Structural Controllability and Controlling Centrality of Temporal Networks

Temporal networks are such networks where nodes and interactions may appear and disappear at various time scales. With the evidence of ubiquity of temporal networks in our economy, nature and society, it''s urgent and significant to focus on its structural controllability as well as the corresponding characteristics, which nowadays is still an untouched topic. We develop graphic tools to study the structural controllability as well as its characteristics, identifying the intrinsic mechanism of the ability of individuals in controlling a dynamic and large-scale temporal network. Classifying temporal trees of a temporal network into different types, we give (both upper and lower) analytical bounds of the controlling centrality, which are verified by numerical simulations of both artificial and empirical temporal networks. We find that the positive relationship between aggregated degree and controlling centrality as well as the scale-free distribution of node''s controlling centrality are virtually independent of the time scale and types of datasets, meaning the inherent robustness and heterogeneity of the controlling centrality of nodes within temporal networks.     

Time-ordered networks reveal limitations to information flow in ant colonies

Background

An important function of many complex networks is to inhibit or promote the transmission of disease, resources, or information between individuals. However, little is known about how the temporal dynamics of individual-level interactions affect these networks and constrain their function. Ant colonies are a model comparative system for understanding general principles linking individual-level interactions to network-level functions because interactions among individuals enable integration of multiple sources of information to collectively make decisions, and allocate tasks and resources.

Methodology/Findings

Here we show how the temporal and spatial dynamics of such individual interactions provide upper bounds to rates of colony-level information flow in the ant Temnothorax rugatulus. We develop a general framework for analyzing dynamic networks and a mathematical model that predicts how information flow scales with individual mobility and group size.

Conclusions/Significance

Using thousands of time-stamped interactions between uniquely marked ants in four colonies of a range of sizes, we demonstrate that observed maximum rates of information flow are always slower than predicted, and are constrained by regulation of individual mobility and contact rate. By accounting for the ordering and timing of interactions, we can resolve important difficulties with network sampling frequency and duration, enabling a broader understanding of interaction network functioning across systems and scales.     

Coupling between Normal Modes Drives Protein Conformational Dynamics: Illustrations Using Allosteric Transitions in Myosin II

Structure-based elastic network models (ENMs) have been remarkably successful in describing conformational transitions in a variety of biological systems. Low-frequency normal modes are usually calculated from the ENM that characterizes elastic interactions between residues in contact in a given protein structure with a uniform force constant. To explore the dynamical effects of nonuniform elastic interactions, we calculate the robustness and coupling of the low-frequency modes in the presence of nonuniform variations in the ENM force constant. The variations in the elastic interactions, approximated here by Gaussian noise, approximately account for perturbation effects of heterogeneous residue-residue interactions or evolutionary sequence changes within a protein family. First-order perturbation theory provides an efficient and qualitatively correct estimate of the mode robustness and mode coupling for finite perturbations to the ENM force constant. The mode coupling analysis and the mode robustness analysis identify groups of strongly coupled modes that encode for protein functional motions. We illustrate the new concepts using myosin II motor protein as an example. The biological implications of mode coupling in tuning the allosteric couplings among the actin-binding site, the nucleotide-binding site, and the force-generating converter and lever arm in myosin isoforms are discussed. We evaluate the robustness of the correlation functions that quantify the allosteric couplings among these three key structural motifs.     

Global protein function prediction from protein-protein interaction networks

Determining protein function is one of the most challenging problems of the post-genomic era. The availability of entire genome sequences and of high-throughput capabilities to determine gene coexpression patterns has shifted the research focus from the study of single proteins or small complexes to that of the entire proteome. In this context, the search for reliable methods for assigning protein function is of primary importance. There are various approaches available for deducing the function of proteins of unknown function using information derived from sequence similarity or clustering patterns of co-regulated genes, phylogenetic profiles, protein-protein interactions (refs. 5-8 and Samanta, M.P. and Liang, S., unpublished data), and protein complexes. Here we propose the assignment of proteins to functional classes on the basis of their network of physical interactions as determined by minimizing the number of protein interactions among different functional categories. Function assignment is proteome-wide and is determined by the global connectivity pattern of the protein network. The approach results in multiple functional assignments, a consequence of the existence of multiple equivalent solutions. We apply the method to analyze the yeast Saccharomyces cerevisiae protein-protein interaction network. The robustness of the approach is tested in a system containing a high percentage of unclassified proteins and also in cases of deletion and insertion of specific protein interactions.     

On the number of protein-protein interactions in the yeast proteome

Using two different approaches, we estimated that on average there are about five interacting partners per protein in the proteome of the yeast Saccharomyces cerevisiae. In the first approach, we used a novel method to model sampling overlap by a Bernoulli process, compared the results of two independent yeast two-hybrid interaction screens and tested the robustness of the estimate. The most stable estimate of five interactors per protein was obtained when the three most highly connected nodes in the protein interaction network were removed from the analysis (eight interactors per protein if those nodes were kept). In the second approach, we analysed a published high-confidence subset of putative interaction data obtained from multiple sources, including large-scale two-hybrid screens, complex purifications, synthetic lethals, correlated gene expression, computational predictions and previous annotations. Strikingly, the estimate was again five interactors per protein. These estimates suggest a range of ~16 000–26 000 different interaction pairs in the yeast, excluding homotypic interactions. We also discuss the approaches to estimating the rate of homotypic interactions.     

Breaking down Complex Saproxylic Communities: Understanding Sub-Networks Structure and Implications to Network Robustness

Saproxylic insect communities inhabiting tree hollow microhabitats correspond with large food webs which simultaneously are constituted by multiple types of plant-animal and animal-animal interactions, according to the use of trophic resources (wood- and insect-dependent sub-networks), or to trophic habits or interaction types (xylophagous, saprophagous, xylomycetophagous, predators and commensals). We quantitatively assessed which properties of specialised networks were present in a complex networks involving different interacting types such as saproxylic community, and how they can be organised in trophic food webs. The architecture, interacting patterns and food web composition were evaluated along sub-networks, analysing their implications to network robustness from random and directed extinction simulations. A structure of large and cohesive modules with weakly connected nodes was observed throughout saproxylic sub-networks, composing the main food webs constituting this community. Insect-dependent sub-networks were more modular than wood-dependent sub-networks. Wood-dependent sub-networks presented higher species degree, connectance, links, linkage density, interaction strength, and were less specialised and more aggregated than insect-dependent sub-networks. These attributes defined high network robustness in wood-dependent sub-networks. Finally, our results emphasise the relevance of modularity, differences among interacting types and interrelations among them in modelling the structure of saproxylic communities and in determining their stability.     

Why do hubs tend to be essential in protein networks?

The protein–protein interaction (PPI) network has a small number of highly connected protein nodes (known as hubs) and many poorly connected nodes. Genome-wide studies show that deletion of a hub protein is more likely to be lethal than deletion of a non-hub protein, a phenomenon known as the centrality-lethality rule. This rule is widely believed to reflect the special importance of hubs in organizing the network, which in turn suggests the biological significance of network architectures, a key notion of systems biology. Despite the popularity of this explanation, the underlying cause of the centrality-lethality rule has never been critically examined. We here propose the concept of essential PPIs, which are PPIs that are indispensable for the survival or reproduction of an organism. Our network analysis suggests that the centrality-lethality rule is unrelated to the network architecture, but is explained by the simple fact that hubs have large numbers of PPIs, therefore high probabilities of engaging in essential PPIs. We estimate that ~ 3% of PPIs are essential in the yeast, accounting for ~ 43% of essential genes. As expected, essential PPIs are evolutionarily more conserved than nonessential PPIs. Considering the role of essential PPIs in determining gene essentiality, we find the yeast PPI network functionally more robust than random networks, yet far less robust than the potential optimum. These and other findings provide new perspectives on the biological relevance of network structure and robustness.     

Novel recurrent neural network for modelling biological networks: Oscillatory p53 interaction dynamics

Understanding the control of cellular networks consisting of gene and protein interactions and their emergent properties is a central activity of Systems Biology research. For this, continuous, discrete, hybrid, and stochastic methods have been proposed. Currently, the most common approach to modelling accurate temporal dynamics of networks is ordinary differential equations (ODE). However, critical limitations of ODE models are difficulty in kinetic parameter estimation and numerical solution of a large number of equations, making them more suited to smaller systems. In this article, we introduce a novel recurrent artificial neural network (RNN) that addresses above limitations and produces a continuous model that easily estimates parameters from data, can handle a large number of molecular interactions and quantifies temporal dynamics and emergent systems properties. This RNN is based on a system of ODEs representing molecular interactions in a signalling network. Each neuron represents concentration change of one molecule represented by an ODE. Weights of the RNN correspond to kinetic parameters in the system and can be adjusted incrementally during network training. The method is applied to the p53-Mdm2 oscillation system – a crucial component of the DNA damage response pathways activated by a damage signal. Simulation results indicate that the proposed RNN can successfully represent the behaviour of the p53-Mdm2 oscillation system and solve the parameter estimation problem with high accuracy. Furthermore, we presented a modified form of the RNN that estimates parameters and captures systems dynamics from sparse data collected over relatively large time steps. We also investigate the robustness of the p53-Mdm2 system using the trained RNN under various levels of parameter perturbation to gain a greater understanding of the control of the p53-Mdm2 system. Its outcomes on robustness are consistent with the current biological knowledge of this system. As more quantitative data become available on individual proteins, the RNN would be able to refine parameter estimation and mapping of temporal dynamics of individual signalling molecules as well as signalling networks as a system. Moreover, RNN can be used to modularise large signalling networks.     

NEXCADE: Perturbation Analysis for Complex Networks

Recent advances in network theory have led to considerable progress in our understanding of complex real world systems and their behavior in response to external threats or fluctuations. Much of this research has been invigorated by demonstration of the 'robust, yet fragile' nature of cellular and large-scale systems transcending biology, sociology, and ecology, through application of the network theory to diverse interactions observed in nature such as plant-pollinator, seed-dispersal agent and host-parasite relationships. In this work, we report the development of NEXCADE, an automated and interactive program for inducing disturbances into complex systems defined by networks, focusing on the changes in global network topology and connectivity as a function of the perturbation. NEXCADE uses a graph theoretical approach to simulate perturbations in a user-defined manner, singly, in clusters, or sequentially. To demonstrate the promise it holds for broader adoption by the research community, we provide pre-simulated examples from diverse real-world networks including eukaryotic protein-protein interaction networks, fungal biochemical networks, a variety of ecological food webs in nature as well as social networks. NEXCADE not only enables network visualization at every step of the targeted attacks, but also allows risk assessment, i.e. identification of nodes critical for the robustness of the system of interest, in order to devise and implement context-based strategies for restructuring a network, or to achieve resilience against link or node failures. Source code and license for the software, designed to work on a Linux-based operating system (OS) can be downloaded at http://www.nipgr.res.in/nexcade_download.html. In addition, we have developed NEXCADE as an OS-independent online web server freely available to the scientific community without any login requirement at http://www.nipgr.res.in/nexcade.html.     

AKT as locus of cancer angiogenic robustness and fragility

Angiogenesis get full robustness in metastatic cancer, relapsed leukemia or lymphoma when complex positive feedback loop signaling systems become integrative. A cancer hypoxic microenvironment generates positive loops inducing formation of the vascular functional shunts. AKT is an upstream angiogenic locus of integrative robustness and fragility activated by the positive loops. AKT controls two downstream nodes the mTOR and NOS in nodal organization of the signaling genes. AKT phosphorylation is regulated by a balance of an oxidant/antioxidant. Targeting AKT locus represents new principle to control integrative angiogenic robustness by the locus chemotherapy. J. Cell. Physiol. 228: 21–24, 2013. © 2012 Wiley Periodicals, Inc.     

Complexity of multitrophic interactions in a grassland ecosystem depends on plant species diversity

1.?We studied the theoretical prediction that a loss of plant species richness has a strong impact on community interactions among all trophic levels and tested whether decreased plant species diversity results in a less complex structure and reduced interactions in ecological networks. 2.?Using plant species-specific biomass and arthropod abundance data from experimental grassland plots (Jena Experiment), we constructed multitrophic functional group interaction webs to compare communities based on 4 and 16 plant species. 427 insect and spider species were classified into 13 functional groups. These functional groups represent the nodes of ecological networks. Direct and indirect interactions among them were assessed using partial Mantel tests. Interaction web complexity was quantified using three measures of network structure: connectance, interaction diversity and interaction strength. 3.?Compared with high plant diversity plots, interaction webs based on low plant diversity plots showed reduced complexity in terms of total connectance, interaction diversity and mean interaction strength. Plant diversity effects obviously cascade up the food web and modify interactions across all trophic levels. The strongest effects occurred in interactions between adjacent trophic levels (i.e. predominantly trophic interactions), while significant interactions among plant and carnivore functional groups, as well as horizontal interactions (i.e. interactions between functional groups of the same trophic level), showed rather inconsistent responses and were generally rarer. 4.?Reduced interaction diversity has the potential to decrease and destabilize ecosystem processes. Therefore, we conclude that the loss of basal producer species leads to more simple structured, less and more loosely connected species assemblages, which in turn are very likely to decrease ecosystem functioning, community robustness and tolerance to disturbance. Our results suggest that the functioning of the entire ecological community is critically linked to the diversity of its component plants species.     

Unique role of dystroglycan in peripheral nerve myelination,nodal structure,and sodium channel stabilization

Dystroglycan is a central component of the dystrophin-glycoprotein complex implicated in the pathogenesis of several neuromuscular diseases. Although dystroglycan is expressed by Schwann cells, its normal peripheral nerve functions are unknown. Here we show that selective deletion of Schwann cell dystroglycan results in slowed nerve conduction and nodal changes including reduced sodium channel density and disorganized microvilli. Additional features of mutant mice include deficits in rotorod performance, aberrant pain responses, and abnormal myelin sheath folding. These data indicate that dystroglycan is crucial for both myelination and nodal architecture. Dystroglycan may be required for the normal maintenance of voltage-gated sodium channels at nodes of Ranvier, possibly by mediating trans interactions between Schwann cell microvilli and the nodal axolemma.     

Exploring biological network structure with clustered random networks

Background  

Complex biological systems are often modeled as networks of interacting units. Networks of biochemical interactions among proteins, epidemiological contacts among hosts, and trophic interactions in ecosystems, to name a few, have provided useful insights into the dynamical processes that shape and traverse these systems. The degrees of nodes (numbers of interactions) and the extent of clustering (the tendency for a set of three nodes to be interconnected) are two of many well-studied network properties that can fundamentally shape a system. Disentangling the interdependent effects of the various network properties, however, can be difficult. Simple network models can help us quantify the structure of empirical networked systems and understand the impact of various topological properties on dynamics.     

Mutual Information Rate and Bounds for It

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.     

High-order interactions maintain or enhance structural robustness of a coffee agroecosystem network

The capacity of highly diverse systems to prevail has proven difficult to explain. In addition to methodological issues, the inherent complexity of ecosystems and issues like multicausality, non-linearity and context-specificity make it hard to establish general and unidirectional explanations. Nevertheless, in recent years, high order interactions have been increasingly discussed as a mechanism that benefits the functioning of highly diverse ecosystems and may add to the mechanisms that explain their persistence. Until now, this idea has been explored by means of hypothetical simulated networks. Here, we test this idea using an updated and empirically documented network for a coffee agroecosystem. We identify potentially key nodes and measure network robustness in the face of node removal with and without incorporation of high order interactions. We find that the system's robustness is either increased or unaffected by the addition of high order interactions, in contrast with randomized counterparts with similar structural characteristics. We also propose a method for representing networks with high order interactions as ordinary graphs and a method for measuring their robustness.     

How scale-free are biological networks.

The concept of scale-free network has emerged as a powerful unifying paradigm in the study of complex systems in biology and in physical and social studies. Metabolic, protein, and gene interaction networks have been reported to exhibit scale-free behavior based on the analysis of the distribution of the number of connections of the network nodes. Here we study 10 published datasets of various biological interactions and perform goodness-of-fit tests to determine whether the given data is drawn from the power-law distribution. Our analysis did not identify a single interaction network that has a nonzero probability of being drawn from the power-law distribution.     

Integrating the Alzheimer's disease proteome and transcriptome: a comprehensive network model of a complex disease

Network models combined with gene expression studies have become useful tools for studying complex diseases like Alzheimer's disease. We constructed a "Core" Alzheimer's disease protein interaction network by human curation of the primary literature. The Core network consisted of 775 nodes and 2,204 interactions. To our knowledge, this is the most comprehensive and accurate protein interaction network yet constructed for Alzheimer's disease. An "Expanded" network was computationally constructed by adding additional proteins that interacted with Core network proteins, and consisted of 4,945 nodes and 26,064 interactions. We then mapped existing gene expression studies to the Core network. This combined data model identified the MAPK/ERK pathway and clathrin-mediated receptor endocytosis as key pathways in Alzheimer's disease. Important proteins in the MAPK/ERK pathway that interacted in the Core network formed a downregulated cluster of nodes, whereas clathrin and several clathrin accessory proteins that interacted in the Core network formed an upregulated cluster of nodes. The MAPK/ERK pathway is a key component in synaptic plasticity and learning, processes disrupted in Alzheimer's. Clathrin and clathrin adaptor proteins are involved in the endocytosis of the APP protein that can lead to increased intracellular levels of amyloid beta peptide, contributing to the progression of Alzheimer's.     

Ant-Plant Interaction in a Tropical Savanna: May the Network Structure Vary over Time and Influence on the Outcomes of Associations?

Plant-animal interactions occur in a community context of dynamic and complex ecological interactive networks. The understanding of who interacts with whom is a basic information, but the outcomes of interactions among associates are fundamental to draw valid conclusions about the functional structure of the network. Ecological networks studies in general gave little importance to know the true outcomes of interactions and how they may change over time. We evaluate the dynamic of an interaction network between ants and plants with extrafloral nectaries, by verifying the temporal variation in structure and outcomes of mutualism for the plant community (leaf herbivory). To reach this goal, we used two tools: bipartite network analysis and experimental manipulation. The networks exhibited the same general pattern as other mutualistic networks: nestedness, asymmetry and low specialization and this pattern was maintained over time, but with internal changes (species degree, connectance and ant abundance). These changes influenced the protection effectiveness of plants by ants, which varied over time. Our study shows that interaction networks between ants and plants are dynamic over time, and that these alterations affect the outcomes of mutualisms. In addition, our study proposes that the set of single systems that shape ecological networks can be manipulated for a greater understanding of the entire system.     

Balance of Interactions Determines Optimal Survival in Multi-Species Communities

We consider a multi-species community modelled as a complex network of populations, where the links are given by a random asymmetric connectivity matrix J, with fraction 1 − C of zero entries, where C reflects the over-all connectivity of the system. The non-zero elements of J are drawn from a Gaussian distribution with mean μ and standard deviation σ. The signs of the elements J _ij reflect the nature of density-dependent interactions, such as predatory-prey, mutualism or competition, and their magnitudes reflect the strength of the interaction. In this study we try to uncover the broad features of the inter-species interactions that determine the global robustness of this network, as indicated by the average number of active nodes (i.e. non-extinct species) in the network, and the total population, reflecting the biomass yield. We find that the network transitions from a completely extinct system to one where all nodes are active, as the mean interaction strength goes from negative to positive, with the transition getting sharper for increasing C and decreasing σ. We also find that the total population, displays distinct non-monotonic scaling behaviour with respect to the product μC, implying that survival is dependent not merely on the number of links, but rather on the combination of the sparseness of the connectivity matrix and the net interaction strength. Interestingly, in an intermediate window of positive μC, the total population is maximal, indicating that too little or too much positive interactions is detrimental to survival. Rather, the total population levels are optimal when the network has intermediate net positive connection strengths. At the local level we observe marked qualitative changes in dynamical patterns, ranging from anti-phase clusters of period 2 cycles and chaotic bands, to fixed points, under the variation of mean μ of the interaction strengths. We also study the correlation between synchronization and survival, and find that synchronization does not necessarily lead to extinction. Lastly, we propose an effective low dimensional map to capture the behavior of the entire network, and this provides a broad understanding of the interplay of the local dynamical patterns and the global robustness trends in the network.