix transmits the stress to the inclusions, has been added to the appendix B of the revised version.

Reviewer #3:

In this manuscript, Dolega and colleagues examine the impact of osmotic pressure versus solid stress (or "global compression" as the authors describe) on proliferation and motility in cell aggregates cultured in 3D gels. They develop a clever method of using dextrans that are small, so they can penetrate the gel, or are large, so that they are excluded from the gel, to exert increased osmotic pressure or solid stress, respectively. They find that solid stress impacts cell proliferation and migration within clusters, whereas increased osmotic pressure has a limited impact.

The question of how solid stress impacts cells is an important question, which is particularly relevant to the context of tumor growth. Approaches to test the impact of uniform solid stress on cells are limited. It is often assumed that modulating osmotic pressure can simulate solid stress. However, the authors show here that this assumption is incorrect. Thus, the approach the authors develop to modulating solid stress, and the finding that solid stress has a different impact than increased osmotic pressure, is important and a nice advance for the field, which is in principle suitable for eLife. This approach could serve as a powerful tool for the community. However, the method and biological results need to be better characterized in order for this manuscript to be suitable for publication in eLife. Additional no mechanistic insights are provided; some mechanistic insight would make the manuscript more impactful.

1) Characterization of method: How do the authors determine the solid stress for the large dextran used? Is it just assumed that whatever osmotic pressure is applied will translate to that amount of solid stress? While this might be the case, these gels are complex, some direct experimental measurement of this would build more confidence (e.g. by using a rheometer to measure negative normal stress of the gels or polyacrlymide hydrogel "reporter" beads). In addition, showing how solid stress varies as a function of big dextran density, and demonstrating the applicability of this idea in another common 3D culture gel system (e.g. collagen, PEG, agarose, or alginate) would facilitate the broader adoption and use of this technique.

Theory: We first would like to conceptually clarify the classical situation of the osmotic compression of a passive poroelastic material. To do so, we first explain theoretically why an osmotic shock with a osmolite that cannot permeate the mesh of the poro-elastic material leads to a mechanical strain (and hence a solid stress) in the material.

In the revised version we experimentally show that this idea is correct on the simple example of Matrigel that is used in experiments of the paper. The experimental part is added as an appendix of the new manuscript.

Poroelasticity is a theory describing the flow of a liquid in a solid deformable porous medium usually called the skeleton. The premise of the theory dates back to Gibbs and was then pioneered by M.A. Biot [Journal of applied physics, vol 12, pp.155-164, 1941]. A justification of the theory from a homogenization perspective as well as its thermodynamic foundations can be found in the textbook of O. Coussy [Coussy, 2004]. While, for convenience of the reviewer, we will here only recall the “small displacements” theory, the same derivation can be followed in the geometrically non-linear setting although it becomes much more technical.

We consider a fluid-infiltrated solid medium which occupies the domain 𝛺, immersed in the fluid. We denote the spatial coordinate r ∈𝛺 and the time t. Inside this domain, in the absence of inertial effects and body forces, balance of momentum reads,where (𝑟,𝑡) is the total –solid plus fluid- stress. We use the classical differential notation where 𝛻. is the divergence operator. The effective rheology of a poro-elastic material can be formulated in the following way. First we relate the stress with the strain and the hydrostatic pore pressure 𝑝(𝑟, 𝑡) (with respect to the pressure in the fluid bath) as

Where the strain is conventionally defined as 𝜀̿ (𝑟, 𝑡) = (𝛻𝑢 + 𝛻𝑢𝑇)/2 with 𝑢(𝑟, 𝑡) the displacement field of the skeleton from the rest state. 𝐼̿ denotes the identity matrix. Relation (2) generalizes the elastic Hooke’s law for a poro-elastic medium.

This description introduces some rheological coefficients:

– 𝐾 is the so-called drained bulk modulus corresponding to deformations of the material at fixed 𝑝 = 0 when the fluid can flow in and out of the skeleton.

– 𝐺 is the shear modulus of the skeleton and is unaffected by the presence of the permeating fluid since fluid cannot resist shear.

– 𝛼 is the Biot-Willis coefficient which measures the amount of pore pressure contributing to total stress. For biological materials this parameter is generally very close to one because they are composed of highly compressible material permeated by an almost incompressible fluid. We shall assume that 𝛼 = 1.

In steady state, the pore pressure equilibrates with the applied osmotic pressure 𝜋𝑑 such that 𝑝 = −𝜋𝑑 (see [Dolega et al., 2020] for a justification ). In the case of a spherical ball, thanks to the symmetries, the solution of the ensuing mechanical problem is

𝜎 (𝑟,𝑡) = 0. This means that the elastic stress in the skeleton is compensated by the pore pressure term 𝑝. Hence, using the constitutive relation (2) , we obtain,

Taking the trace of this equation, we obtain the volumetric strain in the skeleton following the application of 𝜋𝑑 is

This shows that by applying an osmotic pressure to a poro-elastic ball, we induce a solid stress in its skeleton which is exactly −𝜋𝑑. This leads to a constant volumetric strain −𝜋𝑑/𝐾 inside the ball. This is why the drained bulk modulus 𝐾 of the skeleton (as referred to in the mechanics community) is also often also called the osmotic modulus.

Experiments: We experimentally demonstrate that this theoretical idea is applicable to Matrigel in the main paper. We exploited the reviewer's idea of embedding deformable beads in a matrigel scaffold, to experimentally prove that the extracellular matrix is capable of transduce the osmotic pressure into solid stress. These experiments were added in Appendix B of the revised manuscript.

2) Some of the experiments need more detail and statistical analysis:

We thank the reviewer for accurately pointing all those omissions.

Figure 2B, C and D – statistical analysis are needed.

Added in the revised version.

Figure 4A: pattern and/or levels of proliferation should be quantified. Single representative images are not sufficient: quantitative data supported by statistically significant differences are required to make conclusions.

A panel was added to Figure 4 to quantify the density of proliferating cells (Ki67 positive) as a function of the radial position, in the three conditions. The text and the legend were modified accordingly.

Figure 4B: are differences statistically significant? Statistical analyses should be included. Also, representative time series of images could be included.

Statistical analysis and time series of images has been added to Figure 4, in the revised version.

Figure 4C: timelapse studies should be conducted, and timelapse images included, to better display the motion that is described.

There are no images, as the velocity has been measured by Dynamic Light Scattering. In fact, cells cannot be imaged inside the spheroids, as light scattering makes the spheroid opaque beyond the two first cell layers. Thus, we took advantage of this scattering to analyze the light scattered by the spheroids in the forward direction to determine the mean velocities inside the aggregate. The technique is simple, but its explanation would considerably complexify the article. For this reason we refer to the published articles in the manuscript (Brunel, 2017 and Brunel, 2020). Nevertheless, we agree that it is important to quickly explain the technique and to show an example of raw data. Thus, we have added a full subsection "Dynamic Light Scattering and Motile Activity inside MCS" to the Appendix of the revised version.

Figure 5: statistical analysis should be included for D and F.

Statistical analysis has been added to the revised version

Figures 4 and 5: multiple levels of solid stress would be ideal to show the trend.

The choice of using a pressure of 5 kPa was motivated by our previously published experiments (Montel et al., 2012; Brunel et al., 2020) and reported in Author response image 1. Such experiments showed that 5 kPa is the value at which the effect of pressure on proliferation saturates. At lower pressure proliferation and motility inhibition is less clear. Larger pressures do not exacerbate the effect, but appsssssroach the regime of high osmotic pressures, where other cell responses are involved.

We modified the text to better explain these two points. Statistical tests have been added to all plots. We did few experiments at different pressures, which showed qualitatively similar results. However, a precise quantification of the influence of the pressure magnitude in all our experiments would require large statistics and a quantity of work that is beyond our capabilities in a decent amount of time.

Figure 5: do cells extend beyond the periphery of the Matrigel beads?

Cells at the interface often extend outside the MG. Those cells have been excluded from the analysis. Cells shown in the figures do not extend beyond the periphery of MG beads. A sentence was added to the revised manuscript, to precise this point.

3) Mechanistic insights – there are really no mechanistic insights provided as to how increased solid stress might lead to some of the behaviors observed. This is unusual for eLife papers. Even a screen of implicated small molecule inhibitors (e.g. actin, myosin, Rho,.…) could be valuable in generating some general idea into mechanism.

As suggested by the reviewer, we have realized compression experiments after exposure to drugs affecting the cytoskeleton organization and the contractility: Y-27632, Blebbistatin, Cytochalasin D, Nocodazole and Taxol. Unfortunately, cells have no long-term viability, when exposed to those drugs so it was not possible to investigate their impact on cell proliferation and motility. However, it was possible to evaluate how those perturbations affect the compressibility of spheroids to an osmotic compression.

In the experiments, we first expose the MCS to the drug and measure the volume change. Then, we add the big dextran at 5 kPa and measure again the evolution of the MCS volume. We obtained two results:

1) Drugs modify the MCS volume in different manners (see Appendix 1—figure 5) as compared to the control (DMSO). This is in agreement with the fact such pharmacological perturbations are known to impact the single cell volume in different manners (see [Stewart et al., 2011]). Although several mechanisms linking the cytoskeleton and the cell membrane effective permeability have been discovered [Cadart et al., 2019], a theoretical model that would unify these observations is however still lacking to our knowledge. In addition, these drugs can impact not only cell volume, but the compaction of the spheroid by means of cell-cell interactions and contractility thus modify the overall spheroid volume.

2) When dextran is added to the solution, the spheroids get compressed from their initial state (with the drug); such final compression (Dextran+Drug) is comparable to that obtained with dextran alone but the amount of compression with respect to the initial state varies depending on the drug.

Those results are compatible with our idea that the 5 kPa Dextran compression reduces almost to the maximum the inter-cellular space and that cells are then almost fully connective in the final state. Thus, depending on the amount of compression that the drug first creates, the ensuing compression with Dextran will change depending on the available inter-cellular space that remains. For instance, in the presence of cytochalasin, the extra-cellular space is already largely reduced compared to DMSO so when the osmotic compression follows, there is hardly no intercellular space which can still be compressed. This seems to be an additional indication that the MCS compressibility in response to a gentle osmotic pressure is more related to the rheology of the extracellular space than to the internal organization and contractility of the cytoskeleton as we argue in [Dolega et al., 2020]. However, it is difficult to extract from this data a potential mechanism that would explain the effect of mechanical stress in the inter-cellular ECM on the cells motility and proliferation.

Some preliminary experiments indicate that membrane tension evolve under pressure (see also https://www.biorxiv.org/content/10.1101/2021.01.22.427801v1) and may play a major role. Although promising, we still do not have sufficient evidence to support this hypothesis unequivocally.

We don't think these new data add much value to the article, but instead may complicate the message. Thus, unless the reviewer has a different opinion, we added them as additional information.

Key resources table

Reagent type (species) or resource	Designation	Source or reference	Identifiers	Additional information
Cell Line (mouse)	CT26	ATCC CRL-2638	RRID:CVCL_7256
Chemical compound,drug	Matrigel/MG	Corning; 354234
Chemical compound, drug	Small Dextran	Sigma Aldrich; D9260
Chemical compound, drug	Big Dextran	Sigma-Aldrich; D5376
Antibody	Anti-Fibronectin (Monoclonal mouse)	Sigma Aldrich; F7387	RRID:AB_476988	(1:200)
Antibody	Anti-Ki-67 (Polyclonal rabbit)	Sigma Aldrich; AB9260	RRID:AB_2142366	(1:200)