Modularity and robustness of frontal cortical networks

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Modularity of gene-regulatory networks revealed in sea-star development

Evidence that conserved developmental gene-regulatory networks can change as a unit during deutersostome evolution emerges from a study published in BMC Biology. This shows that genes consistently expressed in anterior brain patterning in hemichordates and chordates are expressed in a similar spatial pattern in another deuterostome, an asteroid echinoderm (sea star), but in a completely different developmental context (the animal-vegetal axis). This observation has implications for hypotheses on the type of development present in the deuterostome common ancestor.     

Statistics of weighted brain networks reveal hierarchical organization and Gaussian degree distribution

Whole brain weighted connectivity networks were extracted from high resolution diffusion MRI data of 14 healthy volunteers. A statistically robust technique was proposed for the removal of questionable connections. Unlike most previous studies our methods are completely adapted for networks with arbitrary weights. Conventional statistics of these weighted networks were computed and found to be comparable to existing reports. After a robust fitting procedure using multiple parametric distributions it was found that the weighted node degree of our networks is best described by the normal distribution, in contrast to previous reports which have proposed heavy tailed distributions. We show that post-processing of the connectivity weights, such as thresholding, can influence the weighted degree asymptotics. The clustering coefficients were found to be distributed either as gamma or power-law distribution, depending on the formula used. We proposed a new hierarchical graph clustering approach, which revealed that the brain network is divided into a regular base-2 hierarchical tree. Connections within and across this hierarchy were found to be uncommonly ordered. The combined weight of our results supports a hierarchically ordered view of the brain, whose connections have heavy tails, but whose weighted node degrees are comparable.     

Modularity of cellular networks shows general center-periphery polarization

The modular biology is supposed to be a bridge from the molecular to the systems biology. Using a new approach, it is shown here that the protein interaction networks of yeast Saccharomyces cerevisiae and bacteria Escherichia coli consist of two large-scale modularity layers, central and peripheral, separated by a zone of depressed modularity. This finding based on the analysis of network topology is further supported by the discovery that there are many more Gene Ontology categories (terms) and KEGG biochemical pathways that are overrepresented in the central and peripheral layers than in the intermediate zone. The categories of the central layer are mostly related to nuclear information processing, regulation and cell cycle, whereas the peripheral layer is dealing with various metabolic and energetic processes, transport and cell communication. A similar center-periphery polarization of modularity is found in the protein domain networks ('built-in interactome') and in a powergrid (as a non-biological example). These data suggest a 'polarized modularity' model of cellular networks where the central layer seems to be regulatory and to use information storage of the nucleus, whereas the peripheral layer seems devoted to more specialized tasks and environmental interactions, with a complex 'bus' between the layers.     

Anti-correlations in the degree distribution increase stimulus detection performance in noisy spiking neural networks

Neuronal circuits in the rodent barrel cortex are characterized by stable low firing rates. However, recent experiments show that short spike trains elicited by electrical stimulation in single neurons can induce behavioral responses. Hence, the underlying neural networks provide stability against internal fluctuations in the firing rate, while simultaneously making the circuits sensitive to small external perturbations. Here we studied whether stability and sensitivity are affected by the connectivity structure in recurrently connected spiking networks. We found that anti-correlation between the number of afferent (in-degree) and efferent (out-degree) synaptic connections of neurons increases stability against pathological bursting, relative to networks where the degrees were either positively correlated or uncorrelated. In the stable network state, stimulation of a few cells could lead to a detectable change in the firing rate. To quantify the ability of networks to detect the stimulation, we used a receiver operating characteristic (ROC) analysis. For a given level of background noise, networks with anti-correlated degrees displayed the lowest false positive rates, and consequently had the highest stimulus detection performance. We propose that anti-correlation in the degree distribution may be a computational strategy employed by sensory cortices to increase the detectability of external stimuli. We show that networks with anti-correlated degrees can in principle be formed by applying learning rules comprised of a combination of spike-timing dependent plasticity, homeostatic plasticity and pruning to networks with uncorrelated degrees. To test our prediction we suggest a novel experimental method to estimate correlations in the degree distribution.     

A network with tunable clustering, degree correlation and degree distribution, and an epidemic thereon

A random network model which allows for tunable, quite general forms of clustering, degree correlation and degree distribution is defined. The model is an extension of the configuration model, in which stubs (half-edges) are paired to form a network. Clustering is obtained by forming small completely connected subgroups, and positive (negative) degree correlation is obtained by connecting a fraction of the stubs with stubs of similar (dissimilar) degree. An SIR (Susceptible $\rightarrow $ Infective $\rightarrow $ Recovered) epidemic model is defined on this network. Asymptotic properties of both the network and the epidemic, as the population size tends to infinity, are derived: the degree distribution, degree correlation and clustering coefficient, as well as a reproduction number $R_*$ , the probability of a major outbreak and the relative size of such an outbreak. The theory is illustrated by Monte Carlo simulations and numerical examples. The main findings are that (1) clustering tends to decrease the spread of disease, (2) the effect of degree correlation is appreciably greater when the disease is close to threshold than when it is well above threshold and (3) disease spread broadly increases with degree correlation $\rho $ when $R_*$ is just above its threshold value of one and decreases with $\rho $ when $R_*$ is well above one.     

The dichotomy in degree correlation of biological networks

Most complex networks from different areas such as biology, sociology or technology, show a correlation on node degree where the possibility of a link between two nodes depends on their connectivity. It is widely believed that complex networks are either disassortative (links between hubs are systematically suppressed) or assortative (links between hubs are enhanced). In this paper, we analyze a variety of biological networks and find that they generally show a dichotomous degree correlation. We find that many properties of biological networks can be explained by this dichotomy in degree correlation, including the neighborhood connectivity, the sickle-shaped clustering coefficient distribution and the modularity structure. This dichotomy distinguishes biological networks from real disassortative networks or assortative networks such as the Internet and social networks. We suggest that the modular structure of networks accounts for the dichotomy in degree correlation and vice versa, shedding light on the source of modularity in biological networks. We further show that a robust and well connected network necessitates the dichotomy of degree correlation, suggestive of an evolutionary motivation for its existence. Finally, we suggest that a dichotomous degree correlation favors a centrally connected modular network, by which the integrity of network and specificity of modules might be reconciled.     

Modularity and specialization in bat-fly interaction networks are remarkably consistent across patches within urbanized landscapes and spatial scales

Patterns of specialization and the structure of interactions between bats and ectoparasitic flies have been studied mostly on non-urban environments and at loca...     

随机抽样对蛋白质相互作用网络度分布的影响

蛋白质相互作用(PPI)网络,是目前系统研究蛋白质层面细胞活动的重要工具,PPI网络的度分布是研究复杂网络性质的重要物理量。随着蛋白质相互作用数据量不断的增加,其数据的可靠性是否会对PPI网络的度分布造成影响,并不确定。本文对四种模式生物的PPI网络数据,按照5%的增长比率,随机删除PPI网络的边,来检验随机抽样对PPI网络度分布的影响。结果表明,各种实验数据的误差不会对真实PPI网络的度分布造成干扰,且在目前描述网络度分布的五种函数中,广延指数函数拟合程度最优。     

STORE working memory networks for storage and recall of arbitrary temporal sequences

Neural network models of working memory, called “sustained temporal order recurrent” (STORE) models, are described. They encode the invariant temporal order of sequential events in short-term memory (STM) in a way that mimics cognitive data about working memory, including primacy, recency, and bowed order and error gradients. As new items are presented, the pattern of previously stored items remains invariant in the sense that relative activations remain constant through time. This invariant temporal order code enables all possible groupings of sequential events to be stably learned and remembered in real time, even as new events perturb the system. Such competence is needed to design self-organizing temporal recognition and planning systems in which any subsequence of events may need to be categorized in order to control and predict future behavior or external events. STORE models show how arbitrary event sequences may be invariantly stored, including repeated events. A preprocessor interacts with the working memory to represent event repeats in spatially separate locations. It is shown why at least two processing levels are needed to invariantly store events presented with variable durations and interstimulus intervals. It is also shown how network parameters control the type and shape of primacy, recency, or bowed temporal order gradients that will be stored. Received: 3 November 1992/Accepted in revised form: 2 May 1994     

Low degree metabolites explain essential reactions and enhance modularity in biological networks

Background  

Recently there has been a lot of interest in identifying modules at the level of genetic and metabolic networks of organisms, as well as in identifying single genes and reactions that are essential for the organism. A goal of computational and systems biology is to go beyond identification towards an explanation of specific modules and essential genes and reactions in terms of specific structural or evolutionary constraints.     

Modularity and integration in the hominoid scapula

In this paper, several hypotheses of morphological integration within the hominoid (ape) scapula are tested. In particular, whether the scapula represents a set of developmental tissues sharing tight correlations between constituent parts (i.e., highly integrated) or is more modularly organized (i.e., covariation is greater within regions than between) is tested. Whether the patterns of integration in the scapula have changed over phylogenetic time or in response to selective forces is also examined. Results from two different analyses (matrix correlations and edge deviance) indicate traits comprising the blade and acromion, and to a weaker degree the glenoid, correlate highly with each other. The coracoid exhibits more independence from other parts of the scapula, perhaps reflecting its distinct evolutionary developmental history. Overall, similarity in species-specific patterns of correlation was high between all taxa. Correlation matrix similarity was significantly correlated with functional similarity and morphological distance, but not with phylogenetic distance. These results are congruent with other studies of integration that suggest correlation patterns remain stable over evolutionary time. There are changes associated with phylogeny, but the tight link between functional similarity and phylogenetic distance at this level of comparison presents possible challenges to interpretation. Overall similarities in the pattern of integration in all taxa might be better interpreted as relative strengthening or weakening of trait correlations rather than broadscale changes in the pattern of relationship between developmental regions. Larger sample sizes with greater taxonomic/functional breadth, and finer scale analyses of patterns of correlation are needed to test these hypotheses further.     

Systems biology beyond degree, hubs and scale-free networks: the case for multiple metrics in complex networks

Modeling and topological analysis of networks in biological and other complex systems, must venture beyond the limited consideration of very few network metrics like degree, betweenness or assortativity. A proper identification of informative and redundant entities from many different metrics, using recently demonstrated techniques, is essential. A holistic comparison of networks and growth models is best achieved only with the use of such methods.     

Biological network comparison using graphlet degree distribution

MOTIVATION: Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally infeasible, and thus heuristics, such as the degree distribution, clustering coefficient, diameter, and relative graphlet frequency distribution have been sought. It is easy to demonstrate that two networks are different by simply showing a short list of properties in which they differ. It is much harder to show that two networks are similar, as it requires demonstrating their similarity in all of their exponentially many properties. Clearly, it is computationally prohibitive to analyze all network properties, but the larger the number of constraints we impose in determining network similarity, the more likely it is that the networks will truly be similar. RESULTS: We introduce a new systematic measure of a network's local structure that imposes a large number of similarity constraints on networks being compared. In particular, we generalize the degree distribution, which measures the number of nodes 'touching' k edges, into distributions measuring the number of nodes 'touching' k graphlets, where graphlets are small connected non-isomorphic subgraphs of a large network. Our new measure of network local structure consists of 73 graphlet degree distributions of graphlets with 2-5 nodes, but it is easily extendible to a greater number of constraints (i.e. graphlets), if necessary, and the extensions are limited only by the available CPU. Furthermore, we show a way to combine the 73 graphlet degree distributions into a network 'agreement' measure which is a number between 0 and 1, where 1 means that networks have identical distributions and 0 means that they are far apart. Based on this new network agreement measure, we show that almost all of the 14 eukaryotic PPI networks, including human, resulting from various high-throughput experimental techniques, as well as from curated databases, are better modeled by geometric random graphs than by Erd?s-Rény, random scale-free, or Barabási-Albert scale-free networks. AVAILABILITY: Software executables are available upon request.     

Influence of degree correlations on network structure and stability in protein-protein interaction networks

Background  

The existence of negative correlations between degrees of interacting proteins is being discussed since such negative degree correlations were found for the large-scale yeast protein-protein interaction (PPI) network of Ito et al. More recent studies observed no such negative correlations for high-confidence interaction sets. In this article, we analyzed a range of experimentally derived interaction networks to understand the role and prevalence of degree correlations in PPI networks. We investigated how degree correlations influence the structure of networks and their tolerance against perturbations such as the targeted deletion of hubs.