Invariant and Equivariant Data-driven Methods for Modeling Cellular Dynamics
Abstract
Recent advances in experimental methodologies and large-scale community efforts have led to an explosion of single-cell genomics and imaging data, creating a need for new analytical frameworks capable of extracting meaningful structure and dynamics. In this talk, I will describe our recent efforts to leverage optimal transport, in combination with neural networks and kernel methods, to learn dynamical systems in cellular biology, with a specific focus on processes with invariance and/or equivariance.
In the first part, from a geometric perspective, I will present a sequence of metrics on shape spaces and demonstrate their application to quantifying morphological variability in cellular images during mitosis. This part is based on joint work with Danica J Sutherland (UBC CS) and Khanh Dao Duc (UBC math).
In the second part, I will discuss a method for learning dynamics directly from single-cell transcriptomic data without temporal labels, using neural network architectures to uncover causal gene-regulatory relationships that govern cyclic processes such as the cell cycle. This part is based on joint work with Elana J. Fertig (UMD) and Genevieve Stein-O’Brien (JHU).
