Fig. 1: Transition to order in confined endothelial cells.

a Top: The state of disorder (gray shaded region) and order (beige shaded region) is illustrated by the corresponding velocity field of the confluent endothelial cell layer on a circular pattern (D = 200 µm). Bottom: The steep increase in the angular order parameter (\(\Phi=\frac{1}{N}\,\mathop{\sum }\nolimits_{j=1}^{N}{\hat{v}}_{j}\,{{{{{{\bf{e}}}}}}}_{\varphi {j}}\)) quantifies the transition from the initially disordered to the ordered motion, where \({\hat{v}}_{j}\) denotes the normalized velocity and \({{{{{{\boldsymbol{e}}}}}}}_{\varphi {j}}\) the unit vector in the azimuthal direction of agent cell j in a population of size N. b The space-time representation of a single cell moving on an adhesive line pattern (width = 50 μm). c By plotting the mean migration speed of a single cell against the nucleation frequency of actin waves, we find a positive correlation (n = 20). d Top: A schematic representation of the collective migration of endothelial cells on a ring-shaped adhesive pattern. Below: The space-time representation of a representative subset of the acquired time series of a configuration of 3 cells on a ring (diameter = 300 μm, width = 35 μm), before and after the onset of collective rotation. Adjacent: In the corresponding polar transform, the frequency locked state becomes evident by the uniform vertical spacing between the periodically reappearing polymerizing actin waves with respect to the individual cells and across the collective. The white lines indicate the boundary between individual cells. e Bottom: The correlation parameter C characterizes periods of small standard deviations in frequency and high mean velocities across the population. During phases of ordered, collective migration (beige-shaded region), the correlation parameter C approaches values close to unity and decreases towards zero while the system is in disorder (gray-shaded regions). Top: The corresponding power spectrum density depicts the dominant frequencies present. The main nucleation frequency of polymerizing actin waves is around 4.8 h⁻¹, and the first harmonics are present at around 2.4 h⁻¹. f Top: Representative cell trajectories are shown during individual stages of a CK666 treatment experiment. During the presence of the ARP2/3 inhibiting drug, cells are actively migrating, but the global order is lost. After removing the drug, the carousel-like motion recovers. The transitions between states can be quantitatively identified by the drop and consecutive rise in the angular order parameter (n = 10) (Mean ± SD).