Abstracts Mathematics

Life Together: Modeling the Collective Behavior of Cellular Communities

by Katherine Owens

Our lives as eukaryotic organisms are defined by the collective behaviors of cellular systems. Together groups of cells form intricate structures and accomplish complex tasks. Where an individual cell cycles through growth, reproduction, and death, a group of cells can live more richly. Among other functions, multicellular communities form patterns, share resources, colonize new environments, and even communicate. In this work, I deploy data-driven and classical modeling techniques to understand these collective behaviors in three contexts. First, I consider synchronization in networks of coupled oscillators. Can we learn the rules governing patterns of group behavior exclusively from measurements of the state of the individuals? Towards this goal, I develop a data-driven method for coarse-graining system dynamics even under conditions of spatio-temporal heterogeneity. Next I model tumor growth and it's mitigation via CAR T-cell therapy, a novel cellular based immunotherapy. I develop an ordinary differential equation model for testing combinations of chemotherapeutic preconditioning and CAR T-cell infusion for treating blood cancers. Simulation results and sensitivity analysis support several potential refinements to current clinical protocols. I then extend this ODE model into a reaction-diffusion model, which I use to test local administration of CAR T-cells for the treatment of solid tumors. These simulations suggest that the optimal mode of local administration depends on tumor growth characteristics. In the final chapter, I present a pipeline for high-throughput phenotype quantification from images of yeast patches, including the complexity of pattern formation. I implemented this algorithm in an open source python package, PyPl8, which has enabled novel genetic analysis.