  Chemotaxis enables cells to systematically approach distant targets that emit
a diffusible guiding substance. However, the visual observation of an encounter
between a cell and a target does not necessarily indicate the presence of a
chemotactic approach mechanism, as even a blindly migrating cell can come
across a target by chance. To distinguish between the chemotactic approach and
blind migration, we present an objective method that is based on the analysis
of time-lapse recorded cell migration trajectories. First, we validate our
method with simulated data, demonstrating that it reliably detects the presence
or absence of remote cell-cell interactions. In a second step, we apply the
method to data from three-dimensional collagen gels, interspersed with highly
migratory natural killer (NK) cells that were derived from two different human
donors. We find for one of the donors an attractive interaction between the NK
cells, pointing to a cooperative behavior of these immune cells. When adding
nearly stationary K562 tumor cells to the system, we find a repulsive
interaction between K562 and NK cells for one of the donors. By contrast, we
find attractive interactions between NK cells and an IL-15-secreting variant of
K562 tumor cells. We therefore speculate that NK cells find wild-type tumor
cells only by chance, but are programmed to leave a target quickly after a
close encounter. We provide a freely available Python implementation of our
p-value method that can serve as a general tool for detecting long-range
interactions in collective systems of self-driven agents.
