Mathematica 11

The calculations were performed with Mathematica 11.1 (Wolfram Research). For further details, see S1 Text.
For the simulations shown in Fig 7D (Nanog mutant embryos), we use the cell positions, cells proportions from early Nanog^+/+ or Nanog^+/- embryos (44 embryos; p_GATA6 = 94% and p_NANOG = 78%) and startNumNeigh = 9 to simulate the wild-type situation. For the Nanog mutants, we set the proportion of N+ cells (p_NANOG) to 0.

We used the embryos labelled as “littermate”, available from GitHub [22 (link)]. This resulted in 147 additional data sets (S1 and S2 Tables, data II). Compared to data I, the experimental setup was slightly different. Specifically, a different NANOG antibody was used and the embryos were imaged without being mounted. Given the extra thickness of the samples, the correction of fluorescent decay along the z-axis was required. Furthermore, while the same algorithm was used for the segmentation, a different thresholding method was applied to obtain the four populations (k-means clustering). We used the same cell number-based staging method as the one used for our data set, which resulted in 64 early, 34 mid and 49 late blastocysts. We excluded all NANOG and GATA6 levels from the distribution that were two standard deviations away from the respective mean as we noticed that there were some oversaturated nuclei images. The calculations were performed with Mathematica 11.1 (Wolfram Research). For further details, see S1 Text.

To explore the distribution centered over a geographical region within a country and at each timepoint, we chose a grid of 27 evenly spaced internal points within the country’s minimum and maximum latitude and longitude. For each internal point, we randomly resampled surveys with inclusion probability based on the distance from the specific point (Gaussian kernel with a SD of 2° unless otherwise stated). All calculations were performed in Mathematica 11.1 (Wolfram Research).

The calculations were performed with Mathematica 11.1 (Wolfram Research). Details on the total number of embryos and cells in each population type analysed are shown in S1 and S2 Tables. For further details, see S1 Text and S1 Fig.

The synchronized movies were visualized (Video 2) using custom scripts (Scherf, 2017 ) for Mathematica 11.1 (Wolfram Research Inc., Champaign, Illinois). The raw calcium signal stacks for each time point were normalized and visualized in 3D using direct volume rendering of the resulting intensities. The 3D volume visualizations were then projected to 2D using a standard perspective transform from a defined viewpoint. Animations were created by a smooth interpolation between different viewpoints.

We developed a pipeline for automated image analysis designed to detect single objects (e.g. cells, nuclei, and FAs) and extract their morphological features (Fig 2). For this, the acquired grey-scale images of the actin cytoskeleton, nucleus and FAs were processed and analyzed using a custom-made code written in Mathematica 11.1 (Wolfram Research, Inc., Champaign, USA), which is available as a supplementary file S1 File.

The Spearman’s correlation analysis and bootstrapping were performed in Matlab R2012b (MathWorks). The simulations of the null model were performed with Mathematica 11.1 (Wolfram Research).
To classify the strength of the correlations we used the criteria by Evans [34 ]:
For further details, see S1 Text.