Superstatistical analysis and modelling of heterogeneous random walks

Abstract

Stochastic time series are ubiquitous in nature. In particular, random walks with time-varying statistical properties are found in many scientific disciplines. Here we present a superstatistical approach to analyse and model such heterogeneous random walks. The time-dependent statistical parameters can be extracted from measured random walk trajectories with a Bayesian method of sequential inference. The distributions and correlations of these parameters reveal subtle features of the random process that are not captured by conventional measures, such as the mean-squared displacement or the step width distribution. We apply our new approach to migration trajectories of tumour cells in two and three dimensions, and demonstrate the superior ability of the superstatistical method to discriminate cell migration strategies in different environments. Finally, we show how the resulting insights can be used to design simple and meaningful models of the underlying random processes.

Quantifying Modes of 3D Cell Migration

“…Many 2D analyses of cell migration have been undertaken, and 3D cell migration has been analyzed at the cellular scale [57, 58], providing insight into how the environment affects cell migration strategies over hundreds of micrometers. However, analyzing 3D migration at the subcellular scale brings a new set of challenges, even apart from the need for visualization.…”

Bursts of activity in collective cell migration

“…Wound healing is a typical biological assay to study collective migration of cells under controlled conditions in vitro and is a prototypical experimental method to study active matter (7-10). Experiments performed on soluble collagen (11) or other gels (12), micropatterned (13, 14) and deformable substrates (1) show that cell migration is guided by the substrate structure and stiffness (5,15,16).It has been argued that collective migration properties arise from stresses transmitted between neighboring cells (1) giving rise to longranged stress waves in the monolayer (17,18). Hence the dynamics of an invading cell sheet is ruled by a combination of long-range internal stresses and interactions with the substrate, suggesting an analogy with driven elastic systems moving in a disordered medium such as cracks lines (19,20), imbibition fronts (21), or ferromagnetic domain walls (22).…”

“…Wound healing is a typical biological assay to study collective migration of cells under controlled conditions in vitro and is a prototypical experimental method to study active matter (7)(8)(9)(10). Experiments performed on soluble collagen (11) or other gels (12), micropatterned (13,14) and deformable substrates (1) show that cell migration is guided by the substrate structure and stiffness (5,15,16).…”

Coloring Single Nanoparticle Trajectory in Live Cell with its Own History: a Presuppositionless Preprocessing Approach

“…The data for analysis are often generated from the particle trajectory using subsequence or moving window operation. The general assumption is that during the NP-cell interaction process, the NP motion-state within a short time window is stable or statistically predictable, and different NP states are independent and limited in number (15). These underlying states could be recovered by either numerical fitting or by machine learning based model assignment, where the sub-trajectories are treated as atomistic fragment or event and are generally considered to be isolated from the adjacent ones.…”