Capturing Spatiotemporal Signaling Patterns in Cellular Data with Geometric Scattering Trajectory Homology

Cells communicate with one another through a variety of signaling mechanisms. Exchange of information via these mechanisms allows cells to coordinate their behavior and respond to environmental stress and other stimuli. To facilitate quantitative understanding of complex spatiotemporal signaling activity, we developed Geometric Scattering Trajectory Homology, a general framework that encapsulates time-lapse signals on a cell adjacency graph in a low-dimensional trajectory. We tested this framework using computational models of collective oscillations and calcium signaling in the Drosophila wing imaginal disc, as well as experimental data, including in vitro ERK signaling in human mammary epithelial cells and in vivo calcium signaling from the mouse epidermis and visual cortex. We found that the geometry and topology of the trajectory are related to the degree of synchrony (over space and time), intensity, speed, and quasi-periodicity of the signaling pattern. We recovered model parameters and experimental conditions by training neural networks on trajectory data, showing that our approach preserves information that characterizes various cell types, tissues and drug treatments. We envisage the applicability of our framework in various biological contexts to generate new insights into cell communication. ### Competing Interest Statement The authors have declared no competing interest.