a, Phase-contrast (top) and fluorescence (bottom) images are shown for two live keratocytes stained with TMR-derivatized kabiramide C. The fluorescence intensity reflects the current and past distribution of filament ends, in addition to diffuse background signal from unincorporated probe20. Along the leading edge, the fluorescence intensity is proportional to the local density of actin filaments (see Supplementary Information; 1-µm-wide strips along the leading edge are shown superimposed on the phase-contrast images, with centre and side regions highlighted). b, The average (background-corrected) fluorescence intensity along the strips shown in a is plotted. The cell on the left has a peaked distribution of actin filaments, whereas the actin distribution in the cell on the right is flatter. The ratio of the actin density at the centre (Dc) and sides (Ds; averaged over both sides) of the strip, denoted as Dcs, serves as a robust measure of the peakedness of the distribution. c, The density distribution of pushing actin filaments along the leading edge is approximated as a parabola, with a maximum at the centre. Cells with peaked filamentous actin distributions and, therefore, high Dcs values, have larger regions in which the actin filament density is above the ‘stall’ threshold, and thus have longer protruding front edges (of length x) compared with the length of the stalled/retracting cell sides (y), yielding higher aspect ratios (S = x/y). d, The ratio between actin density at the centre and at the sides, Dcs, is plotted as a function of cell aspect ratio, S. Each data point represents an individual cell. Our model provides a parameter-free prediction of this relationship (red line), which captures the mean trend in the data, plotted as a gaussian-weighted moving average (σ = 0.25; blue line) ± one standard deviation (blue region). Inset: the model of cell shape is illustrated schematically.