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Mathematical Model of Cell Migration: Cell Boundaries and Force Balances
Presenter: Christina Dee
Mentors: Bradford Percy (Mathematics and Statistics), MichelleĀ Starz-Gaiano (Biology)
Abstract:
This research centers on simulation of a cluster of migratory cells among nurse cells toward the oocyte in the egg chamber of Drosophila melanogaster in MATLAB. Cell migration is movement of cells responding to chemical gradients acting as signals. It is integral to daily functions like development and healing; also, progress in studies can lead to findings in cancer metastasis. This organism has a well-studied history and many human homologs in genetics. We asked: How to model cell migration through force balances, and what changes to parameters, equations, and geometry are needed? We captured heterogeneous cells of the egg chamber: including nurse, epithelial, and migratory border cells using interactions between cell membranes and arising via forces, including adhesive, repulsive, and spring forces. We used a volume force to include heterogeneously and realistically sized cells. When cells filled the chamber, we enacted the migratory force, which stems from a chemical gradient signaling, allowing border cells to climb through nurse cells. We solved the force balance equation with Euler's step to capture progression in time. In MATLAB, we coded cell boundaries around cell centers to represent membranes while adapting parameters, equations, and coefficients in order to realistically simulate cell migration.