An integrative cell migration model incorporating focal adhesion (FA) dynamics, cytoskeleton and nucleus remodeling and actin motor activity is developed for predicting cell migration behaviors on 3-dimensional curved surfaces, such as cylindrical lumens in the 3-D extracellular matrix (ECM). The work is motivated by 3-D microfluidic migration experiments suggesting that the migration speed and direction may vary depending on the cross sectional shape of the lumen along which the cell migrates. In this paper, the mechanical structure of the cell is modeled as double elastic membranes of cell and nucleus. The two elastic membranes are connected by stress fibers, which are extended from focal adhesions on the cell surface to the nuclear membrane. The cell deforms and gains traction as transmembrane integrins distributed over the outer cell membrane bind to ligands on the ECM, form focal adhesions, and activate stress fibers. Probabilities at which integrin ligand–receptor bonds are formed as well as ruptures are affected by the surface geometry, resulting in diverse migration behaviors that depend on the curvature of the surface. Monte Carlo simulations of the integrative model reveal that (a) the cell migration speed is dependent on the cross sectional area of the lumen with a maximum speed at a particular diameter or width, (b) as the lumen diameter increases, the cell tends to spread and migrate around the circumference of the lumen, while it moves in the longitudinal direction as the lumen diameter narrows, (c) once the cell moves in one direction, it tends to stay migrating in the same direction despite the stochastic nature of migration. The relationship between the cell migration speed and the lumen width agrees with microfluidic experimental data for cancer cell migration.
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