Geometry, Genetics and Development

Developmental biology has been very successful in determining the genetic 'parts list' required for a fertilized egg to develop into an adult organism. The past few decades have seen great advances in our ability to assay the transcriptional signature of single cells and thus define new cell types, and also track the lineage of cells as they develop and differentiate. Imaging has also advanced in pace. During the last third of the 20th century pure mathematics has shown how to enumerate the types of solutions that can arise from systems of equations whose general properties are very plausibly shared by any model for development. The generic bifurcations that govern transitions among states are very compact and should provide a template for quantitative models of development. The PI has a background in self-organizing stem cell systems that will be the basis for regenerative medicine. The ability to predictively engineer the desired outcomes is a requirement for success. From previous projects with the Brivanlou lab at Rockefeller, the PI is a founder of a biotech company Rumi Scientific, that exploits our self-organizing stem cell technologies to screen for compounds that can revert the phenotypes of single gene diseases where the relevant mutation can readily be engineered into human stem cells. The mathematical analysis of models of development makes the key assumption of genericity, what happens in the absence of parameter tuning, which is plausible for development. Then all generic bifurcations can be enumerated, and each has a simple functional form with a few parameters. While there is no ambiguity about the power of mathematics to describe systems of equations, it is not at all obvious that these descriptions carry over to actual data. Hundreds of genes can be differentially expressed following a bifurcation between two cell types, or lineages, from a common progenitor. These genes are coordinated by a nearly infinite number of cross regulatory interactions, involving all the steps from genome to proteins. Mathematics achieves simplicity by simply positing two states and focuses on the bifurcation point where the lineages start to differentiate and where external manipulations can affect the outcome. Feedbacks that can regulate the proportions of the two lineages are also simply described. The PI will adapt the mathematical viewpoint to analyze data from in-vitro differentiated embryonic stem cells; self-organizing stem cell assemblies 'organoids' that mimic segments of embryonic development; and limb regeneration in amphibian systems. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.