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 Schödinger equation, there are simply too many molecules for this to be useful. Optimal transport provides a set of equations that describe development at the level of cells. This theory is motivated by single-cell measurement technologies, which are ushering in a new era of precision measurement and massive datasets in biology. Techniques like single-cell RNA sequencing can profile cell states at unprecedented molecular resolution. However, these measurements are destructive -- cells must be lysed to measure expression profiles. Therefore, we cannot directly observe the waves of transcriptional patterns that dictate changes in cell type. We introduce a rigorous framework for inferring the developmental trajectories of cells in a dynamically changing, heterogeneous population from static snapshots along a time-course. The framework is based on a simple hypothesis: over short time-scales cells can only change their expression profile by small amounts. We formulate this in precise mathematical terms using optimal transport, and we propose that this optimal transport hypothesis is a fundamental mathematical principle of developmental biology.

About Geoffrey Schiebinger

Geoffrey received his PhD in Statistics in 2016 from the University of California, Berkeley, and pursued postdoctoral studies from 2016-2019 with joint positions at the MIT Center for Statistics and Data Science and the Broad Institute of MIT and Harvard. He was recently promoted to Associate Professor of Mathematics at the University of British Columbia, where he is a member of the Math of Information group, the Mathematical Biology group, and the Probability group. He is also an Associate Member of the UBC School of Biomedical Engineering, and a Specially Appointed Associate Professor at the University of Osaka in Japan.