The complexity of gene expression dynamics revealed by permutation entropy

Background: 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.Results: 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.Conclusions: 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

The complexity of gene expression dynamics revealed by permutation entropy

ABSTRACT: BACKGROUND: 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. RESULTS: 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. CONCLUSIONS: 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

Permutation entropy and its main biomedical and econophysics applications: a review

Entropy is a powerful tool for the analysis of time series, as it allows describing the probability distributions of the possible state of a system, and therefore the information encoded in it. Nevertheless, important information may be codified also in the temporal dynamics, an aspect which is not usually taken into account. The idea of calculating entropy based on permutation patterns (that is, permutations defined by the order relations among values of a time series) has received a lot of attention in the last years, especially for the understanding of complex and chaotic systems. Permutation entropy directly accounts for the temporal information contained in the time series; furthermore, it has the quality of simplicity, robustness and very low computational cost. To celebrate the tenth anniversary of the original work, here we analyze the theoretical foundations of the permutation entropy, as well as the main recent applications to the analysis of economical markets and to the understanding of biomedical systems.Facultad de Ingenierí

Etude expérimentale des dynamiques temporelles du comportement normal et pathologique chez le rat et la souris

155 p.Modern neuroscience highlights the need for designing sophisticated behavioral readout of internal cognitive states. From a thorough analysis of classical behavioral test, my results supports the hypothesis that sensory ypersensitivity might be the cause of other behavioural deficits, and confirm the potassium channel BKCa as a potentially relevant molecular target for the development of drug medication against Fragile X Syndrome/Autism Spectrum Disorders. I have also used an innovative device, based on pressure sensors that can non-invasively detect the slightest animal movement with unprecedented sensitivity and time resolution, during spontaneous behaviour. Analysing this signal with sophisticated computational tools, I could demonstrate the outstanding potential of this methodology for behavioural phenotyping in general, and more specifically for the investigation of pain, fear or locomotion in normal mice and models of neurodevelopmental and neurodegenerative disorders

Simultaneous identification of specifically interacting paralogs and inter-protein contacts by Direct-Coupling Analysis

Understanding protein-protein interactions is central to our understanding of almost all complex biological processes. Computational tools exploiting rapidly growing genomic databases to characterize protein-protein interactions are urgently needed. Such methods should connect multiple scales from evolutionary conserved interactions between families of homologous proteins, over the identification of specifically interacting proteins in the case of multiple paralogs inside a species, down to the prediction of residues being in physical contact across interaction interfaces. Statistical inference methods detecting residue-residue coevolution have recently triggered considerable progress in using sequence data for quaternary protein structure prediction; they require, however, large joint alignments of homologous protein pairs known to interact. The generation of such alignments is a complex computational task on its own; application of coevolutionary modeling has in turn been restricted to proteins without paralogs, or to bacterial systems with the corresponding coding genes being co-localized in operons. Here we show that the Direct-Coupling Analysis of residue coevolution can be extended to connect the different scales, and simultaneously to match interacting paralogs, to identify inter-protein residue-residue contacts and to discriminate interacting from noninteracting families in a multiprotein system. Our results extend the potential applications of coevolutionary analysis far beyond cases treatable so far.Comment: Main Text 19 pages Supp. Inf. 16 page

Hierarchical network structure as the source of power-law frequency spectra (state-trait continua) in living and non-living systems: how physical traits and personalities emerge from first principles in biophysics

What causes organisms to have different body plans and personalities? We address this question by looking at universal principles that govern the morphology and behavior of living systems. Living systems display a small-world network structure in which many smaller clusters are nested within fewer larger ones, producing a fractal-like structure with a power-law cluster size distribution. Their dynamics show similar qualities: the timeseries of inner message passing and overt behavior contain high frequencies or 'states' that are nested within lower frequencies or 'traits'. Here, we argue that the nested modular (power-law) dynamics of living systems results from their nested modular (power-law) network structure: organisms 'vertically encode' the deep spatiotemporal structure of their environments, so that high frequencies (states) are produced by many small clusters at the base of a nested-modular hierarchy and lower frequencies (traits) are produced by fewer larger clusters at its top. These include physical as well as behavioral traits. Nested-modular structure causes higher frequencies to be embedded in lower frequencies, producing power-law dynamics. Such dynamics satisfy the need for efficient energy dissipation through networks of coupled oscillators, which also governs the dynamics of non-living systems (e.g. earthquake dynamics, stock market fluctuations). Thus, we provide a single explanation for power-law frequency spectra in both living and non-living systems. If hierarchical structure indeed produces hierarchical dynamics, the development (e.g. during maturation) and collapse (e.g. during disease) of hierarchical structure should leave specific traces in power-law frequency spectra that may serve as early warning signs to system failure. The applications of this idea range from embryology and personality psychology to sociology, evolutionary biology and clinical medicine

DNA entropy reveals a significant difference in complexity between housekeeping and tissue specific gene promoters

BACKGROUND The complexity of DNA can be quantified using estimates of entropy. Variation in DNA complexity is expected between the promoters of genes with different transcriptional mechanisms; namely housekeeping (HK) and tissue specific (TS). The former are transcribed constitutively to maintain general cellular functions, and the latter are transcribed in restricted tissue and cells types for specific molecular events. It is known that promoter features in the human genome are related to tissue specificity, but this has been difficult to quantify on a genomic scale. If entropy effectively quantifies DNA complexity, calculating the entropies of HK and TS gene promoters as profiles may reveal significant differences. RESULTS Entropy profiles were calculated for a total dataset of 12,003 human gene promoters and for 501 housekeeping (HK) and 587 tissue specific (TS) human gene promoters. The mean profiles show the TS promoters have a significantly lower entropy (p<2.2e-16) than HK gene promoters. The entropy distributions for the 3 datasets show that promoter entropies could be used to identify novel HK genes. CONCLUSION Functional features comprise DNA sequence patterns that are non-random and hence they have lower entropies. The lower entropy of TS gene promoters can be explained by a higher density of positive and negative regulatory elements, required for genes with complex spatial and temporary expression