Exploring epithelial-cell calcium signaling with geometric and topological data analysis
Spatio-temporal calcium imaging is widely used to study neuronal activity. However the function of calcium signaling in epithelial cells is not well understood. We thus explore the underlying fluorescence patterns using a combination of data geometry and topology. We model the epithelial tissue as a graph and use a variant of geometric scattering transform (a multi-level wavelet transform on a graph) to describe the signaling at each time point. We then embed these discriptors using the manifold learning method PHATE in order to capture the entire time-trajectory of calcium signaling. Finally, we use persistent homology computed on the PHATE embedding to quantitatively characterize the trajectory. We demonstrate that scattering coefficients can effectively learn time point embeddings while PHATE can represent relationships between time points. Persistent homology provides a way to quantify differences between signaling dynamics as evidenced by the differences in dynamics between wild type cells and cells that are stalled in a particular cell cycle phase.
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