Towards a Mathematical Theory of Development
This talk introduces a mathematical theory of developmental biology, based on optimal transport. While, in principle, organisms are made of molecules whose motions are described by the Schrödinger equation, there are simply too many molecules for this to be useful. Optimal transport-a fascinating topic in its own right, at the intersection of probability, statistics and optimization-provides a set of equations that describe development at the level of cells. Biology has entered a new era of precision measurement and massive datasets. Techniques like single-cell RNA sequencing (scRNA-seq) and single-cell ATAC-seq have emerged as powerful tools to profile cell states at unprecedented molecular resolution. One of the most exciting prospects associated with this new trove of data is the possibility of studying temporal processes, such as differentiation and development. If we could understand the genetic forces that control embryonic development, then we would have a better idea of how cell types are stabilized throughout adult life and how they destabilize with age or in diseases like cancer. This would be within reach if we could analyze the dynamic changes in gene expression, as populations develop and subpopulations differentiate. However, this is not directly possible with current measurement technologies because they are destructive (e.g. cells must be lysed to measure expression profiles). Therefore, we cannot directly observe the waves of transcriptional patterns that dictate changes in cell type.