Fig. 2: Instantaneous cell flux drives layer formation.

a Schematic illustrations of cell flows driven by the nematic order (left) and polarity (right) around the same +1/2 defect. The dashed circle shows the boundary at which we calculate the velocity and polarity fluxes. The orange arrows show the cell velocity driven by the nematic active force, which is asymmetric due to anisotropic friction¹⁴. The solid black curves illustrate the director field near this defect. The green arrows label the cell polarity. b Two exemplary regions with (A, purple) and without (B, green) second layer formation. For region A, we set the time at which the second layer appeared as t = 0 min, while for B, the time point t = 0 min was chosen arbitrarily. The white circles with a radius of l_p = 12 μm label the boundaries of the selected regions, and they each surround a +1/2 defect. c Polarity flux Φ_p, velocity flux Φ_v, and volume change ΔV in regions A (purple) and B (green). d Mean (curves) polarity flux \(\overline{{\Phi }_{{{\boldsymbol{p}}}}}\), velocity flux \(\overline{{\Phi }_{{{\boldsymbol{v}}}}}\), and volume change \(\overline{\Delta V}\) over multiple regions, each surrounding a +1/2 defect, with (purple) and without (green) second layer formation, and the corresponding standard errors (shaded areas). The expected volume change driven by the mean velocity (Fig. 1c) is shown by the black dot-dashed line, calculated using the experimentally measured \({\Phi }_{\left\langle {{\boldsymbol{v}}}\right\rangle }\) and Eq. (2). The definition of t = 0 min remains the same. e Probability density functions of the polarity flux Φ_p and velocity flux Φ_v within the time window of [−5, 10] min.