Superstatistical analysis and modelling of heterogeneous random walks

Claus Metzner (), Christoph Mark, Julian Steinwachs, Lena Lautscham, Franz Stadler and Ben Fabry
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Claus Metzner: Biophysics Group, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Christoph Mark: Biophysics Group, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Julian Steinwachs: Biophysics Group, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Lena Lautscham: Biophysics Group, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Franz Stadler: Biophysics Group, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Ben Fabry: Biophysics Group, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)

Nature Communications, 2015, vol. 6, issue 1, 1-8

Abstract: 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.

Date: 2015
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DOI: 10.1038/ncomms8516

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