Harmonic Analysis and Differential Equations Seminar: Al Volkening (Purdue)

Speaker:  Al Volkening (Purdue) 

Note: Participants are warmly invited to lunch beforehand with the speaker at the Bread Company at 12:00pm. 

Agent-based, vertex-based, and continuum models of cell behavior in biological patterns

Abstract:
Many natural and social phenomena involve individual agents coming together to create group dynamics, whether the agents are drivers in a traffic jam, cells in a developing tissue, or locusts in a swarm. Here I will focus on two examples of emergent behavior in biology, specifically cell interactions during pattern formation in zebrafish skin and gametophyte development in ferns. Different modeling approaches provide complementary insights into these systems and face different challenges. For example, vertex-based models describe cell shape, while more efficient agent-based models treat cells as particles. In both cases, it can be challenging to broadly characterize the behavior of these biologically detailed models or address questions about model uniqueness—even quantitatively judging messy, cell-based patterns is not straightforward. Continuum models, which track the evolution of cell densities, are more amenable to analysis, but it is often difficult to relate their few parameters to specific cell interactions. In this talk, I will overview our models of cell behavior in biological patterns and discuss our ongoing work combining topological techniques and data-driven methods to more broadly characterize pattern systems and the relationship between different models.