Fig. 1

Definition of coordinate systems of the Kupffer’s vesicle (KV).

(A) Side view of a zebrafish embryo at 5-somite stage (left panel) and its schematic drawing (middle panel), highlighting the KV localization (grey box). The zoom-up box (right panel) shows the schematic transverse section of the KV, depicting the cilia (in green), their rotational orientation (black curved arrows) and the directional flow (thick black arrows). (B) e_m, e_n, e_f are the local basis on the ellipsoid, which are used to define cilia orientation. The vector e_m is aligned along a meridian (blue) from the ventral to the dorsal pole; e_f follows a parallel (red) in the direction of the typical directional flow within the vesicle; e_n is the vector normal to the KV surface and pointing towards the center of the vesicle (green). (C) Cilia 3D orientation is quantified by two angles: θ (tilt angle from the surface normal e_n) and φ (angle between the surface projection of the cilia vector and the meridional direction). (D) 2D flat map representation of the KV surface with coordinates α and β. The origin is set in the anterior pole. The embryonic body plan directions are marked as A (anterior), P (posterior), L (left), R (right), D (dorsal) and V (ventral). The body plan reference frame is defined as vectors e_D, e_L, e_A.