EEG-based functional brain networks: does the network size matter?

Functional connectivity in human brain can be represented as a network using electroencephalography (EEG) signals. These networks--whose nodes can vary from tens to hundreds--are characterized by neurobiologically meaningful graph theory metrics. This study investigates the degree to which various graph metrics depend upon the network size. To this end, EEGs from 32 normal subjects were recorded and functional networks of three different sizes were extracted. A state-space based method was used to calculate cross-correlation matrices between different brain regions. These correlation matrices were used to construct binary adjacency connectomes, which were assessed with regards to a number of graph metrics such as clustering coefficient, modularity, efficiency, economic efficiency, and assortativity. We showed that the estimates of these metrics significantly differ depending on the network size. Larger networks had higher efficiency, higher assortativity and lower modularity compared to those with smaller size and the same density. These findings indicate that the network size should be considered in any comparison of networks across studies.

Synchronous versus asynchronous modeling of gene regulatory networks.

MOTIVATION: In silico modeling of gene regulatory networks has gained some momentum recently due to increased interest in analyzing the dynamics of biological systems. This has been further facilitated by the increasing availability of experimental data on gene-gene, protein-protein and gene-protein interactions. The two dynamical properties that are often experimentally testable are perturbations and stable steady states. Although a lot of work has been done on the identification of steady states, not much work has been reported on in silico modeling of cellular differentiation processes. RESULTS: In this manuscript, we provide algorithms based on reduced ordered binary decision diagrams (ROBDDs) for Boolean modeling of gene regulatory networks. Algorithms for synchronous and asynchronous transition models have been proposed and their corresponding computational properties have been analyzed. These algorithms allow users to compute cyclic attractors of large networks that are currently not feasible using existing software. Hereby we provide a framework to analyze the effect of multiple gene perturbation protocols, and their effect on cell differentiation processes. These algorithms were validated on the T-helper model showing the correct steady state identification and Th1-Th2 cellular differentiation process. AVAILABILITY: The software binaries for Windows and Linux platforms can be downloaded from http://si2.epfl.ch/~garg/genysis.html.

Structural Analysis of Networks

Network analysis naturally relies on graph theory and, more particularly, on the use of node and edge metrics to identify the salient properties in graphs. When building visual maps of networks, these metrics are turned into useful visual cues or are used interactively to filter out parts of a graph while querying it, for instance. Over the years, analysts from different application domains have designed metrics to serve specific needs. Network science is an inherently cross-disciplinary field, which leads to the publication of metrics with similar goals; different names and descriptions of their analytics often mask the similarity between two metrics that originated in different fields. Here, we study a set of graph metrics and compare their relative values and behaviors in an effort to survey their potential contributions to the spatial analysis of networks.

Dynamic simulation of regulatory networks using SQUAD.

BACKGROUND: The ambition of most molecular biologists is the understanding of the intricate network of molecular interactions that control biological systems. As scientists uncover the components and the connectivity of these networks, it becomes possible to study their dynamical behavior as a whole and discover what is the specific role of each of their components. Since the behavior of a network is by no means intuitive, it becomes necessary to use computational models to understand its behavior and to be able to make predictions about it. Unfortunately, most current computational models describe small networks due to the scarcity of kinetic data available. To overcome this problem, we previously published a methodology to convert a signaling network into a dynamical system, even in the total absence of kinetic information. In this paper we present a software implementation of such methodology. RESULTS: We developed SQUAD, a software for the dynamic simulation of signaling networks using the standardized qualitative dynamical systems approach. SQUAD converts the network into a discrete dynamical system, and it uses a binary decision diagram algorithm to identify all the steady states of the system. Then, the software creates a continuous dynamical system and localizes its steady states which are located near the steady states of the discrete system. The software permits to make simulations on the continuous system, allowing for the modification of several parameters. Importantly, SQUAD includes a framework for perturbing networks in a manner similar to what is performed in experimental laboratory protocols, for example by activating receptors or knocking out molecular components. Using this software we have been able to successfully reproduce the behavior of the regulatory network implicated in T-helper cell differentiation. CONCLUSION: The simulation of regulatory networks aims at predicting the behavior of a whole system when subject to stimuli, such as drugs, or determine the role of specific components within the network. The predictions can then be used to interpret and/or drive laboratory experiments. SQUAD provides a user-friendly graphical interface, accessible to both computational and experimental biologists for the fast qualitative simulation of large regulatory networks for which kinetic data is not necessarily available.

Emergence of Cooperation on Static and Dynamic Networks

Game theory is a branch of applied mathematics used to analyze situation where two or more agents are interacting. Originally it was developed as a model for conflicts and collaborations between rational and intelligent individuals. Now it finds applications in social sciences, eco- nomics, biology (particularly evolutionary biology and ecology), engineering, political science, international relations, computer science, and philosophy. Networks are an abstract representation of interactions, dependencies or relationships. Net- works are extensively used in all the fields mentioned above and in many more. Many useful informations about a system can be discovered by analyzing the current state of a network representation of such system. In this work we will apply some of the methods of game theory to populations of agents that are interconnected. A population is in fact represented by a network of players where one can only interact with another if there is a connection between them. In the first part of this work we will show that the structure of the underlying network has a strong influence on the strategies that the players will decide to adopt to maximize their utility. We will then introduce a supplementary degree of freedom by allowing the structure of the population to be modified along the simulations. This modification allows the players to modify the structure of their environment to optimize the utility that they can obtain.

Stochastic models and numerical algorithms for a class of regulatory gene networks.

Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856-860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.