A Transient Model of Confined Cell Migration

Cells utilize different mechanisms for migration depending on their microenvironment. On two-dimensional surfaces, migration is driven by actin polymerization. While in confined channels with high hydraulic resistance, migration can be driven by water permeation. Water permeation is driven by a polarized distribution of membrane proteins, including ion channels and aquaporin. Taking cancer metastasis as an example, breast cancer cells are known to have an overexpression of ion channels and pumps and sometimes migrate through confined environments that have elevated hydraulic pressure. This suggests that breast cancer cells can migrate in an ideal environment for the use of water permeation. Despite the important role of ion and water transport(flux) in cell migration, the mathematical formulation of this mode of migration is relatively new. There are few models that allow the study of how ion and water fluxes through ion channels affect cell migration. We develop a single-cell based model for cell migration capable of studying directional solute fluxes. Model components such as actin polymerization, focal adhesions, polarized distribution of ion channels and pumps, external hydraulic resistance, cytoplasmic flow, and membrane tension are modeled through a set of coupled differential equations and are solved numerically in MATLAB. We anticipate this transient model to shed insight on how parameters related to polymerization, water permeation, and the cell’s environment affect cell velocity and cell length during migration