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Multipole decomposition of surface patterns.

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posted on 2020-12-10, 18:46 authored by André Scholich, Simon Syga, Hernán Morales-Navarrete, Fabián Segovia-Miranda, Hidenori Nonaka, Kirstin Meyer, Walter de Back, Lutz Brusch, Yannis Kalaidzidis, Marino Zerial, Frank Jülicher, Benjamin M. Friedrich

(A, B) Schematic of vectorial and nematic cell polarity, respectively. (C) Multipole decomposition of a distribution on a sphere into spherical harmonics, see Eq (1). (D) Prototypical membrane distribution of vectorial polarity type with respective Mollweide projection and spherical power spectrum. The spherical power spectrum shows the power ||Fi||2 of the each mode Fi corresponding to the contribution from spherical harmonics of order i, i = 0, 1, 2, 3, 4, see Eq (2). (E) Same as panel D but for a ring-like surface distribution. Here, the second mode of the spherical power spectrum dominates. (E’) The second mode of the spherical power spectrum also dominates for the analogous case of a bipolar surface distribution. (F) Spherical projection, Mollweide projection and spherical power spectrum for an epithelial tubular cell from kidney tissue, as well as averaged power spectrum for a population of cells (n = 286, mean±2 ⋅ s.e.m., corresponding to 95% confidence interval). (G) Same as panel F, but for a hepatocyte from mouse liver tissue, as well as a population of hepatocytes (n = 9983).

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