Functional Aspects of the EGF-Induced MAP Kinase Cascade: A Complex Self-Organizing System Approach

The EGF-induced MAP kinase cascade is one of the most important and best characterized networks in intracellular signalling. It has a vital role in the development and maturation of living organisms. However, when deregulated, it is involved in the onset of a number of diseases. Based on a computational model describing a “surface” and an “internalized” parallel route, we use systems biology techniques to characterize aspects of the network’s functional organization. We examine the re-organization of protein groups from low to high external stimulation, define functional groups of proteins within the network, determine the parameter best encoding for input intensity and predict the effect of protein removal to the system’s output response. Extensive functional re-organization of proteins is observed in the lower end of stimulus concentrations. As we move to higher concentrations the variability is less pronounced. 6 functional groups have emerged from a consensus clustering approach, reflecting different dynamical aspects of the network. Mutual information investigation revealed that the maximum activation rate of the two output proteins best encodes for stimulus intensity. Removal of each protein of the network resulted in a range of graded effects, from complete silencing to intense activation. Our results provide a new “vista” of the EGF-induced MAP kinase cascade, from the perspective of complex self-organizing systems. Functional grouping of the proteins reveals an organizational scheme contrasting the current understanding of modular topology. The six identified groups may provide the means to experimentally follow the dynamics of this complex network. Also, the vulnerability analysis approach may be used for the development of novel therapeutic targets in the context of personalized medicine.     

Network 'small-world-ness': a quantitative method for determining canonical network equivalence

Background

Many technological, biological, social, and information networks fall into the broad class of ‘small-world’ networks: they have tightly interconnected clusters of nodes, and a shortest mean path length that is similar to a matched random graph (same number of nodes and edges). This semi-quantitative definition leads to a categorical distinction (‘small/not-small’) rather than a quantitative, continuous grading of networks, and can lead to uncertainty about a network''s small-world status. Moreover, systems described by small-world networks are often studied using an equivalent canonical network model – the Watts-Strogatz (WS) model. However, the process of establishing an equivalent WS model is imprecise and there is a pressing need to discover ways in which this equivalence may be quantified.

Methodology/Principal Findings

We defined a precise measure of ‘small-world-ness’ S based on the trade off between high local clustering and short path length. A network is now deemed a ‘small-world’ if S>1 - an assertion which may be tested statistically. We then examined the behavior of S on a large data-set of real-world systems. We found that all these systems were linked by a linear relationship between their S values and the network size n. Moreover, we show a method for assigning a unique Watts-Strogatz (WS) model to any real-world network, and show analytically that the WS models associated with our sample of networks also show linearity between S and n. Linearity between S and n is not, however, inevitable, and neither is S maximal for an arbitrary network of given size. Linearity may, however, be explained by a common limiting growth process.

Conclusions/Significance

We have shown how the notion of a small-world network may be quantified. Several key properties of the metric are described and the use of WS canonical models is placed on a more secure footing.     

Implications of Network Topology on Stability

In analogy to chemical reaction networks, I demonstrate the utility of expressing the governing equations of an arbitrary dynamical system (interaction network) as sums of real functions (generalized reactions) multiplied by real scalars (generalized stoichiometries) for analysis of its stability. The reaction stoichiometries and first derivatives define the network’s “influence topology”, a signed directed bipartite graph. Parameter reduction of the influence topology permits simplified expression of the principal minors (sums of products of non-overlapping bipartite cycles) and Hurwitz determinants (sums of products of the principal minors or the bipartite cycles directly) for assessing the network’s steady state stability. Visualization of the Hurwitz determinants over the reduced parameters defines the network’s stability phase space, delimiting the range of its dynamics (specifically, the possible numbers of unstable roots at each steady state solution). Any further explicit algebraic specification of the network will project onto this stability phase space. Stability analysis via this hierarchical approach is demonstrated on classical networks from multiple fields.     

The Oral Tolerance as a Complex Network Phenomenon

The phenomenon of oral tolerance refers to a local and systemic state of tolerance induced in the gut after its exposure to innocuous antigens. Recent findings have shown the interrelationship between cellular and molecular components of oral tolerance, but its representation through a network of interactions has not been investigated. Our work aims at identifying the causal relationship of each element in an oral tolerance network, and also to propose a phenomenological model that’s capable of predicting the stochastic behavior of this network when under manipulation. We compared the changes of a “healthy” network caused by “knock-outs” (KOs) in two approaches: an analytical approach by the Perron Frobenius theory; and a computational approach, which we describe within this work in order to find numerical results for the model. Both approaches have shown the most relevant immunological components for this phenomena, that happens to corroborate the empirical results from animal models. Besides explain in a intelligible fashion how the components interacts in a complex manner, we also managed to describe and quantify the importance of KOs that hasn’t been empirically tested.     

Extended CADLIVE: a novel graphical notation for design of biochemical network maps and computational pathway analysis

Biochemical network maps are helpful for understanding the mechanism of how a collection of biochemical reactions generate particular functions within a cell. We developed a new and computationally feasible notation that enables drawing a wide resolution map from the domain-level reactions to phenomenological events and implemented it as the extended GUI network constructor of CADLIVE (Computer-Aided Design of LIVing systEms). The new notation presents ‘Domain expansion’ for proteins and RNAs, ‘Virtual reaction and nodes’ that are responsible for illustrating domain-based interaction and ‘InnerLink’ that links real complex nodes to virtual nodes to illustrate the exact components of the real complex. A modular box is also presented that packs related reactions as a module or a subnetwork, which gives CADLIVE a capability to draw biochemical maps in a hierarchical modular architecture. Furthermore, we developed a pathway search module for virtual knockout mutants as a built-in application of CADLIVE. This module analyzes gene function in the same way as molecular genetics, which simulates a change in mutant phenotypes or confirms the validity of the network map. The extended CADLIVE with the newly proposed notation is demonstrated to be feasible for computational simulation and analysis.     

A Family of Algorithms for Computing Consensus about Node State from Network Data

Biological and social networks are composed of heterogeneous nodes that contribute differentially to network structure and function. A number of algorithms have been developed to measure this variation. These algorithms have proven useful for applications that require assigning scores to individual nodes–from ranking websites to determining critical species in ecosystems–yet the mechanistic basis for why they produce good rankings remains poorly understood. We show that a unifying property of these algorithms is that they quantify consensus in the network about a node''s state or capacity to perform a function. The algorithms capture consensus by either taking into account the number of a target node''s direct connections, and, when the edges are weighted, the uniformity of its weighted in-degree distribution (breadth), or by measuring net flow into a target node (depth). Using data from communication, social, and biological networks we find that that how an algorithm measures consensus–through breadth or depth– impacts its ability to correctly score nodes. We also observe variation in sensitivity to source biases in interaction/adjacency matrices: errors arising from systematic error at the node level or direct manipulation of network connectivity by nodes. Our results indicate that the breadth algorithms, which are derived from information theory, correctly score nodes (assessed using independent data) and are robust to errors. However, in cases where nodes “form opinions” about other nodes using indirect information, like reputation, depth algorithms, like Eigenvector Centrality, are required. One caveat is that Eigenvector Centrality is not robust to error unless the network is transitive or assortative. In these cases the network structure allows the depth algorithms to effectively capture breadth as well as depth. Finally, we discuss the algorithms'' cognitive and computational demands. This is an important consideration in systems in which individuals use the collective opinions of others to make decisions.     

Tinnitus-like “hallucinations” elicited by sensory deprivation in an entropy maximization recurrent neural network

Sensory deprivation has long been known to cause hallucinations or “phantom” sensations, the most common of which is tinnitus induced by hearing loss, affecting 10–20% of the population. An observable hearing loss, causing auditory sensory deprivation over a band of frequencies, is present in over 90% of people with tinnitus. Existing plasticity-based computational models for tinnitus are usually driven by homeostatic mechanisms, modeled to fit phenomenological findings. Here, we use an objective-driven learning algorithm to model an early auditory processing neuronal network, e.g., in the dorsal cochlear nucleus. The learning algorithm maximizes the network’s output entropy by learning the feed-forward and recurrent interactions in the model. We show that the connectivity patterns and responses learned by the model display several hallmarks of early auditory neuronal networks. We further demonstrate that attenuation of peripheral inputs drives the recurrent network towards its critical point and transition into a tinnitus-like state. In this state, the network activity resembles responses to genuine inputs even in the absence of external stimulation, namely, it “hallucinates” auditory responses. These findings demonstrate how objective-driven plasticity mechanisms that normally act to optimize the network’s input representation can also elicit pathologies such as tinnitus as a result of sensory deprivation.     

Establishing a Statistical Link between Network Oscillations and Neural Synchrony

Pairs of active neurons frequently fire action potentials or “spikes” nearly synchronously (i.e., within 5 ms of each other). This spike synchrony may occur by chance, based solely on the neurons’ fluctuating firing patterns, or it may occur too frequently to be explicable by chance alone. When spike synchrony above chances levels is present, it may subserve computation for a specific cognitive process, or it could be an irrelevant byproduct of such computation. Either way, spike synchrony is a feature of neural data that should be explained. A point process regression framework has been developed previously for this purpose, using generalized linear models (GLMs). In this framework, the observed number of synchronous spikes is compared to the number predicted by chance under varying assumptions about the factors that affect each of the individual neuron’s firing-rate functions. An important possible source of spike synchrony is network-wide oscillations, which may provide an essential mechanism of network information flow. To establish the statistical link between spike synchrony and network-wide oscillations, we have integrated oscillatory field potentials into our point process regression framework. We first extended a previously-published model of spike-field association and showed that we could recover phase relationships between oscillatory field potentials and firing rates. We then used this new framework to demonstrate the statistical relationship between oscillatory field potentials and spike synchrony in: 1) simulated neurons, 2) in vitro recordings of hippocampal CA1 pyramidal cells, and 3) in vivo recordings of neocortical V4 neurons. Our results provide a rigorous method for establishing a statistical link between network oscillations and neural synchrony.     

Computing the Local Field Potential (LFP) from Integrate-and-Fire Network Models

Leaky integrate-and-fire (LIF) network models are commonly used to study how the spiking dynamics of neural networks changes with stimuli, tasks or dynamic network states. However, neurophysiological studies in vivo often rather measure the mass activity of neuronal microcircuits with the local field potential (LFP). Given that LFPs are generated by spatially separated currents across the neuronal membrane, they cannot be computed directly from quantities defined in models of point-like LIF neurons. Here, we explore the best approximation for predicting the LFP based on standard output from point-neuron LIF networks. To search for this best “LFP proxy”, we compared LFP predictions from candidate proxies based on LIF network output (e.g, firing rates, membrane potentials, synaptic currents) with “ground-truth” LFP obtained when the LIF network synaptic input currents were injected into an analogous three-dimensional (3D) network model of multi-compartmental neurons with realistic morphology, spatial distributions of somata and synapses. We found that a specific fixed linear combination of the LIF synaptic currents provided an accurate LFP proxy, accounting for most of the variance of the LFP time course observed in the 3D network for all recording locations. This proxy performed well over a broad set of conditions, including substantial variations of the neuronal morphologies. Our results provide a simple formula for estimating the time course of the LFP from LIF network simulations in cases where a single pyramidal population dominates the LFP generation, and thereby facilitate quantitative comparison between computational models and experimental LFP recordings in vivo.     

Performance of Social Network Sensors during Hurricane Sandy

Information flow during catastrophic events is a critical aspect of disaster management. Modern communication platforms, in particular online social networks, provide an opportunity to study such flow and derive early-warning sensors, thus improving emergency preparedness and response. Performance of the social networks sensor method, based on topological and behavioral properties derived from the “friendship paradox”, is studied here for over 50 million Twitter messages posted before, during, and after Hurricane Sandy. We find that differences in users’ network centrality effectively translate into moderate awareness advantage (up to 26 hours); and that geo-location of users within or outside of the hurricane-affected area plays a significant role in determining the scale of such an advantage. Emotional response appears to be universal regardless of the position in the network topology, and displays characteristic, easily detectable patterns, opening a possibility to implement a simple “sentiment sensing” technique that can detect and locate disasters.     

Contact Trees: Network Visualization beyond Nodes and Edges

Node-Link diagrams make it possible to take a quick glance at how nodes (or actors) in a network are connected by edges (or ties). A conventional network diagram of a “contact tree” maps out a root and branches that represent the structure of nodes and edges, often without further specifying leaves or fruits that would have grown from small branches. By furnishing such a network structure with leaves and fruits, we reveal details about “contacts” in our ContactTrees upon which ties and relationships are constructed. Our elegant design employs a bottom-up approach that resembles a recent attempt to understand subjective well-being by means of a series of emotions. Such a bottom-up approach to social-network studies decomposes each tie into a series of interactions or contacts, which can help deepen our understanding of the complexity embedded in a network structure. Unlike previous network visualizations, ContactTrees highlight how relationships form and change based upon interactions among actors, as well as how relationships and networks vary by contact attributes. Based on a botanical tree metaphor, the design is easy to construct and the resulting tree-like visualization can display many properties at both tie and contact levels, thus recapturing a key ingredient missing from conventional techniques of network visualization. We demonstrate ContactTrees using data sets consisting of up to three waves of 3-month contact diaries over the 2004-2012 period, and discuss how this design can be applied to other types of datasets.     

Control of Neuronal Network in Caenorhabditis elegans

Caenorhabditis elegans, a soil dwelling nematode, is evolutionarily rudimentary and contains only ∼ 300 neurons which are connected to each other via chemical synapses and gap junctions. This structural connectivity can be perceived as nodes and edges of a graph. Controlling complex networked systems (such as nervous system) has been an area of excitement for mankind. Various methods have been developed to identify specific brain regions, which when controlled by external input can lead to achievement of control over the state of the system. But in case of neuronal connectivity network the properties of neurons identified as driver nodes is of much importance because nervous system can produce a variety of states (behaviour of the animal). Hence to gain insight on the type of control achieved in nervous system we implemented the notion of structural control from graph theory to C. elegans neuronal network. We identified ‘driver neurons’ which can provide full control over the network. We studied phenotypic properties of these neurons which are referred to as ‘phenoframe’ as well as the ‘genoframe’ which represents their genetic correlates. We find that the driver neurons are primarily motor neurons located in the ventral nerve cord and contribute to biological reproduction of the animal. Identification of driver neurons and its characterization adds a new dimension in controllability of C. elegans neuronal network. This study suggests the importance of driver neurons and their utility to control the behaviour of the organism.     

Discovering Preferential Patterns in Sectoral Trade Networks

We analyze the patterns of import/export bilateral relations, with the aim of assessing the relevance and shape of “preferentiality” in countries’ trade decisions. Preferentiality here is defined as the tendency to concentrate trade on one or few partners. With this purpose, we adopt a systemic approach through the use of the tools of complex network analysis. In particular, we apply a pattern detection approach based on community and pseudocommunity analysis, in order to highlight the groups of countries within which most of members’ trade occur. The method is applied to two intra-industry trade networks consisting of 221 countries, relative to the low-tech “Textiles and Textile Articles” and the high-tech “Electronics” sectors for the year 2006, to look at the structure of world trade before the start of the international financial crisis. It turns out that the two networks display some similarities and some differences in preferential trade patterns: they both include few significant communities that define narrow sets of countries trading with each other as preferential destinations markets or supply sources, and they are characterized by the presence of similar hierarchical structures, led by the largest economies. But there are also distinctive features due to the characteristics of the industries examined, in which the organization of production and the destination markets are different. Overall, the extent of preferentiality and partner selection at the sector level confirm the relevance of international trade costs still today, inducing countries to seek the highest efficiency in their trade patterns.     

The importance of bottlenecks in protein networks: correlation with gene essentiality and expression dynamics

It has been a long-standing goal in systems biology to find relations between the topological properties and functional features of protein networks. However, most of the focus in network studies has been on highly connected proteins (“hubs”). As a complementary notion, it is possible to define bottlenecks as proteins with a high betweenness centrality (i.e., network nodes that have many “shortest paths” going through them, analogous to major bridges and tunnels on a highway map). Bottlenecks are, in fact, key connector proteins with surprising functional and dynamic properties. In particular, they are more likely to be essential proteins. In fact, in regulatory and other directed networks, betweenness (i.e., “bottleneck-ness”) is a much more significant indicator of essentiality than degree (i.e., “hub-ness”). Furthermore, bottlenecks correspond to the dynamic components of the interaction network—they are significantly less well coexpressed with their neighbors than nonbottlenecks, implying that expression dynamics is wired into the network topology.     

The Default Mode Network and the Working Memory Network Are Not Anti-Correlated during All Phases of a Working Memory Task

Introduction

The default mode network and the working memory network are known to be anti-correlated during sustained cognitive processing, in a load-dependent manner. We hypothesized that functional connectivity among nodes of the two networks could be dynamically modulated by task phases across time.

Methods

To address the dynamic links between default mode network and the working memory network, we used a delayed visuo-spatial working memory paradigm, which allowed us to separate three different phases of working memory (encoding, maintenance, and retrieval), and analyzed the functional connectivity during each phase within and between the default mode network and the working memory network networks.

Results

We found that the two networks are anti-correlated only during the maintenance phase of working memory, i.e. when attention is focused on a memorized stimulus in the absence of external input. Conversely, during the encoding and retrieval phases, when the external stimulation is present, the default mode network is positively coupled with the working memory network, suggesting the existence of a dynamically switching of functional connectivity between “task-positive” and “task-negative” brain networks.

Conclusions

Our results demonstrate that the well-established dichotomy of the human brain (anti-correlated networks during rest and balanced activation-deactivation during cognition) has a more nuanced organization than previously thought and engages in different patterns of correlation and anti-correlation during specific sub-phases of a cognitive task. This nuanced organization reinforces the hypothesis of a direct involvement of the default mode network in cognitive functions, as represented by a dynamic rather than static interaction with specific task-positive networks, such as the working memory network.     

Molecular basis for evolving modularity in the yeast protein interaction network

Scale-free networks are generically defined by a power-law distribution of node connectivities. Vastly different graph topologies fit this law, ranging from the assortative, with frequent similar-degree node connections, to a modular structure. Using a metric to determine the extent of modularity, we examined the yeast protein network and found it to be significantly self-dissimilar. By orthologous node categorization, we established the evolutionary trend in the network, from an “emerging” assortative network to a present-day modular topology. The evolving topology fits a generic connectivity distribution but with a progressive enrichment in intramodule hubs that avoid each other. Primeval tolerance to random node failure is shown to evolve toward resilience to hub failure, thus removing the fragility often ascribed to scale-free networks. This trend is algorithmically reproduced by adopting a connectivity accretion law that disfavors like-degree connections for large-degree nodes. The selective advantage of this trend relates to the need to prevent a failed hub from inducing failure in an adjacent hub. The molecular basis for the evolutionary trend is likely rooted in the high-entropy penalty entailed in the association of two intramodular hubs.     

Body composition adaptations to lower-body plyometric training: a systematic review and meta-analysis

The aim of this meta-analysis was to explore the effects of plyometric jump training (PJT) on body composition parameters among males. Relevant articles were searched in the electronic databases PubMed, MEDLINE, WOS, and SCOPUS, using the key words “ballistic”, “complex”, “explosive”, “force-velocity”, “plyometric”, “stretch-shortening cycle”, “jump”, “training”, and “body composition”. We included randomized controlled trials (RCTs) that investigating the effects of PJT in healthy male’s body composition (e.g., muscle mass; body fat), irrespective of age. From database searching 21 RCTs were included (separate experimental groups = 28; pooled number of participants = 594). Compared to control, PJT produced significant increases in total leg muscle volume (small ES = 0.55, p = 0.009), thigh muscle volume (small ES = 0.38, p = 0.043), thigh girth (large ES = 1.78, p = 0.011), calf girth (large ES = 1.89, p = 0.022), and muscle pennation angle (small ES = 0.53, p = 0.040). However, we did not find significant difference between PJT and control for muscle cross-sectional area, body fat, and skinfold thickness. Heterogeneity remained low-to-moderate for most analyses, and using the Egger’s test publication bias was not found in any of the analyses (p = 0.300–0.900). No injuries were reported among the included studies. PJT seems to be an effective and safe mode of exercise for increasing leg muscle volume, thigh muscle volume, thigh and calf girth, and muscle pennation angle. Therefore, PJT may be effective to improve muscle size and architecture, with potential implications in several clinical and sport-related contexts.     

Fine-Scale Dissection of Functional Protein Network Organization by Statistical Network Analysis

Revealing organizational principles of biological networks is an important goal of systems biology. In this study, we sought to analyze the dynamic organizational principles within the protein interaction network by studying the characteristics of individual neighborhoods of proteins within the network based on their gene expression as well as protein-protein interaction patterns. By clustering proteins into distinct groups based on their neighborhood gene expression characteristics, we identify several significant trends in the dynamic organization of the protein interaction network. We show that proteins with distinct neighborhood gene expression characteristics are positioned in specific localities in the protein interaction network thereby playing specific roles in the dynamic network connectivity. Remarkably, our analysis reveals a neighborhood characteristic that corresponds to the most centrally located group of proteins within the network. Further, we show that the connectivity pattern displayed by this group is consistent with the notion of “rich club connectivity” in complex networks. Importantly, our findings are largely reproducible in networks constructed using independent and different datasets.