Dynamics of Unperturbed and Noisy Generalized Boolean Networks

For years, we have been building models of gene regulatory networks, where recent advances in molecular biology shed some light on new structural and dynamical properties of such highly complex systems. In this work, we propose a novel timing of updates in Random and Scale-Free Boolean Networks, inspired by recent findings in molecular biology. This update sequence is neither fully synchronous nor asynchronous, but rather takes into account the sequence in which genes affect each other. We have used both Kauffman's original model and Aldana's extension, which takes into account the structural properties about known parts of actual GRNs, where the degree distribution is right-skewed and long-tailed. The computer simulations of the dynamics of the new model compare favorably to the original ones and show biologically plausible results both in terms of attractors number and length. We have complemented this study with a complete analysis of our systems' stability under transient perturbations, which is one of biological networks defining attribute. Results are encouraging, as our model shows comparable and usually even better behavior than preceding ones without loosing Boolean networks attractive simplicity.Comment: 29 pages, publishe

A Study of NK Landscapes' Basins and Local Optima Networks

We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces (Doye, 2002). We use the well-known family of $NK$ landscapes as an example. In our case the inherent network is the graph where the vertices are all the local maxima and edges mean basin adjacency between two maxima. We exhaustively extract such networks on representative small NK landscape instances, and show that they are 'small-worlds'. However, the maxima graphs are not random, since their clustering coefficients are much larger than those of corresponding random graphs. Furthermore, the degree distributions are close to exponential instead of Poissonian. We also describe the nature of the basins of attraction and their relationship with the local maxima network.Comment: best paper nominatio

Additive Functions in Boolean Models of Gene Regulatory Network Modules

Gene-on-gene regulations are key components of every living organism. Dynamical abstract models of genetic regulatory networks help explain the genome’s evolvability and robustness. These properties can be attributed to the structural topology of the graph formed by genes, as vertices, and regulatory interactions, as edges. Moreover, the actual gene interaction of each gene is believed to play a key role in the stability of the structure. With advances in biology, some effort was deployed to develop update functions in Boolean models that include recent knowledge. We combine real-life gene interaction networks with novel update functions in a Boolean model. We use two sub-networks of biological organisms, the yeast cell-cycle and the mouse embryonic stem cell, as topological support for our system. On these structures, we substitute the original random update functions by a novel threshold-based dynamic function in which the promoting and repressing effect of each interaction is considered. We use a third real-life regulatory network, along with its inferred Boolean update functions to validate the proposed update function. Results of this validation hint to increased biological plausibility of the threshold-based function. To investigate the dynamical behavior of this new model, we visualized the phase transition between order and chaos into the critical regime using Derrida plots. We complement the qualitative nature of Derrida plots with an alternative measure, the criticality distance, that also allows to discriminate between regimes in a quantitative way. Simulation on both real-life genetic regulatory networks show that there exists a set of parameters that allows the systems to operate in the critical region. This new model includes experimentally derived biological information and recent discoveries, which makes it potentially useful to guide experimental research. The update function confers additional realism to the model, while reducing the complexity and solution space, thus making it easier to investigate

The Multiscale Backbone of the Human Phenotype Network Based on Biological Pathways

Background: Networks are commonly used to represent and analyze large and complex systems of interacting elements. In systems biology, human disease networks show interactions between disorders sharing common genetic background. We built pathway-based human phenotype network (PHPN) of over 800 physical attributes, diseases, and behavioral traits; based on about 2,300 genes and 1,200 biological pathways. Using GWAS phenotype-to-genes associations, and pathway data from Reactome, we connect human traits based on the common patterns of human biological pathways, detecting more pleiotropic effects, and expanding previous studies from a gene-centric approach to that of shared cell-processes. Results: The resulting network has a heavily right-skewed degree distribution, placing it in the scale-free region of the network topologies spectrum. We extract the multi-scale information backbone of the PHPN based on the local densities of the network and discarding weak connection. Using a standard community detection algorithm, we construct phenotype modules of similar traits without applying expert biological knowledge. These modules can be assimilated to the disease classes. However, we are able to classify phenotypes according to shared biology, and not arbitrary disease classes. We present examples of expected clinical connections identified by PHPN as proof of principle. Conclusions: We unveil a previously uncharacterized connection between phenotype modules and discuss potential mechanistic connections that are obvious only in retrospect. The PHPN shows tremendous potential to become a useful tool both in the unveiling of the diseases’ common biology, and in the elaboration of diagnosis and treatments

PERFORMANCE AND ROBUSTNESS OF CELLULAR AUTOMATA COMPUTATION ON IRREGULAR NETWORKS

We investigate the performances of collective task-solving capabilities and the robustness of complex networks of automata using the density and synchronization problems as typical cases. We show by computer simulations that evolved Watts–Strogatz small-world networks have superior performance with respect to several kinds of scale-free graphs. In addition, we show that Watts–Strogatz networks are as robust in the face of random perturbations, both transient and permanent, as configuration scale-free networks, while being widely superior to Barabási–Albert networks. This result differs from information diffusion on scale-free networks, where random faults are highly tolerated by similar topologies.Cellular automata, scale-free networks, small-world networks, density task, synchronization task, robustness

Additive functions in boolean models of gene regulatory network modules.

Gene-on-gene regulations are key components of every living organism. Dynamical abstract models of genetic regulatory networks help explain the genome's evolvability and robustness. These properties can be attributed to the structural topology of the graph formed by genes, as vertices, and regulatory interactions, as edges. Moreover, the actual gene interaction of each gene is believed to play a key role in the stability of the structure. With advances in biology, some effort was deployed to develop update functions in Boolean models that include recent knowledge. We combine real-life gene interaction networks with novel update functions in a Boolean model. We use two sub-networks of biological organisms, the yeast cell-cycle and the mouse embryonic stem cell, as topological support for our system. On these structures, we substitute the original random update functions by a novel threshold-based dynamic function in which the promoting and repressing effect of each interaction is considered. We use a third real-life regulatory network, along with its inferred Boolean update functions to validate the proposed update function. Results of this validation hint to increased biological plausibility of the threshold-based function. To investigate the dynamical behavior of this new model, we visualized the phase transition between order and chaos into the critical regime using Derrida plots. We complement the qualitative nature of Derrida plots with an alternative measure, the criticality distance, that also allows to discriminate between regimes in a quantitative way. Simulation on both real-life genetic regulatory networks show that there exists a set of parameters that allows the systems to operate in the critical region. This new model includes experimentally derived biological information and recent discoveries, which makes it potentially useful to guide experimental research. The update function confers additional realism to the model, while reducing the complexity and solution space, thus making it easier to investigate