Quantifying Topological Features and Irregularities in Zebrafish Patterns Using the Sweeping-Plane Filtration

Abstract.

Complex patterns emerge across a wide range of biological systems. While patterns often exhibit remarkable robustness, variation and irregularity exist at multiple scales and can carry important information about the underlying agent interactions driving collective dynamics. Many methods for quantifying patterns focus on large-scale, characteristic features (such as stripe width or spot number), but questions remain on how to characterize messy patterns. In the case of cellular patterns that emerge during development, understanding where patterns are most susceptible to variability may help shed light on cell behavior and the tissue environment. Motivated by these challenges, we introduce methods based on topological data analysis to classify and quantify messy patterns. To compute persistent homology, our methods rely on a sweeping-plane filtration which, in comparison to the Vietoris–Rips filtration, is more rarely applied to self-organization. We demonstrate how results from the sweeping-plane filtration can be interpreted to quantify stripe patterns—with and without interruptions—by analyzing in silico zebrafish skin patterns, and we generate new predictions about which pattern features may be most robust or variable. Our work provides an automated framework for quantifying features and irregularities in complex patterns and highlights how different approaches to persistent homology can provide complementary insight.