Robin Dirk, Jonas L. Fischer, Simon Schardt, Markus J. Ankenbrand, Sabine C. Fischer

• Abstract Cell lineage decisions occur in three-dimensional spatial patterns that are difficult to identify by eye. There is an ongoing effort to replicate such patterns using mathematical modeling. One approach uses long ranging cell-cell communication to replicate common spatial arrangements like checkerboard and engulfing patterns. In this model, the cell-cell communication has been implemented as a signal that disperses throughout the tissue. On the other hand, machine learning models have been developed for pattern recognition and patternAbstract Cell lineage decisions occur in three-dimensional spatial patterns that are difficult to identify by eye. There is an ongoing effort to replicate such patterns using mathematical modeling. One approach uses long ranging cell-cell communication to replicate common spatial arrangements like checkerboard and engulfing patterns. In this model, the cell-cell communication has been implemented as a signal that disperses throughout the tissue. On the other hand, machine learning models have been developed for pattern recognition and pattern reconstruction tasks. We combined synthetic data generated by the mathematical model with spatial summary statistics and deep learning algorithms to recognize and reconstruct cell fate patterns in organoids of mouse embryonic stem cells. Application of Moran’s index and pair correlation functions for in vitro and synthetic data from the model showed local clustering and radial segregation. To assess the patterns as a whole, a graph neural network was developed and trained on synthetic data from the model. Application to in vitro data predicted a low signal dispersion value. To test this result, we implemented a multilayer perceptron for the prediction of a given cell fate based on the fates of the neighboring cells. The results show a 70% accuracy of cell fate imputation based on the nine nearest neighbors of a cell. Overall, our approach combines deep learning with mathematical modeling to link cell fate patterns with potential underlying mechanisms. Author summary Mammalian embryo development relies on organized differentiation of stem cells into different lineages. Particularly at the early stages of embryogenesis, cells of different fates form three-dimensional spatial patterns that are difficult to identify by eye. Pattern quantification and mathematical modeling have produced first insights into potential mechanisms for the cell fate arrangements. However, these approaches have relied on classifications of the patterns such as inside-out or random, or used summary statistics such as pair correlation functions or cluster radii. Deep neural networks allow characterizing patterns directly. Since the tissue context can be readily reproduced by a graph, we implemented a graph neural network to characterize the patterns of embryonic stem cell organoids as a whole. In addition, we implemented a multilayer perceptron model to reconstruct the fate of a given cell based on its neighbors. To train and test the models, we used synthetic data generated by our mathematical model for cell-cell communication. This interplay of deep learning and mathematical modeling in combination with summary statistics allowed us to identify a potential mechanism for cell fate determination in mouse embryonic stem cells. Our results agree with a mechanism with a dispersion of the intercellular signal that links a cell’s fate to those of the local neighborhood.…