Open Collections

Abstract

This thesis presents a computational model for cell motility that integrates biochemical and geometrical mechanisms driving cellular migration. The model describes cell movement as the interplay between membrane activity and forces acting on the membrane. A system of geometric surface partial differential equations is formulated and a two-dimensional framework based on the Evolving Surface Finite Element Method (ESFEM) is developed to capture these processes, restricted to the membrane and excluding external and internal interactions. The study investigates the influence of mechanical parameters, particularly those governing membrane area, and identifies suitable initial conditions and parameter sets required for accurate and consistent simulations. It also explores the role of chemical parameters in shaping cell protrusive structures. The results demonstrate that these mechanical parameters are strongly interdependent and have a significant impact on cell shape and motility. Moreover, the cell can exhibit different modes of motion depending on the dynamics of the chemical species on the membrane. Overall, this work provides new insights into the factors regulating cellular migration and contributes to a deeper understanding of the dynamics underlying cell movement.