Systemic and kinematic properties of Amoeba proteus migration correlate strongly across environments

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Recent work has shown that cell migration is a systemic property of the whole cell, yet how the different properties of a migratory trajectory relate to one another remains largely uncharacterized. Here we quantified the migration of 150 Amoeba proteus cells under three experimental scenarios (absence of stimuli, a direct-current electric field, and a chemotactic peptide gradient) with eleven metrics that describe either the systemic dynamics of the trajectory (long-range correlations, long-term persistence, super-diffusive exploration, regularity of the move steps and memory of the velocity) or its kinematic output (net displacement, straightness and speed). Screening all 55 metric pairs for statistical dependence with distance covariance identified six couplings that held in all three experimental scenarios, besides the pairs linked by definition. Long-term persistence and super-diffusive exploration were coupled with each other, in agreement with the scaling relation expected for self-similar trajectories, and each of them was coupled with the net displacement and the straightness of the trajectory: more persistent and more super-diffusive cells moved farther and along straighter paths. In addition, the long-range correlations of the move steps were coupled with the memory of speed between consecutive steps. All six couplings were positive and monotonic, with no trend reversal over the observed range. The stimuli shifted six of the eleven metrics, the electric field mainly increasing the straightness and the net displacement of the trajectories and the chemical gradient mainly increasing the speed memory, but they left the six couplings intact and reorganized part of the dependence structure around speed. These results show that several systemic and kinematic properties of Amoeba proteus migration are not independent observables but vary together as parts of an integrated system whose couplings are preserved across environments.