  In vivo, cells navigate through complex environments filled with obstacles.
Recently, the term 'topotaxis' has been introduced for navigation along
topographic cues such as obstacle density gradients. Experimental and
mathematical efforts have analyzed topotaxis of single cells in pillared grids
with pillar density gradients. A previous model based on active Brownian
particles has shown that ABPs perform topotaxis, i.e., drift towards lower
pillar densities, due to decreased effective persistence lengths at high
pillars densities. The ABP model predicted topotactic drifts of up to 1% of the
instantaneous speed, whereas drifts of up to 5% have been observed
experimentally. We hypothesized that the discrepancy between the ABP and the
experimental observations could be in 1) cell deformability, and 2) more
complex cell-pillar interactions. Here, we introduce a more detailed model of
topotaxis, based on the Cellular Potts model. To model persistent cells we use
the Act model, which mimicks actin-polymerization driven motility, and a hybrid
CPM-ABP model. Model parameters were fitted to simulate the experimentally
found motion of D. discoideum on a flat surface. For starved D. discoideum,
both CPM variants predict topotactic drifts closer to the experimental results
than the previous ABP model, due to a larger decrease in persistence length.
Furthermore, the Act model outperformed the hybrid model in terms of topotactic
efficiency, as it shows a larger reduction in effective persistence time in
dense pillar grids. Also pillar adhesion can slow down cells and decrease
topotaxis. For slow and less persistent vegetative D. discoideum cells, both
CPMs predicted a similar small topotactic drift. We conclude that deformable
cell volume results in higher topotactic drift compared to ABPs, and that
feedback of cell-pillar collisions on cell persistence increases drift only in
highly persistent cells.
