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Cyclic stretch of the substratum using a shape-memory alloy induces directional migration in Dictyostelium cells
 
Yoshiaki Iwadate1,2 and Shigehiko Yumura1
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Supplementary Material
Supplementary Movie 1. Motion of stretching device using SMA as a power source. (.mov)
To generate the power to stretch the elastic sheet, 4 pieces of coiled SMA were connected in parallel to the left edge of the sheet. The time cycle was 30 s. The movie is shown 5× faster than real time.
Supplementary Movie 2. Dictyostelium cells under the cyclic stretching stimuli. (.mov)
This movie was prepared for demonstration. The densities of cells in this movie were higher than that of the trajectory measurement (see Figure 2 in the main text). The time cycle was 30 s. The movie is shown 10× faster than real time.
Supplementary Movie 3. Migration of Dictyostelium cells under the cyclic stretching stimuli. (.mov)
The images where the substratum shrank in Movie 2 were extracted and accumulated sequentially. The movie is shown 450× faster than real time.

Finite element analysis

We estimated the Poisson's effect and the homogeneity of the deformation of the elastic sheet clamped in the stretching device by finite element analysis (FEA) of the plane stress state. FEA was performed by using VisualFEA software (Intuition Software, Chonbuk, South Korea).

Results and discussion

In elastic sheets, shortening of the sheet perpendicular to the axis of stretch (Poisson's effect) must take place. First, characteristics of the elastic sheet clamped in the new device were determined (Table 1). The change of the length of the sheet indicated as the central perpendicular lines (l and l′ in Figure 1, G and I) by stretching to the horizontal axis was measured. In the range of 5–30% stretching, the ratio of perpendicular shrinkage was 1/4 of the stretching length. This value agrees well with the theoretical value calculated by FEA of the plane stress state, in which Young's modulus and Poisson's ratio were 2.2 MPa and 0.3, respectively. Thus, we assumed that the sheet clamped in the new device behaved as an elastic sheet in which the Poisson's ratio was 0.3. Then, the deformation of the sheet was simulated by FEA (Figure 1, K–N). Figure 1K and 1M show the pseudo-color images of the displacements of each point of the sheet in the stretching direction (Figure 1K) and in the perpendicular direction (Figure 1M), respectively. In this calculation, 30% stretching was applied. The displacements of the sheet along the arrows in Figure 1K and 1M were plotted in Figure 1L and 1N, respectively. The numbers 0 and 1 in Figure 1L and 1N indicate the positions 0 and 1 in Figure 1K and 1M, respectively. As shown in Figure 1L and 1N, the displacements increase linearly from position 0 to 1, suggesting that the mechanical stimulation from the sheet to the cell is uniform throughout the sheet.





To generate an enough force to stretch the elastic sheet, 4 pieces of coiled SMA, 2.2 cm in length, were connected in parallel to the edge of the sheet. The total resistance of the 4 pieces of SMA was ~2.6 ohms. Sequential square voltage pulses with a peak value of 2.6 V were applied to the SMA. This electric application caused cyclic stretching of the elastic sheet. The duty ratio and the time cycle of the cyclic stretching were easily controlled by changing the durations of the 2.6 and 0 V applications. The duty ratio was fixed at 1:1 throughout the experiments. The minimum time cycle of the new stretching device was <5 s. This is comparable in speed to commercially available stretching devices. Typical motion of the device is exhibited in Supplementary Movie S1, in which the stretching ratio and the time cycle are 30% and 30 s, respectively. The kinetic property of the substratum is shown in Figure 1O. The duty ratio (t1:t2 in Figure 1O) was fixed at 1:1. Under this condition, no medium flow was confirmed by the observation of sunken small particles detached from the substratum (data not shown), which indicated that the influence of shear stress to the cells would be negligible.

The costs of the SMA required for making the new stretching device was ~$30 USD. Thus, the total cost of the new device including the electric circuit and the acrylic frame was <$100 USD. This cost is much lower than the price of commercially available products (e.g., FX-4000, Flexcell, NC, USA, and STB-150, Strex, Osaka, Japan; >$10,000). Moreover, the new device has two other advantages: its small size and lack of vibrating noise. In preliminary experiments, we applied the cyclic stretching to the Dictyostelium cells using a motor-driven device (STB-150, Strex, Osaka, Japan). They often detached from the substratum by vibration from the motor because of their weak adhesiveness (data not shown).

Using the new stretching device, we examined whether Dictyostelium cells could sense mechanical stimulations applied through the substratum and whether this influenced migration direction. The cAR1/cAR3 double-mutant cell line was used in this experiment to prevent spontaneous chemotactic response. Dictyostelium cells, developed in BSS for >12 h at 4°C, were dispersed on the elastic sheet and their migrations were recorded during the application of cyclic stretching stimuli (30% stretching ratio and 30 s time cycle; Supplementary Movie S2). As shown in the movie, the cells can be observed clearly at the moment when the sheet shrinks. Thus, only the images from when the sheet shrank were extracted and accumulated sequentially (Supplementary Movie S3). From these sequential images, we analyzed the trajectory and velocity of the cells using plug-ins for ImageJ software (Figure 2). In Figure 2, cyclic stretching was applied horizontally (0–180°). Figure 2, A–D, shows typical trajectories of migrating cells (green lines) under the application of cyclic stretching. Stretching directions are indicated as blue double-headed arrows at the bottom of each figure. The cells tended to migrate perpendicular to the stretching direction (n = 50, from four experiments). The cells migrated upward and downward with the same probability. Figure 2, G and J, shows the trajectories of migrating cells and the frequencies of cell migrating directions (θ), respectively. The migrations of the cells on the fixed sheets under the shrunken state (Figure 2, E and H) and the stretched state (Figure 2, F and I) were observed as controls. As an index of perpendicular migration to the stretching direction, average |sin θ| values in each condition were calculated (3 columns from the left in Figure 3I). The average migrating speeds of cells under the three conditions are summarized in Figure 2K.

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