Extended Data Figure 6: Spindle orientation modelling.
From: Epithelial tricellular junctions act as interphase cell shape sensors to orient mitosis
a, Mitotic cell in the Drosophila pupal notum labelled with Jupiter–GFP to label microtubules (n = 23 cells). White arrows indicate astral microtubules. Yellow arrowheads indicate spindle poles. Scale bar, 1 μm. b, Representation of the different parameters that were varied for the predictions based on the GFP–Mud cortical intensity and shape model to estimate their contribution. L, length of the mitotic spindle; N, number of astral microtubules; 
, the angle covered by the astral microtubules; and 
, the GFP–Mud intensity scaling factor. See also Supplementary Table 1. c–f, Cumulative plots of the differences between the theoretical spindle orientation (
) and the experimental spindle orientation (
) angles in GFP–Mud-expressing cells (same cells as in Fig. 2h) for different spindle lengths (c), microtubule number (d), angular extension of astral microtubules (e) and different scaling factor between the GFP–Mud intensity and mechanical pulling force (f). The GFP–Mud model predictions are mostly independent of spindle length, the number of astral microtubules, the angle covered by the astral microtubules or the scaling factor between GFP–Mud intensity and microtubule pulling force. g, Dependence of model prediction on shape or GFP–Mud effective potential depth (±s.e.m.). The y axis quantitates the difference between the theoretical angle (
) and experimental angle (
) (1, aligned; −1, perpendicular). A larger potential depth corresponds to more deformed cells for the shape model, and to a sharp and anisotropic GFP–Mud distribution for the cortical model. Model predictions improve with potential depth, suggesting the model can capture the effect of GFP–Mud distributions in a dose-dependent manner. n = 140 cells. h, Definitions of the angles used in the analytical calculation of the contribution of different harmonics to the potential 
. The spindle (heavy black line) makes an angle 
with the positive x axis. An astral microtubule (thin black line indicated by the black arrow) projects to the cortex (circle) at an angle 
with respect to the spindle. The same microtubule contacts the cortex an angle 
above the positive x axis. i, Normalized magnitudes 
of the Fourier coefficients of the kernel 
for n even. The magnitudes 
drop off substantially with increasing n, indicating that for many purposes it should be sufficient to approximate the function 
by its lowest, 
mode. To calculate numerical values for the Fourier coefficients, we took the average of the normalized spindle length 
or the n = 140 cells analysed in this paper, obtaining 
; because it is difficult to precisely estimate 
from the available data, coefficients are shown for 
and 
in agreement with the astral microtubule distribution observed in a. j, Schematic illustrating the difference between cell shape and cell TCJ bipolarity measurements. An elongated cell and a rounded cell are overlaid (left panels) and shown side-by-side (middle and right panels). In this example, although the two cells have distinct shapes, they have the same TCJ bipolarity. The upper panels illustrate the measurement of cell shape, which uses all the pixels making up the cell (blue bars). The lower panels illustrate the measurement of TCJ bipolarity (red bars), which is solely based on the angular distribution of the TCJs (red dots), only using the unit vectors 
pointing from the cell centre (black dot) to each cell TCJ. The TCJ bipolarity therefore characterizes TCJ distribution independently of cell shape, and a correlation observed between the two quantities is not due to a shape bias in the TCJ bipolarity measurement.
