Abstract
BackgroundHigh 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.ResultsApplying 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.ConclusionsWe 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.
Highlights
High complexity is considered a hallmark of living systems
We demonstrate that Permutation Entropy (PE) is a simple, yet powerful novel concept to study the dynamics of temporal gene expression profiles and applicable to other types of molecular profile data
We applied the concept of Permutation Entropy (PE) as a metric to assess the complexity of temporal gene expression profiles obtained from abiotic stress time series microarray experiments performed in Arabidopsis thaliana [30]
Summary
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. In the temporal domain, the complexity of molecular processes has not been adequately investigated yet Dynamic phenomena such as the temporal gene expression response to external perturbations as measured in time course genome-scale microarray measurements, while constituting a major research topic, have been analyzed primarily to unravel structural relationships between different groups of genes with the aim to identify important gene sets - for example, for diagnostic purposes - via clustering [4,5,6,7,8] or principal component analysis (PCA) [6,9], or to deduce regulatory transcriptional networks and modules [10,11,12,13], infer relationships between metabolic genes [14,15] as well as to provide a basis for network modeling [16,17]. Introduced approaches ranged from applying unbiased Singular Value Decomposition (SVD, [18]), utilizing the notion of patterns [19] and extracting gene sets that are consistent with simple up/down/unchanged patterns and successions thereof as a means to guided profile clustering [7], and to converting continuous level values into discrete ranks to determine the degree of randomness with regard to rank permutations [20]
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