Chemo-mechanical representation of the coupling between stress-regulated signaling and myosin motor recruit-ment regulated by ECM strain stiffening.

(a) Binding-force generation-unbinding myosin cycle until steady-state realization; (b) schematization of the total free energy contributed by the cell, matrix and interface. The competition among the corresponding energy components determines the optimal cell shape at steady state.

Trizonal model implementation.

(a) Constituents of the 3D and 1D computational domains; (b) 1D trizonal solution for normalized stress vs. equivalent stiffness ratio η _ Ep/E at various tuning parameters of c adopting (nearly) zero to 1, and p = 4; (b) representative example of predicted optimum cell aspect ratio from the lowly motile (lower branch) and highly motile (upper branch) solutions. Cell parameters are identified by E = 1.5 kPa, ν = 0.27, (ς _ ρ0/E, B _ βE, Λ _ α/β) = (0.2, 4.5, 0.8).

Free energy-based stiffness-regulated optimal cell shape at equilibrium state.

(a) Variation of cell–ECM and interfacial free energy components (in reference to the spherical cell) vs. cell body aspect ratioζ at sufficiently large ECM stiffness (η _ EM/E = 5); (b) total free energy difference from superposition of cell–ECM and interfacial contributions; (c,d) lower and upper branch iso-energy contour lines, with their canyons (connected via white lines) denoting optimum aspect ratios (lower-branch canyons are realized entirely atζ = 1). Cell parameters and interfacial contribution are considered E = 1.5 kPa, ν = 0.27, (ς, ℬ, Λ) = (0.2, 5, 0.7) and (γ0, γ1) = (0.2, 0.001) mN/m, δad = 1, respectively. Model tuning parameters are also fixed at (p, c) = (6, 1/3).

Representative cell morphologies showcasing phenotype heterogeneity.

Morphologies of HT1080 cells migrating for 20 hours in 3 mg/ml bovine collagen with and without dual interference of Blebbistatin and 4B4 treatment: (a) example control assay treated with DMSO (0.1%, vehicle control, Sigma Aldrich) and mouse IgG1 isotype (5 µg/mL, BD Bioscience, 557273) controls; (b) example assay treated with Blebbistatin (20 µM, Sigma, 203391) and mouse monoclonal anti-human CD29 (clone 4B4, 5 µg/mL, Beckman Coulter, 6603113). Ellipses indicate cell bodies with their respective aspect ratios (scale bars are 10 µm); (c–f) predicted vs. experimental histograms of cell body aspect ratios: (c) for cells cultured in 1.6 and 3.0 mg/mL collagens, (d) for cells treated with Blebbistatin compared with the DMSO control histogram, (e) for cells treated with 4B4 mAb compared with the IgG1 isotype control histogram, (f) for cells treated with combined Blebbistatin–4B4 mAb, compared with the DMSO–IgG1 control histogram.

Extracellular strain stiffening and stiffness degradation can both instigate malignant phenotypes.

(a) Schematic histological sections of young vs. aged human skin; (b) corresponding schematic cell morphology in young vs. aged skin, with elongation and ECM fiber-mediated protrusion prompted by interactive intracellular contractility, extracellular stiffening and fiber alignment.