Vorticity contours from four distinct cellular systems exhibit the same patterns of scale and conformal invariance, which is recapitulated using a continuum model of an active fluid (IMAGE)

Faculty of Sciences of the University of Lisbon

Vorticity contours from four distinct cellular systems exhibit the same patterns of scale and conformal invariance, which is recapitulated using a continuum model of an active fluid

Caption

a, Perimeter of contours as a function of their radius of gyration for two prokaryotic and two eukaryotic genotypes, including WT P. aeruginosa bacteria (yellow circles) and a hyperpilated ΔpilH P. aeruginosa mutant (blue squares) that individually move faster, and MDCK cells (red diamonds) and MCF-7 human breast cancer cells (purple stars). Here we separately analysed the complete perimeter and accessible external perimeter of the contours (Extended Data Fig. 3). We found that the experimental data for all four genotypes collapsed onto lines with slopes of approximately 7/4 and 4/3 for the two different perimeter measurements. The flow fields produced by a numerical model of active fluids (Methods) generated vorticity contours with a power-law dependency in close agreement with that observed in the experiments. The perimeter and radius of gyration is normalized by the radius of gyration of the largest vorticity cluster in their respective systems Rg,max (Methods). b, Variance in the distribution of the winding angle, plotted here as a function of distance along the curve for the four experimental systems and numerical model, all of which exhibit the same logarithmic scaling with a slope of 6/7 (dashed line). The inset shows the distribution of winding angles for a fixed distance along the contour, which is closely approximated by a Gaussian (dashed line). Both findings are consistent with that predicted for conformally invariant curves, which exhibit the same fractal dimension that we obtained for our data in a. The dashed lines correspond to a slope of 6/7 and a standard Gaussian distribution. The inset also shows that the winding angles are obtained for segments of contours with lengths of 64 (filled symbols) and 512 (empty symbols), and measured relative to the average angle of the contour. Here we show the mean (symbol) and s.d. (error bar) from n > 85 separate measurements of the flow field for each dataset (Methods).

Credit

Benjamin H. Andersen, Francisco M. R. Safara, Valeriia Grudtsyna, Oliver J. Meacock, Simon G. Andersen, William M. Durham, Nuno A. M. Araujo & Amin Doostmohammadi

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