Mechanical forces play important roles at the single-cell and multicellular levels in tissue biology (Farge, 2011; Hoffman et al., 2011), including in the regulation of cell shape and movement (Aegerter-Wilmsen et al., 2012; Legoff et al., 2013; Mao et al., 2013; Clément et al., 2017), cell-cycle progression (Campinho et al., 2013; Streichan et al., 2014), cell-division orientation (di Pietro et al., 2016; Gloerich et al., 2017), and gene expression (Aragona et al., 2013; Benham-Pyle et al., 2015). In general, these effects have been studied by observing the generation of cellular traction forces, or by applying external tensile forces to whole cell populations (Mukundan et al., 2013; Simmons et al., 2011; Tambe et al., 2011; Zaritsky et al., 2015; Micoulet et al., 2005). While a few studies have estimated the shear forces between cells from observations of cellular tractions ( Tambe et al., 2011; Zaritsky et al., 2015), none have perturbed a tissue with direct application of shear loading.

In-plane shear forces exist within any solid material under load, such as between groups of cells in tissues under applied or intrinsic forces. These forces are distinct from shear stresses applied by laminar liquid flow on top of cells that mimic the vasculature. Tissues spontaneously generate internal shear forces to maintain an external force balance (Prost et al., 2015), and biopolymer networks have been observed to pull inward when sheared on a rheometer (Janmey et al., 2007).

In-plane shear forces are thought to affect the collective behavior of migrating cells in epithelial tissues (Tambe et al., 2011; Zaritsky et al., 2015). For example, the ridges that appear in the epithelial tissue forming the pupal Drosophila wing have been attributed to shear forces arising during development (Etournay et al., 2015). In addition, shear forces between migrating cells of the prechordal plate in the zebrafish embryo and cells of the neurectoderm determine the position of the neural anlage (Smutny et al., 2017). These studies suggest that local shear forces between groups of cells are important contributors to global effects in tissue motility and organ patterning. However, how local in-plane shear forces are spread throughout a tissue, which is important for understanding collective tissue behavior, is not understood in part because of the difficulty in applying direct and localized in-plane shear within a tissue.

In order to close this gap, here we examined epithelial mechanics after we applied in-plane shear with a novel silicon device. We determined that in-plane shear produces local deformations that are propagated into a global migratory response that distributes and dissipates forces through oscillations. Confined epithelia, similar to embryos or tumors, have been shown to oscillate (Deforet et al., 2014; Kocgozlu et al., 2016), but the mechanism driving these oscillations is unknown. Such oscillatory behavior may be important as an intrinsic collective cellular process that follows a shear-induced force imbalance, enabling the probing and maintenance of tension homeostasis within a developing tissue.

We designed and deployed a new silicon device (adapted from [Mukundan and Pruitt, 2009]) to apply localized shear to an epithelium while simultaneously observing cell movements and measuring forces across the epithelium (Figure 1A–C; Materials and methods). We fabricated devices from single crystal silicon-on-insulator wafers because silicon does not change elasticity over time (Hopcroft et al., 2010). The device consisted of two parallel 1000 μm x 250 μm suspended planks, one for force actuation and the other for force sensing. Moving the actuation plank applied 100 μm of shear (resulting in about one radian average cellular shear strain in cells near the mid-plane) at the midline of a Madin-Darby Canine Kidney (MDCK) epithelial cell monolayer cultured across the surface of both planks (Figure 1A; Materials and methods). We generated kymographs of cell movements using Particle Image Velocimetry (PIV) (Figure 1B), from which we mapped cell movements in the x- and y-directions relative to shear (Figure 1C; Materials and methods). We calculated force across the monolayer from the displacement of the sensing spring (k_s = 0.93 N/m) (Figure 1—figure supplement 1).

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Following the application of shear, the epithelium did not rupture or tear (Figure 1—figure supplement 2), nor was there significant extrusion of dead cells (Video 1). Throughout the response, cells within the epithelium retained their nearest neighbors, and new cell adhesions were formed only between daughter cells and their neighbors following division (Figure 1—figure supplement 3; Video 2).

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The MDCK epithelium had a collective response to the application of in-plane shear (Figure 1D–G). Cells throughout the epithelium began a collective wave of inward y-direction movement toward the shear-plane, which started at the shear-plane and propagated to the opposite edge of the plank within 45 min at a rate 10x faster than individual cell velocities (290 vs. 30 μm/h; Figure 1D,E). This inward movement was expected because biopolymer networks develop an inward normal stress under applied shear (Janmey et al., 2007). In our live epithelium, cells reversed y-direction movements at 7, 11, and 15 hr after shear with decreasing velocity magnitude: they behaved as a damped oscillator (Figure 1D,E), with cells furthest from the shear-plane exhibiting the most movement in the y-direction (Figure 1E). Reversals in y-direction movement propagated from the shear plane outward at 80–100 μm/h.

Cells adjacent to the shear-plane (2–3 cell layers,<50 μm) were deformed, and moved in the x-direction opposite the applied shear (Figure 1F,G). These x-direction movements diminished within ~1 hr, and stopped after ~3 hr. In this deformation zone, y-direction cell movements were small, outward, and short-lived. Cell oscillations in the y-direction, but not the x-direction, also occurred spontaneously without shear (Figure 1H–K; Video 3), at a cell velocity 3-4x slower than in the presence of applied shear (9 vs. 30 μm/h). It has been previously reported that MDCK cells plated on circular micro-patterns with 500 μm diameter, the same as the width of the two planks in our device, oscillated radially, but the origin and mechanism of propagation of these oscillations were unknown (Deforet et al., 2014; Kocgozlu et al., 2016).

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To examine whether there were changes in individual cell morphology after in-plane shear, we measured cell orientation, eccentricity, area, density, and perimeter over time. We found no changes in cell morphology or periodicity that matched long-term y-direction collective oscillations (Figure 1—figure supplement 4). Thus, inward/outward y-direction oscillations within the epithelium primarily represented collective cell movements rather than changes in individual cell morphology. While the deformation zone (2–3 cell layers) adjacent to the shear-plane exhibited cell-shape changes and horizontal displacement in the x-direction, this physical shear deformation did not occur (Figure 1—figure supplement 3, Figure 1—figure supplement 5) nor propagate to the rest of the monolayer (Figure 1—figure supplement 4A,B). Finally , there was no change in the localization of E-cadherin at cell-cell adhesions of migrating cells due to shear (Figure 1—figure supplement 5).

We sought to connect these experimental data to the mechanical properties of the monolayer by using the known stiffness and displacement of the on-chip sensing plank to extract force as a function of time after shear (Figure 1—figure supplement 1). The measured position of the sensing plank was used to calculate the force experienced by the epithelium from images taken at 30 s intervals from 5 min before to 30 min after shear (Figure 2A). The measured force peaked (F_MAX) immediately after shear, and then relaxed with an exponential decay characteristic of a viscoelastic material, where the time constant, τ, is defined as the time to decay by 63% as the epithelium relaxed and remodeled (Figure 2A).

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Spring and dashpot elements have been used to model the elastic and viscous components of viscoelastic materials, respectively (Micoulet et al., 2005; Mukundan et al., 2013). While these elements are largely sufficient for modeling normal viscoelastic materials and living materials over short time scales, they do not capture the long-term behavior of active, living materials. The MDCK epithelium in our study behaved as a damped oscillator over tens of hours (Figure 1D,E,H and I). Therefore, we inferred that an additional mechanical element was required to capture the time required for mechanical signals to pass through the epithelium, and for the epithelium to generate forces and respond. The addition of a mechanical signal storage and relay element called an inerter, placed in parallel with the viscoelastic components captured these damped oscillations over tens of hours (Figure 2B). The size of the inerter is inversely proportional to the rate of mechanical signal transduction within the epithelium (80–100 μm/h in Figure 1D). The addition of an inerter to viscoelastic elements has been suggested before (Popović et al., 2017), but the configuration presented previously did not support the observed oscillations in this study. In our model, F_INT represents the intrinsic shear force spontaneously generated by an epithelium to maintain an external force balance (Prost et al., 2015), and F_EXT is the extrinsically applied shear force. Fitting our model with and without F_EXT (+Shear, Figure 1D; -Shear, Figure 1H) to observed cell movements, we estimate that the F_INT required to restore a force balance is 4X smaller than F_EXT (Figure 2—figure supplement 1).

To interrogate long-term collective epithelial behavior (Figure 1D and H), we averaged the y-direction cell velocities from kymographs for the +Shear (Figure 1D) and -Shear (Figure 1H) conditions. There was no statistically significant difference in the period or damping rate of oscillations (Figure 2—figure supplement 2C, p<0.05), but the amplitude of oscillations was higher with shear than without shear (Figure 2—figure supplement 2C, p<0.05). We used the MATLAB Simulink/Simscape environment to simulate the behavior of the mechanical models presented in Figure 2B (Figure 2—figure supplement 1; Materials and methods). The simulation (Figure 2C,D, Simulation) captured the observed long-term oscillations and damping after applied shear (Figure 2C,D, Experiment). Our models and simulations are in the y-direction , where they account for the shear forces as an inward step input of force (Janmey et al., 2007).

The role of actomyosin contraction in shear-induced cell movements in the x- and y-directions was tested by adding the myosin II inhibitor blebbistatin (50 μM; (Straight et al., 2003)) 15 min before shear for 1 hr (Figure 3A–G; Video 4) or 1.5 hr after shear for 1 hr (Figure 3—figure supplement 1; Video 5). Addition of blebbistatin before (Figure 3A,B) or after shear (Figure 3—figure supplement 1A,B) inhibited all y-direction oscillatory cell movements, even after washout. Consistent with deformation of a passive material, x-direction cell movements in the 2–3 cell layer deformation zone still occurred after treatment with blebbistatin (Figure 3C,D), although the amount of cell movement was less than in the +Shear condition (Figure 1F,G). Sensing data revealed no statistical difference in F_MAX but a much faster relaxation time (τ = 1.3 min) compared to the +Shear condition (Figure 2—figure supplement 2A, τ = 3.7 min, p<0.01). In our mechanical model, this faster force relaxation time corresponds to decreased damping (c), and the inverse relationship between the size of the inerter and the rate of mechanical signal propagation leads to a much larger inerter value (b) than in the +Shear condition (Figure 3F vs. Figure 2B). As expected, the vertical average of y-velocity kymographs (Figure 3A) did not exhibit any oscillatory behavior (Figure 3G, Experiment). The simulation (Figure 3G, Simulation) captured the absence of oscillations (Figure 3G, Experiment). These results show that temporary loss of actomyosin contraction, before or after shear, decreases damping, suppresses collective oscillatory behavior, and prevents the propagation of cell movements away from the shear-plane.

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Actomyosin contraction is coordinated between cells via linkage to the E-cadherin cell-cell adhesion complex (Yonemura et al., 2010). To distinguish the cytoplasmic actomyosin-anchoring role of E-cadherin from its extracellular, tension-dependent trans-cell adhesion role, we used MDCK cells expressing an E-cadherin extracellular domain mutant (T151 cells [Troxell et al., 2000]). E-cadherin in T151 cells has a truncated, nonfunctional extracellular domain, but an intact plasma membrane-tethered cytosolic tail that binds actin through catenins (Troxell et al., 2000). Importantly, expression of T151 E-cadherin results in the down-regulation of endogenous E-cadherin, but other cell-cell junctions maintain monolayer cohesion (Troxell et al., 2000). Shear did not induce inward/outward y-direction movements of T151 cells (Figure 3H,I; Video 6), unlike the +Shear condition in MDCK cells with normal E-cadherin (Figure 1D,E). This result indicates that extracellular E-cadherin trans-cell adhesion, and not other cell-cell junctions, was specifically required for the propagation of oscillatory y-direction cell movements after shear. Similar to the blebbistatin-treated epithelium of MDCK cells and the +Shear condition, 2–3 layers of T151 cells adjacent to the shear-plane (<50 μm) moved in the x-direction opposite to shear (Figure 3J,K), confirming that passive deformation of the monolayer is independent of E-cadherin trans-cell adhesion. The sensing data (Figure 3L) revealed no statistical difference in F_MAX and τ compared to the +Shear condition (Figure 2—figure supplement 2). In our mechanical model, similar to the blebbistatin-treated MDCK epithelium (Figure 3F), the inverse relationship between the size of the inerter and the rate of signal propagation leads to a much larger inerter value (b) than in the +Shear condition (Figure 3M). The vertical average of y-velocity kymographs (Figure 3H) also did not exhibit any oscillatory behavior (Figure 3N, Experiment), which was also captured by the simulation (Figure 3N, Simulation). Taken together, data from T151 cells demonstrate that damping is unaffected by the loss of E-cadherin trans-cell binding, but E-cadherin transcellular engagement is required to relay the mechanical signal from the shear plane through the epithelium.

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We next examined whether shear-induced cell movements were affected by reducing actin dynamics and increasing actin filament length by adding jasplakinolide (200 nM; (Bubb et al., 1994)) 15 min before shear for 1 h (Figure 4A–G; Video 7); immunofluorescence imaging confirmed that 200 nM jasplakinolide led to the reorganization of long actin filaments in this cell type (Figure 4—figure supplement 1). After shear, jasplakinolide treated cells moved inward in the y-direction at a rate (10 μm/h; Figure 4A) 3x slower than in the + Shear condition with untreated cells (30 μm/h). This inward movement propagated to the edge of the plank at a rate 8x faster than the average cell velocity (80 μm/h vs.10 μm/h), but 3.6x slower than the initial rate in the + Shear condition with untreated cells (290 μm/h, Figure 1D). Jasplakinolide treated cells reversed y-direction movements at 7, 9.5, 13, and 17 hr after shear, but without decreasing velocity magnitude (Figure 4A,B): the magnitude of oscillations was maintained. After jasplakinolide treatment, cell movement in the x-direction was opposite to the applied shear (Figure 4C,D) similar to the +Shear condition with untreated cells (Figure 1F,G), although the x-direction movement propagated to cells further from the shear plane. These results indicate that regulation of actin dynamics and actin polymer length is involved in propagating and damping shear-induced oscillatory cell movements in both the x- and y-directions.

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The sensing data from the jasplakinolide treatment revealed no statistically significant difference in F_MAX, but a much slower (Figure 2—figure supplement 2C, p<0.05) relaxation time (τ = 6.2 min) compared to the +Shear condition with untreated cells (τ = 3.7 min). In our mechanical model, the slower force relaxation time corresponds to an increased damping (c), while the similar rate of mechanical signal propagation (80–100 μm/h) leads to the same inerter value (b) compared to the +Shear condition with untreated cells (Figure 2B). The vertical average (Figure 4G, Experiment) of y-velocity kymographs (Figure 4A) showed that the inward/outward oscillations of jasplakinolide treated cells took much longer (p<0.05) to dampen, although with no statistically significant difference in oscillation period compared to the -Shear or +Shear conditions with untreated cells (Figure 2—figure supplement 2). Again, the simulation (Figure 4G, Simulation) captured the observed long-term oscillations after applied shear (Figure 4G, Experiment). Thus, reduced actin dynamics and longer actin polymer length increased damping and slowed the dissipation of the mechanical signal within the monolayer, leading to prolonged oscillations.

Collectively, our results support the idea that local shear affects the epithelium in two spatially and temporally distinct phases, each with different dependencies on the actin cytoskeleton and E-cadherin-mediated cell-cell adhesion. In one phase, x-direction movements and deformations in 2–3 cell layers adjacent to the shear-plane are independent of the organization and contraction of the actin cytoskeleton, and E-cadherin trans-cell adhesion. These movements last several minutes, and do not oscillate except when actin dynamics are disrupted. In another phase, y-direction cell movements in the epithelium behave as a damped oscillator, requiring actomyosin contraction, actin filament dynamics, and E-cadherin-mediated cell-cell adhesion; these movements persist for tens of hours.

Based upon our simulations and experimental data, we suggest that transient local deformation of 2–3 cell layers adjacent to the shear-plane generates a mechanical event that is relayed across the epithelium over tens of hours. Cell movements at the shear-plane may induce tension on E-cadherin in cells adjacent to the deformation zone, and tension on E-cadherin increases actomyosin contraction and cell stiffening (Borghi et al., 2012; Buckley et al., 2014; le Duc et al., 2010). Therefore, we suggest that the mechanical event from the deformed cells is transmitted throughout the epithelium via direct coupling of actomyosin contraction and E-cadherin cell-cell adhesion (Borghi et al., 2012; Buckley et al., 2014; le Duc et al., 2010; Yonemura et al., 2010). Note that a temporary (1 h) loss of actomyosin contraction blocked long-term (24 h) y-direction cell oscillations even though actomyosin contraction was re-established after blebbistatin washout (+Blebb; Figure 3A). These data indicate that with the loss of actomyosin contractility, the generated mechanical signal dissipated, which enabled the epithelium to immediately reach a new external force balance. We suggest that dissipation of the mechanical signal under the -Shear and +Shear conditions occurred through oscillatory cell movements over >15 h, which gradually damped global cell movements as a new external force balance was reached.

The longer force relaxation time constant for cells treated with jasplakinolide showed that damping was significantly increased (Figure 4E) because of the longer, stable actin filaments that formed in the presence of jaspakinolide (Figure 4—figure supplement 1). Extrapolating from our experimental data (Figure 4G, Experiment) beyond the period of observation indicates that oscillations would have persisted for approximately 80 h after shear. Jasplakinolide stabilizes and increases actin filament length (Bubb et al., 1994), which could generate a more viscous actin network that causes the epithelium to act like a material with longer polymeric chains and high damping (Kim et al., 2016). This change in physical characteristics may also explain why oscillations occurred in the x- as well as the y- direction after jasplakinolide treatment (Figure 4A and C). Thus, normal actin filament dynamics and turnover may be required for oscillation damping and dissipation of the mechanical signal generated by shear, which are required to reach a new force balance.

We can rule out the possibility that changes in cell density over the time of the experiment affected the response of the epithelium to shear. We detected little or no cell extrusion of dead cells (Video 1), and the amount of cell division was similar under all experimental conditions with or without shear (Videos 1 and 3–7). Furthermore, the cell density was between 6,000–10,000 cells/mm², due to temporary local variations, regardless of the application of shear (Figure 1—figure supplement 4vs. Figure 1—figure supplement 6), and either in the presence of blebbistatin (Figure 3—figure supplement 2) or jasplakinolide (Figure 4—figure supplement 2).

Our results suggest a mechanism for the spontaneous oscillation of confined epithelia (Deforet et al., 2014; Kocgozlu et al., 2016), which are important model systems for embryo development and tumor progression. Spontaneously generated shear forces (Prost et al., 2015) in these epithelia produce a normal stress towards the shear plane, (Janmey et al., 2007). These researchers posited that their results were relevant to the study of biological tissues and, indeed, may be applicable to our work because of the short time scales associated with reaching peak force (Figures 2A, 3E, L and 4E). These spontaneously generated shears lead to a force imbalance that is eliminated through the inward/outward oscillation of the epithelium. Here, we reconstituted a similar imbalance by applying a larger external shear force to the epithelium (+Shear), which led to a response similar in type but larger in magnitude to the condition where no external shear force was applied (-Shear). This new understanding was made possible by the ability to apply a localized and quantifiable shear force.

In summary, our novel device and results answer the question of how local shear on cells induces global changes in multicellular organization. Using an intrinsic mechanical signal storage and relay element, we capture the generation of forces by local shear in active, living tissue, and how this signal is propagated and eventually dissipated through oscillatory cell movements. Mechanistically, a force imbalance is generated through local deformation of a few cells by shear. The sensing and restoration of this force imbalance requires tension developed by actomyosin contraction linked to E-cadherin cell-cell adhesion. Our results provide new insights into the mechanical basis of collective cell movement in tissues.

All data generated or analysed during this study are included in the manuscript and supporting files. Source data files and source code have been provided for all figures at: osf.io/kvu5j

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   2. Ehsan Sadeghipour

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   Source data and source code for all figures.

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Author details

1. Ehsan Sadeghipour

   1. Department of Bioengineering, Stanford University, Stanford, United States
   2. Department of Mechanical Engineering, Stanford University, Stanford, United States

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing—original draft, Writing—review and editing

   Contributed equally with

   Miguel A Garcia

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-8686-8315

2. Miguel A Garcia

   Department of Biology, Stanford University, Stanford, United States

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Validation, Visualization, Methodology, Writing—original draft, Writing—review and editing

   Contributed equally with

   Ehsan Sadeghipour

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-4181-5372

3. William James Nelson

   1. Department of Biology, Stanford University, Stanford, United States
   2. Department of Molecular and Cellular Physiology, Stanford University, Stanford, United States

   Contribution

   Conceptualization, Resources, Supervision, Funding acquisition, Investigation, Methodology, Project administration, Writing—review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-3039-3776

4. Beth L Pruitt

   1. Department of Bioengineering, Stanford University, Stanford, United States
   2. Department of Mechanical Engineering, Stanford University, Stanford, United States
   3. Department of Molecular and Cellular Physiology, Stanford University, Stanford, United States
   4. The Stanford Cardiovascular Institute, Stanford University, Stanford, United States
   5. Mechanical Engineering, University of California, Santa Barbara, United States
   6. Biomolecular Science and Engineering, University of California, Santa Barbara, United States
   7. Cellular and Developmental Biology, University of California, Santa Barbara, United States

   Contribution

   Conceptualization, Resources, Supervision, Funding acquisition, Investigation, Methodology, Project administration, Writing—review and editing

   For correspondence

   blp@ucsb.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-4861-2124

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