Chemotaxis and topotaxis add vectorially for amoeboid cell migration

Abstract

3. Data modelling, computational biology and predictive medicine, AbstractCells encounter a wide variety of physical and chemical cues when navigating their native environments. However, their response to multiple simultaneous cues is not yet clear. In particular, the influence of topography, in the presence of a chemotactic gradient, on their migratory behavior is understudied. Here, we investigate the effects of topographical guidance on highly motile amoeboid cell migration (topotaxis) generated by asymmetrically placed micropillars. The micropillar field allows for an additional, natural chemotactic gradient in two different directions, thereby revealing the relevance of topotaxis in the presence of cell migration directed by chemical gradients (chemotaxis). Interestingly, we found that the topotactic drift generated by the pillar field is conserved during chemotaxis. We show that the drifts generated by both these cues add up linearly. A coarse-grained analysis as a function of pillar spacing subsequently revealed that the strength and direction of the topotactic drift is determined by (i) the pore size, (ii) space between pores, and (iii) the effective diffusion constant of the cells. Finally, we argue that topotaxis must be conserved during chemotaxis, as it is an emergent property of both the asymmetric properties of the pillar field and the inherent stochasticity of (biased) amoeboid migration.

Topotaxis of active Brownian particles

“…Specifically, the topotactic velocity in our simulations is in the order of 1% of the intrinsic particle speed (Fig. 2), whereas in the experiments on cells this ratio is approximately 5%, provided that the obstacles are not spaced further apart than the cell size [15]. In order to better understand this surprising efficiency, the topotactic response of several types of persistently moving cells, such as amoeba [60], cancer cells [61], or leukocytes [62], could be compared.…”

“…Finally, although here we demonstrated that topotaxis can be solely driven by the interplay between topographical gradients and persistent random motion, whether this is sufficient to explain cellular topotaxis remains an open problem. A quantitative comparison between our numerical data and experiments on highly motile cells [15] shows, in fact, discrepancies that could be ascribed to the enormously more complex interactions between cells and their environment. Specifically, the topotactic velocity in our simulations is in the order of 1% of the intrinsic particle speed (Fig.…”

“…For instance, how is the picture affected by translational diffusion? Is topotaxis robust against competing directional cues, such as chemotaxis [15]? How sensitive is the performance of topotaxis with respect to the obstacles' shape [18,37,38], the type of motion (e.g., persistent random walk, run-and-tumble, Lévy walk, etc.…”

“…The extent of rotational diffusion is quantified by the rotational diffusion coefficient D r , whereas translational diffusion is neglected under the assumption of large Péclet number: Pe 1. Overall, this set-up provides a reasonable toy model for highly motile cells such as those used in experimental studies of topotaxis [15,46,47]. For a study on the influence of the Péclet number on the motion of ABPs around obstacles, see, for example, Ref.…”

“…For instance, it has been shown that local anisotropy in the underlying substrate, in the form of adhesive ratchets [10][11][12] or three-dimensional structures on the subcellular scale [10,13,14], can lead to directed motion even in the absence of chemical stimuli. More recently, Wondergem and coworkers demonstrated directed migration of single cells using a spatial gradient in the density of cell-sized topographical features [15]. In these experiments, highly motile, persistently migrating cells (i.e., cells performing amoeboid migration) move on a substrate in between microfabricated pillars that act as obstacles and conse- * Corresponding author: giomi@lorentz.leidenuniv.nl quently force the cells to move around them.…”