On the basic computational structure of gene regulatory networks

Gene regulatory networks constitute the first layer of the cellular computation for cell adaptation and surveillance. In these webs, a set of causal relations is built up from thousands of interactions between transcription factors and their target genes. The large size of these webs and their entangled nature make difficult to achieve a global view of their internal organisation. Here, this problem has been addressed through a comparative study for {\em Escherichia coli}, {\em Bacillus subtilis} and {\em Saccharomyces cerevisiae} gene regulatory networks. We extract the minimal core of causal relations, uncovering the hierarchical and modular organisation from a novel dynamical/causal perspective. Our results reveal a marked top-down hierarchy containing several small dynamical modules for \textit{E. coli} and \textit{B. subtilis}. Conversely, the yeast network displays a single but large dynamical module in the middle of a bow-tie structure. We found that these dynamical modules capture the relevant wiring among both common and organism-specific biological functions such as transcription initiation, metabolic control, signal transduction, response to stress, sporulation and cell cycle. Functional and topological results suggest that two fundamentally different forms of logic organisation may have evolved in bacteria and yeast.Comment: This article is published at Molecular Biosystems, Please cite as: Carlos Rodriguez-Caso, Bernat Corominas-Murtra and Ricard V. Sole. Mol. BioSyst., 2009, 5 pp 1617--171

Local Difference Measures between Complex Networks for Dynamical System Model Evaluation

Acknowledgments We thank Reik V. Donner for inspiring suggestions that initialized the work presented herein. Jan H. Feldhoff is credited for providing us with the STARS simulation data and for his contributions to fruitful discussions. Comments by the anonymous reviewers are gratefully acknowledged as they led to substantial improvements of the manuscript.Peer reviewedPublisher PD

Balancing Robustness against the Dangers of Multiple Attractors in a Hopfield-Type Model of Biological Attractors

Background: Many chronic human diseases are of unclear origin, and persist long beyond any known insult or instigating factor. These diseases may represent a structurally normal biologic network that has become trapped within the basin of an abnormal attractor. Methodology/Principal Findings: We used the Hopfield net as the archetypical example of a dynamic biological network. By progressively removing the links of fully connected Hopfield nets, we found that a designated attractor of the nets could still be supported until only slightly more than 1 link per node remained. As the number of links approached this minimum value, the rate of convergence to this attractor from an arbitrary starting state increased dramatically. Furthermore, with more than about twice the minimum of links, the net became increasingly able to support a second attractor. Conclusions/Significance: We speculate that homeostatic biological networks may have evolved to assume a degree of connectivity that balances robustness and agility against the dangers of becoming trapped in an abnormal attractor

Detection of regulator genes and eQTLs in gene networks

Genetic differences between individuals associated to quantitative phenotypic traits, including disease states, are usually found in non-coding genomic regions. These genetic variants are often also associated to differences in expression levels of nearby genes (they are "expression quantitative trait loci" or eQTLs for short) and presumably play a gene regulatory role, affecting the status of molecular networks of interacting genes, proteins and metabolites. Computational systems biology approaches to reconstruct causal gene networks from large-scale omics data have therefore become essential to understand the structure of networks controlled by eQTLs together with other regulatory genes, and to generate detailed hypotheses about the molecular mechanisms that lead from genotype to phenotype. Here we review the main analytical methods and softwares to identify eQTLs and their associated genes, to reconstruct co-expression networks and modules, to reconstruct causal Bayesian gene and module networks, and to validate predicted networks in silico.Comment: minor revision with typos corrected; review article; 24 pages, 2 figure

Structural correlations in bacterial metabolic networks

<p>Abstract</p> <p>Background</p> <p>Evolution of metabolism occurs through the acquisition and loss of genes whose products acts as enzymes in metabolic reactions, and from a presumably simple primordial metabolism the organisms living today have evolved complex and highly variable metabolisms. We have studied this phenomenon by comparing the metabolic networks of 134 bacterial species with known phylogenetic relationships, and by studying a neutral model of metabolic network evolution.</p> <p>Results</p> <p>We consider the 'union-network' of 134 bacterial metabolisms, and also the union of two smaller subsets of closely related species. Each reaction-node is tagged with the number of organisms it belongs to, which we denote organism degree (OD), a key concept in our study. Network analysis shows that common reactions are found at the centre of the network and that the average OD decreases as we move to the periphery. Nodes of the same OD are also more likely to be connected to each other compared to a random OD relabelling based on their occurrence in the real data. This trend persists up to a distance of around five reactions. A simple growth model of metabolic networks is used to investigate the biochemical constraints put on metabolic-network evolution. Despite this seemingly drastic simplification, a 'union-network' of a collection of unrelated model networks, free of any selective pressure, still exhibit similar structural features as their bacterial counterpart.</p> <p>Conclusions</p> <p>The OD distribution quantifies topological properties of the evolutionary history of bacterial metabolic networks, and lends additional support to the importance of horizontal gene transfer during bacterial metabolic evolution where new reactions are attached at the periphery of the network. The neutral model of metabolic network growth can reproduce the main features of real networks, but we observe that the real networks contain a smaller common core, while they are more similar at the periphery of the network. This suggests that natural selection and biochemical correlations can act both to diversify and to narrow down metabolic evolution.</p

A Differential Network Approach to Exploring Differences between Biological States: An Application to Prediabetes

Background: Variations in the pattern of molecular associations are observed during disease development. The comprehensive analysis of molecular association patterns and their changes in relation to different physiological conditions can yield insight into the biological basis of disease-specific phenotype variation. Methodology: Here, we introduce a formal statistical method for the differential analysis of molecular associations via network representation. We illustrate our approach with extensive data on lipoprotein subclasses measured by NMR spectroscopy in 4,406 individuals with normal fasting glucose, and 531 subjects with impaired fasting glucose (prediabetes). We estimate the pair-wise association between measures using shrinkage estimates of partial correlations and build the differential network based on this measure of association. We explore the topological properties of the inferred network to gain insight into important metabolic differences between individuals with normal fasting glucose and prediabetes. Conclusions/Significance: Differential networks provide new insights characterizing differences in biological states. Based on conventional statistical methods, few differences in concentration levels of lipoprotein subclasses were found between individuals with normal fasting glucose and individuals with prediabetes. By performing the differential analysis of networks, several characteristic changes in lipoprotein metabolism known to be related to diabetic dyslipidemias were identified. The results demonstrate the applicability of the new approach to identify key molecular changes inaccessible to standard approaches

A Tutorial in Connectome Analysis: Topological and Spatial Features of Brain Networks

High-throughput methods for yielding the set of connections in a neural system, the connectome, are now being developed. This tutorial describes ways to analyze the topological and spatial organization of the connectome at the macroscopic level of connectivity between brain regions as well as the microscopic level of connectivity between neurons. We will describe topological features at three different levels: the local scale of individual nodes, the regional scale of sets of nodes, and the global scale of the complete set of nodes in a network. Such features can be used to characterize components of a network and to compare different networks, e.g. the connectome of patients and control subjects for clinical studies. At the global scale, different types of networks can be distinguished and we will describe Erd\"os-R\'enyi random, scale-free, small-world, modular, and hierarchical archetypes of networks. Finally, the connectome also has a spatial organization and we describe methods for analyzing wiring lengths of neural systems. As an introduction for new researchers in the field of connectome analysis, we discuss the benefits and limitations of each analysis approach.Comment: Neuroimage, in pres

Correlation Network Analysis Applied to Complex Biofilm Communities

The complexity of the human microbiome makes it difficult to reveal organizational principles of the community and even more challenging to generate testable hypotheses. It has been suggested that in the gut microbiome species such as Bacteroides thetaiotaomicron are keystone in maintaining the stability and functional adaptability of the microbial community. In this study, we investigate the interspecies associations in a complex microbial biofilm applying systems biology principles. Using correlation network analysis we identified bacterial modules that represent important microbial associations within the oral community. We used dental plaque as a model community because of its high diversity and the well known species-species interactions that are common in the oral biofilm. We analyzed samples from healthy individuals as well as from patients with periodontitis, a polymicrobial disease. Using results obtained by checkerboard hybridization on cultivable bacteria we identified modules that correlated well with microbial complexes previously described. Furthermore, we extended our analysis using the Human Oral Microbe Identification Microarray (HOMIM), which includes a large number of bacterial species, among them uncultivated organisms present in the mouth. Two distinct microbial communities appeared in healthy individuals while there was one major type in disease. Bacterial modules in all communities did not overlap, indicating that bacteria were able to effectively re-associate with new partners depending on the environmental conditions. We then identified hubs that could act as keystone species in the bacterial modules. Based on those results we then cultured a not-yet-cultivated microorganism, Tannerella sp. OT286 (clone BU063). After two rounds of enrichment by a selected helper (Prevotella oris OT311) we obtained colonies of Tannerella sp. OT286 growing on blood agar plates. This system-level approach would open the possibility of manipulating microbial communities in a targeted fashion as well as associating certain bacterial modules to clinical traits (e.g.: obesity, Crohn's disease, periodontal disease, etc)

On the dynamics of the adenylate energy system: homeorhesis vs homeostasis.

Biochemical energy is the fundamental element that maintains both the adequate turnover of the biomolecular structures and the functional metabolic viability of unicellular organisms. The levels of ATP, ADP and AMP reflect roughly the energetic status of the cell, and a precise ratio relating them was proposed by Atkinson as the adenylate energy charge (AEC). Under growth-phase conditions, cells maintain the AEC within narrow physiological values, despite extremely large fluctuations in the adenine nucleotides concentration. Intensive experimental studies have shown that these AEC values are preserved in a wide variety of organisms, both eukaryotes and prokaryotes. Here, to understand some of the functional elements involved in the cellular energy status, we present a computational model conformed by some key essential parts of the adenylate energy system. Specifically, we have considered (I) the main synthesis process of ATP from ADP, (II) the main catalyzed phosphotransfer reaction for interconversion of ATP, ADP and AMP, (III) the enzymatic hydrolysis of ATP yielding ADP, and (IV) the enzymatic hydrolysis of ATP providing AMP. This leads to a dynamic metabolic model (with the form of a delayed differential system) in which the enzymatic rate equations and all the physiological kinetic parameters have been explicitly considered and experimentally tested in vitro. Our central hypothesis is that cells are characterized by changing energy dynamics (homeorhesis). The results show that the AEC presents stable transitions between steady states and periodic oscillations and, in agreement with experimental data these oscillations range within the narrow AEC window. Furthermore, the model shows sustained oscillations in the Gibbs free energy and in the total nucleotide pool. The present study provides a step forward towards the understanding of the fundamental principles and quantitative laws governing the adenylate energy system, which is a fundamental element for unveiling the dynamics of cellular life