Properties of metabolic graphs: biological organization or representation artifacts?

Background  

Standard graphs, where each edge links two nodes, have been extensively used to represent the connectivity of metabolic networks. It is based on this representation that properties of metabolic networks, such as hierarchical and small-world structures, have been elucidated and null models have been proposed to derive biological organization hypotheses. However, these graphs provide a simplistic model of a metabolic network's connectivity map, since metabolic reactions often involve more than two reactants. In other words, this map is better represented as a hypergraph. Consequently, a question that naturally arises in this context is whether these properties truly reflect biological organization or are merely an artifact of the representation.     

Osprey: a network visualization system

We have developed a software platform called Osprey for visualization and manipulation of complex interaction networks. Osprey builds data-rich graphical representations that are color-coded for gene function and experimental interaction data. Mouse-over functions allow rapid elaboration and organization of network diagrams in a spoke model format. User-defined large-scale data sets can be readily combined with Osprey for comparison of different methods.     

Osprey: a network visualization system

We have developed a software platform called Osprey for visualization and manipulation of complex interaction networks. Osprey builds data-rich graphical representations that are color-coded for gene function and experimental interaction data. Mouse-over functions allow rapid elaboration and organization of network diagrams in a spoke model format. User-defined large-scale datasets can be readily combined with Osprey for comparison of different methods.     

Dynamical systems for discovering protein complexes and functional modules from biological networks

Recent advances in high throughput experiments and annotations via published literature have provided a wealth of interaction maps of several biomolecular networks, including metabolic, protein-protein, and protein-DNA interaction networks. The architecture of these molecular networks reveals important principles of cellular organization and molecular functions. Analyzing such networks, i.e., discovering dense regions in the network, is an important way to identify protein complexes and functional modules. This task has been formulated as the problem of finding heavy subgraphs, the heaviest k-subgraph problem (k-HSP), which itself is NP-hard. However, any method based on the k-HSP requires the parameter k and an exact solution of k-HSP may still end up as a "spurious" heavy subgraph, thus reducing its practicability in analyzing large scale biological networks. We proposed a new formulation, called the rank-HSP, and two dynamical systems to approximate its results. In addition, a novel metric, called the standard deviation and mean ratio (SMR), is proposed for use in "spurious" heavy subgraphs to automate the discovery by setting a fixed threshold. Empirical results on both the simulated graphs and biological networks have demonstrated the efficiency and effectiveness of our proposal     

On the relationship between emotion and cognition

The current view of brain organization supports the notion that there is a considerable degree of functional specialization and that many regions can be conceptualized as either 'affective' or 'cognitive'. Popular examples are the amygdala in the domain of emotion and the lateral prefrontal cortex in the case of cognition. This prevalent view is problematic for a number of reasons. Here, I will argue that complex cognitive-emotional behaviours have their basis in dynamic coalitions of networks of brain areas, none of which should be conceptualized as specifically affective or cognitive. Central to cognitive-emotional interactions are brain areas with a high degree of connectivity, called hubs, which are critical for regulating the flow and integration of information between regions.     

MODULAR: software for the autonomous computation of modularity in large network sets

Many ecological systems can be represented as networks of interactions. A key feature in these networks is their organization into modules, which are subsets of tightly connected elements. We introduce MODULAR to perform rapid and autonomous calculation of modularity in network sets. MODULAR reads a set of files representing unipartite or bipartite networks, and identifies modules using two different modularity metrics widely used in the ecological networks literature. To estimate modularity, the software offers five optimization methods to the user. The software also includes two null models commonly used in studies of ecological networks to verify how the degree of modularity differs from two distinct theoretical benchmarks.     

Functional significance of the variations in the geometrical organization of tight junction networks.

Using freeze-fracture techniques, we have examined the morpholog of tight junction networks found along the length of the alimentary tract of Xenopus laevis before and after metamorphosis. We have developed the hypothesis, based on these observations, that the geometrical organization of the network determined by the stress-induced shape changes normally experienced by the cells linked by the network. Consistent with this theory, tight junctions can be classified into two distinct types of network organization which differ in their response normal and experimentally induced stress conditions: (a) loosely interconnected networks which can stretch or compress extensively under tension, thereby adapting to stress changes in the tissue; and (b) evenly cross-linked networks which retain their basic morphology under normal stress conditions. The absorptive cells of the large intestine as well as the mucous cells of the gastrointestine or stomach are sealed by the first, flexible type of tight junction. The second type of junctional organization, the evenly cross-connected network, is found between absorptive cells of the small intestine and ciliated cells of the esophagus, and reflects in its constant morphology the relative stability of the apical region of both of these cell types. Networks intermediate between these two types arise when a cell which would normally form a lossely interconnected network borders a cell which tends to form a more evenly cross-linked network, as is found in the esophagus where ciliated and goblet cells adjoin. Despite the change in the animal's diet during metamorphosis from herbivorous to carnivorous, the basic gemetrical organization of the networks associated with each tissue of the alimentary tract remains the same.     

Actin polymerization serves as a membrane domain switch in model lipid bilayers

The ability of cells to mount localized responses to external or internal stimuli is critically dependent on organization of lipids and proteins in the plasma membrane. Involvement of the actin cytoskeleton in membrane organization has been documented, but an active role for actin networks that directly links internal organization of the cytoskeleton with membrane organization has not yet been identified. Here we show that branched actin networks formed on model lipid membranes enriched with the lipid second messenger PIP(2) trigger both temporal and spatial rearrangement of membrane components. Using giant unilamellar vesicles able to separate into two coexisting liquid phases, we demonstrate that polymerization of dendritic actin networks on the membrane induces phase separation of initially homogenous vesicles. This switch-like behavior depends only on the PIP(2)-N-WASP link between the membrane and actin network, and we find that the presence of a preexisting actin network spatially biases the location of phase separation. These results show that dynamic, membrane-bound actin networks alone can control when and where membrane domains form and may actively contribute to membrane organization during cell signaling.     

基因逻辑网络研究进展

海量生物数据的涌现,使得通过数据分析和理论方法探索生物机理成为理论生物学研究的重要途径．特别是对于基因的复杂的功能系统,建立基因网络这种理论方法的意义更为突出．Bowers在蛋白质相互作用的分析中引入了高阶逻辑关系,从而建立了系统发生谱数据的逻辑分析（LAPP）的系统方法．LAPP和通常建立模型的方法不同,它给出了一个从复杂网络的元素（或部件）的表达数据出发,通过逻辑分析,找到元素之间逻辑关联性的建模方法．这种方法能够从蛋白质表达谱数据出发,利用信息熵的算法发现两种蛋白质对一种蛋白质的联合作用,对于发现蛋白质之间新的作用机理有重要意义．由于涉及功能的基因组通常是一个大的群体构成的系统,因此LAPP方法也是一个生成复杂的基因逻辑网络的方法．基因逻辑网络的建立,方便实现通过逻辑调控进行基因调控的目的．这种方法可以应用在很多方面,如物种进化、肿瘤诊疗等等．系统阐述并分析了LAPP方法,并指出其在方法和应用方面的新进展以及评述．     

The individual organization of frontal-hippocampal networks during realization of different behavioral tasks

Four cats were subjected to appetitive instrumental conditioning with light as a conditioned stimulus by the method of "active choice" of the reinforcement quality: short-delay conditioned bar-press responses were followed by bread-meat mixture and the delayed responses--by meat. The animals differed in behavior strategy: four animals preferred bar-pressing with long delay (so called "self-control" group); two animal preferred bar-pressing with short-delay (so called "impulsive" group). Then all the animals were learned to short-delay (1 s) instrumental conditioned reflex to light (CS+) reinforced by meat. The multiunit activity in the frontal cortex and the hippocampus (CA3) was recorded through chronically implanted nichrome-wire semimicroelectrodes. The interactions among the neighboring neurons in the frontal cortex and hippocampus (within the local neuronal networks) and between the neurons of the frontal cortex and hippocampus (distributed neuronal networks of frontal-hippocampal and hippocampal-frontal directions) were evaluated by means of statistical crosscorrelation analysis of the spike trains. Crosscorrelation interneuronal connections in the delay range 0-100 ms were explored. It was shown that the functional organization of the frontal and hippocampal neuronal networks differed in choice behavior and was similar during realization of short-delayed conditioned reflex. We suggest that the local and distributed neural networks of the frontal cortex and hippocampus take part in the realization of cognitive behavior, in particularly in the processes of the decision making.     

Intracellular organelle networks: Understanding their organization and communication through systems-level modeling and analysis

Background

Membrane-bound intracellular organelles are biochemically distinct compartments used by eukaryotic cells for serving specialized physiological functions and organizing their internal environment. Recent studies revealed surprisingly extensive communication between these organelles and highlighted the network nature of their organization and communication. Since organization and communication of the organelles are carried out at the systems level through their networks, systems-level studies are essential for understanding the underlying mechanisms.

Methods

We reviewed recent studies that used systems-level quantitative modeling and analysis to understand organization and communication of intracellular organelle networks.

Results

We first review modeling and analysis studies on how fusion/fission and degradation/biogenesis, two essential and closely related classes of activities of individual organelles, collectively mediate the dynamic organization of their networks. We then turn to another important aspect of the dynamic organization of the organelle networks, namely how organelles are physically connected within their networks, a property referred to as the topology of the networks in mathematics, and summarize some of their distinct properties. Lastly, we briefly review modeling and analysis studies that aim to understand communication between different organelle networks, focusing on cellular calcium homeostasis as an example. We conclude with a brief discussion of future directions for research in this area.

Conclusion

Together, the reviewed studies provide critical insights into how diverse activities of individual organelles collectively mediate the organization and communication of their networks. They demonstrate the essential role of systemslevel modeling and analysis in understanding complex behavior of such networks.

     

The balance of weak and strong interactions in genetic networks

Genetic interactions are being quantitatively characterized in a comprehensive way in several model organisms. These data are then globally represented in terms of genetic networks. How are interaction strengths distributed in these networks? And what type of functional organization of the underlying genomic systems is revealed by such distribution patterns? Here, I found that weak interactions are important for the structure of genetic buffering between signaling pathways in Caenorhabditis elegans, and that the strength of the association between two genes correlates with the number of common interactors they exhibit. I also determined that this network includes genetic cascades balancing weak and strong links, and that its hubs act as particularly strong genetic modifiers; both patterns also identified in Saccharomyces cerevisae networks. In yeast, I further showed a relation, although weak, between interaction strengths and some phenotypic/evolutionary features of the corresponding target genes. Overall, this work demonstrates a non-random organization of interaction strengths in genetic networks, a feature common to other complex networks, and that could reflect in this context how genetic variation is eventually influencing the phenotype.     

A Graph Theoretical Approach to Study the Organization of the Cortical Networks during Different Mathematical Tasks

The two core systems of mathematical processing (subitizing and retrieval) as well as their functionality are already known and published. In this study we have used graph theory to compare the brain network organization of these two core systems in the cortical layer during difficult calculations. We have examined separately all the EEG frequency bands in healthy young individuals and we found that the network organization at rest, as well as during mathematical tasks has the characteristics of Small World Networks for all the bands, which is the optimum organization required for efficient information processing. The different mathematical stimuli provoked changes in the graph parameters of different frequency bands, especially the low frequency bands. More specific, in Delta band the induced network increases it’s local and global efficiency during the transition from subitizing to retrieval system, while results suggest that difficult mathematics provoke networks with higher cliquish organization due to more specific demands. The network of the Theta band follows the same pattern as before, having high nodal and remote organization during difficult mathematics. Also the spatial distribution of the network’s weights revealed more prominent connections in frontoparietal regions, revealing the working memory load due to the engagement of the retrieval system. The cortical networks of the alpha brainwaves were also more efficient, both locally and globally, during difficult mathematics, while the fact that alpha’s network was more dense on the frontparietal regions as well, reveals the engagement of the retrieval system again. Concluding, this study gives more evidences regarding the interaction of the two core systems, exploiting the produced functional networks of the cerebral cortex, especially for the difficult mathematics.     

Comparison of Tree-Child Phylogenetic Networks

Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of nontreelike evolutionary events, like recombination, hybridization, or lateral gene transfer. While much progress has been made to find practical algorithms for reconstructing a phylogenetic network from a set of sequences, all attempts to endorse a class of phylogenetic networks (strictly extending the class of phylogenetic trees) with a well-founded distance measure have, to the best of our knowledge and with the only exception of the bipartition distance on regular networks, failed so far. In this paper, we present and study a new meaningful class of phylogenetic networks, called tree-child phylogenetic networks, and we provide an injective representation of these networks as multisets of vectors of natural numbers, their path multiplicity vectors. We then use this representation to define a distance on this class that extends the well-known Robinson-Foulds distance for phylogenetic trees and to give an alignment method for pairs of networks in this class. Simple polynomial algorithms for reconstructing a tree-child phylogenetic network from its path multiplicity vectors, for computing the distance between two tree-child phylogenetic networks and for aligning a pair of tree-child phylogenetic networks, are provided. They have been implemented as a Perl package and a Java applet, which can be found at http://bioinfo.uib.es/~recerca/phylonetworks/mudistance/.     

Insights into the organization of biochemical regulatory networks using graph theory analyses

Graph theory has been a valuable mathematical modeling tool to gain insights into the topological organization of biochemical networks. There are two types of insights that may be obtained by graph theory analyses. The first provides an overview of the global organization of biochemical networks; the second uses prior knowledge to place results from multivariate experiments, such as microarray data sets, in the context of known pathways and networks to infer regulation. Using graph analyses, biochemical networks are found to be scale-free and small-world, indicating that these networks contain hubs, which are proteins that interact with many other molecules. These hubs may interact with many different types of proteins at the same time and location or at different times and locations, resulting in diverse biological responses. Groups of components in networks are organized in recurring patterns termed network motifs such as feedback and feed-forward loops. Graph analysis revealed that negative feedback loops are less common and are present mostly in proximity to the membrane, whereas positive feedback loops are highly nested in an architecture that promotes dynamical stability. Cell signaling networks have multiple pathways from some input receptors and few from others. Such topology is reminiscent of a classification system. Signaling networks display a bow-tie structure indicative of funneling information from extracellular signals and then dispatching information from a few specific central intracellular signaling nexuses. These insights show that graph theory is a valuable tool for gaining an understanding of global regulatory features of biochemical networks.     

Using Synchronous Boolean Networks to Model Several Phenomena of Collective Behavior

In this paper, we propose an approach for modeling and analysis of a number of phenomena of collective behavior. By collectives we mean multi-agent systems that transition from one state to another at discrete moments of time. The behavior of a member of a collective (agent) is called conforming if the opinion of this agent at current time moment conforms to the opinion of some other agents at the previous time moment. We presume that at each moment of time every agent makes a decision by choosing from the set (where 1-decision corresponds to action and 0-decision corresponds to inaction). In our approach we model collective behavior with synchronous Boolean networks. We presume that in a network there can be agents that act at every moment of time. Such agents are called instigators. Also there can be agents that never act. Such agents are called loyalists. Agents that are neither instigators nor loyalists are called simple agents. We study two combinatorial problems. The first problem is to find a disposition of instigators that in several time moments transforms a network from a state where the majority of simple agents are inactive to a state with the majority of active agents. The second problem is to find a disposition of loyalists that returns the network to a state with the majority of inactive agents. Similar problems are studied for networks in which simple agents demonstrate the contrary to conforming behavior that we call anticonforming. We obtained several theoretical results regarding the behavior of collectives of agents with conforming or anticonforming behavior. In computational experiments we solved the described problems for randomly generated networks with several hundred vertices. We reduced corresponding combinatorial problems to the Boolean satisfiability problem (SAT) and used modern SAT solvers to solve the instances obtained.     

Plasmodium falciparum antigenic variation. Mapping mosaic var gene sequences onto a network of shared, highly polymorphic sequence blocks

Plasmodium falciparum erythrocyte membrane protein 1 (PfEMP1) is a potentially important family of immune targets, encoded by an extremely diverse gene family called var . Understanding of the genetic organization of var genes is hampered by sequence mosaicism that results from a long history of non-homologous recombination. Here we have used software designed to analyse social networks to visualize the relationships between large collections of short var sequences tags sampled from clinical parasite isolates. In this approach, two sequences are connected if they share one or more highly polymorphic sequence blocks. The results show that the majority of analysed sequences including several var -like sequences from the chimpanzee parasite Plasmodium reichenowi can be either directly or indirectly linked together in a single unbroken network. However, the network is highly structured and contains putative subgroups of recombining sequences. The major subgroup contains the previously described group A var genes, previously proposed to be genetically distinct. Another subgroup contains sequences found to be associated with rosetting, a parasite virulence phenotype. The mosaic structure of the sequences and their division into subgroups may reflect the conflicting problems of maximizing antigenic diversity and minimizing epitope sharing between variants while maintaining their host cell binding functions.