The attractor structure of functional connectivity in coupled logistic maps.

Stylized models of dynamical processes on graphs allow us to explore the relationships between network architecture and dynamics, a topic of relevance in a range of disciplines. One strategy is to translate dynamical observations into pairwise relationships of nodes, often called functional connectivity (FC), and quantitatively compare them with network architecture or structural connectivity (SC). Here, we start from the observation that for coupled logistic maps, SC/FC relationships vary strongly with coupling strength. Using symbolic encoding, the mapping of the dynamics onto a cellular automaton, and the subsequent analysis of the resulting attractors, we show that this behavior is invariant under these transformations and can be understood from the attractors of the cellular automaton alone. Interestingly, noise enhances SC/FC correlations by creating a more uniform sampling of attractors. On a methodological level, we introduce cellular automata as a data analysis tool, rather than a simulation model of dynamics on graphs.

Predicting attractors from spectral properties of stylized gene regulatory networks.

How the architecture of gene regulatory networks shapes gene expression patterns is an open question, which has been approached from a multitude of angles. The dominant strategy has been to identify nonrandom features in these networks and then argue for the function of these features using mechanistic modeling. Here we establish the foundation of an alternative approach by studying the correlation of network eigenvectors with synthetic gene expression data simulated with a basic and popular model of gene expression dynamics: Boolean threshold dynamics in signed directed graphs. We show that eigenvectors of the network adjacency matrix can predict collective states (attractors). However, the overall predictive power depends on details of the network architecture, namely the fraction of positive 3-cycles, in a predictable fashion. Our results are a set of statistical observations, providing a systematic step towards a further theoretical understanding of the role of network eigenvectors in dynamics on graphs.

Marine ecosystem shifts with deglacial sea-ice loss inferred from ancient DNA shotgun sequencing.

Sea ice is a key factor for the functioning and services provided by polar marine ecosystems. However, ecosystem responses to sea-ice loss are largely unknown because time-series data are lacking. Here, we use shotgun metagenomics of marine sedimentary ancient DNA off Kamchatka (Western Bering Sea) covering the last ~20,000 years. We traced shifts from a sea ice-adapted late-glacial ecosystem, characterized by diatoms, copepods, and codfish to an ice-free Holocene characterized by cyanobacteria, salmon, and herring. By providing information about marine ecosystem dynamics across a broad taxonomic spectrum, our data show that ancient DNA will be an important new tool in identifying long-term ecosystem responses to climate transitions for improvements of ocean and cryosphere risk assessments. We conclude that continuing sea-ice decline on the northern Bering Sea shelf might impact on carbon export and disrupt benthic food supply and could allow for a northward expansion of salmon and Pacific herring.

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.

Reaction-diffusion models in weighted and directed connectomes.

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.

Inferring missing edges in a graph from observed collective patterns.

Many real-life networks are incomplete. Dynamical observations can allow estimating missing edges. Such procedures, often summarized under the term 'network inference', typically evaluate the statistical correlations among pairs of nodes to determine connectivity. Here, we offer an alternative approach: completing an incomplete network by observing its collective behavior. We illustrate this approach for the case of patterns emerging in reaction-diffusion systems on graphs, where collective behaviors can be associated with eigenvectors of the network's Laplacian matrix. Our method combines a partial spectral decomposition of the network's Laplacian matrix with eigenvalue assignment by matching the patterns to the eigenvectors of the incomplete graph. We show that knowledge of a few collective patterns can allow the prediction of missing edges and that this result holds across a range of network architectures. We present a numerical case study using activator-inhibitor dynamics and we illustrate that the main requirement for the observed patterns is that they are not confined to subsets of nodes, but involve the whole network.

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.

Exploring cocoa bean fermentation mechanisms by kinetic modelling.

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.

Collective patterns and stable misunderstandings in networks striving for consensus without a common value system.

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').

Predictable topological sensitivity of Turing patterns on graphs.

Reaction-diffusion systems implemented as dynamical processes on networks have recently renewed the interest in their self-organized collective patterns known as Turing patterns. We investigate the influence of network topology on the emerging patterns and their diversity, defined as the variety of stationary states observed with random initial conditions and the same dynamics. We show that a seemingly minor change, the removal or rewiring of a single link, can prompt dramatic changes in pattern diversity. The determinants of such critical occurrences are explored through an extensive and systematic set of numerical experiments. We identify situations where the topological sensitivity of the attractor landscape can be predicted without a full simulation of the dynamical equations, from the spectrum of the graph Laplacian and the linearized dynamics. Unexpectedly, the main determinant appears to be the degeneracy of the eigenvalues or the growth rate and not the number of unstable modes.

Contribution of 3D genome topological domains to genetic risk of cancers: a genome-wide computational study.

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.

Cocoa bean fingerprinting via correlation networks.

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.

The economy of chromosomal distances in bacterial gene regulation.

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.

A minimal model for gene expression dynamics of bacterial type II toxin-antitoxin systems.

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.

Two classes of functional connectivity in dynamical processes in networks.

The relationship between network structure and dynamics is one of the most extensively investigated problems in the theory of complex systems of recent years. Understanding this relationship is of relevance to a range of disciplines-from neuroscience to geomorphology. A major strategy of investigating this relationship is the quantitative comparison of a representation of network architecture (structural connectivity, SC) with a (network) representation of the dynamics (functional connectivity, FC). Here, we show that one can distinguish two classes of functional connectivity-one based on simultaneous activity (co-activity) of nodes, the other based on sequential activity of nodes. We delineate these two classes in different categories of dynamical processes-excitations, regular and chaotic oscillators-and provide examples for SC/FC correlations of both classes in each of these models. We expand the theoretical view of the SC/FC relationships, with conceptual instances of the SC and the two classes of FC for various application scenarios in geomorphology, ecology, systems biology, neuroscience and socio-ecological systems. Seeing the organisation of dynamical processes in a network either as governed by co-activity or by sequential activity allows us to bring some order in the myriad of observations relating structure and function of complex networks.

Cocoa origin classifiability through LC-MS data: A statistical approach for large and long-term datasets.

Classification of food samples based upon their countries of origin is an important task in food industry for quality assurance and development of fine flavor products. Liquid chromatography -mass spectrometry (LC-MS) provides a fast technique for obtaining in-depth information about chemical composition of foods. However, in a large dataset that is gathered over a period of few years, multiple, incoherent and hard to avoid sources of variations e.g., experimental conditions, transportation, batch and instrumental effects, etc. pose technical challenges that make the study of origin classification a difficult problem. Here, we use a large dataset gathered over a period of four years containing 297 LC-MS profiles of cocoa sourced from 10 countries to demonstrate these challenges by using two popular multivariate analysis methods: principal component analysis (PCA) and linear discriminant analysis (LDA). We show that PCA provides a limited separation in bean origin, while LDA suffers from a strong non-linear dependence on the set of compounds. Further, we show for LDA that a compound selection criterion based on Gaussian distribution of intensities across samples dramatically enhances origin clustering of samples thereby suggesting possibilities for studying marker compounds in such a disparate dataset through this approach. In essence, we show and develop a new approach that maximizes, avoiding overfitting, the utility of multivariate analysis in a highly complex dataset.

A hexokinase isoenzyme switch in human liver cancer cells promotes lipogenesis and enhances innate immunity.

During the cancerous transformation of normal hepatocytes into hepatocellular carcinoma (HCC), the enzyme catalyzing the first rate-limiting step of glycolysis, namely the glucokinase (GCK), is replaced by the higher affinity isoenzyme, hexokinase 2 (HK2). Here, we show that in HCC tumors the highest expression level of HK2 is inversely correlated to GCK expression, and is associated to poor prognosis for patient survival. To further explore functional consequences of the GCK-to-HK2 isoenzyme switch occurring during carcinogenesis, HK2 was knocked-out in the HCC cell line Huh7 and replaced by GCK, to generate the Huh7-GCK+/HK2- cell line. HK2 knockdown and GCK expression rewired central carbon metabolism, stimulated mitochondrial respiration and restored essential metabolic functions of normal hepatocytes such as lipogenesis, VLDL secretion, glycogen storage. It also reactivated innate immune responses and sensitivity to natural killer cells, showing that consequences of the HK switch extend beyond metabolic reprogramming.

Multi-level assessment of obsessive-compulsive disorder (OCD) reveals relations between neural and neurochemical levels.

BACKGROUND: While considerable progress has been made in exploring the psychological, the neural, and the neurochemical dimensions of OCD separately, their interplay is still an open question, especially their changes during psychotherapy. METHODS: Seventeen patients were assessed at these three levels by psychological questionnaires, fMRI, and venipuncture before and after inpatient psychotherapy. Seventeen controls were scanned at comparable time intervals. First, pre/post treatment changes were investigated for all three levels separately: symptom severity, whole-brain and regional activity, and the concentrations of cortisol, serotonin, dopamine, brain-derived neurotrophic factor (BDNF), and immunological parameters (IL-6, IL-10, TNFα). Second, stepwise linear modeling was used to find relations between the variables of the levels. RESULTS: The obsessive-compulsive, depressive, and overall symptom severity was significantly reduced after psychotherapy. At the neural level, the activity in the anterior cingulate cortex (ACC), in frontal regions, in the precuneus, and in the putamen had significantly decreased. No significant changes were found on the neurochemical level. When connecting the levels, a highly significant model was found that explains the decrease in neural activity of the putamen by increases of the concentrations of cortisol, IL-6, and dopamine. CONCLUSION: Multivariate approaches offer insight on the influences that the different levels of the psychiatric disorder OCD have on each other. More research and adapted models are needed.

Link-usage asymmetry and collective patterns emerging from rich-club organization of complex networks.

In models of excitable dynamics on graphs, excitations can travel in both directions of an undirected link. However, as a striking interplay of dynamics and network topology, excitations often establish a directional preference. Some of these cases of "link-usage asymmetry" are local in nature and can be mechanistically understood, for instance, from the degree gradient of a link (i.e., the difference in node degrees at both ends of the link). Other contributions to the link-usage asymmetry are instead, as we show, self-organized in nature, and strictly nonlocal. This is the case for excitation waves, where the preferential propagation of excitations along a link depends on its orientation with respect to a hub acting as a source, even if the link in question is several steps away from the hub itself. Here, we identify and quantify the contribution of such self-organized patterns to link-usage asymmetry and show that they extend to ranges significantly longer than those ascribed to local patterns. We introduce a topological characterization, the hub-set-orientation prevalence of a link, which indicates its average orientation with respect to the hubs of a graph. Our numerical results show that the hub-set-orientation prevalence of a link strongly correlates with the preferential usage of the link in the direction of propagation away from the hub core of the graph. Our methodology is embedding-agnostic and allows for the measurement of wave signals and the sizes of the cores from which they originate.

Chromosomal origin of replication coordinates logically distinct types of bacterial genetic regulation.

For a long time it has been hypothesized that bacterial gene regulation involves an intricate interplay of the transcriptional regulatory network (TRN) and the spatial organization of genes in the chromosome. Here we explore this hypothesis both on a structural and on a functional level. On the structural level, we study the TRN as a spatially embedded network. On the functional level, we analyze gene expression patterns from a network perspective ("digital control"), as well as from the perspective of the spatial organization of the chromosome ("analog control"). Our structural analysis reveals the outstanding relevance of the symmetry axis defined by the origin (Ori) and terminus (Ter) of replication for the network embedding and, thus, suggests the co-evolution of two regulatory infrastructures, namely the transcriptional regulatory network and the spatial arrangement of genes on the chromosome, to optimize the cross-talk between two fundamental biological processes: genomic expression and replication. This observation is confirmed by the functional analysis based on the differential gene expression patterns of more than 4000 pairs of microarray and RNA-Seq datasets for E. coli from the Colombos Database using complex network and machine learning methods. This large-scale analysis supports the notion that two logically distinct types of genetic control are cooperating to regulate gene expression in a complementary manner. Moreover, we find that the position of the gene relative to the Ori is a feature of very high predictive value for gene expression, indicating that the Ori-Ter symmetry axis coordinates the action of distinct genetic control mechanisms.