Social contagion in a world with asymmetric influence.

Social media has blurred the distinction between news outlets and social networks by giving everyone access to mass communication. We simulate how influencers compete for attention on a social network by spreading information. The network structure occupies an ordered metastable state where one influencer maintains dominance for a sustained period or a fragmented state that divides attention between influencers. Numerical simulations are performed to map the domain of the ordered regime on various network topologies. Mutual coexistence between a few dominating influencers occurs on a scale-free social network. Our findings suggest the perception of fake news as a pervasive problem is endemic to a society where everyone can become a news outlet.

Emergence and decline of scientific paradigms.

Scientific paradigms have a tendency to rise fast and decline slowly. This asymmetry reflects the difficulty in developing a truly original idea, compared to the ease at which a concept can be eroded by numerous modifications. Here we formulate a model for the emergence and spread of ideas which deals with this asymmetry by constraining the ability of agents to return to already abandoned concepts. The model exhibits a fairly regular pattern of global paradigm shifts, where older paradigms are eroded and subsequently replaced by new ones. The model sets the theme for a new class of pattern formation models, where local dynamics breaks the detailed balance in a way that prevents old states from defending themselves against new nucleating or invading states. The model allows for frozen events in terms of the coexistence of multiple metastable states.

Time walkers and spatial dynamics of aging information.

The distribution of information is essential for a living system's ability to coordinate and adapt. Random walkers are often used to model this distribution process and, in doing so, one effectively assumes that information maintains its relevance over time. But the value of information in social and biological systems often decays and must continuously be updated. To capture the spatial dynamics of aging information, we introduce time walkers. A time walker moves like a random walker, but interacts with traces left by other walkers, some representing older information, some newer. The traces form a navigable information landscape which we visualize as a river network. We quantify the dynamical properties of time walkers, and the quality of the information left behind, on a two-dimensional lattice. We show that searching in this landscape is superior to random searching.

Minimal gene regulatory circuits that can count like bacteriophage lambda.

The behavior of living systems is dependent on large dynamical gene regulatory networks (GRNs). However, the functioning of even the smallest GRNs is difficult to predict. The bistable GRN of bacteriophage lambda is able to count to make a decision between lysis and lysogeny on the basis of the number of phages infecting the cell, even though replication of the phage genome eliminates this initial difference. By simulating the behavior of a large number of random transcriptional GRNs, we show that a surprising variety of GRNs can carry out this complex task, including simple CI-Cro-like mutual repression networks. Thus, our study extends the repertoire of simple GRNs. Counterintuitively, the major effect of the addition of CII-like regulation, generally thought to be needed for counting by lambda, was to improve the ability of the networks to complete a simulated prophage induction. Our study suggests that additional regulatory mechanisms to decouple Cro and CII levels may exist in lambda and that infection counting could be widespread among temperate bacteriophages, many of which contain CI-Cro-like circuits.

Pathway identification by network pruning in the metabolic network of Escherichia coli.

MOTIVATION: All metabolic networks contain metabolites, such as ATP and NAD, known as currency metabolites, which take part in many reactions. These are often removed in the study of these networks, but no consensus exists on what actually constitutes a currency metabolite, and it is also unclear how these highly connected nodes contribute to the global structure of the network. RESULTS: In this article, we analyse how the Escherichia coli metabolic network responds to pruning in the form of sequential removal of metabolites with highest degree. As expected this leads to network fragmentation, but the process by which it occurs suggests modularity and long-range correlations within the network. We find that the pruned networks contain longer paths than the random expectation, and that the paths that survive the pruning also exhibit a lower cost (number of involved metabolites) compared with random paths in the full metabolic network. Finally we confirm that paths detected by pruning overlap with known metabolic pathways. We conclude that pruning reveals functional pathways in metabolic networks, where currency metabolites may be seen as ingredients in a well-balanced soup in which main metabolic production lines are immersed. CONTACT: gerlee@nbi.dk SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Reinforced communication and social navigation generate groups in model networks.

To investigate the role of information flow in group formation, we introduce a model of communication and social navigation. We let agents gather information in an idealized network society and demonstrate that heterogeneous groups can evolve without presuming that individuals have different interests. In our scenario, individuals' access to global information is constrained by local communication with the nearest neighbors on a dynamic network. The result is reinforced interests among like-minded agents in modular networks; the flow of information works as a glue that keeps individuals together. The model explains group formation in terms of limited information access and highlights global broadcasting of information as a way to counterbalance this fragmentation. To illustrate how the information constraints imposed by the communication structure affects future development of real-world systems, we extrapolate dynamics from the topology of four social networks.

Oscillations and temporal signalling in cells.

The development of new techniques to quantitatively measure gene expression in cells has shed light on a number of systems that display oscillations in protein concentration. Here we review the different mechanisms which can produce oscillations in gene expression or protein concentration using a framework of simple mathematical models. We focus on three eukaryotic genetic regulatory networks which show 'ultradian' oscillations, with a time period of the order of hours, and involve, respectively, proteins important for development (Hes1), apoptosis (p53) and immune response (NF-kappaB). We argue that underlying all three is a common design consisting of a negative feedback loop with time delay which is responsible for the oscillatory behaviour.

Modeling self-organization of communication and topology in social networks.

This paper introduces a model of self-organization between communication and topology in social networks, with a feedback between different communication habits and the topology. To study this feedback, we let agents communicate to build a perception of a network and use this information to create strategic links. We observe a narrow distribution of links when the communication is low and a system with a broad distribution of links when the communication is high. We also analyze the outcome of chatting, cheating, and lying, as strategies to get better access to information in the network. Chatting, although only adopted by a few agents, gives a global gain in the system. Contrary, a global loss is inevitable in a system with too many liars.

Searchability of networks.

We investigate the searchability of complex systems in terms of their interconnectedness. Associating searchability with the number and size of branch points along the paths between the nodes, we find that scale-free networks are relatively difficult to search, and thus that the abundance of scale-free networks in nature and society may reflect an attempt to protect local areas in a highly interconnected network from nonrelated communication. In fact, starting from a random node, real-world networks with higher order organization like modular or hierarchical structure are even more difficult to navigate than random scale-free networks. The searchability at the node level opens the possibility for a generalized hierarchy measure that captures both the hierarchy in the usual terms of trees as in military structures, and the intrinsic hierarchical nature of topological hierarchies for scale-free networks as in the Internet.

Navigating networks with limited information.

We study navigation with limited information in networks and demonstrate that many real-world networks have a structure which can be described as favoring communication at short distance at the cost of constraining communication at long distance. This feature, which is robust and more evident with limited than with complete information, reflects both topological and possibly functional design characteristics. For example, the characteristics of the networks studied derived from a city and from the Internet are manifested through modular network designs. We also observe that directed navigation in typical networks requires remarkably little information on the level of individual nodes. By studying navigation or specific signaling, we take a complementary approach to the common studies of information transfer devoted to broadcasting of information in studies of virus spreading and the like.

Communication boundaries in networks.

We investigate and quantify the interplay between topology and the ability to send specific signals in complex networks. We find that in a majority of investigated real-world networks the ability to communicate is favored by the network topology at small distances, but disfavored at larger distances. We further suggest how the ability to locate specific nodes can be improved if information associated with the overall traffic in the network is available.

Networks and cities: an information perspective.

Traffic is constrained by the information involved in locating the receiver and the physical distance between sender and receiver. We here focus on the former, and investigate traffic in the perspective of information handling. We replot the road map of cities in terms of the information needed to locate specific addresses and create information city networks with roads mapped to nodes and intersections to links between nodes. These networks have the broad degree distribution found in many other complex networks. The mapping to an information city network makes it possible to quantify the information associated with locating specific addresses.

Epigenetics as a first exit problem.

We develop a framework to discuss the stability of epigenetic states as first exit problems in dynamical systems with noise. We consider in particular the stability of the lysogenic state of the lambda prophage. The formalism defines a quantitative measure of robustness of inherited states.

Thermodynamical implications of a protein model with water interactions.

We refine a protein model that reproduces fundamental aspects of protein thermodynamics. The model exhibits two transitions, hot and cold unfolding. The number of relevant parameters is reduced to three: (1) binding energy of folding relative to the orientational energy of bound water, (2) ratio of degrees of freedom between the folded and unfolded protein chain, and (3) the number of water molecules that can access the hydrophobic parts of the protein interior upon unfolding. By increasing the number of water molecules in the model, the separation between the two peaks in the heat capacity curve comes closer, which is more consistent with experimental data. In the end we show that if we, as a speculative assumption, assign only two distinct energy levels for the bound water molecules, better correspondence with experiments can be obtained.

Hydrogen bonds in polymer folding.

We studied the thermodynamics of a homopolymeric chain with both van der Waals and directed hydrogen bond interaction. The effect of hydrogen bonds is to reduce dramatically the entropy of low-lying states and to give rise to long-range order and to conformations displaying secondary structures. For compact polymers a transition is found between helix-rich states and low-entropy sheet-dominated states. The consequences of this transition for protein folding and, in particular, for the problem of prions are discussed.

Thermodynamics of heat-shock response.

Production of heat-shock proteins is induced when a living cell is exposed to a rise in temperature. The heat-shock response of protein DnaK synthesis in E.coli for temperature shifts T-->T+DeltaT and T-->T-DeltaT is measured as a function of the initial temperature T. We observe a reversed heat shock at low T. The magnitude of the shock increases when one increases the distance to the temperature T0 approximately 23 degrees C, thereby mimicking the nonmonotonous stability of proteins at low temperature. This suggests that stability related to hot as well as cold unfolding of proteins is directly implemented in the biological control of protein folding.

Pathways in two-state protein folding.

Thermodynamic measurements of proteins indicate that the folding to the native state takes place either through stable intermediates or through a two-state process without intermediates. The rather short folding times of proteins indicate that folding is guided through some sequence of contact bindings. We discuss the possibility of reconciling a two-state folding event with a sequential folding process in a schematic model of protein folding. We propose a new dynamical transition temperature that is lower than the temperature at which proteins in equilibrium unfold. This is in qualitative agreement with observations of in vivo protein folding activity quantified by chaperone concentration in Escherichia coli. Finally, we discuss our framework in connection with the unfolding of proteins at low temperatures.

Robustness as an evolutionary principle.

We suggest simulating evolution of complex organisms using a model constrained solely by the requirement of robustness in its expression patterns. This scenario is illustrated by evolving discrete logical networks with epigenetic properties. Evidence for dynamical features in the evolved networks is found that can be related to biological observables.