Multi-cue kinetic model with non-local sensing for cell migration on a fibers network with chemotaxis

Cells perform directed motion in response to external stimuli that they detect by sensing the environment with their membrane protrusions. In particular, several biochemical and biophysical cues give rise to tactic migration in the direction of their specific targets. This defines a multi-cue environment in which cells have to sort and combine different, and potentially competitive, stimuli. We propose a non-local kinetic model for cell migration in presence of two external factors both influencing cell polarization: contact guidance and chemotaxis. We propose two different sensing strategies and we analyze the two resulting models by recovering the appropriate macroscopic limit in different regimes, in order to see how the size of the cell, with respect to the variation of both external fields, influences the overall behavior. Moreover, we integrate numerically the kinetic transport equation in a two-dimensional setting in order to investigate qualitatively various scenarios.