Error and attack tolerance of layered complex networks.

Many complex systems may be described by not one but a number of complex networks mapped on each other in a multi-layer structure. Because of the interactions and dependencies between these layers, the state of a single layer does not necessarily reflect well the state of the entire system. In this paper we study the robustness of five examples of two-layer complex systems: three real-life data sets in the fields of communication (the Internet), transportation (the European railway system), and biology (the human brain), and two models based on random graphs. In order to cover the whole range of features specific to these systems, we focus on two extreme policies of system's response to failures, no rerouting and full rerouting. Our main finding is that multi-layer systems are much more vulnerable to errors and intentional attacks than they appear from a single layer perspective.

Evolutionary games on complex networks : the emergence and maintenance of cooperation

Abstract The object of game theory lies in the analysis of situations where different social actors have conflicting requirements and where their individual decisions will all influence the global outcome. In this framework, several games have been invented to capture the essence of various dilemmas encountered in many common important socio-economic situations. Even though these games often succeed in helping us understand human or animal behavior in interactive settings, some experiments have shown that people tend to cooperate with each other in situations for which classical game theory strongly recommends them to do the exact opposite. Several mechanisms have been invoked to try to explain the emergence of this unexpected cooperative attitude. Among them, repeated interaction, reputation, and belonging to a recognizable group have often been mentioned. However, the work of Nowak and May (1992) showed that the simple fact of arranging the players according to a spatial structure and only allowing them to interact with their immediate neighbors is sufficient to sustain a certain amount of cooperation even when the game is played anonymously and without repetition. Nowak and May's study and much of the following work was based on regular structures such as two-dimensional grids. Axelrod et al. (2002) showed that by randomizing the choice of neighbors, i.e. by actually giving up a strictly local geographical structure, cooperation can still emerge, provided that the interaction patterns remain stable in time. This is a first step towards a social network structure. However, following pioneering work by sociologists in the sixties such as that of Milgram (1967), in the last few years it has become apparent that many social and biological interaction networks, and even some technological networks, have particular, and partly unexpected, properties that set them apart from regular or random graphs. Among other things, they usually display broad degree distributions, and show small-world topological structure. Roughly speaking, a small-world graph is a network where any individual is relatively close, in terms of social ties, to any other individual, a property also found in random graphs but not in regular lattices. However, in contrast with random graphs, small-world networks also have a certain amount of local structure, as measured, for instance, by a quantity called the clustering coefficient. In the same vein, many real conflicting situations in economy and sociology are not well described neither by a fixed geographical position of the individuals in a regular lattice, nor by a random graph. Furthermore, it is a known fact that network structure can highly influence dynamical phenomena such as the way diseases spread across a population and ideas or information get transmitted. Therefore, in the last decade, research attention has naturally shifted from random and regular graphs towards better models of social interaction structures. The primary goal of this work is to discover whether or not the underlying graph structure of real social networks could give explanations as to why one finds higher levels of cooperation in populations of human beings or animals than what is prescribed by classical game theory. To meet this objective, I start by thoroughly studying a real scientific coauthorship network and showing how it differs from biological or technological networks using divers statistical measurements. Furthermore, I extract and describe its community structure taking into account the intensity of a collaboration. Finally, I investigate the temporal evolution of the network, from its inception to its state at the time of the study in 2006, suggesting also an effective view of it as opposed to a historical one. Thereafter, I combine evolutionary game theory with several network models along with the studied coauthorship network in order to highlight which specific network properties foster cooperation and shed some light on the various mechanisms responsible for the maintenance of this same cooperation. I point out the fact that, to resist defection, cooperators take advantage, whenever possible, of the degree-heterogeneity of social networks and their underlying community structure. Finally, I show that cooperation level and stability depend not only on the game played, but also on the evolutionary dynamic rules used and the individual payoff calculations. Synopsis Le but de la théorie des jeux réside dans l'analyse de situations dans lesquelles différents acteurs sociaux, avec des objectifs souvent conflictuels, doivent individuellement prendre des décisions qui influenceront toutes le résultat global. Dans ce cadre, plusieurs jeux ont été inventés afin de saisir l'essence de divers dilemmes rencontrés dans d'importantes situations socio-économiques. Bien que ces jeux nous permettent souvent de comprendre le comportement d'êtres humains ou d'animaux en interactions, des expériences ont montré que les individus ont parfois tendance à coopérer dans des situations pour lesquelles la théorie classique des jeux prescrit de faire le contraire. Plusieurs mécanismes ont été invoqués pour tenter d'expliquer l'émergence de ce comportement coopératif inattendu. Parmi ceux-ci, la répétition des interactions, la réputation ou encore l'appartenance à des groupes reconnaissables ont souvent été mentionnés. Toutefois, les travaux de Nowak et May (1992) ont montré que le simple fait de disposer les joueurs selon une structure spatiale en leur permettant d'interagir uniquement avec leurs voisins directs est suffisant pour maintenir un certain niveau de coopération même si le jeu est joué de manière anonyme et sans répétitions. L'étude de Nowak et May, ainsi qu'un nombre substantiel de travaux qui ont suivi, étaient basés sur des structures régulières telles que des grilles à deux dimensions. Axelrod et al. (2002) ont montré qu'en randomisant le choix des voisins, i.e. en abandonnant une localisation géographique stricte, la coopération peut malgré tout émerger, pour autant que les schémas d'interactions restent stables au cours du temps. Ceci est un premier pas en direction d'une structure de réseau social. Toutefois, suite aux travaux précurseurs de sociologues des années soixante, tels que ceux de Milgram (1967), il est devenu clair ces dernières années qu'une grande partie des réseaux d'interactions sociaux et biologiques, et même quelques réseaux technologiques, possèdent des propriétés particulières, et partiellement inattendues, qui les distinguent de graphes réguliers ou aléatoires. Entre autres, ils affichent en général une distribution du degré relativement large ainsi qu'une structure de "petit-monde". Grossièrement parlant, un graphe "petit-monde" est un réseau où tout individu se trouve relativement près de tout autre individu en termes de distance sociale, une propriété également présente dans les graphes aléatoires mais absente des grilles régulières. Par contre, les réseaux "petit-monde" ont, contrairement aux graphes aléatoires, une certaine structure de localité, mesurée par exemple par une quantité appelée le "coefficient de clustering". Dans le même esprit, plusieurs situations réelles de conflit en économie et sociologie ne sont pas bien décrites ni par des positions géographiquement fixes des individus en grilles régulières, ni par des graphes aléatoires. De plus, il est bien connu que la structure même d'un réseau peut passablement influencer des phénomènes dynamiques tels que la manière qu'a une maladie de se répandre à travers une population, ou encore la façon dont des idées ou une information s'y propagent. Ainsi, durant cette dernière décennie, l'attention de la recherche s'est tout naturellement déplacée des graphes aléatoires et réguliers vers de meilleurs modèles de structure d'interactions sociales. L'objectif principal de ce travail est de découvrir si la structure sous-jacente de graphe de vrais réseaux sociaux peut fournir des explications quant aux raisons pour lesquelles on trouve, chez certains groupes d'êtres humains ou d'animaux, des niveaux de coopération supérieurs à ce qui est prescrit par la théorie classique des jeux. Dans l'optique d'atteindre ce but, je commence par étudier un véritable réseau de collaborations scientifiques et, en utilisant diverses mesures statistiques, je mets en évidence la manière dont il diffère de réseaux biologiques ou technologiques. De plus, j'extrais et je décris sa structure de communautés en tenant compte de l'intensité d'une collaboration. Finalement, j'examine l'évolution temporelle du réseau depuis son origine jusqu'à son état en 2006, date à laquelle l'étude a été effectuée, en suggérant également une vue effective du réseau par opposition à une vue historique. Par la suite, je combine la théorie évolutionnaire des jeux avec des réseaux comprenant plusieurs modèles et le réseau de collaboration susmentionné, afin de déterminer les propriétés structurelles utiles à la promotion de la coopération et les mécanismes responsables du maintien de celle-ci. Je mets en évidence le fait que, pour ne pas succomber à la défection, les coopérateurs exploitent dans la mesure du possible l'hétérogénéité des réseaux sociaux en termes de degré ainsi que la structure de communautés sous-jacente de ces mêmes réseaux. Finalement, je montre que le niveau de coopération et sa stabilité dépendent non seulement du jeu joué, mais aussi des règles de la dynamique évolutionnaire utilisées et du calcul du bénéfice d'un individu.

Synchronizability of EEG-Based Functional Networks in Early Alzheimer's Disease.

Recently graph theory and complex networks have been widely used as a mean to model functionality of the brain. Among different neuroimaging techniques available for constructing the brain functional networks, electroencephalography (EEG) with its high temporal resolution is a useful instrument of the analysis of functional interdependencies between different brain regions. Alzheimer's disease (AD) is a neurodegenerative disease, which leads to substantial cognitive decline, and eventually, dementia in aged people. To achieve a deeper insight into the behavior of functional cerebral networks in AD, here we study their synchronizability in 17 newly diagnosed AD patients compared to 17 healthy control subjects at no-task, eyes-closed condition. The cross-correlation of artifact-free EEGs was used to construct brain functional networks. The extracted networks were then tested for their synchronization properties by calculating the eigenratio of the Laplacian matrix of the connection graph, i.e., the largest eigenvalue divided by the second smallest one. In AD patients, we found an increase in the eigenratio, i.e., a decrease in the synchronizability of brain networks across delta, alpha, beta, and gamma EEG frequencies within the wide range of network costs. The finding indicates the destruction of functional brain networks in early AD.

Linear random knots and their scaling behavior

We present here a nonbiased probabilistic method that allows us to consistently analyze knottedness of linear random walks with up to several hundred noncorrelated steps. The method consists of analyzing the spectrum of knots formed by multiple closures of the same open walk through random points on a sphere enclosing the walk. Knottedness of individual "frozen" configurations of linear chains is therefore defined by a characteristic spectrum of realizable knots. We show that in the great majority of cases this method clearly defines the dominant knot type of a walk, i.e., the strongest component of the spectrum. In such cases, direct end-to-end closure creates a knot that usually coincides with the knot type that dominates the random closure spectrum. Interestingly, in a very small proportion of linear random walks, the knot type is not clearly defined. Such walks can be considered as residing in a border zone of the configuration space of two or more knot types. We also characterize the scaling behavior of linear random knots.

Local optima networks of hard combinatorial landscapes

Combinatorial optimization involves finding an optimal solution in a finite set of options; many everyday life problems are of this kind. However, the number of options grows exponentially with the size of the problem, such that an exhaustive search for the best solution is practically infeasible beyond a certain problem size. When efficient algorithms are not available, a practical approach to obtain an approximate solution to the problem at hand, is to start with an educated guess and gradually refine it until we have a good-enough solution. Roughly speaking, this is how local search heuristics work. These stochastic algorithms navigate the problem search space by iteratively turning the current solution into new candidate solutions, guiding the search towards better solutions. The search performance, therefore, depends on structural aspects of the search space, which in turn depend on the move operator being used to modify solutions. A common way to characterize the search space of a problem is through the study of its fitness landscape, a mathematical object comprising the space of all possible solutions, their value with respect to the optimization objective, and a relationship of neighborhood defined by the move operator. The landscape metaphor is used to explain the search dynamics as a sort of potential function. The concept is indeed similar to that of potential energy surfaces in physical chemistry. Borrowing ideas from that field, we propose to extend to combinatorial landscapes the notion of the inherent network formed by energy minima in energy landscapes. In our case, energy minima are the local optima of the combinatorial problem, and we explore several definitions for the network edges. At first, we perform an exhaustive sampling of local optima basins of attraction, and define weighted transitions between basins by accounting for all the possible ways of crossing the basins frontier via one random move. Then, we reduce the computational burden by only counting the chances of escaping a given basin via random kick moves that start at the local optimum. Finally, we approximate network edges from the search trajectory of simple search heuristics, mining the frequency and inter-arrival time with which the heuristic visits local optima. Through these methodologies, we build a weighted directed graph that provides a synthetic view of the whole landscape, and that we can characterize using the tools of complex networks science. We argue that the network characterization can advance our understanding of the structural and dynamical properties of hard combinatorial landscapes. We apply our approach to prototypical problems such as the Quadratic Assignment Problem, the NK model of rugged landscapes, and the Permutation Flow-shop Scheduling Problem. We show that some network metrics can differentiate problem classes, correlate with problem non-linearity, and predict problem hardness as measured from the performances of trajectory-based local search heuristics.

Flippase (FLP) recombinase-mediated marker recycling in the dermatophyte Arthroderma vanbreuseghemii.

Biological processes can be elucidated by investigating complex networks of relevant factors and genes. However, this is not possible in species for which dominant selectable markers for genetic studies are unavailable. To overcome the limitation in selectable markers for the dermatophyte Arthroderma vanbreuseghemii (anamorph: Trichophyton mentagrophytes), we adapted the flippase (FLP) recombinase-recombination target (FRT) site-specific recombination system from the yeast Saccharomyces cerevisiae as a selectable marker recycling system for this fungus. Taking into account practical applicability, we designed FLP/FRT modules carrying two FRT sequences as well as the flp gene adapted to the pathogenic yeast Candida albicans (caflp) or a synthetic codon-optimized flp (avflp) gene with neomycin resistance (nptII) cassette for one-step marker excision. Both flp genes were under control of the Trichophyton rubrum copper-repressible promoter (PCTR4). Molecular analyses of resultant transformants showed that only the avflp-harbouring module was functional in A. vanbreuseghemii. Applying this system, we successfully produced the Ku80 recessive mutant strain devoid of any selectable markers. This strain was subsequently used as the recipient for sequential multiple disruptions of secreted metalloprotease (fungalysin) (MEP) or serine protease (SUB) genes, producing mutant strains with double MEP or triple SUB gene deletions. These results confirmed the feasibility of this system for broad-scale genetic manipulation of dermatophytes, advancing our understanding of functions and networks of individual genes in these fungi.

Subknots in ideal knots, random knots, and knotted proteins.

We introduce disk matrices which encode the knotting of all subchains in circular knot configurations. The disk matrices allow us to dissect circular knots into their subknots, i.e. knot types formed by subchains of the global knot. The identification of subknots is based on the study of linear chains in which a knot type is associated to the chain by means of a spatially robust closure protocol. We characterize the sets of observed subknot types in global knots taking energy-minimized shapes such as KnotPlot configurations and ideal geometric configurations. We compare the sets of observed subknots to knot types obtained by changing crossings in the classical prime knot diagrams. Building upon this analysis, we study the sets of subknots in random configurations of corresponding knot types. In many of the knot types we analyzed, the sets of subknots from the ideal geometric configurations are found in each of the hundreds of random configurations of the same global knot type. We also compare the sets of subknots observed in open protein knots with the subknots observed in the ideal configurations of the corresponding knot type. This comparison enables us to explain the specific dispositions of subknots in the analyzed protein knots.

Arbuscular mycorrhizal fungi mediate below-ground plant-herbivore interactions: a phylogenetic study

Ecological interactions are complex networks, but have typically been studied in a pairwise fashion. Examining how third-party species can modify the outcome of pairwise interactions may allow us to better predict their outcomes in realistic systems. For instance, arbuscular mycorrhizal fungi (AMF) can affect plant interactions with other organisms, including below-ground herbivores, but the mechanisms underlying these effects remain unclear. Here, we use a comparative, phylogenetically controlled approach to test the relative importance of mycorrhizal colonization and plant chemical defences (cardenolides) in predicting plant survival and the abundance of a generalist below-ground herbivore across 14 species of milkweeds (Asclepias spp.). Plants were inoculated with a mixture of four generalist AMF species or left uninoculated. After 1month, larvae of Bradysia sp. (Diptera: Sciaridae), a generalist below-ground herbivore, colonized plant roots. We performed phylogenetically controlled analyses to assess the influence of AMF colonization and toxic cardenolides on plant growth, mortality and infestation by fungus gnats. Overall, plants inoculated with AMF exhibited greater survival than did uninoculated plants. Additionally, surviving inoculated plants had lower numbers of larvae in their roots and fewer non-AM fungi than surviving uninoculated plants. In phylogenetic controlled regressions, gnat density in roots was better predicted by the extent of root colonized by AMF than by root cardenolide concentration. Taken as a whole, AMF modify the effect of below-ground herbivores on plants in a species-specific manner, independent of changes in chemical defence. This study adds to the growing body of literature demonstrating that mycorrhizal fungi may improve plant fitness by conferring protection against antagonists, rather than growth benefits. In addition, we advocate using comparative analyses to disentangle the roles of shared history and ecology in shaping trait expression and to better predict the outcomes of complex multitrophic interactions.

Knot localization in proteins.

The backbones of proteins form linear chains. In the case of some proteins, these chains can be characterized as forming linear open knots. The knot type of the full chain reveals only limited information about the entanglement of the chain since, for example, subchains of an unknotted protein can form knots and subchains of a knotted protein can form different types of knots than the entire protein. To understand fully the entanglement within the backbone of a given protein, a complete analysis of the knotting within all of the subchains of that protein is necessary. In the present article, we review efforts to characterize the full knotting complexity within individual proteins and present a matrix that conveys information about various aspects of protein knotting. For a given protein, this matrix identifies the precise localization of knotted regions and shows the knot types formed by all subchains. The pattern in the matrix can be considered as a knotting fingerprint of that protein. We observe that knotting fingerprints of distantly related knotted proteins are strongly conserved during evolution and discuss how some characteristic motifs in the knotting fingerprints are related to the structure of the knotted regions and their possible biological role.

Effect of knotting on polymer shapes and their enveloping ellipsoids.

We simulate freely jointed chains to investigate how knotting affects the overall shapes of freely fluctuating circular polymeric chains. To characterize the shapes of knotted polygons, we construct enveloping ellipsoids that minimize volume while containing the entire polygon. The lengths of the three principal axes of the enveloping ellipsoids are used to define universal size and shape descriptors analogous to the squared radius of gyration and the inertial asphericity and prolateness. We observe that polymeric chains forming more complex knots are more spherical and also more prolate than chains forming less complex knots with the same number of edges. We compare the shape measures, determined by the enveloping ellipsoids, with those based on constructing inertial ellipsoids and explain the differences between these two measures of polymer shape.

A high-resolution anatomical atlas of the transcriptome in the mouse embryo.

Ascertaining when and where genes are expressed is of crucial importance to understanding or predicting the physiological role of genes and proteins and how they interact to form the complex networks that underlie organ development and function. It is, therefore, crucial to determine on a genome-wide level, the spatio-temporal gene expression profiles at cellular resolution. This information is provided by colorimetric RNA in situ hybridization that can elucidate expression of genes in their native context and does so at cellular resolution. We generated what is to our knowledge the first genome-wide transcriptome atlas by RNA in situ hybridization of an entire mammalian organism, the developing mouse at embryonic day 14.5. This digital transcriptome atlas, the Eurexpress atlas (http://www.eurexpress.org), consists of a searchable database of annotated images that can be interactively viewed. We generated anatomy-based expression profiles for over 18,000 coding genes and over 400 microRNAs. We identified 1,002 tissue-specific genes that are a source of novel tissue-specific markers for 37 different anatomical structures. The quality and the resolution of the data revealed novel molecular domains for several developing structures, such as the telencephalon, a novel organization for the hypothalamus, and insight on the Wnt network involved in renal epithelial differentiation during kidney development. The digital transcriptome atlas is a powerful resource to determine co-expression of genes, to identify cell populations and lineages, and to identify functional associations between genes relevant to development and disease.

Comparison between computational alanine scanning and per-residue binding free energy decomposition for protein-protein association using MM-GBSA: application to the TCR-p-MHC complex.

Recognition by the T-cell receptor (TCR) of immunogenic peptides (p) presented by Class I major histocompatibility complexes (MHC) is the key event in the immune response against virus-infected cells or tumor cells. A study of the 2C TCR/SIYR/H-2K(b) system using a computational alanine scanning and a much faster binding free energy decomposition based on the Molecular Mechanics-Generalized Born Surface Area (MM-GBSA) method is presented. The results show that the TCR-p-MHC binding free energy decomposition using this approach and including entropic terms provides a detailed and reliable description of the interactions between the molecules at an atomistic level. Comparison of the decomposition results with experimentally determined activity differences for alanine mutants yields a correlation of 0.67 when the entropy is neglected and 0.72 when the entropy is taken into account. Similarly, comparison of experimental activities with variations in binding free energies determined by computational alanine scanning yields correlations of 0.72 and 0.74 when the entropy is neglected or taken into account, respectively. Some key interactions for the TCR-p-MHC binding are analyzed and some possible side chains replacements are proposed in the context of TCR protein engineering. In addition, a comparison of the two theoretical approaches for estimating the role of each side chain in the complexation is given, and a new ad hoc approach to decompose the vibrational entropy term into atomic contributions, the linear decomposition of the vibrational entropy (LDVE), is introduced. The latter allows the rapid calculation of the entropic contribution of interesting side chains to the binding. This new method is based on the idea that the most important contributions to the vibrational entropy of a molecule originate from residues that contribute most to the vibrational amplitude of the normal modes. The LDVE approach is shown to provide results very similar to those of the exact but highly computationally demanding method.

Interregional compensatory mechanisms of motor functioning in progressing preclinical neurodegeneration.

Understanding brain reserve in preclinical stages of neurodegenerative disorders allows determination of which brain regions contribute to normal functioning despite accelerated neuronal loss. Besides the recruitment of additional regions, a reorganisation and shift of relevance between normally engaged regions are a suggested key mechanism. Thus, network analysis methods seem critical for investigation of changes in directed causal interactions between such candidate brain regions. To identify core compensatory regions, fifteen preclinical patients carrying the genetic mutation leading to Huntington's disease and twelve controls underwent fMRI scanning. They accomplished an auditory paced finger sequence tapping task, which challenged cognitive as well as executive aspects of motor functioning by varying speed and complexity of movements. To investigate causal interactions among brain regions a single Dynamic Causal Model (DCM) was constructed and fitted to the data from each subject. The DCM parameters were analysed using statistical methods to assess group differences in connectivity, and the relationship between connectivity patterns and predicted years to clinical onset was assessed in gene carriers. In preclinical patients, we found indications for neural reserve mechanisms predominantly driven by bilateral dorsal premotor cortex, which increasingly activated superior parietal cortices the closer individuals were to estimated clinical onset. This compensatory mechanism was restricted to complex movements characterised by high cognitive demand. Additionally, we identified task-induced connectivity changes in both groups of subjects towards pre- and caudal supplementary motor areas, which were linked to either faster or more complex task conditions. Interestingly, coupling of dorsal premotor cortex and supplementary motor area was more negative in controls compared to gene mutation carriers. Furthermore, changes in the connectivity pattern of gene carriers allowed prediction of the years to estimated disease onset in individuals. Our study characterises the connectivity pattern of core cortical regions maintaining motor function in relation to varying task demand. We identified connections of bilateral dorsal premotor cortex as critical for compensation as well as task-dependent recruitment of pre- and caudal supplementary motor area. The latter finding nicely mirrors a previously published general linear model-based analysis of the same data. Such knowledge about disease specific inter-regional effective connectivity may help identify foci for interventions based on transcranial magnetic stimulation designed to stimulate functioning and also to predict their impact on other regions in motor-associated networks.

Towards robust network based complex systems : from evolutionary cellular automata to biological models

Abstract Sitting between your past and your future doesn't mean you are in the present. Dakota Skye Complex systems science is an interdisciplinary field grouping under the same umbrella dynamical phenomena from social, natural or mathematical sciences. The emergence of a higher order organization or behavior, transcending that expected of the linear addition of the parts, is a key factor shared by all these systems. Most complex systems can be modeled as networks that represent the interactions amongst the system's components. In addition to the actual nature of the part's interactions, the intrinsic topological structure of underlying network is believed to play a crucial role in the remarkable emergent behaviors exhibited by the systems. Moreover, the topology is also a key a factor to explain the extraordinary flexibility and resilience to perturbations when applied to transmission and diffusion phenomena. In this work, we study the effect of different network structures on the performance and on the fault tolerance of systems in two different contexts. In the first part, we study cellular automata, which are a simple paradigm for distributed computation. Cellular automata are made of basic Boolean computational units, the cells; relying on simple rules and information from- the surrounding cells to perform a global task. The limited visibility of the cells can be modeled as a network, where interactions amongst cells are governed by an underlying structure, usually a regular one. In order to increase the performance of cellular automata, we chose to change its topology. We applied computational principles inspired by Darwinian evolution, called evolutionary algorithms, to alter the system's topological structure starting from either a regular or a random one. The outcome is remarkable, as the resulting topologies find themselves sharing properties of both regular and random network, and display similitudes Watts-Strogtz's small-world network found in social systems. Moreover, the performance and tolerance to probabilistic faults of our small-world like cellular automata surpasses that of regular ones. In the second part, we use the context of biological genetic regulatory networks and, in particular, Kauffman's random Boolean networks model. In some ways, this model is close to cellular automata, although is not expected to perform any task. Instead, it simulates the time-evolution of genetic regulation within living organisms under strict conditions. The original model, though very attractive by it's simplicity, suffered from important shortcomings unveiled by the recent advances in genetics and biology. We propose to use these new discoveries to improve the original model. Firstly, we have used artificial topologies believed to be closer to that of gene regulatory networks. We have also studied actual biological organisms, and used parts of their genetic regulatory networks in our models. Secondly, we have addressed the improbable full synchronicity of the event taking place on. Boolean networks and proposed a more biologically plausible cascading scheme. Finally, we tackled the actual Boolean functions of the model, i.e. the specifics of how genes activate according to the activity of upstream genes, and presented a new update function that takes into account the actual promoting and repressing effects of one gene on another. Our improved models demonstrate the expected, biologically sound, behavior of previous GRN model, yet with superior resistance to perturbations. We believe they are one step closer to the biological reality.