Independent regulation of tumor cell migration by matrix stiffness and confinement

Abstract

Tumor invasion and metastasis are strongly regulated by biophysical interactions between tumor cells and the extracellular matrix (ECM). While the influence of ECM stiffness on cell migration, adhesion, and contractility has been extensively studied in 2D culture, extension of this concept to 3D cultures that more closely resemble tissue has proven challenging, because perturbations that change matrix stiffness often concurrently change cellular confinement. This coupling is particularly problematic given that matrix-imposed steric barriers can regulate invasion speed independent of mechanics. Here we introduce a matrix platform based on microfabrication of channels of defined wall stiffness and geometry that allows independent variation of ECM stiffness and channel width. For a given ECM stiffness, cells confined to narrow channels surprisingly migrate faster than cells in wide channels or on unconstrained 2D surfaces, which we attribute to increased polarization of cell-ECM traction forces. Confinement also enables cells to migrate increasingly rapidly as ECM stiffness rises, in contrast with the biphasic relationship observed on unconfined ECMs. Inhibition of nonmuscle myosin II dissipates this traction polarization and renders the relationship between migration speed and ECM stiffness comparatively insensitive to matrix confinement. We test these hypotheses in silico by devising a multiscale mathematical model that relates cellular force generation to ECM stiffness and geometry, which we show is capable of recapitulating key experimental trends. These studies represent a paradigm for investigating matrix regulation of invasion and demonstrate that matrix confinement alters the relationship between cell migration speed and ECM stiffness.

Fig. 1.

Design and creation of microfabricated polyacrylamide channels (μPACs). (A) Schematic of process, including fabrication of a silicon master with topographic patterns of defined size and shape, formation of a PA hydrogel of prescribed elasticity around the features, separation of the PA hydrogel from the master, and seeding of cells. (B) Phase contrast images of device fabricated from 120 kPa PA hydrogel and containing channels composed of pores of varying dimensions. Scale bar = 40 μm.

Fig. 2.

Migration speed versus ECM stiffness and channel width. (A) Migration speed versus channel width for soft, intermediate and stiff ECMs, corresponding to E = 0.4, 10, and 120 kPa. *p < 0.05 with respect to narrow (c_w = 10 μm) channels. (B) Migration speed versus ECM stiffness for narrow, intermediate, and wide channels (c_w = 10, 20, and 40 μm) and flat 2D gels. *p < 0.05 for pairwise comparison between two indicated stiffness values for all given channel widths, including 2D flat gel. n > 35 cells per condition over multiple channels and devices. (C) Phase contrast images of cells migrating inside channels of varying stiffness and width. Scale bar = 40 μm.

Fig. 3.

Morphological polarization of U373 cells on flat 2D gels. (A) Cell polarization measured as aspect ratio of cells cultured on flat unconfined (2D) gels. *p < 0.05 for indicated pairwise comparison; n > 35 cells per condition. (B, C, D) Phase contrast images of cells on 2D flat gels of varying stiffness. Scale bar = 40 μm.

Fig. 4.

Stress fiber alignment and spreading area of cells in defined confinement. Confocal images of F-actin and pMLC distribution for U373-MG cells in (A) narrow channels (c_w = 10 μm), (B) wide channels (c_w = 40 μm), and (C) unconfined flat 2D gels of varying ECM stiffness. Scale bar = 20 μm. (D) projected cell area, (E) F-actin alignment, and (F) coalignment of pMLC immunofluorescence with channel axis as a function of ECM stiffness for varying degrees of confinement. Statistically different pairs (p < 0.05) are indicated by horizontal square brackets. n > 12 cells per condition.

Fig. 5.

Effect of nonmuscle myosin II inhibition on cell motility. (A) Migration speed versus ECM stiffness for varying channel width. n > 30 cells per condition. (B) Phase contrast images of cells inside narrow and wide channels and flat 2D gels of varying stiffness. Scale bar = 40 μm. (C) Confinement sensitivity, Δν, calculated as |ν_narrow - ν_wide|, where ν_narrow and ν_wide are average respective migration speeds for narrow (c_w = 10 μm) and wide (c_w = 40 μm) channels versus ECM stiffness for control and blebbistatin-treated cells. Statistical significance (*p < 0.05) determined by Student’s t test (unpaired, two-tailed, 95% confidence interval).

Fig. 6.

Model predictions and comparison with experiments. Migration speed (v) versus ECM stiffness under (A) control and (B) blebbistatin-treated conditions, where model predictions are plotted as solid lines color-coded for varying degrees of matrix confinement with overlaid symbols and dotted lines corresponding to experimental measurements presented in Figs. 2B and 5A.