The relative efficiency of modular and non-modular networks of different size

Most biological networks are modular but previous work with small model networks has indicated that modularity does not necessarily lead to increased functional efficiency. Most biological networks are large, however, and here we examine the relative functional efficiency of modular and non-modular neural networks at a range of sizes. We conduct a detailed analysis of efficiency in networks of two size classes: ‘small’ and ‘large’, and a less detailed analysis across a range of network sizes. The former analysis reveals that while the modular network is less efficient than one of the two non-modular networks considered when networks are small, it is usually equally or more efficient than both non-modular networks when networks are large. The latter analysis shows that in networks of small to intermediate size, modular networks are much more efficient that non-modular networks of the same (low) connective density. If connective density must be kept low to reduce energy needs for example, this could promote modularity. We have shown how relative functionality/performance scales with network size, but the precise nature of evolutionary relationship between network size and prevalence of modularity will depend on the costs of connectivity.     

Revisiting the variation of clustering coefficient of biological networks suggests new modular structure

ABSTRACT: A central idea in biology is the hierarchical organization of cellular processes. A commonly used method to identify the hierarchical modular organization of network relies on detecting a global signature known as variation of clustering coefficient (so-called modularity scaling). Although several studies have suggested other possible origins of this signature, it is still widely used nowadays to identify hierarchical modularity, especially in the analysis of biological networks. Therefore, a further and systematical investigation of this signature for different types of biological networks is necessary. RESULTS: We analyzed a variety of biological networks and found that the commonly used signature of hierarchical modularity is actually the reflection of spoke-like topology, suggesting a different view of network architecture. We proved that the existence of super-hubs is the origin that the clustering coefficient of a node follows a particular scaling law with degree k in metabolic networks. To study the modularity of biological networks, we systematically investigated the relationship between repulsion of hubs and variation of clustering coefficient. We provided direct evidences for repulsion between hubs being the underlying origin of the variation of clustering coefficient, and found that for biological networks having no anti-correlation between hubs, such as gene co-expression network, the clustering coefficient doesn't show dependence of degree. CONCLUSIONS: Here we have shown that the variation of clustering coefficient is neither sufficient nor exclusive for a network to be hierarchical. Our results suggest the existence of spoke-like modules as opposed to "deterministic model" of hierarchical modularity, and suggest the need to reconsider the organizational principle of biological hierarchy.     

以发育模块重复征用和整合为基础的进化创新机制

进化新征的起源和分化是进化发育生物学研究的核心问题。通过对多细胞生物早期发育调控机制的比较分析,发现亲缘关系较远的生物所共有的一些形态特征受保守的发育调控程序调节（深同源性）。许多创新性状的发生是基于对预先存在的基因或发育调控模块的重复利用和整合。发育基因调控网络在结构和功能上高度模块化,因此不仅可以通过模块拆分和重复征用改变发育程式,而且也增强了调控网络自身的进化力。研究基因调控网络和发育系统的进化动态将有助于更深入地认识生物演化过程中创新性状发生和表型进化的分子机制。     

Relative impacts of environmental variation and evolutionary history on the nestedness and modularity of tree–herbivore networks

Nestedness and modularity are measures of ecological networks whose causative effects are little understood. We analyzed antagonistic plant–herbivore bipartite networks using common gardens in two contrasting environments comprised of aspen trees with differing evolutionary histories of defence against herbivores. These networks were tightly connected owing to a high level of specialization of arthropod herbivores that spend a large proportion of the life cycle on aspen. The gardens were separated by ten degrees of latitude with resultant differences in abiotic conditions. We evaluated network metrics and reported similar connectance between gardens but greater numbers of links per species in the northern common garden. Interaction matrices revealed clear nestedness, indicating subsetting of the bipartite interactions into specialist divisions, in both the environmental and evolutionary aspen groups, although nestedness values were only significant in the northern garden. Variation in plant vulnerability, measured as the frequency of herbivore specialization in the aspen population, was significantly partitioned by environment (common garden) but not by evolutionary origin of the aspens. Significant values of modularity were observed in all network matrices. Trait-matching indicated that growth traits, leaf morphology, and phenolic metabolites affected modular structure in both the garden and evolutionary groups, whereas extra-floral nectaries had little influence. Further examination of module configuration revealed that plant vulnerability explained considerable variance in web structure. The contrasting conditions between the two gardens resulted in bottom-up effects of the environment, which most strongly influenced the overall network architecture, however, the aspen groups with dissimilar evolutionary history also showed contrasting degrees of nestedness and modularity. Our research therefore shows that, while evolution does affect the structure of aspen–herbivore bipartite networks, the role of environmental variations is a dominant constraint.     

PERSPECTIVE: COMPLEX ADAPTATIONS AND THE EVOLUTION OF EVOLVABILITY

The problem of complex adaptations is studied in two largely disconnected research traditions: evolutionary biology and evolutionary computer science. This paper summarizes the results from both areas and compares their implications. In evolutionary computer science it was found that the Darwinian process of mutation, recombination and selection is not universally effective in improving complex systems like computer programs or chip designs. For adaptation to occur, these systems must possess “evolvability,” i.e., the ability of random variations to sometimes produce improvement. It was found that evolvability critically depends on the way genetic variation maps onto phenotypic variation, an issue known as the representation problem. The genotype-phenotype map determines the variability of characters, which is the propensity to vary. Variability needs to be distinguished from variations, which are the actually realized differences between individuals. The genotype-phenotype map is the common theme underlying such varied biological phenomena as genetic canalization, developmental constraints, biological versatility, developmental dissociability, and morphological integration. For evolutionary biology the representation problem has important implications: how is it that extant species acquired a genotype-phenotype map which allows improvement by mutation and selection? Is the genotype-phenotype map able to change in evolution? What are the selective forces, if any, that shape the genotype-phenotype map? We propose that the genotype-phenotype map can evolve by two main routes: epistatic mutations, or the creation of new genes. A common result for organismic design is modularity. By modularity we mean a genotype-phenotype map in which there are few pleiotropic effects among characters serving different functions, with pleiotropic effects falling mainly among characters that are part of a single functional complex. Such a design is expected to improve evolvability by limiting the interference between the adaptation of different functions. Several population genetic models are reviewed that are intended to explain the evolutionary origin of a modular design. While our current knowledge is insufficient to assess the plausibility of these models, they form the beginning of a framework for understanding the evolution of the genotype-phenotype map.     

Modularity in the evolution of yeast protein interaction network

Protein interaction networks are known to exhibit remarkable structures: scale-free and small-world and modular structures. To explain the evolutionary processes of protein interaction networks possessing scale-free and small-world structures, preferential attachment and duplication-divergence models have been proposed as mathematical models. Protein interaction networks are also known to exhibit another remarkable structural characteristic, modular structure. How the protein interaction networks became to exhibit modularity in their evolution? Here, we propose a hypothesis of modularity in the evolution of yeast protein interaction network based on molecular evolutionary evidence. We assigned yeast proteins into six evolutionary ages by constructing a phylogenetic profile. We found that all the almost half of hub proteins are evolutionarily new. Examining the evolutionary processes of protein complexes, functional modules and topological modules, we also found that member proteins of these modules tend to appear in one or two evolutionary ages. Moreover, proteins in protein complexes and topological modules show significantly low evolutionary rates than those not in these modules. Our results suggest a hypothesis of modularity in the evolution of yeast protein interaction network as systems evolution.     

Pairwise alignment of protein interaction networks.

With an ever-increasing amount of available data on protein-protein interaction (PPI) networks and research revealing that these networks evolve at a modular level, discovery of conserved patterns in these networks becomes an important problem. Although available data on protein-protein interactions is currently limited, recently developed algorithms have been shown to convey novel biological insights through employment of elegant mathematical models. The main challenge in aligning PPI networks is to define a graph theoretical measure of similarity between graph structures that captures underlying biological phenomena accurately. In this respect, modeling of conservation and divergence of interactions, as well as the interpretation of resulting alignments, are important design parameters. In this paper, we develop a framework for comprehensive alignment of PPI networks, which is inspired by duplication/divergence models that focus on understanding the evolution of protein interactions. We propose a mathematical model that extends the concepts of match, mismatch, and gap in sequence alignment to that of match, mismatch, and duplication in network alignment and evaluates similarity between graph structures through a scoring function that accounts for evolutionary events. By relying on evolutionary models, the proposed framework facilitates interpretation of resulting alignments in terms of not only conservation but also divergence of modularity in PPI networks. Furthermore, as in the case of sequence alignment, our model allows flexibility in adjusting parameters to quantify underlying evolutionary relationships. Based on the proposed model, we formulate PPI network alignment as an optimization problem and present fast algorithms to solve this problem. Detailed experimental results from an implementation of the proposed framework show that our algorithm is able to discover conserved interaction patterns very effectively, in terms of both accuracies and computational cost.     

The evolution of molecular genetic pathways and networks

There is growing interest in the evolutionary dynamics of molecular genetic pathways and networks, and the extent to which the molecular evolution of a gene depends on its position within a pathway or network, as well as over-all network topology. Investigations on the relationships between network organization, topological architecture and evolutionary dynamics provide intriguing hints as to how networks evolve. Recent studies also suggest that genetic pathway and network structures may influence the action of evolutionary forces, and may play a role in maintaining phenotypic robustness in organisms.     

Modularity in the genetic disease-phenotype network

Similar disease phenotypes are engendered as a result of the modular nature of gene networks; thus we hypothesized that all human genetic disease phenotypes appear in similar modular styles. Network representations of phenotypes make it possible to explore this hypothesis. We investigated the modularity of a network of genetic disease phenotypes. We computationally extracted phenotype modules and found that the modularity is well correlated with a physiological classification of human diseases. We also found correlations between the modularity and functional genomics as well as its connection to drug-target associations.     

The Evolutionary Origins of Hierarchy

Hierarchical organization—the recursive composition of sub-modules—is ubiquitous in biological networks, including neural, metabolic, ecological, and genetic regulatory networks, and in human-made systems, such as large organizations and the Internet. To date, most research on hierarchy in networks has been limited to quantifying this property. However, an open, important question in evolutionary biology is why hierarchical organization evolves in the first place. It has recently been shown that modularity evolves because of the presence of a cost for network connections. Here we investigate whether such connection costs also tend to cause a hierarchical organization of such modules. In computational simulations, we find that networks without a connection cost do not evolve to be hierarchical, even when the task has a hierarchical structure. However, with a connection cost, networks evolve to be both modular and hierarchical, and these networks exhibit higher overall performance and evolvability (i.e. faster adaptation to new environments). Additional analyses confirm that hierarchy independently improves adaptability after controlling for modularity. Overall, our results suggest that the same force–the cost of connections–promotes the evolution of both hierarchy and modularity, and that these properties are important drivers of network performance and adaptability. In addition to shedding light on the emergence of hierarchy across the many domains in which it appears, these findings will also accelerate future research into evolving more complex, intelligent computational brains in the fields of artificial intelligence and robotics.     

Evolution of networks for body plan patterning; interplay of modularity, robustness and evolvability

A major goal of evolutionary developmental biology (evo-devo) is to understand how multicellular body plans of increasing complexity have evolved, and how the corresponding developmental programs are genetically encoded. It has been repeatedly argued that key to the evolution of increased body plan complexity is the modularity of the underlying developmental gene regulatory networks (GRNs). This modularity is considered essential for network robustness and evolvability. In our opinion, these ideas, appealing as they may sound, have not been sufficiently tested. Here we use computer simulations to study the evolution of GRNs' underlying body plan patterning. We select for body plan segmentation and differentiation, as these are considered to be major innovations in metazoan evolution. To allow modular networks to evolve, we independently select for segmentation and differentiation. We study both the occurrence and relation of robustness, evolvability and modularity of evolved networks. Interestingly, we observed two distinct evolutionary strategies to evolve a segmented, differentiated body plan. In the first strategy, first segments and then differentiation domains evolve (SF strategy). In the second scenario segments and domains evolve simultaneously (SS strategy). We demonstrate that under indirect selection for robustness the SF strategy becomes dominant. In addition, as a byproduct of this larger robustness, the SF strategy is also more evolvable. Finally, using a combined functional and architectural approach, we determine network modularity. We find that while SS networks generate segments and domains in an integrated manner, SF networks use largely independent modules to produce segments and domains. Surprisingly, we find that widely used, purely architectural methods for determining network modularity completely fail to establish this higher modularity of SF networks. Finally, we observe that, as a free side effect of evolving segmentation and differentiation in combination, we obtained in-silico developmental mechanisms resembling mechanisms used in vertebrate development.     

Linear Motif-Mediated Interactions Have Contributed to the Evolution of Modularity in Complex Protein Interaction Networks

The modular architecture of protein-protein interaction (PPI) networks is evident in diverse species with a wide range of complexity. However, the molecular components that lead to the evolution of modularity in PPI networks have not been clearly identified. Here, we show that weak domain-linear motif interactions (DLIs) are more likely to connect different biological modules than strong domain-domain interactions (DDIs). This molecular division of labor is essential for the evolution of modularity in the complex PPI networks of diverse eukaryotic species. In particular, DLIs may compensate for the reduction in module boundaries that originate from increased connections between different modules in complex PPI networks. In addition, we show that the identification of biological modules can be greatly improved by including molecular characteristics of protein interactions. Our findings suggest that transient interactions have played a unique role in shaping the architecture and modularity of biological networks over the course of evolution.     

EXTINCTIONS IN HETEROGENEOUS ENVIRONMENTS AND THE EVOLUTION OF MODULARITY

Extinctions of local subpopulations are common events in nature. Here, we ask whether such extinctions can affect the design of biological networks within organisms over evolutionary timescales. We study the impact of extinction events on modularity of biological systems, a common architectural principle found on multiple scales in biology. As a model system, we use networks that evolve toward goals specified as desired input–output relationships. We use an extinction–recolonization model, in which metapopulations occupy and migrate between different localities. Each locality displays a different environmental condition (goal), but shares the same set of subgoals with other localities. We find that in the absence of extinction events, the evolved computational networks are typically highly optimal for their localities with a nonmodular structure. In contrast, when local populations go extinct from time to time, we find that the evolved networks are modular in structure. Modular circuitry is selected because of its ability to adapt rapidly to the conditions of the free niche following an extinction event. This rapid adaptation is mainly achieved through genetic recombination of modules between immigrants from neighboring local populations. This study suggests, therefore, that extinctions in heterogeneous environments promote the evolution of modular biological network structure, allowing local populations to effectively recombine their modules to recolonize niches.     

Connecting the sun to flowering in sunflower adaptation

Species living in seasonal environments often adaptively time their reproduction in response to photoperiod cues. We characterized the expression of genes in the flowering-time regulatory network across wild populations of the common sunflower, Helianthus annuus, that we found to be adaptively differentiated for photoperiod response. The observed clinal variation was associated with changes at multiple hierarchical levels in multiple pathways. Paralogue-specific changes in FT homologue expression and tissue-specific changes in SOC1 homologue expression were associated with loss and reversal of plasticity, respectively, suggesting that redundancy and modularity are gene network characteristics easily exploited by natural selection to produce evolutionary innovation. Distinct genetic mechanisms contribute to convergent evolution of photoperiod responses within sunflower, suggesting regulatory network architecture does not impose strong constraints on the evolution of phenotypic plasticity.     

Revealing evolutionary pathways by fitness landscape reconstruction

The concept of epistasis has since long been used to denote non-additive fitness effects of genetic changes and has played a central role in understanding the evolution of biological systems. Owing to an array of novel experimental methodologies, it has become possible to experimentally determine epistatic interactions as well as more elaborate genotype-fitness maps. These data have opened up the investigation of a host of long-standing questions in evolutionary biology, such as the ruggedness of fitness landscapes and the accessibility of mutational trajectories, the evolution of sex, and the origin of robustness and modularity. Here we review this recent and timely marriage between systems biology and evolutionary biology, which holds the promise to understand evolutionary dynamics in a more mechanistic and predictive manner.     

Sexual reproduction reshapes the genetic architecture of digital organisms

Modularity and epistasis, as well as other aspects of genetic architecture, have emerged as central themes in evolutionary biology. Theory suggests that modularity promotes evolvability, and that aggravating (synergistic) epistasis among deleterious mutations facilitates the evolution of sex. Here, by contrast, we investigate the evolution of different genetic architectures using digital organisms, which are computer programs that self-replicate, mutate, compete and evolve. Specifically, we investigate how genetic architecture is shaped by reproductive mode. We allowed 200 populations of digital organisms to evolve for over 10 000 generations while reproducing either asexually or sexually. For 10 randomly chosen organisms from each population, we constructed and analysed all possible single mutants as well as one million mutants at each mutational distance from 2 to 10. The genomes of sexual organisms were more modular than asexual ones; sites encoding different functional traits had less overlap and sites encoding a particular trait were more tightly clustered. Net directional epistasis was alleviating (antagonistic) in both groups, although the overall strength of this epistasis was weaker in sexual than in asexual organisms. Our results show that sexual reproduction profoundly influences the evolution of the genetic architecture.     

Evolution of complex modular biological networks

Biological networks have evolved to be highly functional within uncertain environments while remaining extremely adaptable. One of the main contributors to the robustness and evolvability of biological networks is believed to be their modularity of function, with modules defined as sets of genes that are strongly interconnected but whose function is separable from those of other modules. Here, we investigate the in silico evolution of modularity and robustness in complex artificial metabolic networks that encode an increasing amount of information about their environment while acquiring ubiquitous features of biological, social, and engineering networks, such as scale-free edge distribution, small-world property, and fault-tolerance. These networks evolve in environments that differ in their predictability, and allow us to study modularity from topological, information-theoretic, and gene-epistatic points of view using new tools that do not depend on any preconceived notion of modularity. We find that for our evolved complex networks as well as for the yeast protein–protein interaction network, synthetic lethal gene pairs consist mostly of redundant genes that lie close to each other and therefore within modules, while knockdown suppressor gene pairs are farther apart and often straddle modules, suggesting that knockdown rescue is mediated by alternative pathways or modules. The combination of network modularity tools together with genetic interaction data constitutes a powerful approach to study and dissect the role of modularity in the evolution and function of biological networks.     

Conserved developmental processes and the formation of evolutionary novelties: examples from butterfly wings

The origin and diversification of evolutionary novelties-lineage-specific traits of new adaptive value-is one of the key issues in evolutionary developmental biology. However, comparative analysis of the genetic and developmental bases of such traits can be difficult when they have no obvious homologue in model organisms. The finding that the evolution of morphological novelties often involves the recruitment of pre-existing genes and/or gene networks offers the potential to overcome this challenge. Knowledge about shared developmental processes obtained from extensive studies in model organisms can then be used to understand the origin and diversification of lineage-specific structures. Here, we illustrate this approach in relation to eyespots on the wings of Bicyclus anynana butterflies. A number of spontaneous mutations isolated in the laboratory affect eyespots, lepidopteran-specific features, and also processes that are shared by most insects. We discuss how eyespot mutants with disturbed embryonic development may help elucidate the genetic pathways involved in eyespot formation, and how venation mutants with altered eyespot patterns might shed light on mechanisms of eyespot development.     

Cortical Folding of the Primate Brain: An Interdisciplinary Examination of the Genetic Architecture,Modularity, and Evolvability of a Significant Neurological Trait in Pedigreed Baboons (Genus Papio)

Folding of the primate brain cortex allows for improved neural processing power by increasing cortical surface area for the allocation of neurons. The arrangement of folds (sulci) and ridges (gyri) across the cerebral cortex is thought to reflect the underlying neural network. Gyrification, an adaptive trait with a unique evolutionary history, is affected by genetic factors different from those affecting brain volume. Using a large pedigreed population of ∼1000 Papio baboons, we address critical questions about the genetic architecture of primate brain folding, the interplay between genetics, brain anatomy, development, patterns of cortical–cortical connectivity, and gyrification’s potential for future evolution. Through Mantel testing and cluster analyses, we find that the baboon cortex is quite evolvable, with high integration between the genotype and phenotype. We further find significantly similar partitioning of variation between cortical development, anatomy, and connectivity, supporting the predictions of tension-based models for sulcal development. We identify a significant, moderate degree of genetic control over variation in sulcal length, with gyrus-shape features being more susceptible to environmental effects. Finally, through QTL mapping, we identify novel chromosomal regions affecting variation in brain folding. The most significant QTL contain compelling candidate genes, including gene clusters associated with Williams and Down syndromes. The QTL distribution suggests a complex genetic architecture for gyrification with both polygeny and pleiotropy. Our results provide a solid preliminary characterization of the genetic basis of primate brain folding, a unique and biomedically relevant phenotype with significant implications in primate brain evolution.     

Network design meets in silico evolutionary biology

Cell fate is programmed through gene regulatory networks that perform several calculations to take the appropriate decision. In silico evolutionary optimization mimics the way Nature has designed such gene regulatory networks. In this review we discuss the basic principles of these evolutionary approaches and how they can be applied to engineer synthetic networks. We summarize the basic guidelines to implement an in silico evolutionary design method, the operators for mutation and selection that iteratively drive the network architecture towards a specified dynamical behavior. Interestingly, as it happens in natural evolution, we show the existence of patterns of punctuated evolution. In addition, we highlight several examples of models that have been designed using automated procedures, together with different objective functions to select for the proper behavior. Finally, we briefly discuss the modular designability of gene regulatory networks and its potential application in biotechnology.