Topological data analysis of zebrafish patterns

Abstract

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 only capture 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 agentlevel 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 a new 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.Keywords topological data analysis | agent-based model | self-organization | pattern quantification | zebrafish arXiv:1910.08433v1 [q-bio.QM]

In situdifferentiation of iridophore crystallotypes underlies zebrafish stripe patterning

“…Signals by melanophores and xanthophores are proposed to determine the specific morphologies adopted by iridophores. Consistent with this idea, quantitative models incorporating proposed dynamic morphological changes of individual iridophores are able to produce stripe patterning and robustness 23,24 .…”

Bespoke Turing Systems

“…Such inference methods have been proposed to quantify aspects of signalling dynamics from observed morphogen concentrations in different taxa (Dewar et al 2010), though again often using phenomenological reaction kinetics that are undoubtedly a caricature of the real morphogen signalling dynamics. Similar ideas have been used to quantify and classify the role of different aspects of agent-based models of pattern formation (such as stochasticity and interactions) in models of zebrafish pigmentation (McGuirl et al 2020). If the underlying morphogen interactions are known, and hence, the nonlinearities are given, then these techniques provide a powerful way for using observations to determine key features of the morphogen dynamics.…”

Tracking collective cell motion by topological data analysis

“…It is possible to calculate the correlation between the cophenetic distance and the distances in the matrix of Fig 18(a) (the cophenetic correlation [ 63 ]). For our simulations, Ward’s hierarchical clustering provides the largest cophenetic correlation when compared with other clustering approaches, such as single-linkage [ 53 ]. Thus, the Ward dendrogram gives the most faithful representation of the distance matrix, which is why we use it.…”

“…In this work, we use techniques of topological data analysis with some data taken from experiments and a modest amount of data from numerical simulations so as to explain techniques and results in a clear manner. However, our techniques are scalable and could be used in studies involving large amounts of data, as, for example, those generated to characterize zebrafish patterns by combining machine learning and topological data analysis [ 53 ].…”