A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks

The human brain is organized in functional modules. Such an organization presents a basic conundrum: Modules ought to be sufficiently independent to guarantee functional specialization and sufficiently connected to bind multiple processors for efficient information transfer. It is commonly accepted that small-world architecture of short paths and large local clustering may solve this problem. However, there is intrinsic tension between shortcuts generating small worlds and the persistence of modularity, a global property unrelated to local clustering. Here, we present a possible solution to this puzzle. We first show that a modified percolation theory can define a set of hierarchically organized modules made of strong links in functional brain networks. These modules are "large-world" self-similar structures and, therefore, are far from being small-world. However, incorporating weaker ties to the network converts it into a small world preserving an underlying backbone of well-defined modules. Remarkably, weak ties are precisely organized as predicted by theory maximizing information transfer with minimal wiring cost. This trade-off architecture is reminiscent of the "strength of weak ties" crucial concept of social networks. Such a design suggests a natural solution to the paradox of efficient information flow in the highly modular structure of the brain.     

A metabolic network in the evolutionary context: multiscale structure and modularity

The enormous complexity of biological networks has led to the suggestion that networks are built of modules that perform particular functions and are "reused" in evolution in a manner similar to reusable domains in protein structures or modules of electronic circuits. Analysis of known biological networks has revealed several modules, many of which have transparent biological functions. However, it remains to be shown that identified structural modules constitute evolutionary building blocks, independent and easily interchangeable units. An alternative possibility is that evolutionary modules do not match structural modules. To investigate the structure of evolutionary modules and their relationship to functional ones, we integrated a metabolic network with evolutionary associations between genes inferred from comparative genomics. The resulting metabolic-genomic network places metabolic pathways into evolutionary and genomic context, thereby revealing previously unknown components and modules. We analyzed the integrated metabolic-genomic network on three levels: macro-, meso-, and microscale. The macroscale level demonstrates strong associations between neighboring enzymes and between enzymes that are distant on the network but belong to the same linear pathway. At the mesoscale level, we identified evolutionary metabolic modules and compared them with traditional metabolic pathways. Although, in some cases, there is almost exact correspondence, some pathways are split into independent modules. On the microscale level, we observed high association of enzyme subunits and weak association of isoenzymes independently catalyzing the same reaction. This study shows that evolutionary modules, rather than pathways, may be thought of as regulatory and functional units in bacterial genomes.     

Resolution limit in community detection

Detecting community structure is fundamental for uncovering the links between structure and function in complex networks and for practical applications in many disciplines such as biology and sociology. A popular method now widely used relies on the optimization of a quantity called modularity, which is a quality index for a partition of a network into communities. We find that modularity optimization may fail to identify modules smaller than a scale which depends on the total size of the network and on the degree of interconnectedness of the modules, even in cases where modules are unambiguously defined. This finding is confirmed through several examples, both in artificial and in real social, biological, and technological networks, where we show that modularity optimization indeed does not resolve a large number of modules. A check of the modules obtained through modularity optimization is thus necessary, and we provide here key elements for the assessment of the reliability of this community detection method.     

Process-based network decomposition reveals backbone motif structure

A central challenge in systems biology today is to understand the network of interactions among biomolecules and, especially, the organizing principles underlying such networks. Recent analysis of known networks has identified small motifs that occur ubiquitously, suggesting that larger networks might be constructed in the manner of electronic circuits by assembling groups of these smaller modules. Using a unique process-based approach to analyzing such networks, we show for two cell-cycle networks that each of these networks contains a giant backbone motif spanning all the network nodes that provides the main functional response. The backbone is in fact the smallest network capable of providing the desired functionality. Furthermore, the remaining edges in the network form smaller motifs whose role is to confer stability properties rather than provide function. The process-based approach used in the above analysis has additional benefits: It is scalable, analytic (resulting in a single analyzable expression that describes the behavior), and computationally efficient (all possible minimal networks for a biological process can be identified and enumerated).     

Modularity of stress response evolution

Responses to extracellular stress directly confer survival fitness by means of complex regulatory networks. Despite their complexity, the networks must be evolvable because of changing ecological and environmental pressures. Although the regulatory networks underlying stress responses are characterized extensively, their mechanism of evolution remains poorly understood. Here, we examine the evolution of three candidate stress response networks (chemotaxis, competence for DNA uptake, and endospore formation) by analyzing their phylogenetic distribution across several hundred diverse bacterial and archaeal lineages. We report that genes in the chemotaxis and sporulation networks group into well defined evolutionary modules with distinct functions, phenotypes, and substitution rates as compared with control sets of randomly chosen genes. The evolutionary modules vary in both number and cohesiveness among the three pathways. Chemotaxis has five coherent modules whose distribution among species shows a clear pattern of interdependence and rewiring. Sporulation, by contrast, is nearly monolithic and seems to be inherited vertically, with three weak modules constituting early and late stages of the pathway. Competence does not seem to exhibit well defined modules either at or below the pathway level. Many of the detected modules are better understood in engineering terms than in protein functional terms, as we demonstrate using a control-based ontology that classifies gene function according to roles such as "sensor," "regulator," and "actuator." Moreover, we show that combinations of the modules predict phenotype, yet surprisingly do not necessarily correlate with phylogenetic inheritance. The architectures of these three pathways are therefore emblematic of different modes and constraints on evolution.     

From molecular to modular cardiology. How to interpret the millions of data that came out from large scale analysis of gene expression?

Cell biology is in transition from reductionism, to a more integrated science which is now preoccupied by molecular interactions acting in modules. Large-scale quantitative analysis of gene expression, including cDNA microarrays and proteomic analysis, is now applied to heart failure and atherosclerosis. The technology is still at the beginning and is limited by variations in the array platforms and gene products as well as sensitivity or specificity of the selected probes. These limitations are progressively going to be reduced, but still they do exist. Biological systems are scale free networks made from genes, proteins or traits that interact one another and form networks and functional modules. Networks emerge through the addition of new nodes which are preferentially attached to more connected nodes to form hubs, according to the "rich-gets-richer" mechanism, and there are large networks which include central genes (nexus). Both hubs and nexus are attractive candidate for targeting new therapy. An important study from King JY et al. (Physiol Genomics 2005; 23: 103-18) exemplifies this concept by showing the first realistic pathways to understand atherosclerosis. The 4 steps of the design are based on histological grading and microarrays analysis and include an association network constructed from PubMed and the construction of sub-networks in which genes whose expression was differentially regulated were indicated. Connectivity analysis networks revealed new important modular pathways. In heart failure, no attempts have been made to organize the data into functional modulus. Since the causes of heart failure are well documented, the problem is to identify functional modules responsible for myocardial dysfunction. Several potential functional modules can be identified so far. Indeed, cardiac remodeling results from two types of changes in gene expression, namelly the reexpression of the foetal programme which has a mechanical origin and several well documented interfering determinants that modified the basic remodelling, including senescence, obesity, diabetes, ischemia, and the neurohormonal reaction.     

An information-theoretic framework for resolving community structure in complex networks

To understand the structure of a large-scale biological, social, or technological network, it can be helpful to decompose the network into smaller subunits or modules. In this article, we develop an information-theoretic foundation for the concept of modularity in networks. We identify the modules of which the network is composed by finding an optimal compression of its topology, capitalizing on regularities in its structure. We explain the advantages of this approach and illustrate them by partitioning a number of real-world and model networks.     

Cognitive relevance of the community structure of the human brain functional coactivation network

There is growing interest in the complex topology of human brain functional networks, often measured using resting-state functional MRI (fMRI). Here, we used a meta-analysis of the large primary literature that used fMRI or PET to measure task-related activation (>1,600 studies; 1985–2010). We estimated the similarity (Jaccard index) of the activation patterns across experimental tasks between each pair of 638 brain regions. This continuous coactivation matrix was used to build a weighted graph to characterize network topology. The coactivation network was modular, with occipital, central, and default-mode modules predominantly coactivated by specific cognitive domains (perception, action, and emotion, respectively). It also included a rich club of hub nodes, located in parietal and prefrontal cortex and often connected over long distances, which were coactivated by a diverse range of experimental tasks. Investigating the topological role of edges between a deactivated and an activated node, we found that such competitive interactions were most frequent between nodes in different modules or between an activated rich-club node and a deactivated peripheral node. Many aspects of the coactivation network were convergent with a connectivity network derived from resting state fMRI data (n = 27, healthy volunteers); although the connectivity network was more parsimoniously connected and differed in the anatomical locations of some hubs. We conclude that the community structure of human brain networks is relevant to cognitive function. Deactivations may play a role in flexible reconfiguration of the network according to cognitive demand, varying the integration between modules, and between the periphery and a central rich club.     

Transmitter and receiver modules in bacterial signaling proteins.

Prokaryotes are capable of sophisticated sensory behaviors. We have detected sequence motifs in bacterial signaling proteins that may act as transmitter or receiver modules in mediating protein-protein communication. These modules appear to retain their functional identities in many protein hosts, implying that they are structurally independent elements. We propose that the fundamental activity characterizing these domains is specific recognition and association of matched modules, accompanied by conformational changes in one or both of the interacting elements. Signal propagation is a natural consequence of this behavior. The versatility of this information-processing strategy is evident in the chemotaxis machinery of Escherichia coli, where proteins containing transmitters or receivers are linked in "dyadic relays" to form complex signaling networks.     

Genome evolution reveals biochemical networks and functional modules

The analysis of completely sequenced genomes uncovers an astonishing variability between species in terms of gene content and order. During genome history, the genes are frequently rear-ranged, duplicated, lost, or transferred horizontally between genomes. These events appear to be stochastic, yet they are under selective constraints resulting from the functional interactions between genes. These genomic constraints form the basis for a variety of techniques that employ systematic genome comparisons to predict functional associations among genes. The most powerful techniques to date are based on conserved gene neighborhood, gene fusion events, and common phylogenetic distributions of gene families. Here we show that these techniques, if integrated quantitatively and applied to a sufficiently large number of genomes, have reached a resolution which allows the characterization of function at a higher level than that of the individual gene: global modularity becomes detectable in a functional protein network. In Escherichia coli, the predicted modules can be bench-marked by comparison to known metabolic pathways. We found as many as 74% of the known metabolic enzymes clustering together in modules, with an average pathway specificity of at least 84%. The modules extend beyond metabolism, and have led to hundreds of reliable functional predictions both at the protein and pathway level. The results indicate that modularity in protein networks is intrinsically encoded in present-day genomes.     

Functionalization of a protosynaptic gene expression network

Assembly of a functioning neuronal synapse requires the precisely coordinated synthesis of many proteins. To understand the evolution of this complex cellular machine, we tracked the developmental expression patterns of a core set of conserved synaptic genes across a representative sampling of the animal kingdom. Coregulation, as measured by correlation of gene expression over development, showed a marked increase as functional nervous systems emerged. In the earliest branching animal phyla (Porifera), in which a nearly complete set of synaptic genes exists in the absence of morphological synapses, these "protosynaptic" genes displayed a lack of global coregulation although small modules of coexpressed genes are readily detectable by using network analysis techniques. These findings suggest that functional synapses evolved by exapting preexisting cellular machines, likely through some modification of regulatory circuitry. Evolutionarily ancient modules continue to operate seamlessly within the synapses of modern animals. This work shows that the application of network techniques to emerging genomic and expression data can provide insights into the evolution of complex cellular machines such as the synapse.     

Networks of spatial genetic variation across species

Spatial patterns of genetic variation provide information central to many ecological, evolutionary, and conservation questions. This spatial variability has traditionally been analyzed through summary statistics between pairs of populations, therefore missing the simultaneous influence of all populations. More recently, a network approach has been advocated to overcome these limitations. This network approach has been applied to a few cases limited to a single species at a time. The question remains whether similar patterns of spatial genetic variation and similar functional roles for specific patches are obtained for different species. Here we study the networks of genetic variation of four Mediterranean woody plant species inhabiting the same habitat patches in a highly fragmented forest mosaic in Southern Spain. Three of the four species show a similar pattern of genetic variation with well-defined modules or groups of patches holding genetically similar populations. These modules can be thought of as the long-sought-after, evolutionarily significant units or management units. The importance of each patch for the cohesion of the entire network, though, is quite different across species. This variation creates a tremendous challenge for the prioritization of patches to conserve the genetic variation of multispecies assemblages.     

Directed evolution can rapidly improve the activity of chimeric assembly-line enzymes

Nonribosomal peptides (NRPs) are produced by NRP synthetase (NRPS) enzymes that function as molecular assembly lines. The modular architecture of NRPSs suggests that a domain responsible for activating a building block could be replaced with a domain from a foreign NRPS to create a chimeric assembly line that produces a new variant of a natural NRP. However, such chimeric NRPS modules are often heavily impaired, impeding efforts to create novel NRP variants by swapping domains from different modules or organisms. Here we show that impaired chimeric NRPSs can be functionally restored by directed evolution. Using rounds of mutagenesis coupled with in vivo screens for NRP production, we rapidly isolated variants of two different chimeric NRPSs with approximately 10-fold improvements in enzyme activity and product yield, including one that produces new derivatives of the potent NRP/polyketide antibiotic andrimid. Because functional restoration in these examples required only modest library sizes (10(3) to 10(4) clones) and three or fewer rounds of screening, our approach may be widely applicable even for NRPSs from genetically challenging hosts.