Fig. 4: Shapes and curvatures fitted with approximate curves.
From: Experimental determination and mathematical modeling of standard shapes of forming autophagosomes

a–d The shapes fitted with polynomial functions of a very early-cup (a), an early-cup (b), a middle-cup (c), and a late-cup (d), in which the line color represents the total curvature. In each panel, the black dots represent the same point set as in Fig. 3e–h, respectively. The unit of length was normalized so that the variance of the point set was one. e A schematic description of the meridional and parallel curvatures relative to the xy-plane, \({J}_{m}\) and \({J}_{p}\), respectively. f–i The meridional (\({J}_{m}\), \(x\ge 0,\) right) and parallel (\({J}_{p}\), \(x\le 0\), left) curvatures of a very early-cup (f), an early-cup (g), a middle-cup (h), and a late-cup (i) are shown by the various line colors; the shape of the fitting curve in each panel is the same as those in panels a–d. j A scatter plot of the meridional outward curvature near the rim obtained by polynomial fitting of individual phagophores. Source data are provided as a Source Data file.