A Mathematical Model for Clustered Cell Migration

Abstract

Clustered cell migration is a crucial biological process involved in oocyte development, tissue healing, and cancer metastasis. We specifically investigated this process in the Drosophila melanogaster after egg fertilization, in which a group of migrating cells, called border cells, move as a cluster from the anterior side of the chamber to the posterior side, where the oocyte resides. We represented each cell through boundary points, which are two-dimensional cartesian coordinates. We developed mathematical representations of the various intra- and intercellular forces within the D. melanogaster, and applied each of these forces to the boundary points of the cells with the use of differential equations. We conducted parameter testing of our model with an initial planar implementation, in which we varied one parameter to obtain viable ranges for each parameter. Then, we used a Latin Hypercube Sampling (LHS) method to investigate the force-balance sensitivity of our system. To do so, we used the High Performance Computing Facility (HPCF) at UMBC to run parallel simulations with each set of of parameters generated using the LHS method.