Figure 4: Directed migration from microscale geometric constraints conforms to diffusion anisotropy behavior.

(A) Example of single particle (representing cells) undergoing a random walk in a geometrically constrained environment that results in increased motility coefficients, and thus mean displacements, in the x direction for a population of cells. Note, cells behind a collective migration front and lateral cell interactions further constrain the system. (B) Model output of normalized migration distance in the x direction over of a range of displacement steps with defined persistence length for a range of channel/pattern widths. Model output is from 100,000 steps/particle averaged over 1000 particles and data is normalized to random walk behavior in the unconstrained 2D configuration. (C) Normalized migration distance for four pattern widths highlighting the increase in migration along the x-direction as the geometric constraint narrows. Data are from the average of 10 runs with 300 particles undergoing 100,000 steps/particle.