Implementation of actin polymerization and depolymerization in a two-dimensional cell migration model and its implications on mammalian cell morphology and velocity.

Cell migration, a pivotal process in wound healing, immune response, and even cancer metastasis, manifests through intricate interplay between morphology, speed, and cytoskeletal dynamics. Mathematical modeling emerges as a powerful tool to dissect these complex interactions. This work presents a two-dimensional immersed boundary model for mammalian cell migration, incorporating both filamentous actin (F-actin) and monomeric actin (G-actin) to explicitly capture polymerization and depolymerization. This model builds upon our previous one-dimensional efforts, now enabling us to explore the impact of G-actin on not just cell velocity but also morphology. We compare predictions from both models, revealing that while the one-dimensional model captures core dynamics along the cell's axis, the two-dimensional model excels in portraying cell shape evolution and transverse variations in actin concentration and velocity. Our findings highlight the crucial role of including G-actin in shaping cell morphology. Actin velocity aligned with migration direction elongates the cell, while velocity normal to the membrane promotes spreading. Importantly, the model establishes a link between these microscopic aspects and macroscopic observables like cell shape, offering a deeper understanding of cell migration dynamics. This work not only provides a more comprehensive picture of cell migration but also paves the way for future studies exploring the interplay of actin dynamics, cell morphology, and biophysical parameters in diverse biological contexts.