The Effect of Substrate Stiffness on Elastic Force Transmission in the Epithelial Monolayers over Short Timescales

Purpose The importance of mechanical forces and microenvironment in guiding cellular behavior has been widely accepted. Together with the extracellular matrix (ECM), epithelial cells form a highly connected mechanical system subjected to various mechanical cues from their environment, such as ECM stiffness, and tensile and compressive forces. ECM stiffness has been linked to many pathologies, including tumor formation. However, our understanding of the effect of ECM stiffness and its heterogeneities on rapid force transduction in multicellular systems has not been fully addressed. Methods We used experimental and computational methods. Epithelial cells were cultured on elastic hydrogels with fluorescent nanoparticles. Single cells were moved by a micromanipulator, and epithelium and substrate deformation were recorded. We developed a computational model to replicate our experiments and quantify the force distribution in the epithelium. Our model further enabled simulations with local stiffness gradients. Results We found that substrate stiffness affects the force transduction and the cellular deformation following an external force. Also, our results indicate that the heterogeneities, e.g., gradients, in the stiffness can substantially influence the strain redistribution in the cell monolayers. Furthermore, we found that the cells’ apico-basal elasticity provides a level of mechanical isolation between the apical cell–cell junctions and the basal focal adhesions. Conclusions Our simulation results show that increased ECM stiffness, e.g., due to a tumor, can mechanically isolate cells and modulate rapid mechanical signaling between cells over distances. Furthermore, the developed model has the potential to facilitate future studies on the interactions between epithelial monolayers and elastic substrates. Supplementary Information The online version of this article (10.1007/s12195-023-00772-0) contains supplementary material, which is available to authorized users.

Figure S3.Vertical cell displacement and focal adhesion, cortical, and junction force propagation from soft to stiff substrate with sharp and shallow stiffness gradients.Vertical cell displacement (a), substrate displacement (b), focal adhesion forces (c), cortical forces (d), and junction forces (e) for the four different stiffness gradients shown in (f).For clarity, the four cases were divided into two figures.The corresponding plots for the uniforms stiffnesses are also shown for comparison.The forces were defined by calculating the mean force from the vertices for each cell, and then assigning the mean force for the cell centers and interpolating the values over the epithelium area.Finally, the force area data was averaged.The shaded region represents the standard deviation for each case.(f) The stiffness gradients for displacement and forces shown in (a)-(e) and (g)-(i).The absolute difference in (g) cell and (h) substrate displacement compared to the uniform 1.1-kPa displacement for stiffness gradients shown in (f).(i) The absolute differences in focal adhesion, cortical, and junction forces for stiffness gradients shown in (f) compared to the forces in the corresponding position with 1.1-kPa substrate.The vertical striping shows the positions of cell boundaries for average sized cells and the positions of the gradients are shown with the lines of corresponding colors at the bottom of each figure.For each set of parameters, n = 15.AU, arbitrary unit.For clarity, the four cases were divided into two figures.The corresponding plots for the uniforms stiffnesses are also shown for comparison.The forces were defined by calculating the mean force from the vertices for each cell, and then assigning the mean force for the cell centers and interpolating the values over the epithelium area.Finally, the force area data was averaged.The shaded region represents the standard deviation for each case.(f) The stiffness gradients for displacement and forces shown in (a)-(e) and (g)-(i).The absolute difference in (g) cell and (h) substrate displacement compared to the uniform 1.1-kPa displacement for stiffness gradients shown in (f).(i) The absolute differences in focal adhesion, cortical, and junction forces for stiffness gradients shown in (f) compared to the forces in the corresponding position with 1.1-kPa substrate.The vertical striping shows the positions of cell boundaries for average sized cells and the positions of the gradients are shown with the lines of corresponding colors at the bottom of each figure.For each set of parameters, n = 15.AU, arbitrary unit.

Figure S2 .
Figure S2.Representative example of cell and substrate forces following a micromanipulation.(a) Cell forces of cells on a 1.1-kPa substrate following the 30-µm micromanipulation.The values are in arbitrary units.The micromanipulation force itself is not shown as it only affected a single cell.(b) Substrate forces following the same micromanipulation.The substrate repulsion force is not shown as it was zero everywhere in the simulated area with this soft substrate.

Figure S4 .
Figure S4.Vertical cell displacement and focal adhesion, cortical, and junction force propagation from soft to stiff substrate with stiffness interface gradients.Vertical cell displacement (a), substrate displacement (b), focal adhesion forces (c), cortical forces (d), and junction forces (e) for the four different stiffness interface gradients shown in (f).For clarity, the four cases were divided into two figures.The corresponding plots for the uniforms stiffnesses are also shown for comparison.The vertical striping shows the positions of cell boundaries for average sized cells and the positions of the interfaces are shown with the arrowheads of corresponding colors at the bottom of each figure.The forces were defined by calculating the mean force from the vertices for each cell, and then assigning the mean force for the cell centers and interpolating the values over the epithelium area.Finally, the force area data was averaged with n = 15 simulations.(f) The stiffness interfaces for displacement and forces shown in (a)-(e).The shaded region represents the standard deviation for each case.The force magnitudes are comparable between each other.AU, arbitrary unit.

Figure S5 .
Figure S5.Vertical cell displacement and focal adhesion, cortical, and junction force propagation from stiff to soft substrate with sharp and shallow stiffness gradients.Vertical cell displacement (a), substrate displacement (b), focal adhesion forces (c), cortical forces (d), and junction forces (e) for the four different stiffness gradients shown in (f).For clarity, the four cases were divided into two figures.The corresponding plots for the uniforms stiffnesses are also shown for comparison.The forces were defined by calculating the mean force from the vertices for each cell, and then assigning the mean force for the cell centers and interpolating the values over the epithelium area.Finally, the force area data was averaged.The shaded region represents the standard deviation for each case.(f) The stiffness gradients for displacement and forces shown in (a)-(e) and (g)-(i).The absolute difference in (g) cell and (h) substrate displacement compared to the uniform 1.1-kPa displacement for stiffness gradients shown in (f).(i) The absolute differences in focal adhesion, cortical, and junction forces for stiffness gradients shown in (f) compared to the forces in the corresponding position with 1.1-kPa substrate.The vertical striping shows the positions of cell boundaries for average sized cells and the positions of the gradients are shown with the lines of corresponding colors at the bottom of each figure.For each set of parameters, n = 15.AU, arbitrary unit.

Figure S6 .
Figure S6.Vertical cell displacement and focal adhesion, cortical, and junction force propagation from stiff to soft substrate with stiffness interface gradients.Vertical cell displacement (a), substrate displacement (b) focal adhesion forces (c), cortical forces (d), and junction forces (e) for the four different stiffness interface gradients shown in (f).For clarity, the four cases were divided into two figures.The corresponding plots for the uniforms stiffnesses are also shown for comparison.The vertical striping shows the positions of cell boundaries for average sized cells and the positions of the interfaces are shown with the arrowheads of corresponding colors at the bottom of each figure.The forces were defined by calculating the mean force from the vertices for each cell, and then assigning the mean force for the cell centers and interpolating the values over the epithelium area.Finally, the force area data was averaged with n = 15 simulations.(f) The stiffness interfaces for displacement and forces shown in (a)-(e).The shaded region represents the standard deviation for each case.The force magnitudes are comparable between each other.AU, arbitrary unit.