Protein networking: insights into global functional organization of proteomes

The formulation of network models from global protein studies is essential to understand the functioning of organisms. Network models of the proteome enable the application of Complex Network Analysis, a quantitative framework to investigate large complex networks using techniques from graph theory, statistical physics, dynamical systems and other fields. This approach has provided many insights into the functional organization of the proteome so far and will likely continue to do so. Currently, several network concepts have emerged in the field of proteomics. It is important to highlight the differences between these concepts, since different representations allow different insights into functional organization. One such concept is the protein interaction network, which contains proteins as nodes and undirected edges representing the occurrence of binding in large-scale protein-protein interaction studies. A second concept is the protein-signaling network, in which the nodes correspond to levels of post-translationally modified forms of proteins and directed edges to causal effects through post-translational modification, such as phosphorylation. Several other network concepts were introduced for proteomics. Although all formulated as networks, the concepts represent widely different physical systems. Therefore caution should be taken when applying relevant topological analysis. We review recent literature formulating and analyzing such networks.     

Graph theoretical analysis of complex networks in the brain

Since the discovery of small-world and scale-free networks the study of complex systems from a network perspective has taken an enormous flight. In recent years many important properties of complex networks have been delineated. In particular, significant progress has been made in understanding the relationship between the structural properties of networks and the nature of dynamics taking place on these networks. For instance, the 'synchronizability' of complex networks of coupled oscillators can be determined by graph spectral analysis. These developments in the theory of complex networks have inspired new applications in the field of neuroscience. Graph analysis has been used in the study of models of neural networks, anatomical connectivity, and functional connectivity based upon fMRI, EEG and MEG. These studies suggest that the human brain can be modelled as a complex network, and may have a small-world structure both at the level of anatomical as well as functional connectivity. This small-world structure is hypothesized to reflect an optimal situation associated with rapid synchronization and information transfer, minimal wiring costs, as well as a balance between local processing and global integration. The topological structure of functional networks is probably restrained by genetic and anatomical factors, but can be modified during tasks. There is also increasing evidence that various types of brain disease such as Alzheimer's disease, schizophrenia, brain tumours and epilepsy may be associated with deviations of the functional network topology from the optimal small-world pattern.     

Brain functional network modeling and analysis based on fMRI: a systematic review

In recent years, the number of patients with neurodegenerative diseases (i.e., Alzheimer’s disease, Parkinson’s disease, mild cognitive impairment) and mental disorders (i.e., depression, anxiety and schizophrenia) have increased dramatically. Researchers have found that complex network analysis can reveal the topology of brain functional networks, such as small-world, scale-free, etc. In the study of brain diseases, it has been found that these topologies have undergoed abnormal changes in different degrees. Therefore, the research of brain functional networks can not only provide a new perspective for understanding the pathological mechanism of neurological and psychiatric diseases, but also provide assistance for the early diagnosis. Focusing on the study of human brain functional networks, this paper reviews the research results in recent years. First, this paper introduces the background of the study of brain functional networks under complex network theory and the important role of topological properties in the study of brain diseases. Second, the paper describes how to construct a brain functional network using neural image data. Third, the common methods of functional network analysis, including network structure analysis and disease classification, are introduced. Fourth, the role of brain functional networks in pathological study, analysis and diagnosis of brain functional diseases is studied. Finally, the paper summarizes the existing studies of brain functional networks and points out the problems and future research directions.     

Using Pareto optimality to explore the topology and dynamics of the human connectome

Graph theory has provided a key mathematical framework to analyse the architecture of human brain networks. This architecture embodies an inherently complex relationship between connection topology, the spatial arrangement of network elements, and the resulting network cost and functional performance. An exploration of these interacting factors and driving forces may reveal salient network features that are critically important for shaping and constraining the brain''s topological organization and its evolvability. Several studies have pointed to an economic balance between network cost and network efficiency with networks organized in an ‘economical’ small-world favouring high communication efficiency at a low wiring cost. In this study, we define and explore a network morphospace in order to characterize different aspects of communication efficiency in human brain networks. Using a multi-objective evolutionary approach that approximates a Pareto-optimal set within the morphospace, we investigate the capacity of anatomical brain networks to evolve towards topologies that exhibit optimal information processing features while preserving network cost. This approach allows us to investigate network topologies that emerge under specific selection pressures, thus providing some insight into the selectional forces that may have shaped the network architecture of existing human brains.     

The functional consequences of mutualistic network architecture

The architecture and properties of many complex networks play a significant role in the functioning of the systems they describe. Recently, complex network theory has been applied to ecological entities, like food webs or mutualistic plant-animal interactions. Unfortunately, we still lack an accurate view of the relationship between the architecture and functioning of ecological networks. In this study we explore this link by building individual-based pollination networks from eight Erysimum mediohispanicum (Brassicaceae) populations. In these individual-based networks, each individual plant in a population was considered a node, and was connected by means of undirected links to conspecifics sharing pollinators. The architecture of these unipartite networks was described by means of nestedness, connectivity and transitivity. Network functioning was estimated by quantifying the performance of the population described by each network as the number of per-capita juvenile plants produced per population. We found a consistent relationship between the topology of the networks and their functioning, since variation across populations in the average per-capita production of juvenile plants was positively and significantly related with network nestedness, connectivity and clustering. Subtle changes in the composition of diverse pollinator assemblages can drive major consequences for plant population performance and local persistence through modifications in the structure of the inter-plant pollination networks.     

Neural networks for perceptual processing: from simulation tools to theories

Neural networks are modelling tools that are, in principle, able to capture the input-output behaviour of arbitrary systems that may include the dynamics of animal populations or brain circuits. While a neural network model is useful if it captures phenomenologically the behaviour of the target system in this way, its utility is amplified if key mechanisms of the model can be discovered, and identified with those of the underlying system. In this review, we first describe, at a fairly high level with minimal mathematics, some of the tools used in constructing neural network models. We then go on to discuss the implications of network models for our understanding of the system they are supposed to describe, paying special attention to those models that deal with neural circuits and brain systems. We propose that neural nets are useful for brain modelling if they are viewed in a wider computational framework originally devised by Marr. Here, neural networks are viewed as an intermediate mechanistic abstraction between 'algorithm' and 'implementation', which can provide insights into biological neural representations and their putative supporting architectures.     

Dynamics on Networks: The Role of Local Dynamics and Global Networks on the Emergence of Hypersynchronous Neural Activity

Graph theory has evolved into a useful tool for studying complex brain networks inferred from a variety of measures of neural activity, including fMRI, DTI, MEG and EEG. In the study of neurological disorders, recent work has discovered differences in the structure of graphs inferred from patient and control cohorts. However, most of these studies pursue a purely observational approach; identifying correlations between properties of graphs and the cohort which they describe, without consideration of the underlying mechanisms. To move beyond this necessitates the development of computational modeling approaches to appropriately interpret network interactions and the alterations in brain dynamics they permit, which in the field of complexity sciences is known as dynamics on networks. In this study we describe the development and application of this framework using modular networks of Kuramoto oscillators. We use this framework to understand functional networks inferred from resting state EEG recordings of a cohort of 35 adults with heterogeneous idiopathic generalized epilepsies and 40 healthy adult controls. Taking emergent synchrony across the global network as a proxy for seizures, our study finds that the critical strength of coupling required to synchronize the global network is significantly decreased for the epilepsy cohort for functional networks inferred from both theta (3–6 Hz) and low-alpha (6–9 Hz) bands. We further identify left frontal regions as a potential driver of seizure activity within these networks. We also explore the ability of our method to identify individuals with epilepsy, observing up to 80 predictive power through use of receiver operating characteristic analysis. Collectively these findings demonstrate that a computer model based analysis of routine clinical EEG provides significant additional information beyond standard clinical interpretation, which should ultimately enable a more appropriate mechanistic stratification of people with epilepsy leading to improved diagnostics and therapeutics.     

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.     

The Human Functional Brain Network Demonstrates Structural and Dynamical Resilience to Targeted Attack

In recent years, the field of network science has enabled researchers to represent the highly complex interactions in the brain in an approachable yet quantitative manner. One exciting finding since the advent of brain network research was that the brain network can withstand extensive damage, even to highly connected regions. However, these highly connected nodes may not be the most critical regions of the brain network, and it is unclear how the network dynamics are impacted by removal of these key nodes. This work seeks to further investigate the resilience of the human functional brain network. Network attack experiments were conducted on voxel-wise functional brain networks and region-of-interest (ROI) networks of 5 healthy volunteers. Networks were attacked at key nodes using several criteria for assessing node importance, and the impact on network structure and dynamics was evaluated. The findings presented here echo previous findings that the functional human brain network is highly resilient to targeted attacks, both in terms of network structure and dynamics.     

Gender-related differences in the dysfunctional resting networks of migraine suffers

Background

Migraine shows gender-specific incidence and has a higher prevalence in females. However, little is known about gender-related differences in dysfunctional brain organization, which may account for gender-specific vulnerability and characteristics of migraine. In this study, we considered gender-related differences in the topological property of resting functional networks.

Methodology/Principal Findings

Data was obtained from 38 migraine patients (18 males and 20 females) and 38 healthy subjects (18 males and 20 females). We used the graph theory analysis, which becomes a powerful tool in investigating complex brain networks on a whole brain scale and could describe functional interactions between brain regions. Using this approach, we compared the brain functional networks between these two groups, and several network properties were investigated, such as small-worldness, network resilience, nodal centrality, and interregional connections. In our findings, these network characters were all disrupted in patients suffering from chronic migraine. More importantly, these functional damages in the migraine-affected brain had a skewed balance between males and females. In female patients, brain functional networks showed worse resilience, more regions exhibited decreased nodal centrality, and more functional connections revealed abnormalities than in male patients.

Conclusions

These results indicated that migraine may have an additional influence on females and lead to more dysfunctional organization in their resting functional networks.     

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

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

Brain Network Evolution after Stroke Based on Computational Experiments

Stroke is a frequently-occurring disease threatening the human nervous system. As a serious debilitation affecting a large-scale, hierarchical, and vastly complex electrochemical system, stroke remains relatively misunderstood. Rehabilitation mechanisms and means have suffered from this lack of systematic understanding. Here we propose an evolution model to simulate the dynamic actual evolvement process of functional brain networks computationally in an effort to address current shortcomings in the state of the field. According to simulation results, we conclude that the brain networks of patients following acute stroke were characterized by lower small worldness and lower quantity of long-distance connections compared with the healthy condition. Moreover, distance penalization may be used to describe the general mechanism of brain network evolution in the acute period after stroke.     

A linear model for characterization of synchronization frequencies of neural networks

The synchronization frequency of neural networks and its dynamics have important roles in deciphering the working mechanisms of the brain. It has been widely recognized that the properties of functional network synchronization and its dynamics are jointly determined by network topology, network connection strength, i.e., the connection strength of different edges in the network, and external input signals, among other factors. However, mathematical and computational characterization of the relationships between network synchronization frequency and these three important factors are still lacking. This paper presents a novel computational simulation framework to quantitatively characterize the relationships between neural network synchronization frequency and network attributes and input signals. Specifically, we constructed a series of neural networks including simulated small-world networks, real functional working memory network derived from functional magnetic resonance imaging, and real large-scale structural brain networks derived from diffusion tensor imaging, and performed synchronization simulations on these networks via the Izhikevich neuron spiking model. Our experiments demonstrate that both of the network synchronization strength and synchronization frequency change according to the combination of input signal frequency and network self-synchronization frequency. In particular, our extensive experiments show that the network synchronization frequency can be represented via a linear combination of the network self-synchronization frequency and the input signal frequency. This finding could be attributed to an intrinsically-preserved principle in different types of neural systems, offering novel insights into the working mechanism of neural systems.     

An Adaptive Complex Network Model for Brain Functional Networks

Brain functional networks are graph representations of activity in the brain, where the vertices represent anatomical regions and the edges their functional connectivity. These networks present a robust small world topological structure, characterized by highly integrated modules connected sparsely by long range links. Recent studies showed that other topological properties such as the degree distribution and the presence (or absence) of a hierarchical structure are not robust, and show different intriguing behaviors. In order to understand the basic ingredients necessary for the emergence of these complex network structures we present an adaptive complex network model for human brain functional networks. The microscopic units of the model are dynamical nodes that represent active regions of the brain, whose interaction gives rise to complex network structures. The links between the nodes are chosen following an adaptive algorithm that establishes connections between dynamical elements with similar internal states. We show that the model is able to describe topological characteristics of human brain networks obtained from functional magnetic resonance imaging studies. In particular, when the dynamical rules of the model allow for integrated processing over the entire network scale-free non-hierarchical networks with well defined communities emerge. On the other hand, when the dynamical rules restrict the information to a local neighborhood, communities cluster together into larger ones, giving rise to a hierarchical structure, with a truncated power law degree distribution.     

Metal hyperaccumulation and hypertolerance: a model for plant evolutionary genomics

In the course of evolution, plants adapted to widely differing metal availabilities in soils and therefore represent an important source of natural variation of metal homeostasis networks. Research on plant metal homeostasis can thus provide insights into the functioning, regulation and adaptation of biological networks. Here, we describe major recent breakthroughs in the understanding of the genetic and molecular basis of metal hyperaccumulation and associated hypertolerance, a naturally selected complex trait which represents an extreme adaptation of the metal homeostasis network. Investigations in this field reveal further the molecular alterations underlying the evolution of natural phenotypic diversity and provide a highly relevant framework for comparative genomics.     

Species traits as drivers of food web structure

The use of functional traits to describe community structure is a promising approach to reveal generalities across organisms and ecosystems. Plant ecologists have demonstrated the importance of traits in explaining community structure, competitive interactions as well as ecosystem functioning. The application of trait‐based methods to more complex communities such as food webs is however more challenging owing to the diversity of animal characteristics and of interactions. The objective of this study was to determine how functional structure is related to food web structure. We consider that food web structure is the result of 1) the match between consumer and resource traits, which determine the occurence of a trophic interaction between them, and 2) the distribution of functional traits in the community. We implemented a statistical approach to assess whether or not 35 466 pairwise interactions between soil organisms are constrained by trait‐matching and then used a Procrustes analysis to investigate correlations between functional indices and network properties across 48 sites. We found that the occurrence of trophic interactions is well predicted by matching the traits of the resource with those of the consumer. Taxonomy and body mass of both species were the most important traits for the determination of an interaction. As a consequence, functional evenness and the variance of certain traits in the community were correlated to trophic complementarity between species, while trait identity, more than diversity, was related to network topology. The analysis was however limited by trait data availability, and a coarse resolution of certain taxonomic groups in our dataset. These limitations explain the importance of taxonomy, as well as the complexity of the statistical model needed. Our results outline the important implications of trait composition on ecological networks, opening promising avenues of research into the relationship between functional diversity and ecosystem functioning in multi‐trophic systems.     

Functional network organization of the human brain

Real-world complex systems may be mathematically modeled as graphs, revealing properties of the system. Here we study graphs of functional brain organization in healthy adults using resting state functional connectivity MRI. We propose two novel brain-wide graphs, one of 264 putative functional areas, the other a modification of voxelwise networks that eliminates potentially artificial short-distance relationships. These graphs contain many subgraphs in good agreement with known functional brain systems. Other subgraphs lack established functional identities; we suggest possible functional characteristics for these subgraphs. Further, graph measures of the areal network indicate that the default mode subgraph shares network properties with sensory and motor subgraphs: it is internally integrated but isolated from other subgraphs, much like a "processing" system. The modified voxelwise graph also reveals spatial motifs in the patterning of systems across the cortex.     

PAFit: A Statistical Method for Measuring Preferential Attachment in Temporal Complex Networks

Preferential attachment is a stochastic process that has been proposed to explain certain topological features characteristic of complex networks from diverse domains. The systematic investigation of preferential attachment is an important area of research in network science, not only for the theoretical matter of verifying whether this hypothesized process is operative in real-world networks, but also for the practical insights that follow from knowledge of its functional form. Here we describe a maximum likelihood based estimation method for the measurement of preferential attachment in temporal complex networks. We call the method PAFit, and implement it in an R package of the same name. PAFit constitutes an advance over previous methods primarily because we based it on a nonparametric statistical framework that enables attachment kernel estimation free of any assumptions about its functional form. We show this results in PAFit outperforming the popular methods of Jeong and Newman in Monte Carlo simulations. What is more, we found that the application of PAFit to a publically available Flickr social network dataset yielded clear evidence for a deviation of the attachment kernel from the popularly assumed log-linear form. Independent of our main work, we provide a correction to a consequential error in Newman’s original method which had evidently gone unnoticed since its publication over a decade ago.