Mostly Biomathematics Lunchtime Seminar

Modeling and analysis of complex systems — with a basis in zebrafish patterns

Speaker: Alexandria Volkening, Assistant Professor, Department of Mathematics and Weldon School of Biomedical Engineering, Purdue University

Location: Warren Weaver Hall 1314

Date: Tuesday, March 7, 2023, 12:45 p.m.


Many natural phenomena involve individuals coming together to create group dynamics, whether the agents are cells in developing tissue or locusts in a swarm. From an applied perspective, self-organization and pattern formation provide an opportunity to develop predictive models that can shed light on unknown agent behaviors. From a mathematical perspective, the stochastic, dynamic behavior of agents in space raises many challenges that call for new methods: How do we quantify qualitative pattern data? How do we build models that capture meaningful biological variability? How do we relate different models? How do we move toward making detailed models more computationally searchable or tractable? My work focuses on first developing models closely to biological data for specific applications, and following this by using an application-centered perspective to raise questions and connect mathematical approaches. In this talk, I will briefly overview some of the biological systems that my group is working with and then discuss skin-pattern formation in zebrafish in more detail. With the longterm biological goal of linking genotype, cell behavior, and phenotype, I will introduce my agent-based models of cell behavior during pattern formation in fish. Because agent-based models are not analytically tractable using traditional methods, I will use zebrafish as a case study to also discuss my current and future work in quantifying pattern data using topological techniques, developing data-driven approaches, and connecting agent-based and PDE models.