Symmetry Breaking, Directed Movement, and Organized Tissue Response from Local Interactions

Abstract: Pattern formation and symmetry breaking have long been areas of interest in applied mathematics. In living systems, these questions take on additional complexities: molecular interactions generate dynamic intracellular structures, individual cells develop persistent migratory behaviors, and populations of cells coordinate their dynamics to produce spatiotemporal patterns. A central question is how do biological systems break symmetry, select among competing dynamical states, and coordinate response across scales?

Using cell doublets as the smallest nontrivial collective unit, I will discuss mathematical models, computational methods, and dynamical systems approaches for investigating how local feedback, geometry, and confinement shape these collective dynamical states. We examine how mechanochemical interactions generate directional and coordinated migration, biases, and how nonlinear feedback and spatial coupling give rise to coherent oscillations, traveling waves, and other patterns. Extending these principles to larger cell clusters and tissues reveals emergent organization with implications for development, wound healing, and limb regeneration. These examples illustrate how mathematical models can bridge scales and uncover principles by which local interactions generate global organization.

astrophysicscomputational biologycomputational engineering, finance, and sciencegeneral mathematicsnonlinear sciencescomputational physicsfluid dynamicsgeneral physics

Audience: researchers in the topic

Northwestern Applied Mathematics Seminar