The integrated development of network complexity modulates the diverse evolutionary mutation rates of individual proteins

The rate of evolution-related mutation varies widely among proteins while the unity of the organism implies an integrated evolution of its protein network. Focusing on the yeast interactome, we monitored the structural impact of amino acid substitution on yeast proteins with reported structure. The impact of mutation in creating or deleting structural markers for interactivity varies across proteins and modulates the evolutionary rates, yielding a unified kinetic law of accumulation of connectivities consistent with an integrated evolution of the interactome.     

Gene Duplication and the Properties of Biological Networks

Patterns of network connection of members of multigene families were examined for two biological networks: a genetic network from the yeast Saccharomyces cerevisiae and a protein–protein interaction network from Caenorhabditis elegans. In both networks, genes belonging to gene families represented by a single member in the genome (“singletons”) were disproportionately represented among the nodes having large numbers of connections. Of 68 single-member yeast families with 25 or more network connections, 28 (44.4%) were located in duplicated genomic segments believed to have originated from an ancient polyploidization event; thus, each of these 28 loci was thus presumably duplicated along with the genomic segment to which it belongs, but one of the two duplicates has subsequently been deleted. Nodes connected to major “hubs” with a large number of connections, tended to be relatively sparsely interconnected among themselves. Furthermore, duplicated genes, even those arising from recent duplication, rarely shared many network connections, suggesting that network connections are remarkably labile over evolutionary time. These factors serve to explain well-known general properties of biological networks, including their scale-free and modular nature. [Reviewing Editor : Dr. Manyuan Long]     

Synchrony based learning rule of Hopfield like chaotic neural networks with desirable structure

In this paper a new learning rule for the coupling weights tuning of Hopfield like chaotic neural networks is developed in such a way that all neurons behave in a synchronous manner, while the desirable structure of the network is preserved during the learning process. The proposed learning rule is based on sufficient synchronization criteria, on the eigenvalues of the weight matrix belonging to the neural network and the idea of Structured Inverse Eigenvalue Problem. Our developed learning rule not only synchronizes all neuron’s outputs with each other in a desirable topology, but also enables us to enhance the synchronizability of the networks by choosing the appropriate set of weight matrix eigenvalues. Specifically, this method is evaluated by performing simulations on the scale-free topology.     

Scale-free dynamics of somatic adaptability in immune system

The long-time dynamics of somatic adaptability in immune system is simulated by a simple physical model defined in the shape space. The immune system described by the model exhibits a scale free behavior as is observed in living systems. The balance between the positive and negative feedbacks of the model leads to a robust immune system where the positive one corresponds to the formation of memory cells and the negative one to immunosuppression. Also the immunosenescence of the system is discussed based on the time-dependence of the epigenetic landscape of the adaptive immune cells in the shape space.     

Scale-free extinction dynamics in spatially structured host-parasitoid systems

Much of the work on extinction events has focused on external perturbations of ecosystems, such as climatic change, or anthropogenic factors. Extinction, however, can also be driven by endogenous factors, such as the ecological interactions between species in an ecosystem. Here we show that endogenously driven extinction events can have a scale-free distribution in simple spatially structured host-parasitoid systems. Due to the properties of this distribution there may be many such simple ecosystems that, although not strictly permanent, persist for arbitrarily long periods of time. We identify a critical phase transition in the parameter space of the host-parasitoid systems, and explain how this is related to the scale-free nature of the extinction process. Based on these results, we conjecture that scale-free extinction processes and critical phase transitions of the type we have found may be a characteristic feature of many spatially structured, multi-species ecosystems in nature. The necessary ingredient appears to be competition between species where the locally inferior type disperses faster in space. If this condition is satisfied then the eventual outcome depends subtly on the strength of local superiority of one species versus the dispersal rate of the other.     

Application of network theory to potential mycorrhizal networks

The concept of a common mycorrhizal network implies that the arrangement of plants and mycorrhizal fungi in a community shares properties with other networks. A network is a system of nodes connected by links. Here we apply network theory to mycorrhizas to determine whether the architecture of a potential common mycorrhizal network is random or scale-free. We analyzed mycorrhizal data from an oak woodland from two perspectives: the phytocentric view using trees as nodes and fungi as links and the mycocentric view using fungi as nodes and trees as links. From the phytocentric perspective, the distribution of potential mycorrhizal links, as measured by the number of ectomycorrhizal morphotypes on trees of Quercus garryana, was random with a short tail, implying that all the individuals of this species are more or less equal in linking to fungi in a potential network. From the mycocentric perspective, however, the distribution of plant links to fungi was scale-free, suggesting that certain fungus species may act as hubs with frequent connections to the network. Parallels exist between social networks and mycorrhizas that suggest future lines of study on mycorrhizal networks.     

Congruent epidemic models for unstructured and structured populations: analytical reconstruction of a 2003 SARS outbreak

Both the threat of bioterrorism and the natural emergence of contagious diseases underscore the importance of quantitatively understanding disease transmission in structured human populations. Over the last few years, researchers have advanced the mathematical theory of scale-free networks and used such theoretical advancements in pilot epidemic models. Scale-free contact networks are particularly interesting in the realm of mathematical epidemiology, primarily because these networks may allow meaningfully structured populations to be incorporated in epidemic models at moderate or intermediate levels of complexity. Moreover, a scale-free contact network with node degree correlation is in accord with the well-known preferred mixing concept. The present author describes a semi-empirical and deterministic epidemic modeling approach that (a) focuses on time-varying rates of disease transmission in both unstructured and structured populations and (b) employs probability density functions to characterize disease progression and outbreak controls. Given an epidemic curve for a historical outbreak, this modeling approach calls for Monte Carlo calculations (that define the average new infection rate) and solutions to integro-differential equations (that describe outbreak dynamics in an aggregate population or across all network connectivity classes). Numerical results are obtained for the 2003 SARS outbreak in Taiwan and the dynamical implications of time-varying transmission rates and scale-free contact networks are discussed in some detail.     

Upstream reciprocity in heterogeneous networks

Many mechanisms for the emergence and maintenance of altruistic behavior in social dilemma situations have been proposed. Indirect reciprocity is one such mechanism, where other-regarding actions of a player are eventually rewarded by other players with whom the original player has not interacted. The upstream reciprocity (also called generalized indirect reciprocity) is a type of indirect reciprocity and represents the concept that those helped by somebody will help other unspecified players. In spite of the evidence for the enhancement of helping behavior by upstream reciprocity in rats and humans, theoretical support for this mechanism is not strong. In the present study, we numerically investigate upstream reciprocity in heterogeneous contact networks, in which the players generally have different number of neighbors. We show that heterogeneous networks considerably enhance cooperation in a game of upstream reciprocity. In heterogeneous networks, the most generous strategy, by which a player helps a neighbor on being helped and in addition initiates helping behavior, first occupies hubs in a network and then disseminates to other players. The scenario to achieve enhanced altruism resembles that seen in the case of the Prisoner's Dilemma game in heterogeneous networks.