  In chemotaxis, cells are modulating their migration patterns in response to
concentration gradients of a guiding substance. Immune cells are believed to
use such chemotactic sensing for remotely detecting and homing in on pathogens.
Considering that an immune cells may encounter a multitude of targets with
vastly different migration properties, ranging from immobile to highly mobile,
it is not clear which strategies of chemotactic pursuit are simultaneously
efficient and versatile. We takle this problem theoretically and define a
tunable response function that maps temporal or spatial concentration gradients
to migration behavior. The seven free parameters of this response function are
optimized numerically with the objective of maximizing search efficiency
against a wide spectrum of target cell properties. Finally, we reverse-engineer
the best-performing parameter sets to uncover the principles of efficient
chemotactic pursuit under different biologically realistic boundary conditions.
Remarkably, the numerical optimization rediscovers chemotactic strategies that
are well-known in biological systems, such as the gradient-dependent swimming
and tumbling modes of E.coli. Some of our results may also be useful for the
design of chemotaxis experiments and for the development of algorithms that
automatically detect and quantify goal oriented behavior in measured immune
cell trajectories.
