Quantifying the degree of persistence in random amoeboid motion based on the Hurst exponent of fractional Brownian motion.
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.
Interdisciplinary Center for Dynamics of Complex Systems, University of Potsdam, Karl-Liebknecht Str. 24/25, D-14476 Potsdam, Germany.
Natallia
N
Makarava
Institute of Mathematics, University of Potsdam, Karl-Liebknecht Str. 24/25, D-14476 Potsdam, Germany.
Stephan
S
Menz
Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht Str. 24/25, D-14476 Potsdam, Germany.
Matthias
M
Theves
Institute of Mathematics, University of Potsdam, Karl-Liebknecht Str. 24/25, D-14476 Potsdam, Germany.
Wilhelm
W
Huisinga
Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht Str. 24/25, D-14476 Potsdam, Germany.
Carsten
C
Beta
Interdisciplinary Center for Dynamics of Complex Systems, University of Potsdam, Karl-Liebknecht Str. 24/25, D-14476 Potsdam, Germany and Institute of Mathematics, University of Potsdam, Karl-Liebknecht Str. 24/25, D-14476 Potsdam, Germany.
Matthias
M
Holschneider
D001499:Bayes Theorem; D004023:Dictyostelium / Q000502:physiology*; D008954:Models, Biological; D009038:Motion; D009068:Movement