Developmental biology has been immensely successful in reducing the seeming miraculous self-organization of a fertilized egg to a fetus and adult to a list of genes and the instructions for their regulation in the noncoding genome. But knowing the parts (essentially all genes) is not commensurate with understanding their capacity to self-organize. Thus, we need to move from reductionism to integration, and physics, particularly condensed matter and statistical physics, has a long and successful history in phenomenological but still quantitative descriptions of Nature. Stem cell technologies allow one to build embryos from cells and thus test one's understanding. New imaging modalities and genetic interventions provide the means to reprogram the earliest steps of development in simple model organisms and quantify the outcomes. Development is about morphogenesis and the progressive specialization of cells as a function of time. The natural mathematical language for dynamics is geometric and the key ideas were formulated in the 20th century. Elements of that work provide a mathematically rigorous landscape analogy to development that enables a very compact phenomenological description that can be fit to data. Prior work by the PI has shown how simply confining stem cells in two dimensions elicits their potential for self-organization, which is surprisingly complex and employs the same cellular communications systems as in the embryo. This project will use the simplicity of synthetic systems and geometrical methods to quantify the genetic systems responsible for self-organization in mammals. Similar mathematical machinery is required to understand recent experiments in the nematode C. elegans that uses RNA interference to reprogram the founder cells in the embryo to new fates. How these new fates accommodate to their ectopic environment provide a strong quantifiable constraint on how the embryo self-organizes and are amenable to phenomenological treatments. The PI will continue to study the exact mutation that leads to Huntington disease in humans, which has a dramatic phenotype in stem cells differentiated on micropatterns.
The Waddington landscape is an oft-cited metaphor for development, particularly when discussing stem cells. A theorem of Smale, plausibly applies to the gene regulatory networks as imagined by Waddington and proves that such systems can be represented by potential flow on a Riemannian manifold. The PI will show the utility of this representation in several examples. It is the only general way to implement our intuition that developmental ‘decisions’ take place in a low dimensional space, and it provides a compact functional form with which to challenge that intuition with data, thus reducing the number of dimensions in which the essential degrees of freedom reside, compared to the standard Michaelis-Menten representations of gene regulatory networks, which typically have many more variables than the dimension of the attractor they describe. The PI's experimental collaborations in stem cells and C.elegans development will provide the means to apply these theoretical representations to data.
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.
