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Abstract Given a large enough volume of data and precise, meaningful categories, training a statistical model to solve a classification problem is straightforward and has become a standard application of machine learning (ML). If the categories are not precise, but rather fuzzy, as in the case of scientific disciplines, the systematic failures of ML classification can be informative about properties of the underlying categories. Here we classify a large volume of academic publications using only the abstract as information. From the publications that are classified differently by journal categories and ML categories (i.e., misclassified publications, when using the journal assignment as ground truth) we construct a network among disciplines. Analysis of these misclassifications provides insight in two topics at the core of the science of science: (1) Mapping out the interplay of disciplines. We show that this misclassification network is informative about the interplay of academic disciplines and it is similar to, but distinct from, a citation-based map of science, where nodes are scientific disciplines and an edge indicates a strong co-citation count between publications in these disciplines. (2) Analyzing the success of interdisciplinarity. By evaluating the citation patterns of publications, we show that misclassification can be linked to interdisciplinarity and, furthermore, that misclassified articles have different citation frequencies than correctly classified articles: In the highest 10 percent of journals in each discipline, these misclassified articles are on average cited more frequently, while in the rest of the journals they are cited less frequently.

Ecosystem responses to prehistoric sea-ice loss are poorly known. Using marine sedimentary ancient DNA form the Bering Sea covering the last ~20,000 years, this study reveals a transition from a sea ice-adapted ecosystem, characterized by diatoms, copepods and codfish, to an ice-free Holocene with cyanobacteria, salmon and herring.

Abstract 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.

Abstract 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.

Abstract Collective phenomena in systems of interacting agents have helped us understand diverse social, ecological and biological observations. The corresponding explanations are challenged by incorrect information processing. In particular, the models typically assume a shared understanding of signals or a common truth or value system, i.e., an agreement of whether the measurement or perception of information is ‘right’ or ‘wrong’. It is an open question whether a collective consensus can emerge without these conditions. Here we introduce a model of interacting agents that strive for consensus, however, each with only a subjective perception of the world. Our communication model does not presuppose a definition of right or wrong and the actors can hence not distinguish between correct and incorrect observations. Depending on a single parameter that governs how responsive the agents are to changing their world-view we observe a transition between an unordered phase of individuals that are not able to communicate with each other and a phase of an emerging shared signalling framework. We find that there are two types of convention-aligned clusters: one, where all social actors in the cluster have the same set of conventions, and one, where neighbouring actors have different but compatible conventions (‘stable misunderstandings’).

Abstract Cocoa products have a remarkable chemical and sensory complexity. However, in contrast to other fermentation processes in the food industry, cocoa bean fermentation is left essentially uncontrolled and is devoid of standardization. Questions of food authenticity and food quality are hence particularly challenging for cocoa. Here we provide an illustration how network science can support food fingerprinting and food authenticity research. Using a large dataset of 140 cocoa samples comprising three cocoa fermentation/processing stages and eight countries, we obtain correlation networks between the cocoa samples by computing measures of pairwise correlation from their liquid chromatography-mass spectrometry (LC-MS) profiles. We find that the topology of correlation networks derived from untargeted LC-MS profiles is indicative of the fermentation and processing stage as well as the origin country of cocoa samples. Progressively increasing the correlation threshold firstly reveals network clusters based on processing stage and later country-based clusters. We present both, qualitative and quantitative evidence through network visualization, network statistics and concepts from machine learning. In our view, this network-based approach for classifying mass spectrometry data has broad applicability beyond cocoa.

Abstract Background Genome-wide association studies have identified statistical associations between various diseases, including cancers, and a large number of single-nucleotide polymorphisms (SNPs). However, they provide no direct explanation of the mechanisms underlying the association. Based on the recent discovery that changes in three-dimensional genome organization may have functional consequences on gene regulation favoring diseases, we investigated systematically the genome-wide distribution of disease-associated SNPs with respect to a specific feature of 3D genome organization: topologically associating domains (TADs) and their borders. Results For each of 449 diseases, we tested whether the associated SNPs are present in TAD borders more often than observed by chance, where chance (i.e., the null model in statistical terms) corresponds to the same number of pointwise loci drawn at random either in the entire genome, or in the entire set of disease-associated SNPs listed in the GWAS catalog. Our analysis shows that a fraction of diseases displays such a preferential localization of their risk loci. Moreover, cancers are relatively more frequent among these diseases, and this predominance is generally enhanced when considering only intergenic SNPs. The structure of SNP-based diseasome networks confirms that localization of risk loci in TAD borders differs between cancers and non-cancer diseases. Furthermore, different TAD border enrichments are observed in embryonic stem cells and differentiated cells, consistent with changes in topological domains along embryogenesis and delineating their contribution to disease risk. Conclusions Our results suggest that, for certain diseases, part of the genetic risk lies in a local genetic variation affecting the genome partitioning in topologically insulated domains. Investigating this possible contribution to genetic risk is particularly relevant in cancers. This study thus opens a way of interpreting genome-wide association studies, by distinguishing two types of disease-associated SNPs: one with an effect on an individual gene, the other acting in interplay with 3D genome organization.

Abstract In the transcriptional regulatory network (TRN) of a bacterium, the nodes are genes and a directed edge represents the action of a transcription factor (TF), encoded by the source gene, on the target gene. It is a condensed representation of a large number of biological observations and facts. Nonrandom features of the network are structural evidence of requirements for a reliable systemic function. For the bacterium Escherichia coli we here investigate the (Euclidean) distances covered by the edges in the TRN when its nodes are embedded in the real space of the circular chromosome. Our work is motivated by ’wiring economy’ research in Computational Neuroscience and starts from two contradictory hypotheses: (1) TFs are predominantly employed for long-distance regulation, while local regulation is exerted by chromosomal structure, locally coordinated by the action of structural proteins. Hence long distances should often occur. (2) A large distance between the regulator gene and its target requires a higher expression level of the regulator gene due to longer reaching times and ensuing increased degradation (proteolysis) of the TF and hence will be evolutionarily reduced. Our analysis supports the latter hypothesis.

Connectomes represent comprehensive descriptions of neural connections in a nervous system to better understand and model central brain function and peripheral processing of afferent and efferent neural signals. Connectomes can be considered as a distinctive and necessary structural component alongside glial, vascular, neurochemical, and metabolic networks of the nervous systems of higher organisms that are required for the control of body functions and interaction with the environment. They are carriers of functional phenomena such as planning behavior and cognition, which are based on the processing of highly dynamic neural signaling patterns. In this study, we examine more detailed connectomes with edge weighting and orientation properties, in which reciprocal neuronal connections are also considered. Diffusion processes are a further necessary condition for generating dynamic bioelectric patterns in connectomes. Based on our precise connectome data, we investigate different diffusion-reaction models to study the propagation of dynamic concentration patterns in control and lesioned connectomes. Therefore, differential equations for modeling diffusion were combined with well-known reaction terms to allow the use of connection weights, connectivity orientation and spatial distances. Three reaction-diffusion systems Gray-Scott, Gierer-Meinhardt and Mimura-Murray were investigated. For this purpose, implicit solvers were implemented in a numerically stable reaction-diffusion system within the framework of neuroVIISAS. The implemented reaction-diffusion systems were applied to a subconnectome which shapes the mechanosensitive pathway that is strongly affected in the multiple sclerosis demyelination disease. It was found that demyelination modeling by connectivity weight modulation changes the oscillations of the target region, i.e. the primary somatosensory cortex, of the mechanosensitive pathway. In conclusion, a new application of reaction-diffusion systems to weighted and directed connectomes has been realized. Because the implementation was realized in the neuroVIISAS framework many possibilities for the study of dynamic reaction-diffusion processes in empirical connectomes as well as specific randomized network models are available now.

Abstract Toxin–antitoxin (TA) modules are part of most bacteria’s regulatory machinery for stress responses and general aspects of their physiology. Due to the interplay of a long-lived toxin with a short-lived antitoxin, TA modules have also become systems of interest for mathematical modelling. Here we resort to previous modelling efforts and extract from these a minimal model of type II TA system dynamics on a timescale of hours, which can be used to describe time courses derived from gene expression data of TA pairs. We show that this model provides a good quantitative description of TA dynamics for the 11 TA pairs under investigation here, while simpler models do not. Our study brings together aspects of Biophysics with its focus on mathematical modelling and Computational Systems Biology with its focus on the quantitative interpretation of ’omics’ data. This mechanistic model serves as a generic transformation of time course information into kinetic parameters. The resulting parameter vector can, in turn, be mechanistically interpreted. We expect that TA pairs with similar mechanisms are characterized by similar vectors of kinetic parameters, allowing us to hypothesize on the mode of action for TA pairs still under discussion.

Many cancers fuel their rapid growth by replacing glucokinase with its higher affinity isoenzyme, hexokinase 2 (HK2), making HK2 an attractive drug target. In this study, Perrin-Cocon and Vidalain et al. use CRISPR/Cas-9 gene editing to reverse this enzymatic switch in human liver cancer cells, and find this restores innate immune function as well as reversing cancer-associated metabolic reprogramming.

Compared with other fermentation processes in food industry, cocoa bean fermentation is uncontrolled and not standardized. A detailed mechanistic understanding can therefore be relevant for cocoa bean quality control. Starting from an existing mathematical model of cocoa bean fermentation we analyse five additional biochemical mechanisms derived from the literature. These mechanisms, when added to the baseline model either in isolation or in combination, were evaluated in terms of their capacity to describe experimental data. In total, we evaluated 32 model variants on 23 fermentation datasets. We interpret the results from two perspectives: (1) success of the potential mechanism, (2) discrimination of fermentation protocols based on estimated parameters. The former provides insight in the fermentation process itself. The latter opens an avenue towards reverse-engineering empirical conditions from model parameters. We find support for two mechanisms debated in the literature: consumption of fructose by lactic acid bacteria and production of acetic acid by yeast. Furthermore, we provide evidence that model parameters are sensitive to differences in the cultivar, temperature control and usage of steel tanks compared with wooden boxes. Our results show that mathematical modelling can provide an alternative to standard chemical fingerprinting in the interpretation of fermentation data.

Modularity is a ubiquitous topological feature of structural brain networks at various scales. Although a variety of potential mechanisms have been proposed, the fundamental principles by which modularity emerges in neural networks remain elusive. We tackle this question with a plasticity model of neural networks derived from a purely topological perspective. Our topological reinforcement model acts enhancing the topological overlap between nodes, that is, iteratively allowing connections between non-neighbor nodes with high neighborhood similarity. This rule reliably evolves synthetic random networks toward a modular architecture. Such final modular structure reflects initial “proto-modules,” thus allowing to predict the modules of the evolved graph. Subsequently, we show that this topological selection principle might be biologically implemented as a Hebbian rule. Concretely, we explore a simple model of excitable dynamics, where the plasticity rule acts based on the functional connectivity (co-activations) between nodes. Results produced by the activity-based model are consistent with the ones from the purely topological rule in terms of the final network configuration and modules composition. Our findings suggest that the selective reinforcement of topological overlap may be a fundamental mechanism contributing to modularity emergence in brain networks. The self-organization of modular structure in brain networks is mechanistically poorly understood. We propose a simple plasticity model based on a fundamental principle, topological reinforcement, which promotes connections between nodes with high neighborhood similarity. Starting from a random network, this mechanism systematically promotes the emergence of modular architecture by enhancing initial weak proto-modules. Furthermore, we show that this topological selection principle can also be implemented in biological neural networks through a Hebbian plasticity rule, where what “fires together, wires together” and, under proper conditions, the results are consistent between both scenarios. We propose the topological reinforcement as a principle contributing to the emergence of modular structure in brain networks. This addresses the gap between previous pure generative and activity-based models of modularity emergence in brain networks, offering a common underlying principle at the topological level.

Abstract The scheduling of processes in a network is a core logistic challenge with a multitude of applications in our complex industrialized world. Often, scheduling decisions are based on incomplete and unreliable information. Here, a simple rule of ’more information, better decisions’ may no longer hold and heuristics balancing global and local information, or centralized and autonomous control, may yield better performance. So far, only anecdotal evidence for the potential benefit of autonomous control in scheduling exists. Here, we explore this hypothesis within a minimal model derived from scheduling principles and the phenomenology of dynamical processes on graphs. In this model, centralized and autonomous control can be represented and quantitatively assessed, performance is well defined and problem complexity can be varied. Our model shows that a balance of centralized and autonomous control can enhance the performance in networks of decision-making entities. The mechanistic insight gained from the model also reveals the limitations of hybrid control setups: We find that communication at a high hierarchy level can give an advantage to centralized control. Counter-intuitively, it arises not from a higher degree of coordination and quicker convergence towards a common solution, but rather from an accelerated sampling of candidate choices leading to a measurable increase in information flow from higher to lower hierarchical levels. Our study allows us to formulate a new view of autonomous control in industrial production and derive a set of suggestions with the potential to enhance performance under realistic conditions of scheduling heuristics of jobs in a production process.

Abstract 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.

Although networks of interacting genes and metabolic reactions are interdependent, they have largely been treated as separate systems. Here the authors apply a statistical framework for interdependent networks to E. coli, and show that it is sensitive to gene and protein perturbations but robust against metabolic changes.

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.

Algorithmic methods for interpreting the collective transcriptome (gene expression) patterns of disease cohorts in the context of biological networks are a cornerstone of systems medicine. The calibration of these algorithms using synthetic data with predefined statistical properties can be a relevant benchmarking procedure, facilitating the choice of the appropriate algorithm and the detailed mechanistic interpretation of the results. Here we present a generative model producing patterns of significantly up- and down-regulated genes for synthetic disease cohorts, in which the statistical agreement between the given biological network and the transcriptome patterns can be tuned. Parameters of this generative model are, among others, the size of the cohort, the number of disease-associated genes, the clustering of differentially expressed genes in the network and the network size. Several properties of the model can be analyzed analytically. In a first application of this generative model to produce test instances, we show that considering the subset of significant expression changes occurring in more than one patient of the cohort as an additional filtering step serves as an efficient noise suppression mechanism to enhance the recall of the signal contained in the data by the network connectivity.

The relationship between the structural connectivity (SC) and functional connectivity (FC) of neural systems is of central importance in brain network science. It is an open question, however, how the SC-FC relationship depends on specific topological features of brain networks or the models used for describing neural dynamics. Using a basic but general model of discrete excitable units that follow a susceptible-excited-refractory activity cycle (SER model), we here analyze how the network activity patterns underlying functional connectivity are shaped by the characteristic topological features of the network. We develop an analytical framework for describing the contribution of essential topological elements, such as common inputs and pacemakers, to the coactivation of nodes, and demonstrate the validity of the approach by comparison of the analytical predictions with numerical simulations of various exemplar networks. The present analytic framework may serve as an initial step for the mechanistic understanding of the contributions of brain network topology to brain dynamics.

Cocoa bean fermentation relies on the sequential activation of several microbial populations, triggering a temporal pattern of biochemical transformations. Understanding this complex process is of tremendous importance as it is known to form the precursors of the resulting chocolate’s flavour and taste. At the same time, cocoa bean fermentation is one of the least controlled processes in the food industry. Here, a quantitative model of cocoa bean fermentation is constructed based on available microbiological and biochemical knowledge. The model is formulated as a system of coupled ordinary differential equations with two distinct types of state variables: (i) metabolite concentrations of glucose, fructose, ethanol, lactic acid and acetic acid and (ii) population sizes of yeast, lactic acid bacteria and acetic acid bacteria. We demonstrate that the model can quantitatively describe existing fermentation time series and that the estimated parameters, obtained by a Bayesian framework, can be used to extract and interpret differences in environmental conditions. The proposed model is a valuable tool towards a mechanistic understanding of this complex biochemical process, and can serve as a starting point for hypothesis testing of new systemic adjustments. In addition to providing the first quantitative mathematical model of cocoa bean fermentation, the purpose of our investigation is to show how differences in estimated parameter values for two experiments allow us to deduce differences in experimental conditions.

The analysis of microbiome compositions in the human gut has gained increasing interest due to the broader availability of data and functional databases and substantial progress in data analysis methods, but also due to the high relevance of the microbiome in human health and disease. While most analyses infer interactions among highly abundant species, the large number of low-abundance species has received less attention. Here we present a novel analysis method based on Boolean operations applied to microbial co-occurrence patterns. We calibrate our approach with simulated data based on a dynamical Boolean network model from which we interpret the statistics of attractor states as a theoretical proxy for microbiome composition. We show that for given fractions of synergistic and competitive interactions in the model our Boolean abundance analysis can reliably detect these interactions. Analyzing a novel data set of 822 microbiome compositions of the human gut, we find a large number of highly significant synergistic interactions among these low-abundance species, forming a connected network, and a few isolated competitive interactions.

Objective: The aim of this article is to outline the role of chaotic dynamics in psychotherapy. Besides some empirical findings of chaos at different time scales, the focus is on theoretical modeling of change processes explaining and simulating chaotic dynamics. It will be illustrated how some common factors of psychotherapeutic change and psychological hypotheses on motivation, emotion regulation, and information processing of the client's functioning can be integrated into a comprehensive nonlinear model of human change processes.Methods: The model combines 5 variables (intensity of emotions, problem intensity, motivation to change, insight and new perspectives, therapeutic success) and 4 parameters into a set of 5 coupled nonlinear difference equations. The results of these simulations are presented as time series, as phase space embedding of these time series (i.e., attractors), and as bifurcation diagrams.Results: The model creates chaotic dynamics, phase transition-like phenomena, bi- or multi-stability, and sensibility of the dynamic patterns on parameter drift. These features are predicted by chaos theory and by Synergetics and correspond to empirical findings. The spectrum of these behaviors illustrates the complexity of psychotherapeutic processes.Conclusion: The model contributes to the development of an integrative conceptualization of psychotherapy. It is consistent with the state of scientific knowledge of common factors, as well as other psychological topics, such as: motivation, emotion regulation, and cognitive processing. The role of chaos theory is underpinned, not only in the world of computer simulations, but also in practice. In practice, chaos demands technologies capable of real-time monitoring and reporting on the nonlinear features of the ongoing process (e.g., its stability or instability). Based on this monitoring, a client-centered, continuous, and cooperative process of feedback and control becomes possible. By contrast, restricted predictability and spontaneous changes challenge the usefulness of prescriptive treatment manuals or other predefined programs of psychotherapy.

Metabolism has frequently been analyzed from a network perspective. A major question is how network properties correlate with biological features like growth rates, flux patterns and enzyme essentiality. Using methods from graph theory as well as established topological categories of metabolic systems, we analyze the essentiality of metabolic reactions depending on the growth medium and identify the topological footprint of these reactions. We find that the typical topological context of a medium-dependent essential reaction is systematically different from that of a globally essential reaction. In particular, we observe systematic differences in the distribution of medium-dependent essential reactions across three-node subgraphs (the network motif signature of medium-dependent essential reactions) compared to globally essential or globally redundant reactions. In this way, we provide evidence that the analysis of metabolic systems on the few-node subgraph scale is meaningful for explaining dynamic patterns. This topological characterization of medium-dependent essentiality provides a better understanding of the interplay between reaction deletions and environmental conditions.

Cellular automata (CA) are a remarkably efficient tool for exploring general properties of complex systems and spatiotemporal patterns arising from local rules. Totalistic cellular automata, where the update rules depend only on the density of neighboring states, are at the same time a versatile tool for exploring dynamical processes on graphs. Here we briefly review our previous results on cellular automata on graphs, emphasizing some systematic relationships between network architecture and dynamics identified in this way. We then extend the investigation towards graphs obtained in a simulated-evolution procedure, starting from Erdő s–Rényi (ER) graphs and selecting for low entropies of the CA dynamics. Our key result is a strong association of low Shannon entropies with a broadening of the graph’s degree distribution.

Time by itself is an interesting topic in biological systems, but when it comes to modelling biology, the abstracted representation of time within a mathematical model is a construction surprisingly prone to ambiguities, counterintuitive phenomena and arbitrary decisions. Identifying different scenarios in which the theoretical representation of time is an issue helps us to understand more about concepts of time, biological complexity and the process of modelling itself. This article tries to describe how the process of modelling corresponds to the selection of a particular time scale from a whole range of time scales contributing to a biological system; how the fundamental units of time in biology, rhythmic oscillations, are dependent on the interaction with other rhythmic systems; how a step from a continuous to a discrete time (i.e. a change of the conceptual representation of time within a model) can greatly enhance the range of dynamic behaviours within the model.

Spatiotemporal patterns often emerge from local interactions in a self-organizing fashion. In biology, the resulting patterns are also subject to the influence of the systematic differences between the system's constituents (biological variability). This regulation of spatiotemporal patterns by biological variability is the topic of our review. We discuss several examples of correlations between cell properties and the self-organized spatiotemporal patterns, together with their relevance for biology. Our guiding, illustrative example will be spiral waves of cAMP in a colony of Dictyostelium discoideum cells. Analogous processes take place in diverse situations (such as cardiac tissue, where spiral waves occur in potentially fatal ventricular fibrillation) so a deeper understanding of this additional layer of self-organized pattern formation would be beneficial to a wide range of applications. One of the most striking differences between pattern-forming systems in physics or chemistry and those in biology is the potential importance of variability. In the former, system components are essentially identical with random fluctuations determining the details of the self-organization process and the resulting patterns. In biology, due to variability, the properties of potentially very few cells can have a driving influence on the resulting asymptotic collective state of the colony. Variability is one means of implementing a few-element control on the collective mode. Regulatory architectures, parameters of signaling cascades, and properties of structure formation processes can be "reverse-engineered" from observed spatiotemporal patterns, as different types of regulation and forms of interactions between the constituents can lead to markedly different correlations. The power of this biology-inspired view of pattern formation lies in building a bridge between two scales: the patterns as a collective state of a very large number of cells on the one hand, and the internal parameters of the single cells on the other.

We study the interplay between correlations, dynamics, and networks for repeated attacks on a socio-economic network. As a model system we consider an insurance scheme against disasters that randomly hit nodes, where a node in need receives support from its network neighbors. The model is motivated by gift giving among the Maasai called Osotua. Survival of nodes under different disaster scenarios (uncorrelated, spatially, temporally and spatio-temporally correlated) and for different network architectures are studied with agent-based numerical simulations. We find that the survival rate of a node depends dramatically on the type of correlation of the disasters: Spatially and spatio-temporally correlated disasters increase the survival rate; purely temporally correlated disasters decrease it. The type of correlation also leads to strong inequality among the surviving nodes. We introduce the concept of disaster masking to explain some of the results of our simulations. We also analyze the subsets of the networks that were activated to provide support after fifty years of random disasters. They show qualitative differences for the different disaster scenarios measured by path length, degree, clustering coefficient, and number of cycles.

The set of regulatory interactions between genes, mediated by transcription factors, forms a species' transcriptional regulatory network (TRN). By comparing this network with measured gene expression data, one can identify functional properties of the TRN and gain general insight into transcriptional control. We define the subnet of a node as the subgraph consisting of all nodes topologically downstream of the node, including itself. Using a large set of microarray expression data of the bacterium Escherichia coli, we find that the gene expression in different subnets exhibits a structured pattern in response to environmental changes and genotypic mutation. Subnets with fewer changes in their expression pattern have a higher fraction of feed-forward loop motifs and a lower fraction of small RNA targets within them. Our study implies that the TRN consists of several scales of regulatory organization: (1) subnets with more varying gene expression controlled by both transcription factors and post-transcriptional RNA regulation and (2) subnets with less varying gene expression having more feed-forward loops and less post-transcriptional RNA regulation.

The slime mold Dictyostelium discoideum is one of the model systems of biological pattern formation. One of the most successful answers to the challenge of establishing a spiral wave pattern in a colony of homogeneously distributed D. discoideum cells has been the suggestion of a developmental path the cells follow (Lauzeral and coworkers). This is a well-defined change in properties each cell undergoes on a longer time scale than the typical dynamics of the cell. Here we show that this concept leads to an inhomogeneous and systematic spatial distribution of spiral waves, which can be predicted from the distribution of cells on the developmental path. We propose specific experiments for checking whether such systematics are also found in data and thus, indirectly, provide evidence of a developmental path.

This study investigates the contributions of network topology features to the dynamic behavior of hierarchically organized excitable networks. Representatives of different types of hierarchical networks as well as two biological neural networks are explored with a three-state model of node activation for systematically varying levels of random background network stimulation. The results demonstrate that two principal topological aspects of hierarchical networks, node centrality and network modularity, correlate with the network activity patterns at different levels of spontaneous network activation. The approach also shows that the dynamic behavior of the cerebral cortical systems network in the cat is dominated by the network's modular organization, while the activation behavior of the cellular neuronal network of Caenorhabditis elegans is strongly influenced by hub nodes. These findings indicate the interaction of multiple topological features and dynamic states in the function of complex biological networks.