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Amoebae explore their environment in a random way, unless external cues like, e. g., nutrients, bias their motion. Even in the absence of cues, however, experimental cell tracks show some degree of persistence. In this paper, we analyzed individual cell tracks in the framework of a linear mixed effects model, where each track is modeled by a fractional Brownian motion, i.e., a Gaussian process exhibiting a long-term correlation structure superposed on a linear trend. The degree of persistence was quantified by the Hurst exponent of fractional Brownian motion. Our analysis of experimental cell tracks of the amoeba Dictyostelium discoideum showed a persistent movement for the majority of tracks. Employing a sliding window approach, we estimated the variations of the Hurst exponent over time, which allowed us to identify points in time, where the correlation structure was distorted ("outliers"). Coarse graining of track data via down-sampling allowed us to identify the dependence of persistence on the spatial scale. While one would expect the (mode of the) Hurst exponent to be constant on different temporal scales due to the self-similarity property of fractional Brownian motion, we observed a trend towards stronger persistence for the down-sampled cell tracks indicating stronger persistence on larger time scales.
Motile eukaryotic cells, such as leukocytes, cancer cells, and amoeba, typically move inside the narrow interstitial spacings of tissue or soil. While most of our knowledge of actin-driven eukaryotic motility was obtained from cells that move on planar open surfaces, recent work has demonstrated that confinement can lead to strongly altered motile behavior. Here, we report experimental evidence that motile amoeboid cells undergo a spontaneous symmetry breaking in confined interstitial spaces. Inside narrow channels, the cells switch to a highly persistent, unidirectional mode of motion, moving at a constant speed along the channel. They remain in contact with the two opposing channel side walls and alternate protrusions of their leading edge near each wall. Their actin cytoskeleton exhibits a characteristic arrangement that is dominated by dense, stationary actin foci at the side walls, in conjunction with less dense dynamic regions at the leading edge. Our experimental findings can be explained based on an excitable network model that accounts for the confinement-induced symmetry breaking and correctly recovers the spatio-temporal pattern of protrusions at the leading edge. Since motile cells typically live in the narrow interstitial spacings of tissue or soil, we expect that the geometry-driven polarity we report here plays an important role for movement of cells in their natural environment.