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.