Fig. 2: Method for analyzing the nematic order on the surface of a multicellular aggregate.
From: Capturing nematic order on tissue surfaces of arbitrary geometry

a, b For selected images of the acquired z-stack (Fig. 1a), a black and white mask is created to identify boundary points (yellow dots). c These points are combined to create a discretization of the aggregate’s surface in 3D (yellow dots). To determine the normal (white arrow) at a given point, a set of neighboring points (purple dots) is required to capture the local shape. This is repeated for every surface point (red arrows). d The normal vector (red arrow) at a surface point (yellow dot) defines the tangent plane at that point. This is translated by 5 μm along the normal vector in the direction of the bulk, resulting in a shallow slice (black plane) of the outer cells of the aggregate. e The xy-image of the acquired z-stack at the surface point (yellow dot) in (d) shows the position of the shallow slice (white line) and the 2D component of the 3D normal vector (red arrow). f A continuous 2D image within the shallow slice in (d) is obtained by linear interpolation of the underlying intensity field. Here, dark areas indicate the actin filaments at the cell borders, while lighter areas of the cells are used to perform the orientation analysis using the standard 2D software, OrientationJ. Nematic directors (red lines) are obtained in the shallow slice, with those in a local area ‘beneath’ the surface point (yellow dot) averaged to define n2D (white line). This director is then translated back to the original surface point, where it is expressed in 3D coordinates, n3D (see Methods - 3D nematic director on the surface). g, h The nematic director field (white lines) covers the entire surface of the 3D multicellular MCF10A aggregate and enables the detection of nematic topological defects. Defects of charge ±1/2 are shown here.