Learning Geometric Models for Developmental Dynamics

Successful development from a single cell to a complex, multicellular organism requires that cells differentiate in a coordinated and organized manner in response to a variety of signaling modalities. While the molecular underpinnings may be complex, the resulting phenomenon, in which a cell decides between one fate or another, is relatively simple. A body of work—rooted in dynamical systems theory—has formalized this notion of cellular decision making as flow in a Waddington-like landscape, in which cells evolve according to gradientlike dynamics within a potential that changes shape in response to a number of signals. We present a framework leveraging neural networks as universal function approximators to infer such a parametrized landscape from gene expression data. Inspired by the success of physics-informed machine learning in data-limited contexts, we enforce principled constraints motivated not by physical laws but by this phenomenological understanding of differentiation. Our data-driven approach infers a governing landscape atop a manifold situated within expression space, thereby describing the dynamics of interest in a biologically meaningful context. The resulting system provides an intuitive, visualizable, and interpretable model of cellular differentiation dynamics.