Analysis, control, and engineering of spatiotemporal  pattern formation
A central problem in developmental biology is to understand how tissues are patterned in time and space - how do identical cells differentiate to form the adult body plan? Patterns often arise from prior asymmetries in developing embryos, but there is also increasing evidence for self-organizing mechanisms that can break the symmetry of an initially homogeneous cell population. These patterning processes are mediated by a small number of signaling molecules, including the TGF-β superfamily members BMP and Nodal. While we have begun to analyze how biophysical properties such as signal diffusion and stability contribute to axis formation and tissue allocation during vertebrate embryogenesis, three key questions remain. First, how does signaling cross-talk control robust patterning in developing tissues? Opposing sources of Nodal and BMP are sufficient to produce secondary zebrafish axes, but it is unclear how the signals interact to orchestrate this mysterious process. Second, how do signaling systems self-organize to pattern tissues in the absence of prior asymmetries? Recent evidence indicates that axis formation in mammalian embryos is independent of maternal and extra-embryonic tissues, but the mechanism underlying this self-organized patterning is unknown. Third, what are the minimal requirements to engineer synthetic self-organizing systems? Our theoretical analyses suggest that self-organizing reaction-diffusion systems are more common and robust than previously thought, but this has so far not been experimentally demonstrated. We will address these questions in zebrafish embryos, mouse embryonic stem cells, and bacterial colonies using a combination of quantitative imaging, optogenetics, mathematical modeling, and synthetic biology. In addition to providing insights into signaling and development, this high-risk/high-gain approach opens exciting new strategies for tissue engineering by providing asymmetric or temporally regulated signaling in organ precursors.