Cells make fate decisions in response to different and dynamic environmental and pathological stimuli. Recent technological breakthroughs have enabled biologists to gather data in previously unthinkable quantities at single cell level. However, synthesizing and analyzing such data require new mathematical and computational tools, and in particular, understanding multiscale cellular dynamics emerging from molecular and genomic scale details demands new multiscale modeling. In this talk, I will present our recent works on analyzing single-cell molecular data, and their connections with cellular and spatial tissue dynamics. Our mathematical approaches bring together optimization, statistical physics, ODEs/PDEs, and stochastic simulations along with machine learning techniques. By utilizing our novel mathematical methods and their integration with new datasets from our collaborators, we are able to investigate several complex systems during development and regeneration to uncover new mechanisms, such as novel beneficial roles of noise and intermediate cellular states, in cell fate determination.
