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.
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.
The images where the substratum shrank in Movie 2 were extracted and accumulated sequentially. The movie is shown 450× faster than real time.
Cells of the Dictyostelium discoideum cAR1/cAR3 [receptors of chemoattractant (cAMP)] double-mutant cell line RI9 (22) were cultured in HL5 medium [1.3% (w/v) bacteriological peptone, 0.75% (w/v) yeast extract, 85.5 mM D-glucose, 3.5 mM Na2HPO412H2O, 3.5 mM KH2PO4, pH 6.4] and developed in Bonner's standard saline (BSS, 10 mM NaCl, 10 mM KCl, 3 mM CaCl2) for >12 h at 4°C.Microscopy
One hundred microliters of cell suspension was settled on the elastic sheet. A 7 mm × 7 mm coverslip (Cat. no. 1; Matsunami, Osaka, Japan) was floated on the droplet to prevent light scattering at the rounded surface of the droplet and improve the observed images (Figure 1C).
Migrating cells plated on the elastic sheet were observed under phase-contrast microscopy using an inverted microscope (TMS, Nikon, Tokyo, Japan) with a 20× objective lens (20/0.4, Nikon, Tokyo, Japan). Images taken by a CCD camera (model no. XC-EI50, Sony, Tokyo, Japan) were transferred to a computer (Macintosh G4, Apple Japan, Tokyo, Japan) at 30-s intervals through a frame grabber board (LG3, Scion, Frederick, MD, USA) and analyzed using ImageJ Ver 1.40 (http://rsbweb.nih.gov/ij) with two plug-ins: Manual Tracking, programmed by Fabrice Cordelieres (Institut Curie, Orsay, France), and a Chemotaxis and Migration Tool, programmed by Gerhard Trapp and Elias Horn (Ibidi, Martinsried, Germany). In this analysis, the angle (θ in Figure 1D) between the horizontal line and the straight line which connected the starting and ending points of a migrating cell was measured. As an index of the directional migration, |sin θ| was calculated. When a cell migrates parallel to the stretching direction, the value should be 0. On the other hand, when a cell migrates perpendicularly, the value should be 1. Frequencies of θ are shown as histograms in Figures 2 and 3. The migrating speed was calculated by dividing the total length of the trajectory by total time. One-way analysis of variance (ANOVA) and multiple comparisons of means (Ryan's method) were applied to examine the differences among the data.
Cyclic stretch of the silicone sheet
To stretch the elastic sheet, we used a coiled SMA (BioMetal Helix150, Toki Corp., Tokyo, Japan) as an actuator. The diameters of the fiber and the coil are 0.15 and 0.62 mm, respectively (Figure 1E). The SMA has two interesting characteristics: (i) after expansion by mechanical force, it contracts and recovers its original shape with the application of heat, and (ii) it demonstrates electric resistance. Thus, the SMA can produce heat by itself according to Joule's law: P = V2/R, where P is the power (watts), V is the potential difference (volt) between the two ends of a piece of SMA, and R is the resistance (ohms) of the SMA. Thus, in response to the application of voltage pulses to the expanded SMA, it contracts due to the self-generated heat. A coiled SMA can be expanded to >2× its original length.
A piece of coiled SMA was connected to one side of the elastic sheet via an acrylic part to prevent heat transfer from the SMA to the sheet and the other side of the sheet was fixed (Figure 1, A, F–I). Sequential voltage square pulses were applied to the coiled SMA (blue single-headed arrow, Figure 1A), which induced cyclic stretching and shrinkage of the elastic sheet (blue doubleheaded arrow, Figure 1A). When the voltage between the two ends of the coiled SMA was high (black dot, Figure 1F), the SMA shrank and the sheet stretched (Figure 1G). On the other hand, when the voltage was low (black dot, Figure 1H), the sheet shrank due to its own elastic force (Figure 1I).
Voltage pulses were applied using a simple self-made electric power circuit (Figure 1J). An astable multi-vibrator circuit with NE555 (Texas Instruments, Dallas, TX, USA) was used as a source of voltage pulses. When the time cycle was shorter than 20 s, a fan (Figure 1, A and J) was used for cooling the SMA to release the contractile force quickly. The time of the cooling was optimized by a one-shot multi-vibrator circuit with a power operational amplifier, TA7272 (Toshiba, Tokyo, Japan).
The silicone sheet and SMA were settled in an acrylic frame. The frame was made from an acrylic board using a NC milling machine (COBRA 2520; Original Mind, Nagano, Japan). The costs of the electric circuit and the acrylic frame were <$50 USD and <$20 USD, respectively. It took less than 1 day to make the electric circuit and the acrylic frame.