  Upcoming immunotherapies for cancer treatment rely on the ability of the
immune system to detect and eliminate tumors in the body. A highly simplified
version of this process can be studied in a Petri dish: starting with a random
distribution of immune and tumor cells, it can be observed in detail how
individual immune cells migrate towards nearby tumor cells, establish contact,
and attack. Nevertheless, it remains unclear whether the immune cells find
their targets by chance, or if they approach them 'on purpose', using remote
sensing mechanisms such as chemotaxis. In this work, we present methods to
infer the strength and range of long-range cell-cell interactions from
time-lapse recorded cell trajectories, using a maximum likelihood method to fit
the model parameters. First, we model the interactions as a distance-dependent
'force' that attracts immune cells towards their nearest tumor cell. While this
approach correctly recovers the interaction parameters of simulated cells with
constant migration properties, it detects spurious interactions in the case of
independent cells that spontaneously change their migration behavior over time.
We therefore use an alternative approach that models the interactions by
distance-dependent probabilities for positive and negative turning angles of
the migrating immune cell. We demonstrate that the latter approach finds the
correct interaction parameters even with temporally switching cell migration.
