Clustered Cell Migration: Modeling Boundary Forces

Abstract

We present a mathematical model of cell migration using complex boundaries and force balance methods. Our goal is to answer how one represents membrane tension interactions in a mathematical model for individual cells with complex boundaries. We seek to determine how we can realistically combine and create different forces to affect cell migration in a complex mathematical model for clustered border cells and what parameters are needed to correctly simulate this. We extend a previous model with different forces of adhesion, repulsion, and migration using functions to measure the amount of overlap between boundary points of cells. Furthermore, we create volume, spring, and curvature forces to control the size and shape of cells and the distance between boundary points. We adjust force balances, parameters, equations, and code accordingly to realistically simulate migration and interpret the progression of cell displacement over time. From this, we develop a more efficient model and create a partial simulation of cell migration in a new complex model. Furthermore, we find a more ideal force balance and move closer to a full simulation. From our work and collaborations with Dr. Starz-Gaiano’s lab, we suggest that extracellular geometry can have a significant impact on cluster migration [8]