Fig 1.
Aligned fibers cause faster and directed cell motion.
Representative epithelial monolayer expanding over 16hr (gray region indicates initial position, t = 0 hr) on gels with (a) aligned fibers (AF) and (b) random fibers (RF). (c,d) Corresponding individual cell trajectories, with color-coded mean cell speed in x-direction. Kymographs of cell velocity component in x-direction (vx) for AF (e) and RF (f).). Plot showing temporal evolution of the leading-edge (average of left and right edges) contour for monolayer migrating on AF (g) and RF (h) Kymographs for velocity strain rate for AF (i) and RF (j). Plot showing temporal evolution of
(averaged across a 100 μm wide strip at the monolayer midline) on AF (k) and RF (l). (m) Plot comparing time-averaged (m = 157) spatial autocorrelation function of vx for AF (red) and RF (blue) for n = 3. (n) plot comparing four-point susceptibility χ4 versus Δt between AF and RF. (o) Scatter plots of aspect ratio (AR) versus area for cells on AF (m = 56117) and RF (m = 39447). (p) Plot comparing cellular area distribution on AF and RF. Refer to statistical methods section for description about m and n.
Fig 2.
Aligned fibers cause force-effective collective migration.
Representative phase contrast images of monolayer expanding on (a) AF and (b) RF. Representative heatmaps of traction component Tx for (c) AF and (d) RF. Kymographs for Tx on (e) AF and (f) RF. Representative heatmaps of traction component Ty for (g) AF and (h) RF. Kymographs for Ty on (i) AF and (j) RF. Kymographs for monolayer stress component σxx on (k) AF and (l) RF. (m) Plot comparing strain energy between AF and RF (m = 157) across n = 3 (*****P = 1.98x10-84). (n) Plot comparing Tx with Ty for AF and RF (both Tx and Ty averaged across m = 157 and n = 3). (o) Plot comparing time-averaged (m = 157) spatial evolution of Tx along the normalized width of the monolayer (n = 3) between AF and RF. (p) Plot comparing time averaged (m = 157) spatial correlation function of average-normal stresses between AF and RF (n = 3). Refer to statistical methods section for description about m and n.
Fig 3.
Aligned fibers cause higher Plithotaxis within monolayer.
Representative monolayer overlaid with Principal stress ellipse which are color-coded for alignment angle φ between major axis of principle stress ellipse and direction of cellular velocity on AF (a) and RF (b). (c-f) Comparison of alignment angle φ distribution between AF and RF for quintiles based on distance from the leading edge with (c) being farthest quintile and (f) being closest quintile. For all quintiles, φ distributions are significantly different between AF and RF (p<0.001 for c-e, p<0.05 for f). Cumulative probability distribution curves (red to blue refers to quintiles at decreasing distance from leading edge, m>1000) for monolayer migrating on AF (h) and RF (i). Kymographs for monolayer shear stress (σxy) for AF (j) and RF (k).
Fig 4.
Aligned fibers cause higher fluidization within monolayer.
Plot showing temporal evolution of σxx (averaged across a 100 μm wide strip at the monolayer midline) on AF (a) and RF (b). Plot showing temporal evolution of cellular area on AF (c) and RF (d). Plot showing temporal evolution of on AF (e) and RF (f). Polygons approximating cell shapes for representative monolayer migrating on AF (g) and RF (h). Histogram showing temporal evolution of cell division frequency (averaged across a 100 μm wide strip at the monolayer midline) on AF (i) and RF (j). Histogram showing spatial distribution of cell division frequency (averaged over the entire duration of migration) on AF (k) and RF (l). Plot showing temporal evolution of leading-edge traction (averaged across 3/4th of the monolayer width) on AF (m) and averaged across 1/4th of the monolayer width on RF (n).
Fig 5.
Faster force-effective migration despite reducing substrate stiffness and duration of collagen alignment.
Phase contrast images of cell monolayer migrating of softer (a) AF and (b) RF. (c, d) Maps of velocity component vx. (e, f) Maps of traction component Tx. (g, h) Maps of monolayer stress component σxx. Kymographs of (i, j) velocity component vx, (k, l) traction component Tx, and (m, n) monolayer stress component σxx.
Fig 6.
Single contraction simulation shows that ligand connectivity leads to an increase in migration efficiency.
(a) Schematic of one-dimensional model of epithelial cells represented by springs sliding viscously over rigid ligand springs fixed to substrate springs, after self-propelling forces applied at leader nodes. Schematics showing differences in force balance among cell-ligand forces (Fc-l), ligand-ligand forces (Fl-l) and ligand-substrate forces (Fl-s) between connected ligand (b) and disconnected ligand (c). Forces are depicted as green arrows. Simulated kymographs of (d,e) velocity, (f,g) traction for connected (left) and disconnected (right) ligands for single contraction experiment. Plots showing velocity evolution at the leading edge for connected ligand (h) during the single contraction event for disconnected ligand (i). Plots showing traction evolution at the leading edge for connected ligand (j) during the single contraction event for disconnected ligand (k).
Fig 7.
Parameter scan shows migration efficiency is conserved across parameter space.
(a) Plot comparing migration efficiency (velocity gained/traction exerted) versus cell stiffness across connected and disconnected ligand. (b) Plot comparing migration efficiency (velocity gained/traction exerted) versus cell damping constant across connected and disconnected ligand. (c) Plot comparing migration efficiency (velocity gained/traction exerted) versus substrate stiffness across connected and disconnected ligand. (d) Plot showing evolution of migration efficiency (velocity gained/traction exerted) versus varying ligand connectivity for disconnected ligand condition. Migration efficiency was measured for the initial 5 hours of migration for all data points.
Fig 8.
Fluidization within monolayer further increases migration efficiency.
Simulated kymographs of (a) velocity, (b) traction and (c) strain-rate for connected ligand condition without fluidization. Simulated kymographs of (d) velocity, (e) traction and (f) strain-rate for connected ligand condition with fluidization. Simulated kymographs of (g) velocity, (h) traction and (i) strain-rate for connected ligand condition with fluidization and spatial variation in cell stiffness and damping constant. Plot showing spatial variation in threshold division strain across the cell nodes in silico (j). Plot showing spatial variation in spring stiffness across the cell nodes in silico (k). Plot showing spatial variation in damping constant across the cell nodes in silico (l). Plot comparing migration efficiency (velocity gained/traction exerted) for ‘no fluidization’, ‘fluidization’ and ‘fluidization with spatial variation in stiffness and damping’ across connected and disconnected ligand conditions (m).
Fig 9.
Physical model showing force-effective fast migration due to rapid contractility stabilization by fiber connectivity.
Plot comparing spatial variation in spring stiffness across the cells between connected and disconnected ligand conditions (a). Plot comparing spatial variation in damping constant across the cell nodes between connected and disconnected ligand conditions (b). Plot comparing spatial variation in threshold division strain across the cells between connected and disconnected ligand conditions (c). Simulated kymographs of (d, e) velocity, (g, h) traction, (j, k) shear-stress and (m, n) strain-rate kymograph for connected (left) and disconnected (right) ligands. Plot comparing temporal evolution of leading-edge velocity (f) and traction (i) between connected and disconnected condition. Plot comparing average velocity and traction between connected and disconnected condition (l). Plot comparing four-point susceptibility (χ4) versus Δt for simulated results (o).
Fig 10.
Model capturing the phenomenon of Haptotaxis and depicting ligand connectivity to be superior in terms of migration efficiency when compared to ligand continuity.
(a) Schematic of one-dimensional model showing direction of increasing ligand binding probability (ρl) from right-to-left, discussed further in supplementary section. Simulated kymographs for (b) velocity, (c) traction and (d) strain-rate for α = 0.04. Simulated kymographs for (e) velocity, (f) traction and (g) strain-rate for α = 0.003. Simulated kymographs for (h) velocity, (i) traction and (j) strain-rate for connected ligand condition. Plot showing spatial variation of ligand binding probability (ρl(xc)) for different values of α (k). Plot showing shift in center of mass of the cell mesh migrating on ligand mesh having different ρl(xc) corresponding to different values of α (l). Plot comparing migration efficiency for cell mesh migrating on ligand mesh having different values of α (shown in plot k) (m).
Fig 11.
Model capturing the phenomenon of Durotaxis and showing higher rate of contractility stabilization is sufficient to capture the phenomenon.
(a) Schematic of one-dimensional model showing direction of increasing substrate stiffness (ks) from left-to-right, discussed further in supplementary section. Simulated kymographs for (b) velocity, (c) traction and (d) strain-rate for durotaxis stiffness range of 0.06 nN/μm < ks < 12.3 nN/μm. Simulated kymographs for (e) velocity, (f) traction and (g) strain-rate for uniformly stiff substrates (ks = 12.3 nN/μm). Simulated kymographs for (h) velocity, (i) traction and (j) strain-rate for uniformly soft substrates (ks = 0.06 nN/μm). Plot showing different spatial variation of substrate stiffness (ks(xs)) used for testing the durotaxis model (k). Plot showing shift in center of mass of the cell mesh migrating on substrate mesh having different variations in ks(xs) (shown in plot k) (l).