A simplified model to test the hypothesis that strain rate triggers cellular directional response.

<p>(<b>A</b>) A qualitative description by a simple model of the relations between velocity, acceleration, strain rate, and directionality. Simulated particle velocity in the direction of the wound <i>V₊</i>(<i>t</i>) (solid purple line), acceleration (dashed line), and linker attachment probability in the direction of the wound <i>ρ</i>(<i>t</i>) (solid yellow line). (<b>B</b>) Strain rate triggers a directional response (model calculation). Calculated ratio of the directional velocity parallel (<i>V_∥</i>) to the directional velocity toward The wound (<i>V₊</i>) as the acceleration wave propagates, for increasing sharpness of the wave (decreasing σ in Supporting <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003747#pcbi.1003747.s001" target="_blank">Text S1</a>), corresponding to a wave that is either sharper or with same σ but with larger overall peak acceleration leading to higher final velocity. Both give higher strain-rate and higher directionality according to our proposed relation of directionality on linker occupation (purple curve versus yellow curve as control). (<b>C–D</b>) Experimental results: scatter plot comparison of directionality: <i>V₊ vs</i>. <i>V_∥</i>. Each dot in the scatter plot represents an element (<i>t</i>,<i>d</i>) in the two Corresponding spatiotemporal maps. The results presented here were accumulated over all available experiments (N = 5 for HGF/SF treated cells, N = 6 for control cells). HGF/SF-treated DA3 cells migrate in an enhanced directional manner (<b>D</b>), compared to control cells (<b>C</b>), similarly to the corresponding theoretical purple and yellow plot in (<b>B</b>). (<b>E</b>) Morphology of single DA3 cells as function of time and distance from the wound. Average cell area (left panel) and eccentricity (elongation, right panel) as function of time. Cells stretch to become larger and more elongated as the acceleration and strain-rate wave traverses the monolayer. When the wave passes to deeper cells, enhanced directionality is lost (<b>B</b>) theoretically, (<b>C</b>) and (<b>D</b>) experimentally), but the cells keep maintaining their elongated morphology. (<b>F</b>) Subjective single cells observations served as another indication for the validity of the experimental and theoretic results. Visualization of manual cell tracking (each cell marker with a different color) show that cells elongate to the direction of the wound edge followed by migration in a directional manner upon arrival of the waves. Time is in the format hh:mm. The corresponding video is freely available at “The Cell: an Image Library”, <a href="http://www.cellimagelibrary.org/images/46351" target="_blank">http://www.cellimagelibrary.org/images/46351</a>.