The interdependent network of gene regulation and metabolism is robust where it needs to be

Recent advances in the metabolic engineering and physiological opportunities for microbial synthesis of L-aspartic acid family amino acids: A review

L-aspartic acid, L-threonine, L-isoleucine, l-lysine, and L-methionine constitute the l-aspartate amino acids (AFAAs). Except for L-aspartic acid, these are essential amino acids that cannot be synthesized by humans or animals themselves. E. coli and C. glutamicum are the main model organisms for AFAA production. It is necessary to reconstitute microbial cell factories and the physiological state of industrial fermentation cells for in-depth research into strains with higher AFAA production levels and optimal growth states. Considering that the anabolic pathways of the AFAAs and engineering modifications have rarely been reviewed in the latest progress, this work reviews the central metabolic pathways of two strains and strategies for the metabolic engineering of AFAA synthetic pathways. The challenges posed by microbial physiology in AFAA production and possible strategies to address them, as well as future research directions for constructing strains with high AFAA production levels, are discussed in this review article.

Evaluating the Structural Robustness of Large-Scale Emerging Industry with Blurring Boundaries

The present large-scale emerging industry evolves into a form of an open system with blurring boundaries. However, when complex structures with numerous nodes and connections encounter an open system with blurring boundaries, it becomes much more challenging to effectively depict the structure of an emerging industry, which is the precondition for robustness evaluation. Therefore, this study proposes a novel framework based on a data-driven percolation process and complex network theory to depict the network skeleton and thus evaluate the structural robustness of large-scale emerging industries. The empirical data we used are actual firm-level transaction data in the Chinese new energy vehicle industry in 2019, 2020, and 2021. We applied our method to explore the transformation of structural robustness in the Chinese new energy vehicle industry in pre-COVID (2019), under-COVID (2020), and post-COVID (2021) eras. We unveil that the Chinese new energy vehicle industry became more robust against random attacks in the post-COVID era than in pre-COVID.

Network location and clustering of genetic mutations determine chronicity in a stylized model of genetic diseases

In a highly simplified view, a disease can be seen as the phenotype emerging from the interplay of genetic predisposition and fluctuating environmental stimuli. We formalize this situation in a minimal model, where a network (representing cellular regulation) serves as an interface between an input layer (representing environment) and an output layer (representing functional phenotype). Genetic predisposition for a disease is represented as a loss of function of some network nodes. Reduced, but non-zero, output indicates disease. The simplicity of this genetic disease model and its deep relationship to percolation theory allows us to understand the interplay between disease, network topology and the location and clusters of affected network nodes. We find that our model generates two different characteristics of diseases, which can be interpreted as chronic and acute diseases. In its stylized form, our model provides a new view on the relationship between genetic mutations and the type and severity of a disease.

Modern vaccine development via reverse vaccinology to combat antimicrobial resistance

With the continuous evolution of bacteria, the global antimicrobial resistance health threat is causing millions of deaths yearly. While depending on antibiotics as a primary treatment has its merits, there are no effective alternatives thus far in the pharmaceutical market against some drug-resistant bacteria. In recent years, vaccinology has become a key topic in scientific research. Combining with the growth of technology, vaccine research is seeing a new light where the process is made faster and more efficient. Although less discussed, bacterial vaccine is a feasible strategy to combat antimicrobial resistance. Some vaccines have shown promising results with good efficacy against numerous multidrug-resistant strains of bacteria. In this review, we aim to discuss the findings from studies utilizing reverse vaccinology for vaccine development against some multidrug-resistant bacteria, as well as provide a summary of multi-year bacterial vaccine studies in clinical trials. The advantages of reverse vaccinology in the generation of new bacterial vaccines are also highlighted. Meanwhile, the limitations and future prospects of bacterial vaccine concludes this review.

From Isles of Königsberg to Islets of Langerhans: Examining the Function of the Endocrine Pancreas Through Network Science

Islets of Langerhans are multicellular microorgans located in the pancreas that play a central role in whole-body energy homeostasis. Through secretion of insulin and other hormones they regulate postprandial storage and interprandial usage of energy-rich nutrients. In these clusters of hormone-secreting endocrine cells, intricate cell-cell communication is essential for proper function. Electrical coupling between the insulin-secreting beta cells through gap junctions composed of connexin36 is particularly important, as it provides the required, most important, basis for coordinated responses of the beta cell population. The increasing evidence that gap-junctional communication and its modulation are vital to well-regulated secretion of insulin has stimulated immense interest in how subpopulations of heterogeneous beta cells are functionally arranged throughout the islets and how they mediate intercellular signals. In the last decade, several novel techniques have been proposed to assess cooperation between cells in islets, including the prosperous combination of multicellular imaging and network science. In the present contribution, we review recent advances related to the application of complex network approaches to uncover the functional connectivity patterns among cells within the islets. We first provide an accessible introduction to the basic principles of network theory, enumerating the measures characterizing the intercellular interactions and quantifying the functional integration and segregation of a multicellular system. Then we describe methodological approaches to construct functional beta cell networks, point out possible pitfalls, and specify the functional implications of beta cell network examinations. We continue by highlighting the recent findings obtained through advanced multicellular imaging techniques supported by network-based analyses, giving special emphasis to the current developments in both mouse and human islets, as well as outlining challenges offered by the multilayer network formalism in exploring the collective activity of islet cell populations. Finally, we emphasize that the combination of these imaging techniques and network-based analyses does not only represent an innovative concept that can be used to describe and interpret the physiology of islets, but also provides fertile ground for delineating normal from pathological function and for quantifying the changes in islet communication networks associated with the development of diabetes mellitus.

Asymmetry-induced order in multilayer networks

Symmetries naturally occur in real-world networks and can significantly influence the observed dynamics. For instance, many synchronization patterns result from the underlying network symmetries, and high symmetries are known to increase the stability of synchronization. Yet here we find that general macroscopic features of network solutions such as regularity can be induced by breaking their symmetry of interactions. We demonstrate this effect in an ecological multilayer network where the topological asymmetries occur naturally. These asymmetries rescue the system from chaotic oscillations by establishing stable periodic orbits and equilibria. We call this phenomenon asymmetry-induced order and uncover its mechanism by analyzing both analytically and numerically the absence of dynamics on the system's synchronization manifold. Moreover, the bifurcation scenario describing the route from chaos to order is also disclosed. We demonstrate that this result also holds for generic node dynamics by analyzing coupled paradigmatic Rössler and Lorenz systems.

Comparative Analyses of Gene Co-expression Networks: Implementations and Applications in the Study of Evolution

Similarities and differences in the associations of biological entities among species can provide us with a better understanding of evolutionary relationships. Often the evolution of new phenotypes results from changes to interactions in pre-existing biological networks and comparing networks across species can identify evidence of conservation or adaptation. Gene co-expression networks (GCNs), constructed from high-throughput gene expression data, can be used to understand evolution and the rise of new phenotypes. The increasing abundance of gene expression data makes GCNs a valuable tool for the study of evolution in non-model organisms. In this paper, we cover motivations for why comparing these networks across species can be valuable for the study of evolution. We also review techniques for comparing GCNs in the context of evolution, including local and global methods of graph alignment. While some protein-protein interaction (PPI) bioinformatic methods can be used to compare co-expression networks, they often disregard highly relevant properties, including the existence of continuous and negative values for edge weights. Also, the lack of comparative datasets in non-model organisms has hindered the study of evolution using PPI networks. We also discuss limitations and challenges associated with cross-species comparison using GCNs, and provide suggestions for utilizing co-expression network alignments as an indispensable tool for evolutionary studies going forward.

Modeling the Th17 and Tregs Paradigm: Implications for Cancer Immunotherapy

CD4 + T cell differentiation is governed by gene regulatory and metabolic networks, with both networks being highly interconnected and able to adapt to external stimuli. Th17 and Tregs differentiation networks play a critical role in cancer, and their balance is affected by the tumor microenvironment (TME). Factors from the TME mediate recruitment and expansion of Th17 cells, but these cells can act with pro or anti-tumor immunity. Tregs cells are also involved in tumor development and progression by inhibiting antitumor immunity and promoting immunoevasion. Due to the complexity of the underlying molecular pathways, the modeling of biological systems has emerged as a promising solution for better understanding both CD4 + T cell differentiation and cancer cell behavior. In this review, we present a context-dependent vision of CD4 + T cell transcriptomic and metabolic network adaptability. We then discuss CD4 + T cell knowledge-based models to extract the regulatory elements of Th17 and Tregs differentiation in multiple CD4 + T cell levels. We highlight the importance of complementing these models with data from omics technologies such as transcriptomics and metabolomics, in order to better delineate existing Th17 and Tregs bifurcation mechanisms. We were able to recompilate promising regulatory components and mechanisms of Th17 and Tregs differentiation under normal conditions, which we then connected with biological evidence in the context of the TME to better understand CD4 + T cell behavior in cancer. From the integration of mechanistic models with omics data, the transcriptomic and metabolomic reprograming of Th17 and Tregs cells can be predicted in new models with potential clinical applications, with special relevance to cancer immunotherapy.

Percolation on feature-enriched interconnected systems

Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or sequentially ordered by specific topological descriptors. However, in the vast majority of empirical applications, it is required to dismantle the network following more sophisticated protocols, for instance, by combining topological properties and non-topological node metadata. We propose a novel mathematical framework to fill this gap: networks are enriched with features and their nodes are removed according to the importance in the feature space. We consider features of different nature, from ones related to the network construction to ones related to dynamical processes such as epidemic spreading. Our framework not only provides a natural generalization of percolation but, more importantly, offers an accurate way to test the robustness of networks in realistic scenarios.

Internetwork connectivity of molecular networks across species of life

Molecular interactions are studied as independent networks in systems biology. However, molecular networks do not exist independently of each other. In a network of networks approach (called multiplex), we study the joint organization of transcriptional regulatory network (TRN) and protein-protein interaction (PPI) network. We find that TRN and PPI are non-randomly coupled across five different eukaryotic species. Gene degrees in TRN (number of downstream genes) are positively correlated with protein degrees in PPI (number of interacting protein partners). Gene-gene and protein-protein interactions in TRN and PPI, respectively, also non-randomly overlap. These design principles are conserved across the five eukaryotic species. Robustness of the TRN-PPI multiplex is dependent on this coupling. Functionally important genes and proteins, such as essential, disease-related and those interacting with pathogen proteins, are preferentially situated in important parts of the human multiplex with highly overlapping interactions. We unveil the multiplex architecture of TRN and PPI. Multiplex architecture may thus define a general framework for studying molecular networks. This approach may uncover the building blocks of the hierarchical organization of molecular interactions.

Robustness and lethality in multilayer biological molecular networks

Robustness is a prominent feature of most biological systems. Most previous related studies have been focused on homogeneous molecular networks. Here we propose a comprehensive framework for understanding how the interactions between genes, proteins and metabolites contribute to the determinants of robustness in a heterogeneous biological network. We integrate heterogeneous sources of data to construct a multilayer interaction network composed of a gene regulatory layer, a protein-protein interaction layer, and a metabolic layer. We design a simulated perturbation process to characterize the contribution of each gene to the overall system's robustness, and find that influential genes are enriched in essential and cancer genes. We show that the proposed mechanism predicts a higher vulnerability of the metabolic layer to perturbations applied to genes associated with metabolic diseases. Furthermore, we find that the real network is comparably or more robust than expected in multiple random realizations. Finally, we analytically derive the expected robustness of multilayer biological networks starting from the degree distributions within and between layers. These results provide insights into the non-trivial dynamics occurring in the cell after a genetic perturbation is applied, confirming the importance of including the coupling between different layers of interaction in models of complex biological systems.

Neuroenergetics and "General Intelligence": A Systems Biology Perspective

David C. Geary proposed the efficiency of mitochondrial processes, especially the production of energy, as the most fundamental biological mechanism contributing to individual differences in general intelligence (g). While the efficiency of mitochondrial functioning is undoubtedly an important and highly interesting factor, I outline several reasons why other main factors of neuroenergetics should not be neglected and why a systems biology perspective should be adopted. There are many advantages for research on intelligence to focus on individual differences in the capability of the overall brain metabolism system to produce the energy currency adenosine triphosphate (ATP): higher predictive strength than single mechanisms, diverse possibilities for experimental manipulation, measurement with existing techniques and answers to unresolved questions because of multiple realizability. Many of these aspects are especially important for research on developmental processes and the building and refining of brain networks for adaptation. Focusing too much on single parts of the system, like the efficiency of mitochondrial functioning, carries the danger of missing important information about the role of neuroenergetics in intelligence and valuable research opportunities.

Construction, comparison and evolution of networks in life sciences and other disciplines

Network approaches have become pervasive in many research fields. They allow for a more comprehensive understanding of complex relationships between entities as well as their group-level properties and dynamics. Many networks change over time, be it within seconds or millions of years, depending on the nature of the network. Our focus will be on comparative network analyses in life sciences, where deciphering temporal network changes is a core interest of molecular, ecological, neuropsychological and evolutionary biologists. Further, we will take a journey through different disciplines, such as social sciences, finance and computational gastronomy, to present commonalities and differences in how networks change and can be analysed. Finally, we envision how borrowing ideas from these disciplines could enrich the future of life science research.

Asymmetry in interdependence makes a multilayer system more robust against cascading failures

Multilayer networked systems are ubiquitous in nature and engineering, and the robustness of these systems against failures is of great interest. A main line of theoretical pursuit has been percolation-induced cascading failures, where interdependence between network layers is conveniently and tacitly assumed to be symmetric. In the real world, interdependent interactions are generally asymmetric. To uncover and quantify the impact of asymmetry in interdependence on network robustness, we focus on percolation dynamics in double-layer systems and implement the following failure mechanism: Once a node in a network layer fails, the damage it can cause depends not only on its position in the layer but also on the position of its counterpart neighbor in the other layer. We find that the characteristics of the percolation transition depend on the degree of asymmetry, where the striking phenomenon of a switch in the nature of the phase transition from first to second order arises. We derive a theory to calculate the percolation transition points in both network layers, as well as the transition switching point, with strong numerical support from synthetic and empirical networks. Not only does our work shed light on the factors that determine the robustness of multilayer networks against cascading failures, but it also provides a scenario by which the system can be designed or controlled to reach a desirable level of resilience.

Universal behavior of cascading failures in interdependent networks

Catastrophic and major disasters in real-world systems, such as blackouts in power grids or global failures in critical infrastructures, are often triggered by minor events which originate a cascading failure in interdependent graphs. We present here a self-consistent theory enabling the systematic analysis of cascading failures in such networks and encompassing a broad range of dynamical systems, from epidemic spreading, to birth-death processes, to biochemical and regulatory dynamics. We offer testable predictions on breakdown scenarios, and, in particular, we unveil the conditions under which the percolation transition is of the first-order or the second-order type, as well as prove that accounting for dynamics in the nodes always accelerates the cascading process. Besides applying directly to relevant real-world situations, our results give practical hints on how to engineer more robust networked systems.

Chronic kidney disease: Biomarker diagnosis to therapeutic targets

Chronic kidney disease (CKD), characterized as renal dysfunction, is recognized as a major public health problem with high morbidity and mortality worldwide. Unfortunately, there are no obvious clinical symptoms in early stage disease until severe damage has occurred. Further complicating early diagnosis and treatment is the lack of sensitive and specific biomarkers. As such, novel biomarkers are urgently needed. Metabolomics has shown an increasing potential for identifying underlying disease mechanisms, facilitating clinical diagnosis and developing pharmaceutical treatments for CKD. Recent advances in metabolomics revealed that CKD was closely associated with the dysregulation of numerous metabolites, such as amino acids, lipids, nucleotides and glycoses, that might be exploited as potential biomarkers. In this review, we summarize recent metabolomic applications based on animal model studies and in patients with CKD and highlight several biomarkers that may play important roles in diagnosis, intervention and development of new therapeutic strategies.

Control of multilayer biological networks and applied to target identification of complex diseases

BACKGROUND

Networks have been widely used to model the structures of various biological systems. The ultimate aim of research on biological networks is to steer biological system structures to desired states by manipulating signals. Despite great advances in the linear control of single-layer networks, it has been observed that many complex biological systems have a multilayer networked structure and extremely complicated nonlinear processes.

RESULT

In this study, we propose a general framework for controlling nonlinear dynamical systems with multilayer networked structures by formulating the problem as a minimum union optimization problem. In particular, we offer a novel approach for identifying the minimal driver nodes that can steer a multilayered nonlinear dynamical system toward any desired dynamical attractor. Three disease-related biology multilayer networks are used to demonstrate the effectiveness of our approaches. Moreover, in the set of minimum driver nodes identified by the algorithm we proposed, we confirmed that some nodes can act as drug targets in the biological experiments. Other nodes have not been reported as drug targets; however, they are also involved in important biological processes from existing literature.

CONCLUSIONS

The proposed method could be a promising tool for determining higher drug target enrichment or more meaningful steering nodes for studying complex diseases.

A system-wide network reconstruction of gene regulation and metabolism in Escherichia coli

Genome-scale metabolic models have become a fundamental tool for examining metabolic principles. However, metabolism is not solely characterized by the underlying biochemical reactions and catalyzing enzymes, but also affected by regulatory events. Since the pioneering work of Covert and co-workers as well as Shlomi and co-workers it is debated, how regulation and metabolism synergistically characterize a coherent cellular state. The first approaches started from metabolic models, which were extended by the regulation of the encoding genes of the catalyzing enzymes. By now, bioinformatics databases in principle allow addressing the challenge of integrating regulation and metabolism on a system-wide level. Collecting information from several databases we provide a network representation of the integrated gene regulatory and metabolic system for Escherichia coli, including major cellular processes, from metabolic processes via protein modification to a variety of regulatory events. Besides transcriptional regulation, we also take into account regulation of translation, enzyme activities and reactions. Our network model provides novel topological characterizations of system components based on their positions in the network. We show that network characteristics suggest a representation of the integrated system as three network domains (regulatory, metabolic and interface networks) instead of two. This new three-domain representation reveals the structural centrality of components with known high functional relevance. This integrated network can serve as a platform for understanding coherent cellular states as active subnetworks and to elucidate crossover effects between metabolism and gene regulation.

Bond percolation in coloured and multiplex networks

Percolation in complex networks is a process that mimics network degradation and a tool that reveals peculiarities of the network structure. During the course of percolation, the emergent properties of networks undergo non-trivial transformations, which include a phase transition in the connectivity, and in some special cases, multiple phase transitions. Such global transformations are caused by only subtle changes in the degree distribution, which locally describe the network. Here we establish a generic analytic theory that describes how structure and sizes of all connected components in the network are affected by simple and colour-dependent bond percolations. This theory predicts locations of the phase transitions, existence of wide critical regimes that do not vanish in the thermodynamic limit, and a phenomenon of colour switching in small components. These results may be used to design percolation-like processes, optimise network response to percolation, and detect subtle signals preceding network collapse.

Percolation is a tool used to investigate a network’s response as random links are removed. Here the author presents a generic analytic theory to describe how percolation properties are affected in coloured networks, where the colour can represent a network feature such as multiplexity or the belonging to a community.

Interaction paths promote module integration and network-level robustness of spliceosome to cascading effects

The functionality of distinct types of protein networks depends on the patterns of protein-protein interactions. A problem to solve is understanding the fragility of protein networks to predict system malfunctioning due to mutations and other errors. Spectral graph theory provides tools to understand the structural and dynamical properties of a system based on the mathematical properties of matrices associated with the networks. We combined two of such tools to explore the fragility to cascading effects of the network describing protein interactions within a key macromolecular complex, the spliceosome. Using S. cerevisiae as a model system we show that the spliceosome network has more indirect paths connecting proteins than random networks. Such multiplicity of paths may promote routes to cascading effects to propagate across the network. However, the modular network structure concentrates paths within modules, thus constraining the propagation of such cascading effects, as indicated by analytical results from the spectral graph theory and by numerical simulations of a minimal mathematical model parameterized with the spliceosome network. We hypothesize that the concentration of paths within modules favors robustness of the spliceosome against failure, but may lead to a higher vulnerability of functional subunits, which may affect the temporal assembly of the spliceosome. Our results illustrate the utility of spectral graph theory for identifying fragile spots in biological systems and predicting their implications.

Feedbacks from the metabolic network to the genetic network reveal regulatory modules in E. coli and B. subtilis

The genetic regulatory network (GRN) plays a key role in controlling the response of the cell to changes in the environment. Although the structure of GRNs has been the subject of many studies, their large scale structure in the light of feedbacks from the metabolic network (MN) has received relatively little attention. Here we study the causal structure of the GRNs, namely the chain of influence of one component on the other, taking into account feedback from the MN. First we consider the GRNs of E. coli and B. subtilis without feedback from MN and illustrate their causal structure. Next we augment the GRNs with feedback from their respective MNs by including (a) links from genes coding for enzymes to metabolites produced or consumed in reactions catalyzed by those enzymes and (b) links from metabolites to genes coding for transcription factors whose transcriptional activity the metabolites alter by binding to them. We find that the inclusion of feedback from MN into GRN significantly affects its causal structure, in particular the number of levels and relative positions of nodes in the hierarchy, and the number and size of the strongly connected components (SCCs). We then study the functional significance of the SCCs. For this we identify condition specific feedbacks from the MN into the GRN by retaining only those enzymes that are essential for growth in specific environmental conditions simulated via the technique of flux balance analysis (FBA). We find that the SCCs of the GRN augmented by these feedbacks can be ascribed specific functional roles in the organism. Our algorithmic approach thus reveals relatively autonomous subsystems with specific functionality, or regulatory modules in the organism. This automated approach could be useful in identifying biologically relevant modules in other organisms for which network data is available, but whose biology is less well studied.

Complexity and irreducibility of dynamics on networks of networks

We study numerically the dynamics of a network of all-to-all-coupled, identical sub-networks consisting of diffusively coupled, non-identical FitzHugh-Nagumo oscillators. For a large range of within- and between-network couplings, the network exhibits a variety of dynamical behaviors, previously described for single, uncoupled networks. We identify a region in parameter space in which the interplay of within- and between-network couplings allows for a richer dynamical behavior than can be observed for a single sub-network. Adjoining this atypical region, our network of networks exhibits transitions to multistability. We elucidate bifurcations governing the transitions between the various dynamics when crossing this region and discuss how varying the couplings affects the effective structure of our network of networks. Our findings indicate that reducing a network of networks to a single (but bigger) network might not be accurate enough to properly understand the complexity of its dynamics.

Control principles for complex biological networks

Networks have been widely used to model the structure of various biological systems. Currently, a series of approaches have been developed to construct reliable biological networks. However, the ultimate understanding of a biological system is to steer its states to the desired ones by imposing signals. The control process is dominated by the intrinsic structure and the dynamic propagation. To understand the underlying mechanisms behind the life process, the control theory can be applied to biological networks with specific target requirements. In this article, we first introduce the structural controllability of complex networks and discuss its advantages and disadvantages. Then, we review the effective control to meet the specific requirements for complex biological networks. Moreover, we summarize the existing methods for finding the unique minimum set of driver nodes via the optimal control for complex networks. Finally, we discuss the relationships between biological networks and structural controllability, effective control and optimal control. Moreover, potential applications of general control principles are pointed out.

In Silico Prediction of Large-Scale Microbial Production Performance: Constraints for Getting Proper Data-Driven Models

Industrial bioreactors range from 10.000 to 700.000 L and characteristically show different zones of substrate availabilities, dissolved gas concentrations and pH values reflecting physical, technical and economic constraints of scale-up. Microbial producers are fluctuating inside the bioreactors thereby experiencing frequently changing micro-environmental conditions. The external stimuli induce responses on microbial metabolism and on transcriptional regulation programs. Both may deteriorate the expected microbial production performance in large scale compared to expectations deduced from ideal, well-mixed lab-scale conditions. Accordingly, predictive tools are needed to quantify large-scale impacts considering bioreactor heterogeneities. The review shows that the time is right to combine simulations of microbial kinetics with calculations of large-scale environmental conditions to predict the bioreactor performance. Accordingly, basic experimental procedures and computational tools are presented to derive proper microbial models and hydrodynamic conditions, and to link both for bioreactor modeling. Particular emphasis is laid on the identification of gene regulatory networks as the implementation of such models will surely gain momentum in future studies.

Spontaneous repulsion in the A+B→0 reaction on coupled networks

We study the transient dynamics of an A+B→0 process on a pair of randomly coupled networks, where reactants are initially separated. We find that, for sufficiently small fractions q of cross couplings, the concentration of A (or B) particles decays linearly in a first stage and crosses over to a second linear decrease at a mixing time t_{x}. By numerical and analytical arguments, we show that for symmetric and homogeneous structures t_{x}∝(〈k〉/q)log(〈k〉/q) where 〈k〉 is the mean degree of both networks. Being this behavior is in marked contrast with a purely diffusive process, where the mixing time would go simply like 〈k〉/q, we identify the logarithmic slowing down in t_{x} to be the result of a spontaneous mechanism of repulsion between the reactants A and B due to the interactions taking place at the networks' interface. We show numerically how this spontaneous repulsion effect depends on the topology of the underlying networks.

Connectivity and complex systems: learning from a multi-disciplinary perspective

In recent years, parallel developments in disparate disciplines have focused on what has come to be termed connectivity; a concept used in understanding and describing complex systems. Conceptualisations and operationalisations of connectivity have evolved largely within their disciplinary boundaries, yet similarities in this concept and its application among disciplines are evident. However, any implementation of the concept of connectivity carries with it both ontological and epistemological constraints, which leads us to ask if there is one type or set of approach(es) to connectivity that might be applied to all disciplines. In this review we explore four ontological and epistemological challenges in using connectivity to understand complex systems from the standpoint of widely different disciplines. These are: (i) defining the fundamental unit for the study of connectivity; (ii) separating structural connectivity from functional connectivity; (iii) understanding emergent behaviour; and (iv) measuring connectivity. We draw upon discipline-specific insights from Computational Neuroscience, Ecology, Geomorphology, Neuroscience, Social Network Science and Systems Biology to explore the use of connectivity among these disciplines. We evaluate how a connectivity-based approach has generated new understanding of structural-functional relationships that characterise complex systems and propose a 'common toolbox' underpinned by network-based approaches that can advance connectivity studies by overcoming existing constraints.