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Abstract Asymmetric nanotopography with sub-cellular dimensions has recently demonstrated the ability to provide a unidirectional bias in cell migration. The details of this guidance depend on the type of cell studied and the design of the nanotopography. This behavior is not yet well understood, so there is a need for a predictive description of cell migration on such nanotopography that captures both the initiation of migration, and the way cell migration evolves. Here, we employ a three-dimensional, physics-based model to study cell guidance on asymmetric nanosawteeth. In agreement with experimental data, our model predicts that asymmetric sawteeth lead to spontaneous motion. Our model demonstrates that the nanosawteeth induce a unidirectional bias in guidance direction that is dependent upon actin polymerization rate and sawtooth dimensions. Motivated by this model, an analysis of previously reported experimental data indicates that the degree of guidance by asymmetric nanosawteeth increases with the cell velocity. 

Abstract Cell movement in vivo is typically characterized by strong confinement and heterogeneous, three-dimensional environments. Such external constraints on cell motility are known to play important roles in many vital processes e.g. during development, differentiation, and the immune response, as well as in pathologies like cancer metastasis. Here we develop a physics-driven three-dimensional computational modeling framework that describes lamellipodium-based motion of cells in arbitrarily shaped and topographically structured surroundings. We use it to investigate the primary in vitro model scenarios currently studied experimentally: motion in vertical confinement, confinement in microchannels, as well as motion on fibers and on imposed modulations of surface topography. We find that confinement, substrate curvature and topography modulate the cell’s speed, shape and actin organization and can induce changes in the direction of motion along axes defined by the constraints. Our model serves as a benchmark to systematically explore lamellipodium-based motility and its interaction with the environment.