Quantifying the degree of persistence in random amoeboid motion based on the Hurst exponent of fractional Brownian motion

Abstract

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.

Modeling random crawling, membrane deformation and intracellular polarity of motile amoeboid cells

“…The resulting center-of-mass motion can be also described in terms of stochastic differential equations derived directly from the experimentally recorded trajectories [ 14 – 17 ]. These approaches were extended to biased random movement in a chemoattractant gradient [ 18 ] and highlight non-Brownian features of Dictyostelium locomotion [ 19 ].…”

Symmetry Breaking during Cell Movement in the Context of Excitability, Kinetic Fine-Tuning and Memory of Pseudopod Formation

“…Cells have persistent movement, meaning that new pseudopods are extended in a similar direction as previous pseudopods. Since pseudopods are extended perpendicular to the cell surface, the tendency to move in the same direction implies that new pseudopods start nearby previous pseudopods [ 2 , 31 , 32 , 33 , 34 ]. Somehow cells have a memory of the place in the cell where they extended previous pseudopod(s).…”

Analytical representation of Gaussian processes in the A−T plane

“…VI A-VI F do not exhaust the possible applications of the A − T plane in regard to constraining the value of H, or classifying time series. Some other interesting instances include, but are not restricted to: ferro-and paramagnetic states of the Heisenberg model that exhibit H ∼ 1 and H ∼ 0.5, respectively [52], and should be easily distinguishable in the A − T plane; a photonic integrated circuit yields 0.2 H 0.8 for varied electric field of the feedback, coupled with chaotic behavior [53]; cataclysmic variable stars observed in X-rays exhibit long-term memory, H > 0.5, suggesting the accretion is driven by magnetic fields [54]; football matches can follow the rules of fBm with H ∼ 0.7 [55]; persistence of amoeboid motion [56] as well as Nitzschia sp. diatoms [57]; Solar wind proton density fluctuations are characterized by H ∼ 0.8, placing constraints on the models of kinetic turbulence [58]; values H > 0.5 were computed for epileptic patients' brain activity, quantified via magnetoencephalographic recordings, and appear to be a promising additional diagnostic tool for identifying epileptogenic zones in presurgical evaluation [59].…”