Self-correcting networks: function, robustness, and motif distributions in biological signal processing

Triadic signatures of global human mobility networks

Global refugee and migrant flows form complex networks with serious consequences for both sending and receiving countries as well as those in between. While several basic network properties of these networks have been documented, their finer structural character remains under-studied. One such structure is the triad significance profile (TSP). In this study, the TSPs of global refugee and migrant flow networks are assessed. Results indicate that the migrant flow network's size and TSP remain stable over the years; its TSP shares patterns with social networks such as trade networks. In contrast, the refugee network has been more dynamic and structurally unstable; its TSP shares patterns with networks in the information-processing superfamily, which includes many biological networks. Our findings demonstrate commonality between migrant and social networks as well as between refugee and biological networks, pointing to possible interdisciplinary collaboration-e.g., application of biological network theories to refugee network dynamics-, potentially furthering theoretical development with respect to both network theory and theories on human mobility.

Local topological features of robust supply networks

The design of robust supply and distribution systems is one of the fundamental challenges at the interface of network science and logistics. Given the multitude of performance criteria, real-world constraints, and external influences acting upon such a system, even formulating an appropriate research question to address this topic is non-trivial. Here we present an abstraction of a supply and distribution system leading to a minimal model, which only retains stylized facts of the systemic function and, in this way, allows us to investigate the generic properties of robust supply networks. On this level of abstraction, a supply and distribution system is the strategic use of transportation to eliminate mismatches between production patterns (i.e., the amounts of goods produced at each production site of a company) and demand patterns (i.e., the amount of goods consumed at each location). When creating networks based on this paradigm and furthermore requiring the robustness of the system with respect to the loss of transportation routes (edge of the network) we see that robust networks are built from specific sets of subgraphs, while vulnerable networks display a markedly different subgraph composition. Our findings confirm a long-standing hypothesis in the field of network science, namely, that network motifs-statistically over-represented small subgraphs-are informative about the robust functioning of a network. Also, our findings offer a blueprint for enhancing the robustness of real-world supply and distribution systems.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s41109-022-00470-2.

Modeling of inter-organizational coordination dynamics in resilience planning of infrastructure systems: A multilayer network simulation framework

This paper proposes and tests a multilayer framework for simulating the network dynamics of inter-organizational coordination among interdependent infrastructure systems (IISs) in resilience planning. Inter-organizational coordination among IISs (such as transportation, flood control, and emergency management) would greatly affect the effectiveness of resilience planning. Hence, it is important to examine and understand the dynamics of coordination in networks of organizations within and across various systems in resilience planning. To capture the dynamic nature of coordination frequency and the heterogeneity of organizations, this paper proposes a multilayer network simulation framework enabling the characterization of inter-organizational coordination dynamics within and across IISs. In the proposed framework, coordination probabilities are utilized to approximate the varying levels of collaboration among organizations. Based on these derived collaborations, the simulation process perturbs intra-layer or inter-layer links and unveils the level of inter-organizational coordination within and across IISs. To test the proposed framework, the study examined a multilayer collaboration network of 35 organizations from five infrastructure systems within Harris County, Texas, based on the data gathered from a survey in the aftermath of Hurricane Harvey. The results indicate that prior to Hurricane Harvey: (1) coordination among organizations across different infrastructure systems is less than the coordination within the individual systems; (2) organizations from the community development system had a low level of coordination for hazard mitigation with organizations in flood control and transportation systems; (3) achieving a greater level of coordination among organizations across infrastructure systems is more difficult and would require a greater frequency of interaction (compared to within-system coordination). The results show the capability of the proposed multilayer network simulation framework to examine inter-organizational coordination dynamics at the system level (e.g., within and across IISs). The assessment of inter-organizational coordination within and across IISs sheds light on important organizational interdependencies in IISs and leads to recommendations for improving the resilience planning process.

SUMO-regulated transcription: challenging the dogma

The small ubiquitin-like modifier SUMO regulates many aspects of cellular physiology to maintain cell homeostasis, both under normal conditions and during cell stress. Components of the transcriptional apparatus and chromatin are among the most prominent SUMO substrates. The prevailing view is that SUMO serves to repress transcription. However, as we will discuss in this review, this model needs to be refined, because recent studies have revealed that SUMO can also have profound positive effects on transcription.

Understanding genetic variation - the value of systems biology

Pharmacology is currently transformed by the vast amounts of genome-associated information available for system-level interpretation. Here I review the potential of systems biology to facilitate this interpretation, thus paving the way for the emerging field of systems pharmacology. In particular, I will show how gene regulatory and metabolic networks can serve as a framework for interpreting high throughput data and as an interface to detailed dynamical models. In addition to the established connectivity analyses of effective networks, I suggest here to also analyze higher order architectural properties of effective networks.

Autonomous learning by simple dynamical systems with delayed feedback

A general scheme for the construction of dynamical systems able to learn generation of the desired kinds of dynamics through adjustment of their internal structure is proposed. The scheme involves intrinsic time-delayed feedback to steer the dynamics towards the target performance. As an example, a system of coupled phase oscillators, which can, by changing the weights of connections between its elements, evolve to a dynamical state with the prescribed (low or high) synchronization level, is considered and investigated.

Identifying emerging motif in growing networks

As function units, network motifs have been detected to reveal evolutionary mechanisms of complex systems, such as biological networks, food webs, engineering networks and social networks. However, emergence of motifs in growing networks may be problematic due to large fluctuation of subgraph frequency in the initial stage. This paper contributes to present a method which can identify the emergence of motif in growing networks. Based on the Erdös-Rényi(E-R) random null model, the variation rate of expected frequency of subgraph at adjacent time points was used to define the suitable detection range for motif identification. Upper and lower boundaries of the range were obtained in analytical form according to a chosen risk level. Then, the statistical metric Z-score was extended to a new one,, which effectively reveals the statistical significance of subgraph in a continuous period of time. In this paper, a novel research framework of motif identification was proposed, defining critical boundaries for the evolutionary process of networks and a significance metric of time scale. Finally, an industrial ecosystem at Kalundborg was adopted as a case study to illustrate the effectiveness and convenience of the proposed methodology.

The ecology of collective behavior

Networks of local interactions regulate biological systems. Ecological constraints set by resource distribution, operating costs, and the threat of rupture produce similar collective behavior in ants, cells, and gene transcription.

Similar patterns of interaction, such as network motifs and feedback loops, are used in many natural collective processes, probably because they have evolved independently under similar pressures. Here I consider how three environmental constraints may shape the evolution of collective behavior: the patchiness of resources, the operating costs of maintaining the interaction network that produces collective behavior, and the threat of rupture of the network. The ants are a large and successful taxon that have evolved in very diverse environments. Examples from ants provide a starting point for examining more generally the fit between the particular pattern of interaction that regulates activity, and the environment in which it functions.

Evolutionary design of non-frustrated networks of phase-repulsive oscillators

Evolutionary optimisation algorithm is employed to design networks of phase-repulsive oscillators that achieve an anti-phase synchronised state. By introducing the link frustration, the evolutionary process is implemented by rewiring the links with probability proportional to their frustration, until the final network displaying a unique non-frustrated dynamical state is reached. Resulting networks are bipartite and with zero clustering. In addition, the designed non-frustrated anti-phase synchronised networks display a clear topological scale. This contrasts usually studied cases of networks with phase-attractive dynamics, whose performance towards full synchronisation is typically enhanced by the presence of a topological hierarchy.

Reverse engineering biomolecular systems using -omic data: challenges, progress and opportunities

Recent advances in high-throughput biotechnologies have led to the rapid growing research interest in reverse engineering of biomolecular systems (REBMS). 'Data-driven' approaches, i.e. data mining, can be used to extract patterns from large volumes of biochemical data at molecular-level resolution while 'design-driven' approaches, i.e. systems modeling, can be used to simulate emergent system properties. Consequently, both data- and design-driven approaches applied to -omic data may lead to novel insights in reverse engineering biological systems that could not be expected before using low-throughput platforms. However, there exist several challenges in this fast growing field of reverse engineering biomolecular systems: (i) to integrate heterogeneous biochemical data for data mining, (ii) to combine top-down and bottom-up approaches for systems modeling and (iii) to validate system models experimentally. In addition to reviewing progress made by the community and opportunities encountered in addressing these challenges, we explore the emerging field of synthetic biology, which is an exciting approach to validate and analyze theoretical system models directly through experimental synthesis, i.e. analysis-by-synthesis. The ultimate goal is to address the present and future challenges in reverse engineering biomolecular systems (REBMS) using integrated workflow of data mining, systems modeling and synthetic biology.

Artefacts in statistical analyses of network motifs: general framework and application to metabolic networks

Few-node subgraphs are the smallest collective units in a network that can be investigated. They are beyond the scale of individual nodes but more local than, for example, communities. When statistically over- or under-represented, they are called network motifs. Network motifs have been interpreted as building blocks that shape the dynamic behaviour of networks. It is this promise of potentially explaining emergent properties of complex systems with relatively simple structures that led to an interest in network motifs in an ever-growing number of studies and across disciplines. Here, we discuss artefacts in the analysis of network motifs arising from discrepancies between the network under investigation and the pool of random graphs serving as a null model. Our aim was to provide a clear and accessible catalogue of such incongruities and their effect on the motif signature. As a case study, we explore the metabolic network of Escherichia coli and show that only by excluding ever more artefacts from the motif signature a strong and plausible correlation with the essentiality profile of metabolic reactions emerges.

Information processing in social insect networks

Investigating local-scale interactions within a network makes it possible to test hypotheses about the mechanisms of global network connectivity and to ask whether there are general rules underlying network function across systems. Here we use motif analysis to determine whether the interactions within social insect colonies resemble the patterns exhibited by other animal associations or if they exhibit characteristics of biological regulatory systems. Colonies exhibit a predominance of feed-forward interaction motifs, in contrast to the densely interconnected clique patterns that characterize human interaction and animal social networks. The regulatory motif signature supports the hypothesis that social insect colonies are shaped by selection for network patterns that integrate colony functionality at the group rather than individual level, and demonstrates the utility of this approach for analysis of selection effects on complex systems across biological levels of organization.

Agricultural trade networks and patterns of economic development

International trade networks are manifestations of a complex combination of diverse underlying factors, both natural and social. Here we apply social network analytics to the international trade network of agricultural products to better understand the nature of this network and its relation to patterns of international development. Using a network tool known as triadic analysis we develop triad significance profiles for a series of agricultural commodities traded among countries. Results reveal a novel network "superfamily" combining properties of biological information processing networks and human social networks. To better understand this unique network signature, we examine in more detail the degree and triadic distributions within the trade network by country and commodity. Our results show that countries fall into two very distinct classes based on their triadic frequencies. Roughly 165 countries fall into one class while 18, all highly isolated with respect to international agricultural trade, fall into the other. Only Vietnam stands out as a unique case. Finally, we show that as a country becomes less isolated with respect to number of trading partners, the country's triadic signature follows a predictable trajectory that may correspond to a trajectory of development.

Subgraph fluctuations in random graphs

The pattern of over- and under-representations of three-node subgraphs has become a standard method of characterizing complex networks and evaluating how this intermediate level of organization contributes to network function. Understanding statistical properties of subgraph counts in random graphs, their fluctuations, and their interdependences with other topological attributes is an important prerequisite for such investigations. Here we introduce a formalism for predicting subgraph fluctuations induced by perturbations of unidirectional and bidirectional edge densities. On this basis we predict the over- and under-representation of subgraphs arising from a density mismatch between a network and the corresponding pool of randomized graphs serving as a null model. Such mismatches occur, for example, in modular and hierarchical graphs.

Robust network clocks: design of genetic oscillators as a complex combinatorial optimization problem

Complex combinatorial optimization can be used to design network systems having desired dynamics and that are robust against structural perturbations. Here genetic networks exhibiting limit-cycle oscillations with prescribed periods and, furthermore, that are robust against the deletion of links and nodes or the application of noise are constructed. Large ensembles of robust genetic clocks with different periods could thus be obtained, and some of their statistical properties have been investigated. Similar methods can be used to design robust network oscillators of various origins.

Network connectivity during mergers and growth: optimizing the addition of a module

The principal eigenvalue λ of a network's adjacency matrix often determines dynamics on the network (e.g., in synchronization and spreading processes) and some of its structural properties (e.g., robustness against failure or attack) and is therefore a good indicator for how "strongly" a network is connected. We study how λ is modified by the addition of a module, or community, which has broad applications, ranging from those involving a single modification (e.g., introduction of a drug into a biological process) to those involving repeated additions (e.g., power-grid and transit development). We describe how to optimally connect the module to the network to either maximize or minimize the shift in λ, noting several applications of directing dynamics on networks.

Introduction to focus issue: design and control of self-organization in distributed active systems

Spatiotemporal self-organization is found in a wide range of distributed dynamical systems. The coupling of the active elements in these systems may be local or global or within a network, and the interactions may be diffusive or nondiffusive in nature. The articles in this focus issue describe biological and chemical systems designed to exhibit spatiotemporal dynamics and the control of such dynamics through feedback methods.