Scale-free Organization Research Articles

Temporal Signatures of Criticality in Human Cortical Excitability as Probed by Early Somatosensory Responses.

Brain responses vary considerably from moment to moment, even to identical sensory stimuli. This has been attributed to changes in instantaneous neuronal states determining the system's excitability. Yet the spatiotemporal organization of these dynamics remains poorly understood. Here we test whether variability in stimulus-evoked activity can be interpreted within the framework of criticality, which postulates dynamics of neural systems to be tuned toward the phase transition between stability and instability as is reflected in scale-free fluctuations in spontaneous neural activity. Using a novel noninvasive approach in 33 male human participants, we tracked instantaneous cortical excitability by inferring the magnitude of excitatory postsynaptic currents from the N20 component of the somatosensory evoked potential. Fluctuations of cortical excitability demonstrated long-range temporal dependencies decaying according to a power law across trials, a hallmark of systems at critical states. As these dynamics covaried with changes in prestimulus oscillatory activity in the alpha band (8-13 Hz), we establish a mechanistic link between ongoing and evoked activity through cortical excitability and argue that the co-emergence of common temporal power laws may indeed originate from neural networks poised close to a critical state. In contrast, no signatures of criticality were found in subcortical or peripheral nerve activity. Thus, criticality may represent a parsimonious organizing principle of variability in stimulus-related brain processes on a cortical level, possibly reflecting a delicate equilibrium between robustness and flexibility of neural responses to external stimuli.SIGNIFICANCE STATEMENT Variability of neural responses in primary sensory areas is puzzling, as it is detrimental to the exact mapping between stimulus features and neural activity. However, such variability can be beneficial for information processing in neural networks if it is of a specific nature, namely, if dynamics are poised at a so-called critical state characterized by a scale-free spatiotemporal structure. Here, we demonstrate the existence of a link between signatures of criticality in ongoing and evoked activity through cortical excitability, which fills the long-standing gap between two major directions of research on neural variability: the impact of instantaneous brain states on stimulus processing on the one hand and the scale-free organization of spatiotemporal network dynamics of spontaneous activity on the other.

Investigation of the role of ion channels in human pancreatic β-cell hubs: A mathematical modeling study

In many cellular networks, the structure of the network follows a scale-free organization, where a limited number of cells are strongly coupled to other cells. These cells are called hub cells and their critical roles are well accepted. Despite their importance, there have been only a few studies investigating the characteristic features of these cells. In this paper, a computational approach is proposed to study the possible role of different ion channels in distinguishing between the hub and non-hub cells. The results show that the P/Q-type and T-type calcium channels may have an especial role in the β-cell hubs because the high-level expressions of these channels make a pancreatic β-cell more potent to force other coupled cells to follow it. In addition, in order to consider the variation of the coupling strength with voltage, a novel mathematical model is proposed for the gap junction coupling between the pancreatic β-cells. The proposed approach is validated based on the data from the literature.

Targeting protein-protein interactions using methods of cheminformatics

We have recently mapped the protein interaction networks of methicillin-resistant Staphylococcus aureus that revealed its scale-free organization with characteristic presence of highly-connected hub proteins that are critical for bacterial survival [1]. Here we report the discovery of highly selective nanomolar inhibitors for one such hub target - staphylococcal pyruvate kinase. The lead compound has been identified through synergetic combination of methods of high-throughput screening and cheminformatics; its further synthetic modifications resulted in much improved antimicrobial properties. Further lead optimization yielded drug candidates with picomolar activity against methicillin-resistant Staphylococcus aureus. Considering a notable lack of recent reports on novel antibacterial targets and cognate antibacterial compounds, this study provides a valuable perspective on the development of a new generation of antimicrobials. Equally noteworthy, the results of the current work highlight the importance of cheminformatics-driven exploration of chemical space around initial high throughput screening hits.

Cheminformatics-Driven Discovery of Selective, Nanomolar Inhibitors for Staphylococcal Pyruvate Kinase

We have recently mapped the protein interaction network of methicillin-resistant Staphylococcus aureus (MRSA), which revealed its scale-free organization with characteristic presence of highly connected hub proteins that are critical for bacterial survival. Here we report the discovery of inhibitors that are highly potent against one such hub target, staphylococcal pyruvate kinase (PK). Importantly, the developed compounds demonstrate complete selectivity for the bacterial enzyme compared to all human orthologues. The lead 91nM inhibitor IS-130 has been identified through ligand-based cheminformatic exploration of a chemical space around micromolar hits initially generated by experimental screening. The following crystallographic study resulted in identification of a tetrameric MRSA PK structure where IS-130 is bound to the interface between the protein's subunits. This newly described binding pocket is not present in otherwise highly similar human orthologues and can be effectively utilized for selective inhibition of bacterial PK. The following synthetic modifications of IS-130, guided by structure-based molecular modeling, resulted in the development of MRSA PK inhibitors with much improved antimicrobial properties. Considering a notable lack of recent reports on novel antibacterial targets and cognate antibacterial compounds, this study provides a valuable perspective on the development of a new generation of antimicrobials. Equally noteworthy, the results of the current work highlight the importance of rigorous cheminformatics-based exploration of the results of high-throughput experiments.

Chemical Basis of Metabolic Network Organization

Although the metabolic networks of the three domains of life consist of different constituents and metabolic pathways, they exhibit the same scale-free organization. This phenomenon has been hypothetically explained by preferential attachment principle that the new-recruited metabolites attach preferentially to those that are already well connected. However, since metabolites are usually small molecules and metabolic processes are basically chemical reactions, we speculate that the metabolic network organization may have a chemical basis. In this paper, chemoinformatic analyses on metabolic networks of Kyoto Encyclopedia of Genes and Genomes (KEGG), Escherichia coli and Saccharomyces cerevisiae were performed. It was found that there exist qualitative and quantitative correlations between network topology and chemical properties of metabolites. The metabolites with larger degrees of connectivity (hubs) are of relatively stronger polarity. This suggests that metabolic networks are chemically organized to a certain extent, which was further elucidated in terms of high concentrations required by metabolic hubs to drive a variety of reactions. This finding not only provides a chemical explanation to the preferential attachment principle for metabolic network expansion, but also has important implications for metabolic network design and metabolite concentration prediction.

Structural Preferential Attachment: Network Organization beyond the Link

We introduce a mechanism which models the emergence of the universal properties of complex networks, such as scale independence, modularity and self-similarity, and unifies them under a scale-free organization beyond the link. This brings a new perspective on network organization where communities, instead of links, are the fundamental building blocks of complex systems. We show how our simple model can reproduce social and information networks by predicting their community structure and more importantly, how their nodes or communities are interconnected, often in a self-similar manner.

Mapping the Protein Interaction Network in Methicillin-Resistant Staphylococcus aureus

Mortality attributable to infection with methicillin-resistant Staphylococcus aureus (MRSA) has now overtaken the death rate for AIDS in the United States, and advances in research are urgently needed to address this challenge. We report the results of the systematic identification of protein-protein interactions for the hospital-acquired strain MRSA-252. Using a high-throughput pull-down strategy combined with quantitative proteomics to distinguish specific from nonspecific interactors, we identified 13,219 interactions involving 608 MRSA proteins. Consecutive analyses revealed that this protein interaction network (PIN) exhibits scale-free organization with the characteristic presence of highly connected hub proteins. When clinical and experimental antimicrobial targets were queried in the network, they were generally found to occupy peripheral positions in the PIN with relatively few interacting partners. In contrast, the hub proteins identified in this MRSA PIN that are essential for network integrity and stability have largely been overlooked as drug targets. Thus, this empirical MRSA-252 PIN provides a rich source for identifying critical proteins essential for network stability, many of which can be considered as prospective antimicrobial drug targets.

THE ONTOGENY OF SCALE-FREE SYNTAX NETWORKS: PHASE TRANSITIONS IN EARLY LANGUAGE ACQUISITION

Language development in children provides a window to understand the transition from protolanguage to language. Here we present the first analysis of the emergence of syntax in terms of complex networks. A previously unreported, sharp transition is shown to occur around two years of age from a (pre-syntactic) tree-like structure to a scale-free, small world syntax network. The development of these networks thus reveals a nonlinear dynamical pattern where the global topology of syntax graphs shifts from a hierarchical, tree-like pattern, to a scale-free organization. Such change seems difficult to be explained under a self-organization framework. Instead, it actually supports the presence of some underlying innate component, as early suggested by some authors.

Small-world and scale-free organization of voxel-based resting-state functional connectivity in the human brain

The brain is a complex dynamic system of functionally connected regions. Graph theory has been successfully used to describe the organization of such dynamic systems. Recent resting-state fMRI studies have suggested that inter-regional functional connectivity shows a small-world topology, indicating an organization of the brain in highly clustered sub-networks, combined with a high level of global connectivity. In addition, a few studies have investigated a possible scale-free topology of the human brain, but the results of these studies have been inconclusive. These studies have mainly focused on inter-regional connectivity, representing the brain as a network of brain regions, requiring an arbitrary definition of such regions. However, using a voxel-wise approach allows for the model-free examination of both inter-regional as well as intra-regional connectivity and might reveal new information on network organization. Especially, a voxel-based study could give information about a possible scale-free organization of functional connectivity in the human brain. Resting-state 3 Tesla fMRI recordings of 28 healthy subjects were acquired and individual connectivity graphs were formed out of all cortical and sub-cortical voxels with connections reflecting inter-voxel functional connectivity. Graph characteristics from these connectivity networks were computed. The clustering-coefficient of these networks turned out to be much higher than the clustering-coefficient of comparable random graphs, together with a short average path length, indicating a small-world organization. Furthermore, the connectivity distribution of the number of inter-voxel connections followed a power-law scaling with an exponent close to 2, suggesting a scale-free network topology. Our findings suggest a combined small-world and scale-free organization of the functionally connected human brain. The results are interpreted as evidence for a highly efficient organization of the functionally connected brain, in which voxels are mostly connected with their direct neighbors forming clustered sub-networks, which are held together by a small number of highly connected hub-voxels that ensure a high level of overall connectivity.

Inferring genetic regulatory networks of the inflammatory bowel disease in human peripheral blood mononuclear cells

Cell phenotypes are determined by groups of functionally related genes. Microarray profiling of gene expression provides us response of cellular state to its perturbation. Several methods for uncovering a cellular network show reliable network reconstruction. In this study, we present reconstruction of gene regulatory network of inflammation bowel disease in human peripheral blood mononuclear cell. The microarray based on Affymetrix Gene Chip Human Genome U133 Array Set HG-U133A is processed and applied network reconstruction algorithm, ARACNe. As a result, we will show that inferred network composed of 450 nodes and 2017 edges is roughly scale-free network and hierarchical organization. The major hub, CCNL2 (cyclin A2), in inferred network is shown to be associated with inflammatory function as well as apoptotic function.

Comparative QSAR- and Fragments Distribution Analysis of Drugs, Druglikes, Metabolic Substances, and Antimicrobial Compounds

A number of binary QSAR models have been developed using methods of artificial neural networks, k-nearest neighbors, linear discriminative analysis, and multiple linear regression and have been compared for their ability to recognize five types of chemical compounds that include conventional drugs, inactive druglikes, antimicrobial substituents, and bacterial and human metabolites. Thus, 20 binary classifiers have been created using a variety of 'inductive' and traditional 2D QSAR descriptors which allowed up to 99% accurate separation of the studied groups of activities. The comparison of the performance by four computational approaches demonstrated that the neural nets result in generally more accurate predictions, followed closely by k-nearest neighbors methods. It has also been demonstrated that complementation of 'inductive' descriptors with conventional QSAR parameters does not generally improve the quality of resulting solutions, conforming high predictive ability of 'inductive' variables. The conducted comparative QSAR analysis based on a novel linear optimization approach has helped to identify the extent of overlapping between the studied groups of compounds, such as cross-recognition of bacterial metabolites and antimicrobial compounds reflecting their immanent resemblance and similar origin. Human metabolites have been characterized as a very distinctive class of substances, separated from all other groups in the descriptors space and exhibiting different QSAR behavior. The analysis of unique structural fragments and substituents revealed inhomogeneous scale-free organization of human metabolites illustrating the fact that certain molecular scaffolds (such as sugars and nucleotides) may be strongly favored by natural evolution. The established scale-free organization of human metabolites has been contemplated as a factor of their unique positioning in the descriptors space and their distinctive QSAR properties. It is anticipated that the study may bring additional insight into QSAR determinants for conventional drugs, inactive chemicals, and metabolic substances and may help in rationalizing design and discovery of novel antimicrobials and human therapeutics with improved, metabolite-like properties.

Wrestling with pleiotropy: Genomic and topological analysis of the yeast gene expression network

The vast majority (>95%) of single-gene mutations in yeast affect not only the expression of the mutant gene, but also the expression of many other genes. These data suggest the presence of a previously uncharacterized "gene expression network"--a set of interactions between genes which dictate gene expression in the native cell environment. Here, we quantitatively analyze the gene expression network revealed by microarray expression data from 273 different yeast gene deletion mutants.(1) We find that gene expression interactions form a robust, error-tolerant "scale-free" network, similar to metabolic pathways(2) and artificial networks such as power grids and the internet.(3-5) Because the connectivity between genes in the gene expression network is unevenly distributed, a scale-free organization helps make organisms resistant to the deleterious effects of mutation, and is thus highly adaptive. The existence of a gene expression network poses practical considerations for the study of gene function, since most mutant phenotypes are the result of changes in the expression of many genes. Using principles of scale-free network topology, we propose that fragmenting the gene expression network via "genome-engineering" may be a viable and practical approach to isolating gene function.

Scale‐free networks in biology: new insights into the fundamentals of evolution?*

Scale-free network models describe many natural and social phenomena. In particular, networks of interacting components of a living cell were shown to possess scale-free properties. A recent study((1)) compares the system-level properties of metabolic and information networks in 43 archaeal, bacterial and eukaryal species and claims that the scale-free organization of these networks is more conserved during evolution than their content.