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The complexity of gene expression dynamics revealed by permutation entropy

Xiaoliang Sun15, Yong Zou2, Victoria Nikiforova1, Jürgen Kurths234 and Dirk Walther1*

Author Affiliations

1 Max Planck Institute for Molecular Plant Physiology, Am Mühlenberg 1, 14476 Potsdam-Golm, Germany

2 Potsdam Institute for Climate Impact Research, P.O. Box 60120314412 Potsdam, Germany

3 Department of Physics, Humboldt University Berlin, Newtonstraße 1512489 Berlin, Germany

4 Institute of Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen, UK

5 Molecular Systems Biology, University of Vienna, Althanstr. 14 1090 Vienna, Austria

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BMC Bioinformatics 2010, 11:607  doi:10.1186/1471-2105-11-607

Published: 22 December 2010



High complexity is considered a hallmark of living systems. Here we investigate the complexity of temporal gene expression patterns using the concept of Permutation Entropy (PE) first introduced in dynamical systems theory. The analysis of gene expression data has so far focused primarily on the identification of differentially expressed genes, or on the elucidation of pathway and regulatory relationships. We aim to study gene expression time series data from the viewpoint of complexity.


Applying the PE complexity metric to abiotic stress response time series data in Arabidopsis thaliana, genes involved in stress response and signaling were found to be associated with the highest complexity not only under stress, but surprisingly, also under reference, non-stress conditions. Genes with house-keeping functions exhibited lower PE complexity. Compared to reference conditions, the PE of temporal gene expression patterns generally increased upon stress exposure. High-complexity genes were found to have longer upstream intergenic regions and more cis-regulatory motifs in their promoter regions indicative of a more complex regulatory apparatus needed to orchestrate their expression, and to be associated with higher correlation network connectivity degree. Arabidopsis genes also present in other plant species were observed to exhibit decreased PE complexity compared to Arabidopsis specific genes.


We show that Permutation Entropy is a simple yet robust and powerful approach to identify temporal gene expression profiles of varying complexity that is equally applicable to other types of molecular profile data.