Fig 1.
Non-elastic remodeling occurs in the course of minutes and depends on crosslinking in 3D biopolymer networks.
(a) Z-projected confocal images of human cells including HUVECs and MDA-MB-231s suspended in 3D biopolymer networks of fibrin (3 mg/mL) and collagen (1.5 mg/mL), respectively. For fibrin gels, crosslinking was lowered using a transglutaminase inhibitor (DDITS, 0.2 mM). White arrows indicate the assumption of the type of deformation, overall (elastic and non-elastic) or elastic only, expected between two force configurations. Scale bar, 20 μm. (b, c) Quantification of the effect of crosslinking in terms of (b) displacement length (N = 8 cells per condition) and in terms of (c) densification factor (N = 7 cells per condition). Times (1h, 2h, 3h and 4 hours) are defined as the time after Cytochalasin D is removed and prior to decellularization. Decell. indicates at least 1 hour after decellularization. (d) Representative ECM remodeling dynamics by MDA-MB-231 cells for two different collagen gel densities. To assess the dynamics without the possible delay in force generation due to drug washout, Cytochalasin D pre-treatment was not used in these experiments. The average matrix displacement length in a ROI (~30x30 μm2) containing the cell and the newly recruited ECM fibers is obtained starting at the reference configuration shortly after seeding. These relatively fast dynamics measurements are calculated from time-lapse images of projected z-stacks. (e) Summary of RI for all cell-matrix pairs studied.
Fig 2.
Mechanical signaling through long-range displacement propagation is cell-matrix specific and can be modified by remodeling.
(a) 3D displacement vectors from the FIDVC algorithm, color-coded according to the magnitude of the cumulative displacement, for three representative cells in the three different matrices tested. Cumulative displacement includes both elastic and plastic components over the duration of the ECM remodeling process. (b) Normalized displacement length vs. distance from the cell membrane for the matrix cases analyzed (N = 5 cells per condition, with displacement lengths vs. distance being averaged from four radial directions per cell). A theoretical representation for isotropic materials, decaying as (distance)-2, is shown for comparison. (c) 3D displacement fields for a representative case of a breast cancer cell in collagen: (left) force recovery with matrix remodeling, with cumulative displacements being both plastic and elastic; (center) the plastic (non-elastic) component; and (right) force relaxation after decellularization, with displacements presumed to be the elastic component.
Fig 3.
ECM recruitment by dynamic actin-driven processes.
(a) Representative confocal images of HUVECs suspended in 3D biopolymer networks of fibrin (3 mg/mL) fixed and stained after 4h treatment with several cytoskeletal drugs and inhibitors. Blue is DAPI, red is phalloidin, and cyan is the fluorescently labeled fibrin fibers. Scale bar is 20 μm. (b) Statistical comparison for all treatments with drugs, in terms of densification factor (N>15 cells per case; ** p<0.01with one-way ANOVA with post-hoc Tukey HSD Test). (c) Computational simulation of an ECM fiber network shows network morphology before (left) and after (right) the application of loading forces near the left boundary. Colors on fibers indicate tension level according to the color bar (-300 to 300pN). Yellow spots are crosslinks (places where fiber-fiber crosslinking can occur). See also S4 Video and S5 Video. (d) Overlay of the time evolution of fiber concentration profiles, normalized by the initial concentration, in the force-loading direction as loading forces are exerted from the left boundary. Loading forces mimic dynamic filopodia pulling from the loading boundary, such that fibers within 2μm of that boundary experience a force pulling them toward the boundary. As new fibers or fiber segments move within that distance, new loading forces are exerted on them. Different colored curves represent different normalized times of: 0 (lower blue, uniform), 0.03 (red), 0.37 (yellow), 0.7 (purple, dashed), 1.03 (green), 1.37 (light blue), 1.7 (magenta), 2.03 (blue), where time is normalized to the total time of force application (starting at right after 0 and ending at 1). Some relaxation occurs after applied forces end, but matrix remodeling here is not reversed. The simulation setup is 100pN loading per fiber segment in the loading region, 1x crosslink zero-force unbinding rate, 0.3x crosslink mechanosensitivity, and 1x crosslink density (see S1 Table for default values). (e) MDA-MB-231 cells expressing fluorescent F-actin (green, left) inside a 3D collagen matrix (white, middle) with a concentration of 1.5mg/mL display many dynamic actin protrusions (blue arrows). Overlay image of actin and collagen is on the right. Images are maximum intensity z-stack projections. The scale bar is 20μm. See also S3 Video. (f) Schematic of ECM recruitment by dynamic filopodia. Step 1: Filopodia attach to fibers in the vicinity of the cell (loading zone). Step 2: Filopodia contract, via actomyosin-based contractile forces, pulling attached fibers toward the cell and breaking force-sensitive crosslinks. Step 3: New filopodia form and attach to new fiber regions in the loading zone. Step 4: Contraction cycle repeats, further pulling ECM fibers toward the cell. This dynamic filopodial force loading condition is applied in our discrete network simulations.
Fig 4.
ECM recruitment profiles from discrete network simulations showing dependence on loading forces and crosslink concentration.
(a) Normalized ECM concentration within the region 0–3μm from the cell vs. time (normalized by the duration of force application) for different loading forces (per fiber), as indicated by the arrows and color legend (in pN). (b) Peak normalized ECM concentration in the accumulation region as a function of the loading force. For the simulations of (a,b), the relative crosslink zero-force unbinding rate is 1x, the relative crosslink mechanosensitivity is 0.3x, and the relative crosslink density is 1x. (c) Normalized ECM concentration within the accumulation region vs. time for different relative crosslink concentrations, as indicated by the arrows and color legend. (d) Peak normalized ECM concentration in the accumulation region as a function of the relative crosslink concentration. In (c,d) the loading force is 100pN, the relative crosslink zero-force unbinding rate is 0.1x, and the relative crosslink mechanosensitivity is 0.3x. See S4 Fig for statistics of triplicate simulations for selected configurations. See S1 Table for 1x values of relative parameters.
Fig 5.
Stress generation in the dynamic ECM from discrete network simulations.
(a) Overall stress vs. time in the ECM network during dynamic force loading for different loading force magnitudes as indicated by the arrows and color legend (in pN). (b) Peak stress in the network as a function of the loading force. (c) Ratio between the stress immediately before stopping loading forces (t = 1) and peak stress as a function of the loading force magnitude. (a,b,c) correspond to the same simulations as Fig 4A and 4B. (d) Overall stress vs. time in the ECM network during dynamic force loading for different relative crosslink concentrations as indicated by the arrows and color legend. (e) Peak stress in the network as a function of the relative crosslink concentration. (f) Ratio between the stress immediately before stopping loading forces (t = 1) and peak stress as a function of the relative crosslink concentration. (d,e,f) correspond to the same simulations as Fig 4C and 4D. Statistical assessment from triplicate simulations are shown in S6 Fig.
Fig 6.
Comparison of simulations and experiments.
Experimental profiles for fibrin and collagen intensities over time are compared with simulations for varying crosslink concentration. For consistency, the accumulation zone for measuring ECM density is here set to 5μm from the cell/loading surface for both experiments and simulations. For simulations, loading forces are stopped at the normalized time of 1. For experiments, time is normalized to 4 hrs, when the intensity levels appear to plateau, and experimental data points after the normalized time of 1 indicate post-decellularization as in Fig 1. Different colored curves represent simulation results with different crosslinker concentrations, as indicated in the legend. Simulation results are from the same conditions and data as in Fig 4C. Circles are experimental data, and error bars are SEM, with N = 5 cells per experimental condition.
Fig 7.
A strain-dependent plastic softening with elastic damage constitutive law recapitulates the effect of crosslinking in fibrous matrices.
(a) Schematic of the constitutive viscoplasticity of the Norton Van’t Hoff type used to model the ECM. (Parameters provided in S2 Table). (b) The model is modified and alternatively tested to include phenomenologically the features of damage, simulating breakage of crosslinks with tensile strain, and plastic softening, simulating the drop in yield stress with plastic strain. (c) The constitutive model is implemented in the commercial finite element solver ABAQUS using existing standard viscoplastic material models and custom subroutine implementation for the damage model. An axisymmetric mesh is shown to model the ECM around a contracting cell. The zoom inset shows the surface where the load is applied to simulate the action of filopodia farther away from the edge. (d) Von Mises equivalent stress and (e) displacement length for the continuum viscoplasticity cases with or without damage and softening. Displacement lengths are calculated at the cell-ECM interface, and Von Mises stresses are calculated at approximately 5μm from the loading surface (toward the ECM), which exhibits mostly tensile stress states. In (d) the boundary applied loading history is plotted, with * showing the typical time discretization for the FE analysis. Loading starts at 0 and stops at the normalized time of 1. (f) Recoverability index at the cell-ECM interface (elastic deformation divided by total deformation) for the cases with or without damage and softening, along with the experimental data from Fig 1E for comparison. (g) Plastic equivalent strain for the cases with or without damage and softening, all calculated at the cell-ECM interface. (h) Recoverability index and damage radius, i.e. the radius up to regions with half-max damage (as pictured in S10 Fig), as a function of the magnitude of the applied load p. (i) Recoverability index and damage radius as a function of the creep loading time during which the load is kept constant (p = 0.1 kPa).