Failure tolerance of motif structure in biological networks

Complex networks serve as generic models for many biological systems that have been shown to share a number of common structural properties such as power-law degree distribution and small-worldness. Real-world networks are composed of building blocks called motifs that are indeed specific subgraphs of (usually) small number of nodes. Network motifs are important in the functionality of complex networks, and the role of some motifs such as feed-forward loop in many biological networks has been heavily studied. On the other hand, many biological networks have shown some degrees of robustness in terms of their efficiency and connectedness against failures in their components. In this paper we investigated how random and systematic failures in the edges of biological networks influenced their motif structure. We considered two biological networks, namely, protein structure network and human brain functional network. Furthermore, we considered random failures as well as systematic failures based on different strategies for choosing candidate edges for removal. Failure in the edges tipping to high degree nodes had the most destructive role in the motif structure of the networks by decreasing their significance level, while removing edges that were connected to nodes with high values of betweenness centrality had the least effect on the significance profiles. In some cases, the latter caused increase in the significance levels of the motifs.     

Rich Club Organization of Macaque Cerebral Cortex and Its Role in Network Communication

Graph-theoretical analysis of brain connectivity data has revealed significant features of brain network organization across a range of species. Consistently, large-scale anatomical networks exhibit highly nonrandom attributes including an efficient small world modular architecture, with distinct network communities that are interlinked by hub regions. The functional importance of hubs motivates a closer examination of their mutual interconnections, specifically to examine the hypothesis that hub regions are more densely linked than expected based on their degree alone, i.e. forming a central rich club. Extending recent findings of rich club topology in the cat and human brain, this report presents evidence for the existence of rich club organization in the cerebral cortex of a non-human primate, the macaque monkey, based on a connectivity data set representing a collation of numerous tract tracing studies. Rich club regions comprise portions of prefrontal, parietal, temporal and insular cortex and are widely distributed across network communities. An analysis of network motifs reveals that rich club regions tend to form star-like configurations, indicative of their central embedding within sets of nodes. In addition, rich club nodes and edges participate in a large number of short paths across the network, and thus contribute disproportionately to global communication. As rich club regions tend to attract and disperse communication paths, many of the paths follow a characteristic pattern of first increasing and then decreasing node degree. Finally, the existence of non-reciprocal projections imposes a net directional flow of paths into and out of the rich club, with some regions preferentially attracting and others dispersing signals. Overall, the demonstration of rich club organization in a non-human primate contributes to our understanding of the network principles underlying neural connectivity in the mammalian brain, and further supports the hypothesis that rich club regions and connections have a central role in global brain communication.     

Do Brain Networks Evolve by Maximizing Their Information Flow Capacity?

We propose a working hypothesis supported by numerical simulations that brain networks evolve based on the principle of the maximization of their internal information flow capacity. We find that synchronous behavior and capacity of information flow of the evolved networks reproduce well the same behaviors observed in the brain dynamical networks of Caenorhabditis elegans and humans, networks of Hindmarsh-Rose neurons with graphs given by these brain networks. We make a strong case to verify our hypothesis by showing that the neural networks with the closest graph distance to the brain networks of Caenorhabditis elegans and humans are the Hindmarsh-Rose neural networks evolved with coupling strengths that maximize information flow capacity. Surprisingly, we find that global neural synchronization levels decrease during brain evolution, reflecting on an underlying global no Hebbian-like evolution process, which is driven by no Hebbian-like learning behaviors for some of the clusters during evolution, and Hebbian-like learning rules for clusters where neurons increase their synchronization.     

Colored motifs reveal computational building blocks in the C. elegans brain

Background

Complex networks can often be decomposed into less complex sub-networks whose structures can give hints about the functional organization of the network as a whole. However, these structural motifs can only tell one part of the functional story because in this analysis each node and edge is treated on an equal footing. In real networks, two motifs that are topologically identical but whose nodes perform very different functions will play very different roles in the network.

Methodology/Principal Findings

Here, we combine structural information derived from the topology of the neuronal network of the nematode C. elegans with information about the biological function of these nodes, thus coloring nodes by function. We discover that particular colorations of motifs are significantly more abundant in the worm brain than expected by chance, and have particular computational functions that emphasize the feed-forward structure of information processing in the network, while evading feedback loops. Interneurons are strongly over-represented among the common motifs, supporting the notion that these motifs process and transduce the information from the sensor neurons towards the muscles. Some of the most common motifs identified in the search for significant colored motifs play a crucial role in the system of neurons controlling the worm''s locomotion.

Conclusions/Significance

The analysis of complex networks in terms of colored motifs combines two independent data sets to generate insight about these networks that cannot be obtained with either data set alone. The method is general and should allow a decomposition of any complex networks into its functional (rather than topological) motifs as long as both wiring and functional information is available.     

Brain Anatomical Network and Intelligence

Intuitively, higher intelligence might be assumed to correspond to more efficient information transfer in the brain, but no direct evidence has been reported from the perspective of brain networks. In this study, we performed extensive analyses to test the hypothesis that individual differences in intelligence are associated with brain structural organization, and in particular that higher scores on intelligence tests are related to greater global efficiency of the brain anatomical network. We constructed binary and weighted brain anatomical networks in each of 79 healthy young adults utilizing diffusion tensor tractography and calculated topological properties of the networks using a graph theoretical method. Based on their IQ test scores, all subjects were divided into general and high intelligence groups and significantly higher global efficiencies were found in the networks of the latter group. Moreover, we showed significant correlations between IQ scores and network properties across all subjects while controlling for age and gender. Specifically, higher intelligence scores corresponded to a shorter characteristic path length and a higher global efficiency of the networks, indicating a more efficient parallel information transfer in the brain. The results were consistently observed not only in the binary but also in the weighted networks, which together provide convergent evidence for our hypothesis. Our findings suggest that the efficiency of brain structural organization may be an important biological basis for intelligence.     

The development of a noisy brain

Early in life, brain development carries with it a large number of structural changes that impact the functional interactions of distributed neuronal networks. Such changes enhance information processing capacity, moving the brain from a deterministic system to one that is more stochastic. The evidence from empirical studies with EEG and functional MRI suggests that this stochastic property is a result of an increased number of possible functional network configurations for a given situation. This is captured in the variability of endogenous and evoked responses or "brain noise ". In empirical data from infants and children, brain noise increases with maturation and correlates positively with stable behavior and accuracy. The noise increase is best explained through increased noise from network level interactions with a concomitant decrease of local noise. In old adults, brain noise continues to change, although the pattern of changes is not as global as in early development. The relation between high brain noise and stable behavior is maintained, but the relationships differ by region, suggesting changes in local dynamics that then impact potential network configurations. These data, when considered in concert with our extant modeling work, suggest that maturational changes in brain noise represent the enhancement offunctional network potential--the brain's dynamic repertoire.     

CytoKavosh: A Cytoscape Plug-In for Finding Network Motifs in Large Biological Networks

Network motifs are small connected sub-graphs that have recently gathered much attention to discover structural behaviors of large and complex networks. Finding motifs with any size is one of the most important problems in complex and large networks. It needs fast and reliable algorithms and tools for achieving this purpose. CytoKavosh is one of the best choices for finding motifs with any given size in any complex network. It relies on a fast algorithm, Kavosh, which makes it faster than other existing tools. Kavosh algorithm applies some well known algorithmic features and includes tricky aspects, which make it an efficient algorithm in this field. CytoKavosh is a Cytoscape plug-in which supports us in finding motifs of given size in a network that is formerly loaded into the Cytoscape work-space (directed or undirected). High performance of CytoKavosh is achieved by dynamically linking highly optimized functions of Kavosh's C++ to the Cytoscape Java program, which makes this plug-in suitable for analyzing large biological networks. Some significant attributes of CytoKavosh is efficiency in time usage and memory and having no limitation related to the implementation in motif size. CytoKavosh is implemented in a visual environment Cytoscape that is convenient for the users to interact and create visual options to analyze the structural behavior of a network. This plug-in can work on any given network and is very simple to use and generates graphical results of discovered motifs with any required details. There is no specific Cytoscape plug-in, specific for finding the network motifs, based on original concept. So, we have introduced for the first time, CytoKavosh as the first plug-in, and we hope that this plug-in can be improved to cover other options to make it the best motif-analyzing tool.     

GAT: a graph-theoretical analysis toolbox for analyzing between-group differences in large-scale structural and functional brain networks

In recent years, graph theoretical analyses of neuroimaging data have increased our understanding of the organization of large-scale structural and functional brain networks. However, tools for pipeline application of graph theory for analyzing topology of brain networks is still lacking. In this report, we describe the development of a graph-analysis toolbox (GAT) that facilitates analysis and comparison of structural and functional network brain networks. GAT provides a graphical user interface (GUI) that facilitates construction and analysis of brain networks, comparison of regional and global topological properties between networks, analysis of network hub and modules, and analysis of resilience of the networks to random failure and targeted attacks. Area under a curve (AUC) and functional data analyses (FDA), in conjunction with permutation testing, is employed for testing the differences in network topologies; analyses that are less sensitive to the thresholding process. We demonstrated the capabilities of GAT by investigating the differences in the organization of regional gray-matter correlation networks in survivors of acute lymphoblastic leukemia (ALL) and healthy matched Controls (CON). The results revealed an alteration in small-world characteristics of the brain networks in the ALL survivors; an observation that confirm our hypothesis suggesting widespread neurobiological injury in ALL survivors. Along with demonstration of the capabilities of the GAT, this is the first report of altered large-scale structural brain networks in ALL survivors.     

Exploring the repertoire of RNA secondary motifs using graph theory; implications for RNA design

Understanding the structural repertoire of RNA is crucial for RNA genomics research. Yet current methods for finding novel RNAs are limited to small or known RNA families. To expand known RNA structural motifs, we develop a two-dimensional graphical representation approach for describing and estimating the size of RNA’s secondary structural repertoire, including naturally occurring and other possible RNA motifs. We employ tree graphs to describe RNA tree motifs and more general (dual) graphs to describe both RNA tree and pseudoknot motifs. Our estimates of RNA’s structural space are vastly smaller than the nucleotide sequence space, suggesting a new avenue for finding novel RNAs. Specifically our survey shows that known RNA trees and pseudoknots represent only a small subset of all possible motifs, implying that some of the ‘missing’ motifs may represent novel RNAs. To help pinpoint RNA-like motifs, we show that the motifs of existing functional RNAs are clustered in a narrow range of topological characteristics. We also illustrate the applications of our approach to the design of novel RNAs and automated comparison of RNA structures; we report several occurrences of RNA motifs within larger RNAs. Thus, our graph theory approach to RNA structures has implications for RNA genomics, structure analysis and design.     

Efficient sampling algorithm for estimating subgraph concentrations and detecting network motifs

SUMMARY: Biological and engineered networks have recently been shown to display network motifs: a small set of characteristic patterns that occur much more frequently than in randomized networks with the same degree sequence. Network motifs were demonstrated to play key information processing roles in biological regulation networks. Existing algorithms for detecting network motifs act by exhaustively enumerating all subgraphs with a given number of nodes in the network. The runtime of such algorithms increases strongly with network size. Here, we present a novel algorithm that allows estimation of subgraph concentrations and detection of network motifs at a runtime that is asymptotically independent of the network size. This algorithm is based on random sampling of subgraphs. Network motifs are detected with a surprisingly small number of samples in a wide variety of networks. Our method can be applied to estimate the concentrations of larger subgraphs in larger networks than was previously possible with exhaustive enumeration algorithms. We present results for high-order motifs in several biological networks and discuss their possible functions. AVAILABILITY: A software tool for estimating subgraph concentrations and detecting network motifs (mfinder 1.1) and further information is available at http://www.weizmann.ac.il/mcb/UriAlon/     

Do motifs reflect evolved function?--No convergent evolution of genetic regulatory network subgraph topologies

Methods that analyse the topological structure of networks have recently become quite popular. Whether motifs (subgraph patterns that occur more often than in randomized networks) have specific functions as elementary computational circuits has been cause for debate. As the question is difficult to resolve with currently available biological data, we approach the issue using networks that abstractly model natural genetic regulatory networks (GRNs) which are evolved to show dynamical behaviors. Specifically one group of networks was evolved to be capable of exhibiting two different behaviors ("differentiation") in contrast to a group with a single target behavior. In both groups we find motif distribution differences within the groups to be larger than differences between them, indicating that evolutionary niches (target functions) do not necessarily mold network structure uniquely. These results show that variability operators can have a stronger influence on network topologies than selection pressures, especially when many topologies can create similar dynamics. Moreover, analysis of motif functional relevance by lesioning did not suggest that motifs were of greater importance to the functioning of the network than arbitrary subgraph patterns. Only when drastically restricting network size, so that one motif corresponds to a whole functionally evolved network, was preference for particular connection patterns found. This suggests that in non-restricted, bigger networks, entanglement with the rest of the network hinders topological subgraph analysis.     

Predicting candidate genomic sequences that correspond to synthetic functional RNA motifs

Riboswitches and RNA interference are important emerging mechanisms found in many organisms to control gene expression. To enhance our understanding of such RNA roles, finding small regulatory motifs in genomes presents a challenge on a wide scale. Many simple functional RNA motifs have been found by in vitro selection experiments, which produce synthetic target-binding aptamers as well as catalytic RNAs, including the hammerhead ribozyme. Motivated by the prediction of Piganeau and Schroeder [(2003) Chem. Biol., 10, 103–104] that synthetic RNAs may have natural counterparts, we develop and apply an efficient computational protocol for identifying aptamer-like motifs in genomes. We define motifs from the sequence and structural information of synthetic aptamers, search for sequences in genomes that will produce motif matches, and then evaluate the structural stability and statistical significance of the potential hits. Our application to aptamers for streptomycin, chloramphenicol, neomycin B and ATP identifies 37 candidate sequences (in coding and non-coding regions) that fold to the target aptamer structures in bacterial and archaeal genomes. Further energetic screening reveals that several candidates exhibit energetic properties and sequence conservation patterns that are characteristic of functional motifs. Besides providing candidates for experimental testing, our computational protocol offers an avenue for expanding natural RNA's functional repertoire.     

Dynamic properties of network motifs contribute to biological network organization

Biological networks, such as those describing gene regulation, signal transduction, and neural synapses, are representations of large-scale dynamic systems. Discovery of organizing principles of biological networks can be enhanced by embracing the notion that there is a deep interplay between network structure and system dynamics. Recently, many structural characteristics of these non-random networks have been identified, but dynamical implications of the features have not been explored comprehensively. We demonstrate by exhaustive computational analysis that a dynamical property—stability or robustness to small perturbations—is highly correlated with the relative abundance of small subnetworks (network motifs) in several previously determined biological networks. We propose that robust dynamical stability is an influential property that can determine the non-random structure of biological networks.     

Efficient detection of network motifs

Motifs in a given network are small connected subnetworks that occur in significantly higher frequencies than would be expected in random networks. They have recently gathered much attention as a concept to uncover structural design principles of complex networks. Kashtan et al. [Bioinformatics, 2004] proposed a sampling algorithm for performing the computationally challenging task of detecting network motifs. However, among other drawbacks, this algorithm suffers from a sampling bias and scales poorly with increasing subgraph size. Based on a detailed analysis of the previous algorithm, we present a new algorithm for network motif detection which overcomes these drawbacks. Furthermore, we present an efficient new approach for estimating the frequency of subgraphs in random networks that, in contrast to previous approaches, does not require the explicit generation of random networks. Experiments on a testbed of biological networks show our new algorithms to be orders of magnitude faster than previous approaches, allowing for the detection of larger motifs in bigger networks than previously possible and thus facilitating deeper insight into the field     

Evolutionarily conserved networks of residues mediate allosteric communication in proteins

A fundamental goal in cellular signaling is to understand allosteric communication, the process by which signals originating at one site in a protein propagate reliably to affect distant functional sites. The general principles of protein structure that underlie this process remain unknown. Here, we describe a sequence-based statistical method for quantitatively mapping the global network of amino acid interactions in a protein. Application of this method for three structurally and functionally distinct protein families (G protein-coupled receptors, the chymotrypsin class of serine proteases and hemoglobins) reveals a surprisingly simple architecture for amino acid interactions in each protein family: a small subset of residues forms physically connected networks that link distant functional sites in the tertiary structure. Although small in number, residues comprising the network show excellent correlation with the large body of mechanistic data available for each family. The data suggest that evolutionarily conserved sparse networks of amino acid interactions represent structural motifs for allosteric communication in proteins.     

In silico evolution of functional modules in biochemical networks

Understanding the large reaction networks found in biological systems is a daunting task. One approach is to divide a network into more manageable smaller modules, thus simplifying the problem. This is a common strategy used in engineering. However, the process of identifying biological modules is still in its infancy and very little is understood about the range and capabilities of motif structures found in biological modules. In order to delineate these modules, a library of functional motifs has been generated via in silico evolution techniques. On the basis of their functional forms, networks were evolved from four broad areas: oscillators, bistable switches, homeostatic systems and frequency filters. Some of these motifs were constructed from simple mass action kinetics, others were based on Michaelis-Menten kinetics as found in protein/protein networks and the remainder were based on Hill equations as found in gene/protein interaction networks. The purpose of the study is to explore the capabilities of different network architectures and the rich variety of functional forms that can be generated. Ultimately, the library may be used to delineate functional motifs in real biological networks.     

RAG: RNA-As-Graphs database--concepts, analysis, and features

MOTIVATION: Understanding RNA's structural diversity is vital for identifying novel RNA structures and pursuing RNA genomics initiatives. By classifying RNA secondary motifs based on correlations between conserved RNA secondary structures and functional properties, we offer an avenue for predicting novel motifs. Although several RNA databases exist, no comprehensive schemes are available for cataloguing the range and diversity of RNA's structural repertoire. RESULTS: Our RNA-As-Graphs (RAG) database describes and ranks all mathematically possible (including existing and candidate) RNA secondary motifs on the basis of graphical enumeration techniques. We represent RNA secondary structures as two-dimensional graphs (networks), specifying the connectivity between RNA secondary structural elements, such as loops, bulges, stems and junctions. We archive RNA tree motifs as 'tree graphs' and other RNAs, including pseudoknots, as general 'dual graphs'. All RNA motifs are catalogued by graph vertex number (a measure of sequence length) and ranked by topological complexity. The RAG inventory immediately suggests candidates for novel RNA motifs, either naturally occurring or synthetic, and thereby might stimulate the prediction and design of novel RNA motifs. AVAILABILITY: The database is accessible on the web at http://monod.biomath.nyu.edu/rna     

The S4 genome segment of baboon reovirus is bicistronic and encodes a novel fusion-associated small transmembrane protein

We demonstrate that the S4 genome segment of baboon reovirus (BRV) contains two sequential partially overlapping open reading frames (ORFs), both of which are functional in vitro and in virus-infected cells. The 15-kDa gene product (p15) of the 5"-proximal ORF induces efficient cell-cell fusion when expressed by itself in transfected cells, suggesting that p15 is the only viral protein required for induction of syncytium formation by BRV. The p15 protein is a small, hydrophobic, basic, integral membrane protein, properties shared with the p10 fusion-associated small transmembrane (FAST) proteins encoded by avian reovirus and Nelson Bay reovirus. As with p10, the BRV p15 protein is also a nonstructural protein and, therefore, is not involved in virus entry. Sequence analysis indicates that p15 shares no significant sequence similarity with the p10 FAST proteins and contains a unique repertoire and arrangement of sequence-predicted structural and functional motifs. These motifs include a functional N-terminal myristylation consensus sequence, an N-proximal proline-rich motif, two potential transmembrane domains, and an intervening polybasic region. The unique structural properties of p15 suggest that this protein is a novel member of the new family of FAST proteins.