Agent-based modeling of skin-pattern formation in fish
Because fish patterns emerge from cell interactions, an agent-based approach is natural. I model cells as point masses and couple deterministic movement (by ODEs) with stochastic rules for cell birth, death, and transitions in type on growing domains. Our models allow us to propose unknown signals behind cell behavior and offer experimentally-testable predictions about Danio evolution and zebrafish mutants.- A Volkening.
Linking genotype, cell behavior, and phenotype: multidisciplinary perspectives with a basis in zebrafish patterns.
Current Opinion in Genetics and Development, 63:78-85, 2020. - A Volkening, MR Abbott*, N Chandra*, B Dubois*, F Lim*, D Sexton*, B Sandstede.
Modeling stripe formation on growing zebrafish tailfins.
Bulletin of Mathematical Biology, 82:56, 2020. (arXiv copy) - A Volkening, B Sandstede.
Iridophores as a source of robustness in zebrafish stripes and variability in Danio patterns.
Nature Communications 9:3231, 2018. - A Volkening, B Sandstede.
Modelling stripe formation in zebrafish: an agent-based approach.
Journal of the Royal Society Interface 12(112):20150812, 2015.
Collaborators:
Björn Sandstede (Brown University), Addie Harrison* (University of Arizona), Gisela Hoxha* (Brown University), Gil Parnon* (Oregon State University), Madison Russell* (University of Buffalo), Berke Türkay* (Brown University), Madeline Abbott* (University of Michigan), Neil Chandra* (Facebook), Bethany Dubois* (D.E. Shaw Research), Francesca Lim* (Citizens Bank), Dorothy Sexton* (Emsi)
*Asterisk denotes undergraduate students mentored
Image analysis to describe pigment-cell size and shape in vivo
Pigment cells can grow in time and come in sub-types with distinct shapes. By analyzing in vivo fish images from the Nüsslein-Volhard lab, we are characterizing how cell size and shape are distributed in fish patterns. We use image-processing and machine-learning methods to extract cells from fish images.Collaborators:
Hans Georg Frohnhöfer (Max Planck Institute for Developmental Biology), Uwe Irion (Max Planck Institute for Developmental Biology), Christiane Nüsslein-Volhard lab (Max Planck Institute for Developmental Biology), Marco Podobnik (Max Planck Institute for Developmental Biology), Harita Duggirala* (Northwestern University), Olivia Dunne* (Northwestern University)
*Asterisk denotes undergraduate students mentored
Topological data analysis to quantify cell-based patterns
Because my agent-based models couple cell movement with stochastic
fluctuations in the number and types of cells present, the number of differential equations
changes randomly in time. Together with the rule-based nature of many cell interactions,
this makes the models difficult to analyze using traditional approaches. To address this,
we have been developing automated, interpretable, cell-
based methods for quantitatively describing patterns. We utilize persistent homology,
clustering, and principal component analysis to provide summary statistics of pattern features.
Publications:
- MR McGuirl, A Volkening, B Sandstede.
Topological data analysis of zebrafish patterns.
Proceedings of the National Academy of Sciences of the USA. 117(10):5113-5124, 2020.
Collaborators:
Melissa R. McGuirl (Spotify), Björn Sandstede (Brown University)
Continuum models of cell dynamics with nonlocal interactions
While agent-based models are closely related to the underlying application, these stochastic, rule-based systems are challenging to analyze using traditional techniques. In contrast, continuum limits lend themselves to analysis. To combine the benefits of both approaches, we are developing PDE models of zebrafish patterning based on my previous agent-based models of zebrafish. Because pigment cell interactions on the zebrafish skin occur at both short and long range, our models take the form of non-local conservations laws (or aggregation equations) and feature non-local reaction terms (modeled using convolution terms).
Collaborators:
José A. Carrillo (University of Oxford), Markus Schmidtchen (TU Dresden), Chandrasekhar Venkataraman (University of Sussex)
Identifying pattern transitions in cellular-automaton models using a TDA approach
Because many agent- and lattice-based models (whether for zebrafish or other applications) involve stochastic fluctuations in the number of agents in time, these models are not analytically tractable using traditional techniques. At the same time, agent-based models often have many parameters. I am interested in developing approaches to more comprehensively describe the patterns that emerge from agent-based models under different parameters. By applying our topological methods to minimal models of pattern formation in zebrafish, we are working to identify regions of parameter space associated with transitions (e.g., spots to stripes). Collaborators:
Nathan Elbaum* (Brown University), Samuel Maffa* (Brown University), Björn Sandstede (Brown University)
*Asterisk denotes undergraduate students mentored
Mechanistic modeling of pigment-cell communication
Cells communicate using many different mechanisms, including gap junctions, potassium channels, cellular extensions of various lengths, and uptake of diffusing morphogens. Most of my work on fish patterns has focused on buidling phenomenological models: rather than describing the specific way two cells are communicating, I predict which types of cells are communicating and at what distance away. To bring my models closer to the biology and investigate how different mechanisms of stochastic communication affect pattern robustnes, I am interested in accounting for the mechanisms of cell communication. As part of a Lorentz Center workshop project that I led, I am working with a group to investigate how the success of cellular signalling depends on the local environment.Collaborators:
Jolene Britton (UC Riverside), Loann Collet (University of Montreal), Francesco Pancaldi (UC Riverside), Sachin Rawat (StartUs Insights), Robyn Shuttleworth (University of Saskatchewan)