Statistical signatures of microorganism motility under environmental stress

The motility of microorganisms and small aquatic organisms provides a natural framework for studying active matter and its response to environmental perturbations. In this work, we experimentally investigate the trajectories of Paramecium caudatum and Artemia salina individuals under controlled laboratory conditions. Using video microscopy, we track the motion of organisms at low population densities and reconstruct individual trajectories over time. In addition to baseline conditions, we analyze stressed environments in which Paramecium caudatum are exposed to a toxic agent and Artemia salina are placed in distilled water. To characterize the statistical properties of the motion, we compute several trajectory-based metrics, including the mean square displacement, velocity and displacement distributions, average velocities, persistence times and lengths, tortuosity, and radius of gyration. These observables allow us to quantify changes in motility patterns across species, densities, and environmental conditions. To further interpret the observed dynamics, we develop coarse-grained stochastic models with parameters extracted directly from the experimental data. While P. caudatum is described within a run-and-tumble framework, including reversal events under stress, A. salina requires a run-and-tumble-like description with persistent orientational noise, accounting for the continuous directional fluctuations observed during its runs. The models reproduce the main trajectory-level observables used for quantitative comparison, namely tortuosity and radius of gyration. This combined experimental and modeling approach provides insight into how environmental stress modifies locomotion statistics. Our results highlight systematic differences in the statistical signatures of motion across conditions and organisms, suggesting that trajectory-based metrics may serve as indicators of physiological stress. Beyond their biological relevance, this work provides an accessible framework for active matter experiments in which individual-level statistics can be directly measured and modeled.