Lyapunov exponent of the random frequency oscillator: cumulant expansion approach

We consider a one-dimensional harmonic oscillator with a random frequency, focusing on both the standard and the generalized Lyapunov exponents, $\lambda$ and $\lambda^\star$ respectively. We discuss the numerical difficulties that arise in the numerical calculation of $\lambda^\star$ in the case of strong intermittency. When the frequency corresponds to a Ornstein-Uhlenbeck process, we compute analytically $\lambda^\star$ by using a cumulant expansion including up to the fourth order. Connections with the problem of finding an analytical estimate for the largest Lyapunov exponent of a many-body system with smooth interactions are discussed.Comment: 6 pages, 4 figures, to appear in J. Phys. Conf. Series - LAWNP0

A Genome-Wide Analysis of Promoter-Mediated Phenotypic Noise in Escherichia coli

Gene expression is subject to random perturbations that lead to fluctuations in the rate of protein production. As a consequence, for any given protein, genetically identical organisms living in a constant environment will contain different amounts of that particular protein, resulting in different phenotypes. This phenomenon is known as “phenotypic noise.” In bacterial systems, previous studies have shown that, for specific genes, both transcriptional and translational processes affect phenotypic noise. Here, we focus on how the promoter regions of genes affect noise and ask whether levels of promoter-mediated noise are correlated with genes' functional attributes, using data for over 60% of all promoters in Escherichia coli. We find that essential genes and genes with a high degree of evolutionary conservation have promoters that confer low levels of noise. We also find that the level of noise cannot be attributed to the evolutionary time that different genes have spent in the genome of E. coli. In contrast to previous results in eukaryotes, we find no association between promoter-mediated noise and gene expression plasticity. These results are consistent with the hypothesis that, in bacteria, natural selection can act to reduce gene expression noise and that some of this noise is controlled through the sequence of the promoter region alon

An Atlas of the Speed of Copy Number Changes in Animal Gene Families and Its Implications

The notion that gene duplications generating new genes and functions is commonly accepted in evolutionary biology. However, this assumption is more speculative from theory rather than well proven in genome-wide studies. Here, we generated an atlas of the rate of copy number changes (CNCs) in all the gene families of ten animal genomes. We grouped the gene families with similar CNC dynamics into rate pattern groups (RPGs) and annotated their function using a novel bottom-up approach. By comparing CNC rate patterns, we showed that most of the species-specific CNC rates groups are formed by gene duplication rather than gene loss, and most of the changes in rates of CNCs may be the result of adaptive evolution. We also found that the functions of many RPGs match their biological significance well. Our work confirmed the role of gene duplication in generating novel phenotypes, and the results can serve as a guide for researchers to connect the phenotypic features to certain gene duplications

GLADX: An Automated Approach to Analyze the Lineage-Specific Loss and Pseudogenization of Genes

A well-established ancestral gene can usually be found, in one or multiple copies, in different descendant species. Sometimes during the course of evolution, all the representatives of a well-established ancestral gene disappear in specific lineages; such gene losses may occur in the genome by deletion of a DNA fragment or by pseudogenization. The loss of an entire gene family in a given lineage may reflect an important phenomenon, and could be due either to adaptation, or to a relaxation of selection that leads to neutral evolution. Therefore, the lineage-specific gene loss analyses are important to improve the understanding of the evolutionary history of genes and genomes. In order to perform this kind of study from the increasing number of complete genome sequences available, we developed a unique new software module called GLADX in the DAGOBAH framework, based on a comparative genomic approach. The software is able to automatically detect, for all the species of a phylum, the presence/absence of a representative of a well-established ancestral gene, and by systematic steps of re-annotation, confirm losses, detect and analyze pseudogenes and find novel genes. The approach is based on the use of highly reliable gene phylogenies, of protein predictions and on the analysis of genomic mutations. All the evidence associated to evolutionary approach provides accurate information for building an overall view of the evolution of a given gene in a selected phylum. The reliability of GLADX has been successfully tested on a benchmark analysis of 14 reported cases. It is the first tool that is able to fully automatically study the lineage-specific losses and pseudogenizations. GLADX is available at http://ioda.univ-provence.fr/IodaSite/gladx/

Discovering local patterns of co - evolution: computational aspects and biological examples

<p>Abstract</p> <p>Background</p> <p>Co-evolution is the process in which two (or more) sets of orthologs exhibit a similar or correlative pattern of evolution. Co-evolution is a powerful way to learn about the functional interdependencies between sets of genes and cellular functions and to predict physical interactions. More generally, it can be used for answering fundamental questions about the evolution of biological systems.</p> <p>Orthologs that exhibit a strong signal of co-evolution in a certain part of the evolutionary tree may show a mild signal of co-evolution in other branches of the tree. The major reasons for this phenomenon are noise in the biological input, genes that gain or lose functions, and the fact that some measures of co-evolution relate to rare events such as positive selection. Previous publications in the field dealt with the problem of finding sets of genes that co-evolved along an entire underlying phylogenetic tree, without considering the fact that often co-evolution is local.</p> <p>Results</p> <p>In this work, we describe a new set of biological problems that are related to finding patterns of <it>local </it>co-evolution. We discuss their computational complexity and design algorithms for solving them. These algorithms outperform other bi-clustering methods as they are designed specifically for solving the set of problems mentioned above.</p> <p>We use our approach to trace the co-evolution of fungal, eukaryotic, and mammalian genes at high resolution across the different parts of the corresponding phylogenetic trees. Specifically, we discover regions in the fungi tree that are enriched with positive evolution. We show that metabolic genes exhibit a remarkable level of co-evolution and different patterns of co-evolution in various biological datasets.</p> <p>In addition, we find that protein complexes that are related to gene expression exhibit non-homogenous levels of co-evolution across different parts of the <it>fungi </it>evolutionary line. In the case of mammalian evolution, signaling pathways that are related to <it>neurotransmission </it>exhibit a relatively higher level of co-evolution along the <it>primate </it>subtree.</p> <p>Conclusions</p> <p>We show that finding local patterns of co-evolution is a computationally challenging task and we offer novel algorithms that allow us to solve this problem, thus opening a new approach for analyzing the evolution of biological systems.</p

2R and remodeling of vertebrate signal transduction engine

<p>Abstract</p> <p><b>Background</b></p> <p>Whole genome duplication (WGD) is a special case of gene duplication, observed rarely in animals, whereby all genes duplicate simultaneously through polyploidisation. Two rounds of WGD (2R-WGD) occurred at the base of vertebrates, giving rise to an enormous wave of genetic novelty, but a systematic analysis of functional consequences of this event has not yet been performed.</p> <p><b>Results</b></p> <p>We show that 2R-WGD affected an overwhelming majority (74%) of signalling genes, in particular developmental pathways involving receptor tyrosine kinases, Wnt and transforming growth factor-β ligands, G protein-coupled receptors and the apoptosis pathway. 2R-retained genes, in contrast to tandem duplicates, were enriched in protein interaction domains and multifunctional signalling modules of Ras and mitogen-activated protein kinase cascades. 2R-WGD had a fundamental impact on the cell-cycle machinery, redefined molecular building blocks of the neuronal synapse, and was formative for vertebrate brains. We investigated 2R-associated nodes in the context of the human signalling network, as well as in an inferred ancestral pre-2R (AP2R) network, and found that hubs (particularly involving negative regulation) were preferentially retained, with high connectivity driving retention. Finally, microarrays and proteomics demonstrated a trend for gradual paralog expression divergence independent of the duplication mechanism, but inferred ancestral expression states suggested preferential subfunctionalisation among 2R-ohnologs (2ROs).</p> <p><b>Conclusions</b></p> <p>The 2R event left an indelible imprint on vertebrate signalling and the cell cycle. We show that 2R-WGD preferentially retained genes are associated with higher organismal complexity (for example, locomotion, nervous system, morphogenesis), while genes associated with basic cellular functions (for example, translation, replication, splicing, recombination; with the notable exception of cell cycle) tended to be excluded. 2R-WGD set the stage for the emergence of key vertebrate functional novelties (such as complex brains, circulatory system, heart, bone, cartilage, musculature and adipose tissue). A full explanation of the impact of 2R on evolution, function and the flow of information in vertebrate signalling networks is likely to have practical consequences for regenerative medicine, stem cell therapies and cancer treatment.</p

Why Is the Correlation between Gene Importance and Gene Evolutionary Rate So Weak?

One of the few commonly believed principles of molecular evolution is that functionally more important genes (or DNA sequences) evolve more slowly than less important ones. This principle is widely used by molecular biologists in daily practice. However, recent genomic analysis of a diverse array of organisms found only weak, negative correlations between the evolutionary rate of a gene and its functional importance, typically measured under a single benign lab condition. A frequently suggested cause of the above finding is that gene importance determined in the lab differs from that in an organism's natural environment. Here, we test this hypothesis in yeast using gene importance values experimentally determined in 418 lab conditions or computationally predicted for 10,000 nutritional conditions. In no single condition or combination of conditions did we find a much stronger negative correlation, which is explainable by our subsequent finding that always-essential (enzyme) genes do not evolve significantly more slowly than sometimes-essential or always-nonessential ones. Furthermore, we verified that functional density, approximated by the fraction of amino acid sites within protein domains, is uncorrelated with gene importance. Thus, neither the lab-nature mismatch nor a potentially biased among-gene distribution of functional density explains the observed weakness of the correlation between gene importance and evolutionary rate. We conclude that the weakness is factual, rather than artifactual. In addition to being weakened by population genetic reasons, the correlation is likely to have been further weakened by the presence of multiple nontrivial rate determinants that are independent from gene importance. These findings notwithstanding, we show that the principle of slower evolution of more important genes does have some predictive power when genes with vastly different evolutionary rates are compared, explaining why the principle can be practically useful despite the weakness of the correlation

Gene Promoter Evolution Targets the Center of the Human Protein Interaction Network

Assessing the contribution of promoters and coding sequences to gene evolution is an important step toward discovering the major genetic determinants of human evolution. Many specific examples have revealed the evolutionary importance of cis-regulatory regions. However, the relative contribution of regulatory and coding regions to the evolutionary process and whether systemic factors differentially influence their evolution remains unclear. To address these questions, we carried out an analysis at the genome scale to identify signatures of positive selection in human proximal promoters. Next, we examined whether genes with positively selected promoters (Prom+ genes) show systemic differences with respect to a set of genes with positively selected protein-coding regions (Cod+ genes). We found that the number of genes in each set was not significantly different (8.1% and 8.5%, respectively). Furthermore, a functional analysis showed that, in both cases, positive selection affects almost all biological processes and only a few genes of each group are located in enriched categories, indicating that promoters and coding regions are not evolutionarily specialized with respect to gene function. On the other hand, we show that the topology of the human protein network has a different influence on the molecular evolution of proximal promoters and coding regions. Notably, Prom+ genes have an unexpectedly high centrality when compared with a reference distribution (P = 0.008, for Eigenvalue centrality). Moreover, the frequency of Prom+ genes increases from the periphery to the center of the protein network (P = 0.02, for the logistic regression coefficient). This means that gene centrality does not constrain the evolution of proximal promoters, unlike the case with coding regions, and further indicates that the evolution of proximal promoters is more efficient in the center of the protein network than in the periphery. These results show that proximal promoters have had a systemic contribution to human evolution by increasing the participation of central genes in the evolutionary process

Evolutionary Genomics Reveals Lineage-Specific Gene Loss and Rapid Evolution of a Sperm-Specific Ion Channel Complex: CatSpers and CatSperβ

The mammalian CatSper ion channel family consists of four sperm-specific voltage-gated Ca2+ channels that are crucial for sperm hyperactivation and male fertility. All four CatSper subunits are believed to assemble into a heteromultimeric channel complex, together with an auxiliary subunit, CatSperβ. Here, we report a comprehensive comparative genomics study and evolutionary analysis of CatSpers and CatSperβ, with important correlation to physiological significance of molecular evolution of the CatSper channel complex. The development of the CatSper channel complex with four CatSpers and CatSperβ originated as early as primitive metazoans such as the Cnidarian Nematostella vectensis. Comparative genomics revealed extensive lineage-specific gene loss of all four CatSpers and CatSperβ through metazoan evolution, especially in vertebrates. The CatSper channel complex underwent rapid evolution and functional divergence, while distinct evolutionary constraints appear to have acted on different domains and specific sites of the four CatSper genes. These results reveal unique evolutionary characteristics of sperm-specific Ca2+ channels and their adaptation to sperm biology through metazoan evolution

Loss of Genetic Redundancy in Reductive Genome Evolution

Biological systems evolved to be functionally robust in uncertain environments, but also highly adaptable. Such robustness is partly achieved by genetic redundancy, where the failure of a specific component through mutation or environmental challenge can be compensated by duplicate components capable of performing, to a limited extent, the same function. Highly variable environments require very robust systems. Conversely, predictable environments should not place a high selective value on robustness. Here we test this hypothesis by investigating the evolutionary dynamics of genetic redundancy in extremely reduced genomes, found mostly in intracellular parasites and endosymbionts. By combining data analysis with simulations of genome evolution we show that in the extensive gene loss suffered by reduced genomes there is a selective drive to keep the diversity of protein families while sacrificing paralogy. We show that this is not a by-product of the known drivers of genome reduction and that there is very limited convergence to a common core of families, indicating that the repertoire of protein families in reduced genomes is the result of historical contingency and niche-specific adaptations. We propose that our observations reflect a loss of genetic redundancy due to a decreased selection for robustness in a predictable environment