Stem cells (SC) have the potential to revolutionize medicine by facilitating the regeneration or replacement of damaged tissues. Crucial for the use of hSC in medicine is control over inter-cell communication, since those pathways are the ones responsible for making patterns and integrating the fate of a cell with its environment. In this project the PI will develop quantitative models of how spatial patterns arise and evolve in populations of stem cells. The predictions of these models will be tested experimentally. The understanding of the spatial patterns formed by stem cells will be used to understand cell-cell communication and how cells interact with their environment that is very important in biology, medicine, and bioengineering.<br/><br/>Recently an assay was developed for differentiating hSC on micropatterned surfaces, that generates the precursors to ectoderm, mesoderm, endoderm, etc. tissues in a spatial arrangement that recapitulates the embryo. This assay permits easy time lapse imaging of stem colonies while the cells signal to each other, move, and acquire distinct patterns of gene expression. Cells can be engineered to produce specific signals on demand and then mixed with naive cells and the emergent patterns followed over time. The relevant signals are generally present at too low a level to be observed directly, so a complex modeling procedure is needed to infer them from the response of the receiving cells. Critical for the success of any modeling in this area are succinct representations for the activity of the hundreds of genes that pattern an embryo. Modern mathematics provides the template for such models, and a separate project will test their application to the development of an organ in the nematode C.elegans. Through a collaboration, this project has access to many hSC lines with fluorescent tags on the genes that mediate cell signaling, and Physicists learn how to derive such lines themselves. Image processing systems developed in house are integrated with experiments to ask whether quantitative and predictive models formulated with only a few variables and guided by geometry are feasible. The goal is an algorithm to select among the infinite combinations of signaling molecules, their concentrations, and the time and duration of their application, the most efficient way to derive any desired cell or tissue from pluripotent cells.