Towards a Mathematical Theory of Development

To be held at ESB 2012 and on Zoom: https://ubc.zoom.us/j/68285564037?pwd=R2ZpLy9uc2pUYldHT3laK3orakg0dz09 Meeting ID: 682 8556 4037 Passcode: 636252

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.