Abstract
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 shortimescale, but, by draining the water out of the extracellular matrix, the global one imposes a residual compressive mechanical stress on the cells over a longtimescale, 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 noncellular 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 reimplanting 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 (FernandezSanchez et al., 2010; Nia et al., 2017). Such pathophysiological 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 cellcycle 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 1000fold 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).
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
Selectivecompression 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 ${\mathrm{\Pi}}_{d}$ exerted using large dextran molecules considerably reduces the proliferation of cells inside multicellular spheroids. The effect was visible starting from ${\mathrm{\Pi}}_{d}=\text{500 Pa}$ and saturated at ${\mathrm{\Pi}}_{d}\simeq 5\text{kPa}$. Unless explicitly stated, the experiments described in this article were performed at ${\mathrm{\Pi}}_{d}\simeq 5\text{kPa}$, 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 ${R}_{g}$ 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 ${\mathrm{\Pi}}_{d}=5\text{kPa}$ (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.
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 ${\mathrm{\Pi}}_{d}=5$ kPa (Monnier et al., 2016), individual CT26 cells are submitted to ${\mathrm{\Pi}}_{d}=15$ kPa. At this pressure, we measured a relative compression $\mathrm{\Delta}{V}_{c}/{V}_{c}=3.8\pm 0.8\%$ (Figure 2c) , where ${V}_{c}$ is the cell volume and $\mathrm{\Delta}{V}_{c}$ the volume loss upon the application of ${\mathrm{\Pi}}_{d}$. This compression indicates that CT26 cells have an effective osmotic modulus ${K}_{c}=$ 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 ${\mathrm{\Pi}}_{d}=5$ 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 ${K}_{s}\simeq $ 30 kPa, 15folds 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 ${\mathrm{\Pi}}_{d}=10$ 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 ${\mathrm{\Pi}}_{d}$ 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 ${\mathrm{\Pi}}_{d}$ in both conditions. Our model, detailed in Appendix 6.5, essentially couples a classical active pumpandleak 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 poroelastic 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 mechanosensitive nature of ion channels.
We show in Appendix A.5 that, for realistic estimates of the model parameters, the application of ${\mathrm{\Pi}}_{d}$ 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 ${\mathrm{\Pi}}_{e}$ is the osmotic pressure of ions in the culture medium and $\beta \simeq 0.1$ is a nondimensional 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 (${\mathrm{\Pi}}_{d}\ll {\mathrm{\Pi}}_{e}\simeq 500$ kPa), the relative change of volume $\mathrm{\Delta}{V}_{c}/{V}_{c}$ is negligible. More quantitatively, formula (Equation 1) provides the estimate of the osmotic modulus of a cell ${K}_{c}=(1\beta ){\mathrm{\Pi}}_{e}\simeq 450$ 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 by
where $G$ 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 ${\mathrm{\Pi}}_{d}\simeq 5$ 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: ${T}_{\text{small}}\simeq 20\text{Pa}\ll {T}_{\text{big}}\simeq 5\text{kPa}$ 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 twophoton 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 ${\mathrm{\Pi}}_{d}=$ 40 kPa for small dextran and to ${\mathrm{\Pi}}_{d}=$ 15 kPa for the big ones.
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 quasiincompressible. The volume reduction of the aggregate induced by a 15 kPa pressure did not differ much from the one obtained with a ${\mathrm{\Pi}}_{d}=5$ 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 (${\mathrm{\Pi}}_{d}$ = 0 kPa, ${\mathrm{\Pi}}_{d}$ = 5 kPa small dextran, and ${\mathrm{\Pi}}_{d}$ = 5 kPa big dextran). Proliferating cells were immunostained for Ki67, a nuclear antigen present during the cell cycle, but absent in G0 phase (Gerdes et al., 1984). Whereas cells in control MCS (${\mathrm{\Pi}}_{d}=0$ 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 Ki67positive 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 Ki67positive 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—source data 1
 https://cdn.elifesciences.org/articles/63258/elife63258fig4data1v2.mat

Figure 4—source data 2
 https://cdn.elifesciences.org/articles/63258/elife63258fig4data2v2.mat

Figure 4—source data 3
 https://cdn.elifesciences.org/articles/63258/elife63258fig4data3v2.mat

Figure 4—source data 4
 https://cdn.elifesciences.org/articles/63258/elife63258fig4data4v2.xlsx
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 ${\mathrm{\Pi}}_{d}$ = 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 (${\mathrm{\Pi}}_{d}=5$ 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 4fg) show that both proliferation and motility remained similar, before and after the addition of dextran at a final pressure ${\mathrm{\Pi}}_{d}\simeq $ 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 ${\mathrm{\Pi}}_{d}=5$ 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 minispheroids, which suggests that ECM compression has a direct effect on the cellECM 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.
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 $\simeq 40$ 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 hoechststained 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, $\mathrm{\u25b3}$), 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, $\mathrm{\square}$). 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 matrixbound 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 af 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 wellknown 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 mechanosensitive 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 ${K}_{ECM}\simeq $ 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 cellcell 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 cellcell 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 nontrivial and nonlinear 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 strechedactivated channels (Nam et al., 2019). As integrindependent 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; BrodersBondon 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
Request a detailed protocolCT26 (mouse colon adenocarcinoma cells, ATCC CRL2638); American Type Culture Collection were cultured under 37°C, 5% CO_{2} 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; SigmaAldrich, 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
Request a detailed protocolThe 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 (twofold 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
Request a detailed protocolMatrigel beads (Matrigel Corning, Ref: 354234) were prepared using vortex method (Dolega et al., 2017). Oil phase of HFE7500/PFPEPEG (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 (singlecell volume measurements)
Request a detailed protocolCell volume was obtained using Fluorescence Exclusion microscopy (Cadart et al., 2017; ZlotekZlotkiewicz 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 Polyllysine (sigma) for 30 min to 1 hr, washed with PBS, then washed with dH_{2}O, 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 CO_{2} 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 100μmdiameter 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
Request a detailed protocolSpheroids 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 CO_{2} independent medium. Before acquisition, medium supplemented with 2 g/L FITCdextran (10 kDa from Sigma Aldrich) was injected to label the intercellular space. Medium exchange was performed manually using large inlets (<1 mm) during twophoton acquisition. Acquisitions were performed at 37°C on a Nikon C1 twophoton microscope coupled with a femtosecond laser at 780 nm with a 40x waterimmersion (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 PLLgPEG (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 $d{H}_{2}O$ 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
Request a detailed protocolExperiments 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
Request a detailed protocolTo quantify cell migration in Matrigel, individual cells were observed by phase contrast microscopy. Zstacks 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
Request a detailed protocolSpheroids 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 polyLlysine 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 antimouse 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
Request a detailed protocolStudent’s ttest (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.
Appendix 1
A Theoretical model of the osmotic compression of a single cell nested in matrigel
Our aim is to qualitatively understand the nature of the steady state mechanical stress and displacement of a cell nested in a matrix in two paradigmatic situations:
When some small osmolytes (typically dextran) that can permeate the matrix pores are introduced in the solution,
When some big osmolytes that are excluded from the matrix are introduced in the solution.
The matrix is a meshwork of biopolymers permeated by an aquaeous solution containing ions. These ions can also permeate the cell cytoplasm via specific channels and pumps integrated in the plasmic membrane (Hoffmann et al., 2009; Lang et al., 1998). For simplicity, we restrict our theoretical description to Na^{+}, K^{+}, and Cl^{–} ions which have specific channels and a well studied pump (Therien and Blostein, 2000) which actively pumps out three sodium ions in exchange of having two potassium ions in. Attached right under the cell membrane via some specific crosslinkers (DizMuñoz et al., 2010), the cell cortex is a thin ’musclelike’ actin network crosslinked by passive and contractile crosslinkers such as myosin II. The cortex has been shown to be an important regulator of the cell surface tension (Clark and Paluch, 2011; Salbreux et al., 2012) as exemplified during motility (Hawkins et al., 2011; Farutin et al., 2019) and cell morphogenesis (Turlier et al., 2014; Sedzinski et al., 2011; Tinevez et al., 2009; Charras et al., 2008). The cell membrane and cortex enclose the cytoplasm a meshwork of macromolecules permeated by water and containing the aforementioned ions. See Appendix 1—figure 6 for a scheme of the model.
For simplicity we assume a spherical geometry with a cell of radius r_{c} inside a matrix ball of radius r_{m}. Each point in the space $\mathbf{x}$ can therefore be localized by its radial position $\mathbf{x}=r{\mathbf{e}}_{r}$ where $\mathbf{e}}_{r$ is radial unit vector. We assume a spherical symmetry of the problem such that all the introduced physical fields are independent of the angular coordinates θ and φ. Throughout this text, we restrict ourselves to a linear theory which typically holds when the deformation in the matrix is assumed to remain sufficiently small. A more quantitative theory would require to take into account both the nonlinear aspects of the matrix deformation and the osmotic pressure created by the polymer.
A.1 Conservation laws at the cellmatrix interface
Water conservation
From KedemKatchalsky theory (Staverman, 1952; Kedem and Katchalsky, 1958; Kedem and Katchalsky, 1963; Baranowski, 1991; Elmoazzen et al., 2009), assuming that the aquaeous solvent moves through specific and passive channels, the aquaporins (Day et al., 2014), we can express the incoming water flux ${\mathbf{\mathbf{j}}}_{w}$ in the cell at $r={r}_{c}$ as (Yi et al., 2003; Hui et al., 2014; Strange, 1993; Hoffmann et al., 2009; Mori, 2012; Cadart et al., 2019):
where ${\mathrm{\Pi}}_{m,c}$ denote the osmotic pressures in the matrix phase and the cell while ${p}_{m,c}$ are the hydrostatic pressures defined with respect to the external (i.e. atmospheric) pressure. The socalled filtration coefficient ${L}_{p}$ is related to the permeability of aquaporins. In a dilute approximation which we again assume for simplicity, the osmotic pressure is dominated by the small molecules in solution and thus reads
where ${k}_{B}$ is the Boltzmann constant, $T$ the temperature, ${N}_{c,m}$, ${K}_{c,m}$ and ${C}_{c,m}$ are the (number) concentrations of sodium, potassium and chloride in the cytoplasm and the extracellular medium and ${D}_{m}$ is the extracellular Dextran (necessary small as big are excluded) concentration in the matrix phase. We neglect in (Equation 5) the osmotic contribution associated with the large macromolecules composing the cell organelles and the cytoskeleton compared to the ionic contributions. In a similar manner, the osmotic contribution of the matrix polymer is also neglected. At steady state, the water flux vanishes (${\mathbf{\mathbf{j}}}_{w}=0$) leading to the relation at $r={r}_{c}$,
Ions conservation
As each ion travels through the plasma membrane via specific channels and pumps, the intensities of each ionic current at $r={r}_{c}$ is given by NernstPlanck laws (Mori, 2012),
where ${g}_{N,K,C}$ are the respective conductivities of ions, v_{c} is the cell membrane potential, $q$ is the elementary charge and j_{p} is the pumping rate associated to the NaK pump on the membrane which is playing a fundamental role for cellular volume control (Hoffmann et al., 2009). The factors 3 and 2 are related to the stochiometry of the sodium potassium pump. Again, in steady state, currents ${i}_{N,K,C}=0$, leading to the GibbsDonnan equilibrium:
where the active potentials related to the pumping activity ${v}_{N,K}$ are ${v}_{N}=3q{j}_{p}/{g}_{N}$ and ${v}_{K}=2q{j}_{p}/{g}_{K}$.
Supposing that the cell membrane capacitance is vanishingly small (Mori, 2012), we can neglect the presence of surface charges and impose an electroneutrality constraint for the intracellular medium:
where z_{c} is the average number of (negative in the physiological $\text{pH}=7.4$ conditions) electric charges carried by macromolecules inside the cell and ${\rho}_{c}$ is their density. As macromolecules are trapped inside the cell membrane, we can express ${\rho}_{c}={X}_{c}/(4\pi {r}_{c}^{3}/3)$ where ${X}_{c}$ is the number of macromolecules which is fixed at short timescale and only increases slowly through synthesis as the amount of dry mass doubles during the cell cycle (Cadart et al., 2019).
Force balance
At the interface between the cell and the matrix $(r={r}_{c})$, we can express the mechanical balance as
In (Equation 10), ${\mathbf{\mathbf{\Sigma}}}_{c}^{\text{bulk}}$ is the Cauchy stress in the cytoplasm which we decompose into ${\mathbf{\mathbf{\Sigma}}}_{c}^{\text{bulk}}={\mathbf{\mathbf{\Sigma}}}_{c}^{\text{skel}}{p}_{c}\text{\mathbf{I}}$, with a first contribution due to the cytoskeleton and a second contribution due to the hydrostatic pressure in the cytosol. The identity matrix is denoted I. The contribution due to the mechanical resistance of the cortex and membrane is denoted ${\sigma}_{c}^{\text{surf}}$. In our spherical geometry, we can express ${\sigma}_{c}^{\text{surf}}=2{\gamma}_{c}/{r}_{c}$ where ${\gamma}_{c}$ is a surface tension in the cell contour. Finally ${\mathbf{\mathbf{\Sigma}}}_{m}$ is the stress in the matrix phase for which we postulate a poroelastic behavior such that, ${\mathbf{\mathbf{\Sigma}}}_{m}={\mathbf{\mathbf{\Sigma}}}_{m}^{\text{el}}({\u03f5}_{m}){p}_{m}\text{\mathbf{I}}$ (the Biot coefficient [Coussy, 2004] is assumed to be one). where
is the Hooke’s law with ${\mathbf{\mathbf{E}}}_{m}$ the (small) elastic strain in the matrix, $G$ the shear modulus and ${K}_{d}$ the drained bulk modulus.
In the absence of cytoskeleton and external matrix (Equation 10) reduces to Laplace law:
and more generally reads,
Such relation provides the hydrostatic pressure jump at the cell membrane $(r={r}_{c})$ entering in the osmotic balance (Equation 6) and, combining (Equation 6) and (Equation 12), we obtain
Conservation laws in the extracellular matrix
Water conservation
Assuming that the extracellular fluid follows a Darcy law, mass conservation of the incompressible water permeating the matrix can be expressed as
where $n$ is the matrix porosity, κ the matrix permeability and μ the fluid viscosity. At steady state, ${\partial}_{t}n=0$ and (Equation 14) is associated with no flux boundary conditions at r_{c} and r_{m} given by
It follows that p_{m} is homogeneous in the matrix and its value is imposed by a relation similar to (Equation 6) with an infinitely permeable membrane at r_{m} :
In (Equation 15), ${\mathrm{\Pi}}_{e}$ is the external osmotic pressure which reads
where ${N}_{e}$, ${K}_{e}$ and ${C}_{e}$ denote the ions concentrations in the external solution and ${D}_{e}$ the concentration of Dextran added to the external solution.
Ions conservation
As we are interested in the steadystate only, the PoissonNernst fluxes of ions concentrations in the matrix locally vanish leading to:
where ${v}_{m}(r)$ is the electrostatic potential in the matrix.
As v_{m} is defined up to an additive constant, we chose that ${v}_{m}({r}_{m})=0$ and, imposing the continuity of ions concentrations at the transition between the matrix and the external solution ${{N}_{m}}_{{r}_{m}}={N}_{e}$, ${{K}_{m}}_{{r}_{m}}={K}_{e}$ and ${{C}_{m}}_{{r}_{m}}={C}_{e}$, we obtain
Next, we again suppose for simplicity that the capacitance of both the porous matrix and the external media are vanishingly small leading to the electroneutrality constraints
where z_{m} is the number of negative charges carried by the biopolymer chains forming the matrix and ${\rho}_{m}$ is their density. As we use uncharged Dextran, its concentration does not enter in expressions (Equation 18). Using, (Equation 17) in tandem with (Equation 18), we obtain
Reinjecting this expression into (Equation 17), we obtain the steady state concentrations of ions in the matrix phase:
Next, we make the realistic assumption that the chloride concentration (number of ions per unit volume) is much larger than the density of fixed charges carried by the polymer chains (number charges per unit volume): ${z}_{m}{\rho}_{m}/{C}_{e}\ll 1$. Indeed using the rough estimates of Section 'Cell volume in the reference situation', the average number of charge carried per amino acid is 0.06 and the typical concentration of matrix is 5 g/l. As the molar mass of an amino acid is roughly 150 g/mol, we can estimate in moles that ${z}_{m}{\rho}_{m}\simeq 2$ mM while ${C}_{e}\simeq 100$ mM. We can thus simplify (Equation 20) up to first order to obtain,
As a result, we obtain that the only steady state contribution of
is imposed by Dextran since the ions only start to contribute to this difference at second order in the small parameter ${z}_{m}{\rho}_{m}/{C}_{e}$. We therefore conclude that, in good approximation, $\mathrm{\Pi}$ vanishes for small Dextran molecules that can permeate the matrix and equates to the imposed and known quantity ${k}_{B}T{D}_{e}$ for big Dextran molecules that cannot enter the matrix pores.
It then follows from Equation 15 that the hydrostatic pressure equilibrates with the imposed osmotic pressure,
Force balance
Using the spherical symmetry of the problem, the only non vanishing components of the stress tensor are ${\mathbf{\mathbf{\Sigma}}}_{m}^{rr}$ and ${\mathbf{\mathbf{\Sigma}}}_{m}^{\theta \theta}={\mathbf{\mathbf{\Sigma}}}_{m}^{\phi \phi}$. Therefore, the local stress balance reads
Assuming a small enough displacement, the nonvanishing components of the strain tensor are given by, ${\mathbf{\mathbf{E}}}_{m}^{rr}=\partial {u}_{r}/\partial r$ and ${\mathbf{\mathbf{E}}}_{m}^{\theta \theta}={\mathbf{\mathbf{E}}}_{m}^{\phi \phi}={u}_{r}/r$ where u_{r} is the radial (and only nonvanishing) displacement component from an homogeneous reference configuration corresponding to a situation where the matrix is not subjected to any external loading and ${r}_{c,m}={R}_{c,m}$. Using the poroelastic constitutive behavior (Equation 11), u_{r} satisfies
This equation is supplemented with the traction free boundary condition at $r={r}_{m}$
Combined with (Equation 23), the two above Equations (24) and (25) lead to the solution
where the introduced constants ${\u03f5}^{0}$ is found using the displacement continuity at the cell matrix interface:
with $u$ given by the change of the cell radius from a reference configuration with radius ${R}_{c}$. The general expression of u_{r} therefore reads,
leading to the following form of the total mechanical stress in the surrounding matrix:
A.3 Formulation of the model
Combining (Equation 5) with (Equation 13) and taking into account (Equation 21), we obtain the relation linking the cell mechanics and the osmotic pressures inside the cell and outside the matrix:
We suppose that the stress in the cytoskeleton is regulated at a homeostatic tension such that ${\mathbf{\mathbf{\Sigma}}}_{c}^{\text{skel}}{\mathbf{\mathbf{e}}}_{r}.{\mathbf{\mathbf{e}}}_{r}\stackrel{\text{def}}{=}{\mathrm{\Sigma}}_{a}$ is a fixed given constant modeling the spontaneous cell contractility. We can then linearize the cell mechanical contributions close to ${r}_{c}={R}_{c}$ to obtain
where ${\stackrel{~}{\mathrm{\Sigma}}}_{a}={\mathrm{\Sigma}}_{a}+2{\gamma}_{c}/{R}_{c}$ and the effective cell mechanical stiffness is ${k}_{c}=2{\gamma}_{c}/{R}_{c}^{2}$.
Using (Equation 23) and (Equation 29) close to ${r}_{c,m}={R}_{c,m}$ we can express,
We therefore finally get the linear relation,
where,
In the limit where ${R}_{m}\gg {R}_{c}$,
Next, using (Equation 8) and (Equation 21) and neglecting ${z}_{m}{\rho}_{m}/{C}_{e}\ll 1$ we obtain the relation linking the externally controlled osmolarity with the cell and matrix mechanics:
In a similar way, we combine (Equation 8) with (Equation 9) with again (Equation 21) in the limit where ${z}_{m}{\rho}_{m}/{C}_{e}\ll 1$ to express the electroneutrality condition
where we have additionally linearized the right handside close to ${r}_{c}={R}_{c}$.
The two Equations (31) and (32) constitute our final model.
A.4 Cell volume in the reference situation
We begin by computing the cell radius and the cell membrane potential in the reference configuration where by definition $u=0$ and $\mathrm{\Pi}={D}_{e}=0$ as no Dextran is present at all. In this case, we solve for the membrane potential ${v}_{c}\stackrel{\text{def}}{=}{V}_{c}$ and radius ${R}_{c}$ in (Equation 31) and (Equation 32) to find their reference values. This computation strictly follows Hoppensteadt and Peskin, 2012.
Defining the nondimensional parameters,
we find the reference radius and membrane potential,
and
Given that the typical concentration of chloride ions outside the cell is of the order of 100 milimolar, the osmotic pressure ${k}_{B}T{C}_{e}$ is of the order ${10}^{5}\text{Pa}$ (i.e. an atmosphere). In sharp contrast, the typical mechanical stresses in the cytoskeleton and the cortex are of the order of ${10}^{2}{10}^{3}\text{Pa}$(Julicher et al., 2007). Therefore, the nondimensional parameter σ is of the order of $\sigma \sim {10}^{3}$ and will be neglected in the following. We then finally obtain the reference values,
The pumping rate enables the cell to maintain a finite a volume. When ${j}_{p}\to 0$, $\beta \to 1$ and the cell swells to infinity because nothing balances the osmotic pressure due to the macromolecules trapped inside. So it is expected that dead cells will swell and lyse. The same happens if the pumping rate is to high. Indeed, as the membrane permeability of potassium is higher than the one of sodium, if the pumping rate is very high, a lot of potassium ions will be brought in (more than sodium ions will be expelled out) and to equilibrate osmolarity with the exterior, water will swell the cell until it bursts. Between these to unphysiological situations, computing the variation of volume with respect to the pumping rate, one gets that this variation vanishes when,
At such pumping rate, the volume is less sensitive to small variations in the pumping rate that may occur.
Rough estimates
The computation of the effective charge carried by macromolecules is complex. The folding of proteins and the electrostatic screening of charges between them (Manning effect) plays a role. See (Barrat and Joanny, 1997) for a review. We can still make a rough estimate in the following way. We assume that macromolecules are mostly proteins. At physiological $\text{pH}=7.4$, three types of aminoacids carry a positive charge, Lysine (7%), Arginine (5.3%), Histidine (0.7%) while two others Aspartate (9.9%) and Glutamate (10.8%) carry a negative charge. Added to this, Histidine has a $\text{pKa}=6$ smaller than the pH so the ratio of [histidine neutral base]/[histidine charged acid] is ${10}^{\text{pH}\text{pKa}}=25$. Hence the contribution of histidine may be neglected. The occurrence of the aforementioned amino acids in the formation of proteins is also known. The average length of proteins is roughly 400 amino acids. We subsequently obtain the average effective number of negative charges as,
Such estimate needs to be refined and account for sugars and other macromolecules which carry more negative charges per chain but a interval from ${z}_{c}=10$ to ${z}_{c}=100$ charges is a plausible estimate.
The estimate of β requires the knowledge of the physiological external concentration of ions ${C}_{e}=150\text{mM}$, ${N}_{e}=140\text{mM}$ and ${K}_{e}=10\text{mM}$ as well as conductances of sodium and potassium ions through the plasmic membrane. Here, again the situation is complicated since the dynamical opening of channels due to some change in the membrane potential (Hodgkin and Huxley, 1952) as well as the mechanical opening mediated by membrane stretching can play a role and affect these quantities. Nevertheless a rough estimate can be given (Yi et al., 2003)
Also the pump rate is estimated in Luo and Rudy, 1991,
This pump rate is in good agreement with the optimal pump rate predicted by the model,
This leads to an estimate of
The density of macromolecules inside the cell is then found to be ${\rho}_{c}=3\times {10}^{6}$ macromolecules per $\mu {\text{m}}^{3}$ which is a correct order of magnitude (Milo, 2013). To further check the soundness of the above theory we can also compute the membrane potential and obtain ${V}_{c}=73$ mV in good agreement with classical values .
A.5 Osmotic compression of the cell
We now consider the case where, from the reference configuration, we impose an additional osmotic pressure in the external solution with Dextran polymers ${\mathrm{\Pi}}_{d}={k}_{B}T{D}_{e}$. We recall that according to formula (Equation 22), $\mathrm{\Pi}=0$ for small Dextran molecules while $\mathrm{\Pi}={\mathrm{\Pi}}_{d}$ for big Dextran molecules.
We use (Equation 31) and (Equation 32) to compute the ensuing small displacement $u$. Assuming in good approximation that the osmotic pressure imposed by chloride ions is much larger (10^{5} Pa) than the mechanical resistance of the cell cortex and the external matrix (10^{3} Pa) ${k}_{B}T{C}_{e}\gg \stackrel{~}{k}{R}_{c}$ we find that,
Strinkingly, making the realistic simplifying assumptions that ${K}_{d}\gg G$ and ${R}_{m}\gg {R}_{c}$, leads to the same displacement of the cell membrane in the two situations of small and big Dextran:
showing that the two different osmotic loading are not distinguishable at that level. The main text relation (Equation 1) is obtained by assuming that the osmotic pressure of negatively charged ions is half the osmotic pressure of all ions.
However, the mechanical stress applied of the cell is completely different in both situations. For small Dextran, the mechanical stress confining the cell reads,
while for big Dextran it reads,
Since ${T}^{\text{small}}\ll {\mathrm{\Pi}}_{d}$ by at least one order of magnitude, the most important feature that changes between small and big Dextran is that ${T}^{\text{small}}>0$ while ${T}^{\text{big}}<0$. The physical picture behind this is that small Dextran compresses the cell without draining the water out of the matrix. Therefore, the cell behaves as a small inclusion which volume is reduced by the osmotic compression. In response, the matrix is elastically pulling back to balance the stress at the interface. In contrast, for big Dextran, the water is drained out of the matrix which therefore compresses the cell.
Notice that, like the membrane displacement, the variation of the membrane potential $v\stackrel{\text{def}}{=}{v}_{c}{V}_{c}$ is the same in the two situations:
where we have made the same previous simplifying assumptions that ${k}_{B}T{C}_{e}\gg \stackrel{~}{k}{R}_{c}$, ${K}_{d}\gg G$ and ${R}_{m}\gg {R}_{c}$. Again such variation is negligibly small in our conditions where ${D}_{e}\ll {C}_{e}$ by several order of magnitudes. This further indicates that the biological response of the cell in response to a big Dextran compression has a mechanical rather than an electrostatic origin.
B Mechanical transmission of the stress through Matrigel
The purpose of this appendix is to verify that an extracellular matrix effectively transmits the mechanical stresses to the cells within it. To this end, we embedded soft polyacrylamide (PA) beads in a matrigel scaffold (see Appendix 1—figure 7a), before compressing the whole scaffold either with small or with big dextran. The polyacrylamide beads were fabricated as detailed in Dolega et al., 2017, they have a typical size of 20–50 μm, a bulk modulus modulus ${K}_{PA}\simeq $ 15 kPa and are fluorescently labelled. We evaluated the volume reduction of the PA beads by imaging them before and after compression (Appendix 1—figure 7b). The bead volume was estimated by measuring the surface of its equatorial section, and assuming that the compression is isotropic. This assumption is valid only for beads located at the top of the dropled (z > 1 mm), where the interaction with the substrate is negligible. The bead volume change $\mathrm{\Delta}V/V$ (Appendix 1—figure 7c) is measured under three experimental conditions:
The culture medium is replaced by fresh medium with identical osmotic pressure (Control, n = 20 beads),
The medium is replaced by fresh medium supplemented with small Dextran at ${\mathrm{\Pi}}_{d}$ = 5 kPa (Small, n = 20),
The fresh medium is supplemented with big Dextran at ${\mathrm{\Pi}}_{d}$ = 5 kPa (Big, n = 18),
We observe that, when the MG is compressed by big dextran moelecules, the PA beads are also lose 25% of their volume, even though they are not directly in contact with the osmolytes (green). Such a volume loss is compatible with a mechanical pressure applied of the beads of few kPa (Dolega et al., 2017) and shows that the externally applied osmotic pressure results in a similar mechanical pressure applied on the beads through the drainage and compression of the MG meshwork. In contrast, if the dextran molecules are small enough to penetrate the MG and the PA beads, no mechanical stress is exerted on the inclusions (blue).
C Interstitial space
C.1 Volume fraction of the intestitial space
To evaluate the volume fraction of the interstitial space in multicellular spheroids (MCS), we supplement the culture medium with sulforhodamineB, a hydrophilic fluorophore that stains the extracellular space without penetrating the cells. From confocal sections of MCS (Appendix 1—figure 3a) we determine the thickness of the thin layer between two adjacent cells. By fitting the intensity profile to a Gaussian distribution (Appendix 1—figure 3b), and taking into account that the instrumental function (resolution 270 nm) broadens the profile, we estimate the extracellular layer to 0.9 ± 0.1 μm (histogram in Appendix 1—figure 3c; N = 132). With an average cell diameter of 20 μm, we evaluate that the fraction of extracellular space is approximately ${n}_{m}={V}_{m}/{V}_{0}=14\pm 5\%$.
C.2 Compression of ECM in the interstitial space of MCS
The evolution of the rheological properties of ECM filling the interstitial space of MCS is very difficult to evaluate, as the interstitial layer is extremely thin (see previous section). However, we can empirically define an exclusionsize (i.e. porosity), above which globular molecules do not penetrate the gel. To evaluate this exclusionsize, we dip the MCS in a solution containing fluorescent tracers with different radii. As shown in Appendix 1—figure 4a, tracers with ${R}_{S}$ = 4.4 nm and ${R}_{S}$ = 5.8 nm permeate the extracellular space of the MCS but not those larger than 14.8 nm. In order to quantify the relative amount of tracers inside the MCS, we compare the average fluorescence measured inside the MCS, $\u27e8{I}_{In}\u27e9$ and in the surrounding solution $\u27e8{I}_{Out}\u27e9$. Appendix 1—figure 4b reports the relative intensities $\u27e8{I}_{In}\u27e9$/$\u27e8{I}_{Out}\u27e9$ , obtained respectively at an external osmotic pressure ${\mathrm{\Pi}}_{d}=0$ Pa and at ${\mathrm{\Pi}}_{d}=5$ kPa. In both cases, the fluorescence level lowers with large tracers. From the results presented in this section, we deduce that:
The intercellular space is rich in fibronectin, a protein constitutive of the extracellular matrix;
The intercellular space has a porosity comparable to that of matrigel gelified in vitro;
The exclusion size of the intercellular space slightly decreases under compression, indicating a moderate compaction of the extracellular matrix.
D Cell volume
In order to estimate how cells react to an overall compression of the whole MCS, we measure the cell volume change within the aggregate. Cell contours are manually segmented from stack piles obtained with twophoton imaging. Manual segmentation is performed with Amira software. Cell volume is extracted before and after application of osmotic pressure for the same cell in order the measure its compression. Spherical cells are excluded of the analysis as they may undergo cell division and display rapid volume changes. Cells larger than 7000 μm^{3} are also discarded from the analysis as they may be two cells rather than one. The results are reported in Appendix 1—figure 5 and show that cells appear to be compressed both by small (40 kPa) and big (15 kPa) dextran molecules. The pressures are chosen to match with the experiments presented in Figure 3 of the main article. Notice that this method is much less accurate than the fluorescence exclusion’ method used to determine the volume of individual cells. The results have to be taken as qualitative.
E Matrigel bulk modulus
In this section, we estimate the bulk modulus of the extracellular matrix. As interstitial ECM is difficult to characterize insitu, we use matrigel (MG) beads to roughly estimate the rheological properties of ECM. Consistently with native ECM, large Dextran molecules were also excluded from microbeads made of MG suggesting an equivalent effective permeability (Dolega et al., 2021). To determine the bulk modulus of MG beads, we follow their compression at different dextran concentration. To facilitate the measurement, the beads are doped with fluorescent nanoparticles. In Appendix 1—figure 6, we display the volume decrease $V/{V}_{0}$ of MG beads as a function of the osmotic stresses, between 15 and 500 Pa (V_{0} being the bead volume before compression). The continuous line represents the best fit to a MooneyRivlin model, the derivative of which represent the bulk modulus ${K}_{m}$(Rivlin and Saunders, 1951). For small deformations, the best fit is obtained for a bulk modulus ${K}_{m}=450\pm 100$ Pa.
F Dynamic light scattering and motile activity inside MCS
The scope of this section is to illustrate how to determine cell motility inside an opaque multicellular aggregate. Previous works already indicate that pressure affects cell motility in multicellular spheroids, but the observations are limited to either the superficial layer (Alessandri et al., 2013) or to the longterm centripetal motion (Delarue et al., 2013). Recently, we developed a method to measure the cell velocity in the deep layers of MCS without using confocal microscopy, which is limited in terms of sample thickness and observation time. In our setup (Brunel et al., 2017; Brunel et al., 2020; Appendix 1—figure 7a), the MCS is observed by phase contrast (Appendix 1—figure 7c) and is simultaneously illuminated with an infrared laser (850 nm). The light scattered by the MCS in the forward direction produces an interference pattern, which is collected by a camera (Appendix 1—figure 7b). From the of temporal fluctuations of this pattern (signal shown in Appendix 1—figure 7d and its autocorrelation function in Appendix 1—figure 7e), one computes the average velocity of cells, moving inside the MCS. It has to be noticed that this technique, an evolution of the Dynamic Light Scattering, provides information on the 3D motility, and not only on the 2D motion as previously measured by Alessandri et al., 2013 at the surface of MCS. With this method, we measure the average speed in the three cases of interest: without pressure, when a pressure is selectively applied on the cells, but not on the ECM (small Dextran), and when the pressure is applied to the whole MCS (big Dextran). The results are shown in Appendix 1—figure 7f and g: whereas the average speed is comparable in the first two cases (10 ± 1 μm/hr; magenta and cyan), it is reduced by a factor of two when the compression is exerted on the entire MCS (4.8 ± 0.5 μm/hr, blue).
G Cytoskeleton and compressibility
Aggregate compressibility depends primarily on three elements: the compressibility of the cells, that of the extracellular matrix, and the volumetric ratio between the two. In this section, we want to evaluate how the rheology of the cytoskeleton contributes to the apparent compressibility of MCS. To do so, we prepare six 96wells plates of identical spheroids. To avoid the formation of a necrotic core, the MCS initial radius does not exceed 200 µm. Subsequently, five drugs and beg dextran molecules (2 MDa) are added to the different plates:
Y27632 ROCK inhibitor, to reduce cell contractility,
Blebbistatin, to inhibit actomyosin activity,
Cytochlasin D, to inhibit actin polymerization,
Nocodazole, to promote microtubule depolymerization,
Paclitaxel, to impede microtubule depolymerization.
As a control, a subset of spheroids are exposed either to the drug alone, without dextran in solution or to Dimethyl Sulfoxide (DMSO). The MCS volumes are obtained by measuring the surface of their equatorial planes and considering them as a perfectly spherical object. The volume is measured before adding the drug, then 45 min after exposure to the drug alone (gray in Appendix 1—figure 8) or to the drug supplemented with dextran (green in Appendix 1—figure 8) and normalized to the initial volume of each MCS.
We observe that drugs modify the MCS volume in different manners (see the figure below) as compared to the control (DMSO). This is in agreement with the fact such pharmacological perturbations are kwown to impact the singlecell volume in different maners (Stewart et al., 2011). 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 amout of compression with respect to the intial state varies depending on the drug.
This result is compatible with our idea the 5 kPa Dextran compression reduces almost to the maximum the intercellular space and that cells are then almost fully connective in the final state. Thus, depeding on the amount of compression that the drug first creates, the ensuing compression with Dextran will change depending on the available intercellular space that remains. For instance, in the presence of cytochalasin, the extracellular space is already largely reduced compared to DMSO so when the osmotic compression follows, their 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., 2021.
Data availability
Data relating to figures 2, 3, 4, 5 and appendix B are available at https://osf.io/n6ra2/?view_only=059da2ebcd064b75bd12c0c2008b9a6a.

Open Science FrameworkID n6ra2. Extracellular matrix in multicellular aggregates.
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Decision letter

Aleksandra M WalczakSenior Editor; École Normale Supérieure, France

Chase P BroederszReviewing Editor; Arnold Sommerfeld Center for Theoretical Physics, LMU Munich, Germany
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 mechanosensory function of the extracellular matrix to regulate cell behavior in 3D environments.
Decision letter after peer review:
Thank you for submitting your article "Extracellular 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 COVID19 (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 nonpenetrating 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 “Selectivecompression 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.
https://doi.org/10.7554/eLife.63258.sa1Author response
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 2to8 g/l, the MG density has a nonmeasurable 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 longterm project, as the chemistry of the extracellular matrix is poorly known and its rheology depends in a nontrivial 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 nonspecific 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 poresize 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.
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 “Selectivecompression 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 nonregular 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 Sphase.
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 K_{PA}~15 kPa, which is considerably higher than that of MG K_{MG}<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 poroelastic 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.155164, 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 nonlinear setting although it becomes much more technical.
We consider a fluidinfiltrated 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 $\phantom{\rule{0.222em}{0ex}}\stackrel{\u033f}{\sigma}$ (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 poroelastic 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 + 𝛻𝑢^{𝑇})/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 poroelastic medium.
This description introduces some rheological coefficients:
– 𝐾 is the socalled 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 BiotWillis 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 𝜋_{𝑑} such that 𝑝 = −𝜋_{𝑑} (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 𝜋_{𝑑} is
This shows that by applying an osmotic pressure to a poroelastic ball, we induce a solid stress in its skeleton which is exactly −𝜋_{𝑑}. This leads to a constant volumetric strain −𝜋_{𝑑}/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: Y27632, Blebbistatin, Cytochalasin D, Nocodazole and Taxol. Unfortunately, cells have no longterm 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 cellcell 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 intercellular 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 intercellular space that remains. For instance, in the presence of cytochalasin, the extracellular 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 intercellular 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.
https://doi.org/10.7554/eLife.63258.sa2Article and author information
Author details
Funding
Agence Nationale de la Recherche (ANR13BSV5000801)
 Giovanni Cappello
Centre National de la Recherche Scientifique (MechanoBio 2018)
 Giovanni Cappello
Ligue Contre le Cancer
 Sylvain Monnier
Institut National de la Santé et de la Recherche Médicale (PC201407)
 Giovanni Cappello
Centre National de la Recherche Scientifique
 Pierre Recho
The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.
Acknowledgements
We warmly thank J Prost and F Jülicher for drawing our attention to the potential impact of the poroelasticity in MCS, A Dawid and J Revilloud for the valuable suggestion to set up the proliferation assay in MG, C Verdier for the valuable exchanges about the evolution of the ECM rheology under stress, and T Boudou for the many fruitful discussion and careful proofreading of the manuscript. This work was supported by the Agence Nationale pour la Recherche (Grant ANR13BSV5000801), by the Institut National de la Santé et de la Recherche Médicale (Grant PC201407), by the Centre National de la Recherche Scientifique (Grant MechanoBio 2018), by the Comité de HauteSavoie de la Ligue contre le Cancer, and by a CNRS Momentum grant (PR).
Senior Editor
 Aleksandra M Walczak, École Normale Supérieure, France
Reviewing Editor
 Chase P Broedersz, Arnold Sommerfeld Center for Theoretical Physics, LMU Munich, Germany
Publication history
 Received: September 19, 2020
 Accepted: March 8, 2021
 Accepted Manuscript published: March 11, 2021 (version 1)
 Version of Record published: April 23, 2021 (version 2)
Copyright
© 2021, Dolega et al.
This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.
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