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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.

SUBMITTER: Metzner C

PROVIDER: S-EPMC4491834 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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Publications

Superstatistical analysis and modelling of heterogeneous random walks.

Metzner Claus C Mark Christoph C Steinwachs Julian J Lautscham Lena L Stadler Franz F Fabry Ben B

Nature communications 20150625

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 proc ...[more]

PMID: 26108639

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Project description:Analysis of co-expressed gene sets typically involves testing for enrichment of different annotations or 'properties' such as biological processes, pathways, transcription factor binding sites, etc., one property at a time. This common approach ignores any known relationships among the properties or the genes themselves. It is believed that known biological relationships among genes and their many properties may be exploited to more accurately reveal commonalities of a gene set. Previous work has sought to achieve this by building biological networks that combine multiple types of gene-gene or gene-property relationships, and performing network analysis to identify other genes and properties most relevant to a given gene set. Most existing network-based approaches for recognizing genes or annotations relevant to a given gene set collapse information about different properties to simplify (homogenize) the networks.We present a network-based method for ranking genes or properties related to a given gene set. Such related genes or properties are identified from among the nodes of a large, heterogeneous network of biological information. Our method involves a random walk with restarts, performed on an initial network with multiple node and edge types that preserve more of the original, specific property information than current methods that operate on homogeneous networks. In this first stage of our algorithm, we find the properties that are the most relevant to the given gene set and extract a subnetwork of the original network, comprising only these relevant properties. We then re-rank genes by their similarity to the given gene set, based on a second random walk with restarts, performed on the above subnetwork. We demonstrate the effectiveness of this algorithm for ranking genes related to Drosophila embryonic development and aggressive responses in the brains of social animals.DRaWR was implemented as an R package available at veda.cs.illinois.edu/DRaWR.blatti@illinois.eduSupplementary data are available at Bioinformatics online.

Dataset Information

Superstatistical analysis and modelling of heterogeneous random walks.

Publications

Superstatistical analysis and modelling of heterogeneous random walks.

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