Abstract
The spatial arrangement of variant phenotypes during stem cell division plays a crucial role in the self-organization of cell tissues. The patterns observed in these cellular assemblies, where multiple phenotypes vie for space and resources, are largely influenced by a mixture of different diffusible chemical signals. This complex process is carried out within a chronological framework of interplaying intracellular and intercellular events. This includes receiving external stimulants, whether secreted by other individuals or provided by the environment, interpreting these environmental signals, and incorporating the information to designate cell fate. Here, given two distinct signaling patterns generated by Turing systems, we investigated the spatial distribution of differentiating cells that use these signals as external cues for modifying the production rates. By proposing a computational map, we show that there is a correspondence between the multiple signaling and developmental cellular patterns. In other words, the model provides an appropriate prediction for the final structure of the differentiated cells in a multi-signal, multi-cell environment. Conversely, when a final snapshot of cellular patterns is given, our algorithm can partially identify the signaling patterns that influenced the formation of the cellular structure, provided that the governing dynamic of the signaling patterns is already known.