Mathematical Modeling of the Loss of Germ Cells and Intercellular Bridges in Germ Cell Clones.

The model was written in MATLAB using undirected graph algorithms in which each cell is considered a “node” and each connection or bridge is considered an “edge”. Adjacency matrices describing the connectivity of the cells in cysts were created using Cytoscape, all remaining adjacency matrices were created manually. Simulations of two models describing the mechanisms of cyst fragmentation were performed: random cell loss and random bridge loss. Using each clone from E14.5 (n = 41) as an initial model input sample, 250 trials were run with random cell or bridge removal in a manner that results in an average loss that corresponds with the experimental loss of cells or bridges across multiple trials (See SI Appendix, Supplemental Files 1 and 2 for additional details). Each mechanism was tested to compare the resulting population of hundreds of simulated broken-down cysts (in silico E17.5) to the E17.5 cyst structure data (in vivo E17.5, n = 29). The same approach was used to model random cell loss and random bridge loss in E17.5 clones (n = 29), the resulting population of hundreds of simulated broken-down cysts (in silico P0) was compared to the P0 cyst structure data (in vivo P0, n = 22). The connectivity of the cells is given by the degree distribution, where the degree of a cell is the number of bridges it has (or the number of other cells to which it is connected) and the degree distribution is the percentage of cells in a clone with 0, 1, 2, 3, or 4 bridges. The averages of each cell number were calculated by multiplying with total cell numbers from in vivo data. For each summary statistic, a two-sample t test with a 0.05-significance level was used to test the null hypothesis that the data came from independent random samples from normal distributions with equal means and equal but unknown variances.