Figure 1

Cell migration assay under nonadhesive tilted micropillars. (a) Design of the assay [see Fig. 3 in the Supplemental Material [17] ]. (b) SEM image of tilted pillars, $\alpha =70°$, $d=10\mu \mathrm{m}$, $h=12\mu \mathrm{m}$. (c) Overlay of phase contrast image and Hoechst staining (nucleus, green) of an NHDF cell confined under tilted pillars.Reuse & Permissions

Figure 2

(a) Typical tracks (starting at the origin) of cells moving under tilted pillars. (b) Angle histogram of the instantaneous direction of migration ($N=252$ cells from 12 movies, $n=78800$ single steps). (c) Median speed as a function of the instantaneous direction of migration ($N=452$ cells from 12 movies, $n=100949$ single steps). In (b) and (c) 0° is the direction of pillar tilt. In (a)–(c) the pillars’ geometry is $d=10\mu \mathrm{m}$, $h=10\mu \mathrm{m}$, $\alpha =65°$.Reuse & Permissions

Figure 3

(a) Measurement method for the direction and orientation bias quantified in (b) and (c). Bias is calculated with $\mathrm{bias}=({\#}_1-{\#}_2)/({\#}_1+{\#}_2)$ where ${\#}_i$ is the number of cells scored in region $i$ around their initial position after $4H$; 100% ($-100\%$) means that all cells are in region 1 (2) after $4H$. (b) Migration bias in controls and for different migration setups. Pillar geometries ($d$, $h$, $\alpha$) are ($5\mu \mathrm{m}$, $5\mu \mathrm{m}$, 90°) for straight pillars, ($5\mu \mathrm{m}$, $5\mu \mathrm{m}$, 45°) for tilted pillars, and ($5\mu \mathrm{m}$, $6.5\mu \mathrm{m}$, 60°) for soft environment. (c) Migration bias for cells confined under tilted pillars of various geometries and under microprisms of $2\mu \mathrm{m}$ in depth, $3\mu \mathrm{m}$ above cells. In (b) and (c) $N$ corresponds to the number of cells, $n$ to the number of single steps. Significance of the bias is given according to the ${\chi }^2$ test on the single steps: * is $p<0.05$, ** is $p<0.01$, **** is $p<0.0001$, ○ is $p<{10}^{-8}$.Reuse & Permissions

Figure 4

(a) Model: deformation of an elastic sphere (the cell nucleus) in a sawtooth profile (top) and the corresponding energy profile (bottom). (b) Top view drawing of pillars and definition of axes and directions used in distribution maps (bottom). Fwd, Bwd, L, and R give the directions used in the rest of the figure. Experimental distribution maps of the center of mass of nuclei as a function of the cell speed and axis of migration (bottom). (c) Theoretical distribution of nuclei predicted by the model (left) and measured (right) for the three speed (force for the model) regimes I–III. Vertical lines indicate the positions of the pillars [minimum of $h(x)$, see (a)]. Inset in the middle right graph shows the median speed of the nucleus as a function of the position of its center of mass and its direction of motion (speeds are normalized by the median speed). Values used in theoretical curves are as follows: in regime I, $FL=0.1\Delta U_E$; in II, $FL=6\Delta U_E$; in III, $FL=30\Delta U_E$. (d) Speed ratio $v_{+}/v_{-}$, as a function of the median instantaneous speed $v$. (e) Model prediction of $v_{+}/v_{-}$ as a function of rescaled force $FL/\Delta U_E$. Data set used for all graphs is the same as in Fig. 2.Reuse & Permissions