Phylogenetic analysis of modularity in protein interaction networks

Background  

In systems biology, comparative analyses of molecular interactions across diverse species indicate that conservation and divergence of networks can be used to understand functional evolution from a systems perspective. A key characteristic of these networks is their modularity, which contributes significantly to their robustness, as well as adaptability. Consequently, analysis of modular network structures from a phylogenetic perspective may be useful in understanding the emergence, conservation, and diversification of functional modularity.     

Module detection in complex networks using integer optimisation

Background  

The detection of modules or community structure is widely used to reveal the underlying properties of complex networks in biology, as well as physical and social sciences. Since the adoption of modularity as a measure of network topological properties, several methodologies for the discovery of community structure based on modularity maximisation have been developed. However, satisfactory partitions of large graphs with modest computational resources are particularly challenging due to the NP-hard nature of the related optimisation problem. Furthermore, it has been suggested that optimising the modularity metric can reach a resolution limit whereby the algorithm fails to detect smaller communities than a specific size in large networks.     

Emergence and maintenance of functional modules in signaling pathways

Background  

While detection and analysis of functional modules in biological systems have received great attention in recent years, we still lack a complete understanding of how such modules emerge. One theory is that systems must encounter a varying selection (i.e. environment) in order for modularity to emerge. Here, we provide an alternative and simpler explanation using a realistic model of biological signaling pathways and simulating their evolution.     

Metabolic robustness and network modularity: a model study

Background

Several studies have mentioned network modularity—that a network can easily be decomposed into subgraphs that are densely connected within and weakly connected between each other—as a factor affecting metabolic robustness. In this paper we measure the relation between network modularity and several aspects of robustness directly in a model system of metabolism.

Methodology/Principal Findings

By using a model for generating chemical reaction systems where one can tune the network modularity, we find that robustness increases with modularity for changes in the concentrations of metabolites, whereas it decreases with changes in the expression of enzymes. The same modularity scaling is true for the speed of relaxation after the perturbations.

Conclusions/Significance

Modularity is not a general principle for making metabolism either more or less robust; this question needs to be addressed specifically for different types of perturbations of the system.     

<Emphasis FontCategory="SansSerif">Investigation on changes of modularity and robustness by edge-removal mutations in signaling networks</Emphasis>

Background

Biological networks consisting of molecular components and interactions are represented by a graph model. There have been some studies based on that model to analyze a relationship between structural characteristics and dynamical behaviors in signaling network. However, little attention has been paid to changes of modularity and robustness in mutant networks.

Results

In this paper, we investigated the changes of modularity and robustness by edge-removal mutations in three signaling networks. We first observed that both the modularity and robustness increased on average in the mutant network by the edge-removal mutations. However, the modularity change was negatively correlated with the robustness change. This implies that it is unlikely that both the modularity and the robustness values simultaneously increase by the edge-removal mutations. Another interesting finding is that the modularity change was positively correlated with the degree, the number of feedback loops, and the edge betweenness of the removed edges whereas the robustness change was negatively correlated with them. We note that these results were consistently observed in randomly structure networks. Additionally, we identified two groups of genes which are incident to the highly-modularity-increasing and the highly-robustness-decreasing edges with respect to the edge-removal mutations, respectively, and observed that they are likely to be central by forming a connected component of a considerably large size. The gene-ontology enrichment of each of these gene groups was significantly different from the rest of genes. Finally, we showed that the highly-robustness-decreasing edges can be promising edgetic drug-targets, which validates the usefulness of our analysis.

Conclusions

Taken together, the analysis of changes of robustness and modularity against edge-removal mutations can be useful to unravel novel dynamical characteristics underlying in signaling networks.

     

An exploratory data analysis method to reveal modular latent structures in high-throughput data

Background  

Modular structures are ubiquitous across various types of biological networks. The study of network modularity can help reveal regulatory mechanisms in systems biology, evolutionary biology and developmental biology. Identifying putative modular latent structures from high-throughput data using exploratory analysis can help better interpret the data and generate new hypotheses. Unsupervised learning methods designed for global dimension reduction or clustering fall short of identifying modules with factors acting in linear combinations.     

Modular co-evolution of metabolic networks

Background  

The architecture of biological networks has been reported to exhibit high level of modularity, and to some extent, topological modules of networks overlap with known functional modules. However, how the modular topology of the molecular network affects the evolution of its member proteins remains unclear.     

Identifying protein complexes based on density and modularity in protein-protein interaction network

Background

Identifying protein complexes is crucial to understanding principles of cellular organization and functional mechanisms. As many evidences have indicated that the subgraphs with high density or with high modularity in PPI network usually correspond to protein complexes, protein complexes detection methods based on PPI network focused on subgraph's density or its modularity in PPI network. However, dense subgraphs may have low modularity and subgraph with high modularity may have low density, which results that protein complexes may be subgraphs with low modularity or with low density in the PPI network. As the density-based methods are difficult to mine protein complexes with low density, and the modularity-based methods are difficult to mine protein complexes with low modularity, both two methods have limitation for identifying protein complexes with various density and modularity.

Results

To identify protein complexes with various density and modularity, including those have low density but high modularity and those have low modularity but high density, we define a novel subgraph's fitness, f _ρ , as f _ρ = (density) ^ρ *(modularity)^1-ρ, and propose a novel algorithm, named LF_PIN, to identify protein complexes by expanding seed edges to subgraphs with the local maximum fitness value. Experimental results of LF-PIN in S.cerevisiae show that compared with the results of fitness equal to density (ρ = 1) or equal to modularity (ρ = 0), the LF-PIN identifies known protein complexes more effectively when the fitness value is decided by both density and modularity (0<ρ<1). Compared with the results of seven competing protein complex detection methods (CMC, Core-Attachment, CPM, DPClus, HC-PIN, MCL, and NFC) in S.cerevisiae and E.coli, LF-PIN outperforms other seven methods in terms of matching with known complexes and functional enrichment. Moreover, LF-PIN has better performance in identifying protein complexes with low density or with low modularity.

Conclusions

By considering both the density and the modularity, LF-PIN outperforms other protein complexes detection methods that only consider density or modularity, especially in identifying known protein complexes with low density or low modularity.

     

Increased entropy of signal transduction in the cancer metastasis phenotype

Background  

The statistical study of biological networks has led to important novel biological insights, such as the presence of hubs and hierarchical modularity. There is also a growing interest in studying the statistical properties of networks in the context of cancer genomics. However, relatively little is known as to what network features differ between the cancer and normal cell physiologies, or between different cancer cell phenotypes.     

Functional brain network modularity captures inter- and intra-individual variation in working memory capacity

Background

Cognitive abilities, such as working memory, differ among people; however, individuals also vary in their own day-to-day cognitive performance. One potential source of cognitive variability may be fluctuations in the functional organization of neural systems. The degree to which the organization of these functional networks is optimized may relate to the effective cognitive functioning of the individual. Here we specifically examine how changes in the organization of large-scale networks measured via resting state functional connectivity MRI and graph theory track changes in working memory capacity.

Methodology/Principal Findings

Twenty-two participants performed a test of working memory capacity and then underwent resting-state fMRI. Seventeen subjects repeated the protocol three weeks later. We applied graph theoretic techniques to measure network organization on 34 brain regions of interest (ROI). Network modularity, which measures the level of integration and segregation across sub-networks, and small-worldness, which measures global network connection efficiency, both predicted individual differences in memory capacity; however, only modularity predicted intra-individual variation across the two sessions. Partial correlations controlling for the component of working memory that was stable across sessions revealed that modularity was almost entirely associated with the variability of working memory at each session. Analyses of specific sub-networks and individual circuits were unable to consistently account for working memory capacity variability.

Conclusions/Significance

The results suggest that the intrinsic functional organization of an a priori defined cognitive control network measured at rest provides substantial information about actual cognitive performance. The association of network modularity to the variability in an individual''s working memory capacity suggests that the organization of this network into high connectivity within modules and sparse connections between modules may reflect effective signaling across brain regions, perhaps through the modulation of signal or the suppression of the propagation of noise.     

The effect of flower position on variation and covariation in floral traits in a wild hermaphrodite plant

Background  

Floral traits within plants can vary with flower position or flowering time. Within an inflorescence, sexual allocation of early produced basal flowers is often female-biased while later produced distal flowers are male-biased. Such temporal adjustment of floral resource has been considered one of the potential advantages of modularity (regarding a flower as a module) in hermaphrodites. However, flowers are under constraints of independent evolution of a given trait. To understand flower diversification within inflorescences, here we examine variation and covariation in floral traits within racemes at the individual and the maternal family level respectively in an alpine herb Aconitum gymnandrum (Ranunculaceae).     

Phenotypic plasticity and morphological integration in a marine modular invertebrate

Background  

Colonial invertebrates such as corals exhibit nested levels of modularity, imposing a challenge to the depiction of their morphological evolution. Comparisons among diverse Caribbean gorgonian corals suggest decoupling of evolution at the polyp vs. branch/internode levels. Thus, evolutionary change in polyp form or size (the colonial module sensu stricto) does not imply a change in colony form (constructed of modular branches and other emergent features). This study examined the patterns of morphological integration at the intraspecific level. Pseudopterogorgia bipinnata (Verrill) (Octocorallia: Gorgoniidae) is a Caribbean shallow water gorgonian that can colonize most reef habitats (shallow/exposed vs. deep/protected; 1–45 m) and shows great morphological variation.     

ALC: automated reduction of rule-based models

Background

Combinatorial complexity is a challenging problem for the modeling of cellular signal transduction since the association of a few proteins can give rise to an enormous amount of feasible protein complexes. The layer-based approach is an approximative, but accurate method for the mathematical modeling of signaling systems with inherent combinatorial complexity. The number of variables in the simulation equations is highly reduced and the resulting dynamic models show a pronounced modularity. Layer-based modeling allows for the modeling of systems not accessible previously.

Results

ALC (Automated Layer Construction) is a computer program that highly simplifies the building of reduced modular models, according to the layer-based approach. The model is defined using a simple but powerful rule-based syntax that supports the concepts of modularity and macrostates. ALC performs consistency checks on the model definition and provides the model output in different formats (C MEX, MATLAB, Mathematica and SBML) as ready-to-run simulation files. ALC also provides additional documentation files that simplify the publication or presentation of the models. The tool can be used offline or via a form on the ALC website.

Conclusion

ALC allows for a simple rule-based generation of layer-based reduced models. The model files are given in different formats as ready-to-run simulation files.     

Structural characterization of genomes by large scale sequence-structure threading: application of reliability analysis in structural genomics

Background  

We establish that the occurrence of protein folds among genomes can be accurately described with a Weibull function. Systems which exhibit Weibull character can be interpreted with reliability theory commonly used in engineering analysis. For instance, Weibull distributions are widely used in reliability, maintainability and safety work to model time-to-failure of mechanical devices, mechanisms, building constructions and equipment.     

Determining modular organization of protein interaction networks by maximizing modularity density

Background

With ever increasing amount of available data on biological networks, modeling and understanding the structure of these large networks is an important problem with profound biological implications. Cellular functions and biochemical events are coordinately carried out by groups of proteins interacting each other in biological modules. Identifying of such modules in protein interaction networks is very important for understanding the structure and function of these fundamental cellular networks. Therefore, developing an effective computational method to uncover biological modules should be highly challenging and indispensable.

Results

The purpose of this study is to introduce a new quantitative measure modularity density into the field of biomolecular networks and develop new algorithms for detecting functional modules in protein-protein interaction (PPI) networks. Specifically, we adopt the simulated annealing (SA) to maximize the modularity density and evaluate its efficiency on simulated networks. In order to address the computational complexity of SA procedure, we devise a spectral method for optimizing the index and apply it to a yeast PPI network.

Conclusions

Our analysis of detected modules by the present method suggests that most of these modules have well biological significance in context of protein complexes. Comparison with the MCL and the modularity based methods shows the efficiency of our method.

     

The modular organization of roe deer (<Emphasis Type="Italic">Capreolus capreolus</Emphasis>) body during ontogeny: the effects of sex and habitat

Background

As a small artiodactyl, the roe deer (Capreolus capreolus L.) is characterized by biological plasticity and great adaptability demonstrated by their survival under a wide variety of environmental conditions. In order to depict patterns of phenotypic variation of roe deer body this study aims to quantify variation during ontogenetic development and determine how sex-specific reproductive investment and non-uniform habitat differences relate to phenotypic variation and do these differential investments mold the patterns of phenotypic variation through modular organisation.

Results

Patterns of phenotypic correlation among body traits change during the ontogeny of roe deer, with differential influence of sex and habitat type. Modularity was found to be a feature of closed habitats with trunk+forelimbs+hindlimbs as the best supported integration/modularity hypothesis for both sexes. The indices of integration and evolvability vary with habitat type, age and sex where increased integration is followed by decreased evolvability.

Conclusion

This is the first study that quantifies patterns of correlation in the roe deer body and finds pronounced changes in correlation structure during ontogeny affected by sex and habitat type. The correlation structure of the roe deer body is developmentally written over the course of ontogeny but we do not exclude the influence of function on ontogenetic changes. Modularity arises with the onset of reproduction (subadults not being modular) and is differentially expressed in males and females from different habitats. Both adult males and females show modularity in primordial, closed habitats. Overall, all these findings are important as they provide support to the idea that modularity can evolve at the population level and change fast within a species.

     

SpectralNET – an application for spectral graph analysis and visualization

Background  

Graph theory provides a computational framework for modeling a variety of datasets including those emerging from genomics, proteomics, and chemical genetics. Networks of genes, proteins, small molecules, or other objects of study can be represented as graphs of nodes (vertices) and interactions (edges) that can carry different weights. SpectralNET is a flexible application for analyzing and visualizing these biological and chemical networks.     

Invariant properties of mycobiont-photobiont networks in Antarctic lichens

Aim

Lichens are often regarded as paradigms of mutualistic relationships. However, it is still poorly known how lichen-forming fungi and their photosynthetic partners interact at a community scale. We explored the structure of fungus-alga networks of interactions in lichen communities along a latitudinal transect in continental Antarctica. We expect these interactions to be highly specialized and, consequently, networks with low nestedness degree and high modularity.

Location

Transantarctic Mountains from 76° S to 85° S (continental Antarctica).

Time Period

Present.

Major Taxa Studied

Seventy-seven species of lichen-forming fungi and their photobionts.

Methods

DNA barcoding of photobionts using nrITS data was conducted in 756 lichen specimens from five regions along the Transantarctic Mountains. We built interaction networks for each of the five studied regions and a metaweb for the whole area. We explored the specialization of both partners using the number of partners a species interacts with and the specialization parameter d'. Network architecture parameters such as nestedness, modularity and network specialization parameter H₂' were studied in all networks and contrasted through null models. Finally, we measured interaction turnover along the latitudinal transect.

Results

We recovered a total of 842 interactions. Differences in specialization between partners were not statistically significant. Fungus-alga interaction networks showed high specialization and modularity, as well as low connectance and nestedness. Despite the large turnover in interactions occurring among regions, network parameters were not correlated with latitude.

Main Conclusions

The interaction networks established between fungi and algae in saxicolous lichen communities in continental Antarctica showed invariant properties along the latitudinal transect. Rewiring is an important driver of interaction turnover along the transect studied. Future work should answer whether the patterns observed in our study are prevalent in other regions with milder climates and in lichen communities on different substrates.