Figure 2. Contraction speed depends on geometry.

(a) Final contraction ratio C_fin/C_init (red) and maximal contraction velocity (black) of initially identical circles (radius C_init=388 μm) depends on the number of stimulation cycles n, corresponding to the density of active motors. Solid lines represent our calculations quantified by the ratio of spring coefficients for which we find K=C_fin/C_init (Supplementary Equation 1 with P=11% and K_∞=0.15) and (Supplementary Equation 19), both as a function of n. (b) Maximum contraction velocity versus the initial distance between boundaries for symmetric patterns (diameter for circles denoted as coloured circles and the width in the middle for squares denoted as black squares) at identical n=20. Solid lines represent linear fits in accordance with Supplementary Equation 15 of our minimal dynamic model, where is proportional to the initial distance between boundaries. The inset shows the radii of activated circles as a function of time for the corresponding colour coded circles. (c) Internal dynamics during the onset of contraction of a full square (half-width X_init=290 μm) after n=5 stimulation cycles. Colour coded are the velocities of contractile structures along the x–coordinate obtained by PIV (Supplementary Fig. 4). The boundary velocities increase to their temporal maxima in the course of time before approaching equilibrium in the long term. To visualize the symmetry and the size reduction of the contraction we show the z-projection of the corresponding three-dimensional plot. (d) To determine where and when motor activity results in a contraction, the local velocity gradients dν_x/dx for three regions (Pos.0, Pos.1 and Pos.2) with increasing distance to one of the interfaces (0 μm, 100 μm and 200 μm) are calculated from the data in c (indicated by the grey arrows, region width is 30 μm) and plotted over time. Close to the interface the contraction rate is high after activation and stays constant. With increasing distance to the boundary the contraction rate is close to zero and gets increased to the contraction rate measured for the boundary. Hence, motors initially contract structures only at the interface and the global ability to contract penetrates the activated area from there. We find that the maximal velocity of the boundary is observed when the centre region exhibits the initial boundary contraction rate (here at t≈16–20 min).