Topological data analysis of zebrafish patterns

Significance While pattern formation has been studied extensively using experiments and mathematical models, methods for quantifying self-organization are limited to manual inspection or global measures in many applications. Our work introduces a methodology for automatically quantifying patterns that arise due to agent interactions. We combine topological data analysis and machine learning to provide a collection of summary statistics describing patterns on both microscopic and macroscopic scales. We apply our methodology to study zebrafish patterns across thousands of model simulations, allowing us to make quantitative predictions about the types of pattern variability present in wild-type and mutant zebrafish. Our work helps address the widespread challenge of quantifying agent-based patterns and opens up possibilities for large-scale analysis of biological data and mathematical models. Self-organized pattern behavior is ubiquitous throughout nature, from fish schooling to collective cell dynamics during organism development. Qualitatively these patterns display impressive consistency, yet variability inevitably exists within pattern-forming systems on both microscopic and macroscopic scales. Quantifying variability and measuring pattern features can inform the underlying agent interactions and allow for predictive analyses. Nevertheless, current methods for analyzing patterns that arise from collective behavior capture only macroscopic features or rely on either manual inspection or smoothing algorithms that lose the underlying agent-based nature of the data. Here we introduce methods based on topological data analysis and interpretable machine learning for quantifying both agent-level features and global pattern attributes on a large scale. Because the zebrafish is a model organism for skin pattern formation, we focus specifically on analyzing its skin patterns as a means of illustrating our approach. Using a recent agent-based model, we simulate thousands of wild-type and mutant zebrafish patterns and apply our methodology to better understand pattern variability in zebrafish. Our methodology is able to quantify the differential impact of stochasticity in cell interactions on wild-type and mutant patterns, and we use our methods to predict stripe and spot statistics as a function of varying cellular communication. Our work provides an approach to automatically quantifying biological patterns and analyzing agent-based dynamics so that we can now answer critical questions in pattern formation at a much larger scale.