Robustness of cooperation on scale-free networks under continuous topological change

Conflict Dynamics in Scale-Free Networks with Degree Correlations and Hierarchical Structure

We present a study of the dynamic interactions between actors located on complex networks with scale-free and hierarchical scale-free topologies with assortative mixing, that is, correlations between the degree distributions of the actors. The actor's state evolves according to a model that considers its previous state, the inertia to change, and the influence of its neighborhood. We show that the time evolution of the system depends on the percentage of cooperative or competitive interactions. For scale-free networks, we find that the dispersion between actors is higher when all interactions are either cooperative or competitive, while a balanced presence of interactions leads to a lower separation. Moreover, positive assortative mixing leads to greater divergence between the states, while negative assortative mixing reduces this dispersion. We also find that hierarchical scale-free networks have both similarities and differences when compared with scale-free networks. Hierarchical scale-free networks, like scale-free networks, show the least divergence for an equal mix of cooperative and competitive interactions between actors. On the other hand, hierarchical scale-free networks, unlike scale-free networks, show much greater divergence when dominated by cooperative rather than competitive actors, and while the formation of a rich club (adding links between hubs) with cooperative interactions leads to greater divergence, the divergence is much less when they are fully competitive. Our findings highlight the importance of the topology where the interaction dynamics take place, and the fact that a balanced presence of cooperators and competitors makes the system more cohesive, compared to the case where one strategy dominates.

Invasion of Cooperation in Scale-Free Networks: Accumulated versus Average Payoffs

It is well known that cooperation cannot be an evolutionarily stable strategy for a non-iterative game in a well-mixed population. In contrast, structured populations favor cooperation, since cooperators can benefit each other by forming local clusters. Previous studies have shown that scale-free networks strongly promote cooperation. However, little is known about the invasion mechanism of cooperation in scale-free networks. To study microscopic and macroscopic behaviors of cooperators' invasion, we conducted computational experiments on the evolution of cooperation in scale-free networks where, starting from all defectors, cooperators can spontaneously emerge by mutation. Since the evolutionary dynamics are influenced by the definition of fitness, we tested two commonly adopted fitness functions: accumulated payoff and average payoff. Simulation results show that cooperation is strongly enhanced with the accumulated payoff fitness compared to the average payoff fitness. However, the difference between the two functions decreases as the average degree increases. As the average degree increases, cooperation decreases for the accumulated payoff fitness, while it increases for the average payoff fitness. Moreover, for the average payoff fitness, low-degree nodes play a more important role in spreading cooperative strategies than for the accumulated payoff fitness.

Constructing Robust Cooperative Networks using a Multi-Objective Evolutionary Algorithm

The design and construction of network structures oriented towards different applications has attracted much attention recently. The existing studies indicated that structural heterogeneity plays different roles in promoting cooperation and robustness. Compared with rewiring a predefined network, it is more flexible and practical to construct new networks that satisfy the desired properties. Therefore, in this paper, we study a method for constructing robust cooperative networks where the only constraint is that the number of nodes and links is predefined. We model this network construction problem as a multi-objective optimization problem and propose a multi-objective evolutionary algorithm, named MOEA-Net_rc, to generate the desired networks from arbitrary initializations. The performance of MOEA-Net_rc is validated on several synthetic and real-world networks. The results show that MOEA-Net_rc can construct balanced candidates and is insensitive to the initializations. MOEA-Net_rc can find the Pareto fronts for networks with different levels of cooperation and robustness. In addition, further investigation of the robustness of the constructed networks revealed the impact on other aspects of robustness during the construction process.

Population Fluctuation Promotes Cooperation in Networks

We consider the problem of explaining the emergence and evolution of cooperation in dynamic network-structured populations. Building on seminal work by Poncela et al., which shows how cooperation (in one-shot prisoner's dilemma) is supported in growing populations by an evolutionary preferential attachment (EPA) model, we investigate the effect of fluctuations in the population size. We find that a fluctuating model - based on repeated population growth and truncation - is more robust than Poncela et al.'s in that cooperation flourishes for a wider variety of initial conditions. In terms of both the temptation to defect, and the types of strategies present in the founder network, the fluctuating population is found to lead more securely to cooperation. Further, we find that this model will also support the emergence of cooperation from pre-existing non-cooperative random networks. This model, like Poncela et al.'s, does not require agents to have memory, recognition of other agents, or other cognitive abilities, and so may suggest a more general explanation of the emergence of cooperation in early evolutionary transitions, than mechanisms such as kin selection, direct and indirect reciprocity.

Identification of important interacting proteins (IIPs) in Plasmodium falciparum using large-scale interaction network analysis and in-silico knock-out studies

Background

Plasmodium falciparum causes the most severe form of malaria and affects 3.2 million people annually. Due to the increasing incidence of resistance to existing drugs, there is a growing need to discover new and more effective drugs against malaria. Despite the global importance of P. falciparum, vast majority of its proteins are uncharacterized experimentally. Application of newer approaches using several “omics” data has become successful for exploring the biological interactions underlying cellular processes. Till date not many system level study has been published using P. falciparum protein protein interaction. Hence, the purpose of this study is to develop a standardized pipeline for structural, functional, and topographical analysis of large scale protein protein interaction network (PPIN) in order to identify proteins important for network topology and integrity. Here, P. falciparum PPIN has been utilized as a model for better understanding of the molecular mechanisms of survival and pathogenesis of malaria parasite.

Methods

Various graph theoretical approaches were implemented to identify highly interacting hub and central proteins that are crucial for network integrity. Further, potential network perturbing proteins via an in-silico knock-out (KO) analysis to isolate important interacting proteins (IIPs), which in principle, can elicit significant impact on the global and local environments of the P. falciparum interaction network.

Results

177 hubs and 132 central proteins were identified from the malarial (proteins: 1607; interactions: 4750) PPI networks. Using the in-silico knock-out exercise 131 and 99 global and local network perturbing proteins were also identified. Finally, 271 proteins from P. falciparum were shortlisted as important interacting proteins (IIPs), which not only play crucial role in intra-pathogen network integrity, stage specificity but also interact with various human proteins involved in multiple metabolic pathways within the host cell. These IIPs could be used as potential drug targets in malarial research.

Conclusion

Graph theoretical analysis of PPIN can be a very useful approach to identify proteins that are important for regulation of the interactions required for an organism’s survival. Important interacting proteins (IIPs) identified using P. falciparum PPIN provides a useful dataset containing probable candidates for future drug target analysis.

Electronic supplementary material

The online version of this article (doi:10.1186/s12936-015-0562-1) contains supplementary material, which is available to authorized users.