Statistical signatures of microorganism motility under environmental stress
The motility of microorganisms provides a natural framework for studying active matter and its response to environmental perturbations. We experimentally investigate the trajectories of \textit{Paramecium caudatum} and \textit{Artemia salina} under controlled conditions. Using video microscopy, we reconstruct individual trajectories over time. Beyond baseline conditions, we analyze stressed environments where \textit{P. caudatum} are exposed to a toxic agent and \textit{A. salina} are placed in distilled water. To characterize the motion, we compute trajectory-based metrics, including mean square displacement, velocity distributions, persistence times, tortuosity, and radius of gyration. These observables quantify changes in motility patterns across species and conditions. To interpret the dynamics, we develop coarse-grained stochastic models parameterized directly from experimental data. \textit{P. caudatum} is described within a run-and-tumble framework, including reversal events under stress. In contrast, \textit{A. salina} requires a run-and-tumble-like description with persistent orientational noise, accounting for continuous directional fluctuations during runs. The models reproduce the main trajectory-level observables used for comparison, namely tortuosity and radius of gyration. This combined approach provides insight into how environmental stress modifies locomotion statistics. Our results highlight systematic differences in the statistical signatures of motion, suggesting that trajectory metrics may serve as indicators of physiological stress. This work provides an accessible framework for active matter experiments where individual-level statistics can be directly measured and modeled.