Interplay between Topology and Dynamics in Excitation Patterns on Hierarchical Graphs

In a recent publication (Müller-Linow et al., 2008) two types of correlations between network topology and dynamics have been observed: waves propagating from central nodes and module-based synchronization. Remarkably, the dynamic behavior of hierarchical modular networks can switch from one of these modes to the other as the level of spontaneous network activation changes. Here we attempt to capture the origin of this switching behavior in a mean-field model as well in a formalism, where excitation waves are regarded as avalanches on the graph

Unravelling topological determinants of excitable dynamics on graphs using analytical mean-field approaches

(peer-reviewed, accepted 2019-05-14)International audienceWe present our use of analytical mean-field approaches in investigating how the interplay between graph topology and excitable dynamics produce spatio-temporal patterns. We first detail the derivation of mean-field equations for a few simple model situations, mainly 3-state discrete-time excitable dynamics with an absolute or a relative excita-tion threshold. Comparison with direct numerical simulation shows that their solution satisfactorily predicts the steady-state excitation density. In contrast, they often fail to capture more complex dynamical features, however we argue that the analysis of this failure is in itself insightful, by pinpointing the key role of mechanisms neglected in the mean-field approach. Moreover, we show how second-order mean-field approaches, in which a topological object (e.g. a cycle or a hub) is considered as embedded in a mean-field surrounding, allow us to go beyond the spatial homogenization currently associated with plain mean-field calculations. The confrontation between these refined analytical predictions and simulation quantitatively evidences the specific contribution of this topological object to the dynamics. Mathematics Subject Classification (2010). Primary 05C82; Secondary 92C42

Predicting attractors from spectral properties of stylized gene regulatory networks

How the architecture of gene regulatory networks ultimately shapes gene expression patterns is an open question, which has been approached from a multitude of angles. The dominant strategy has been to identify non-random features in these networks and then argue for the function of these features using mechanistic modelling. Here we establish the foundation of an alternative approach by studying the correlation of eigenvectors with synthetic gene expression data simulated with a basic and popular model of gene expression dynamics -- attractors of Boolean threshold dynamics in signed directed graphs. Eigenvectors of the graph Laplacian are known to explain collective dynamical states (stationary patterns) in Turing dynamics on graphs. In this study, we show that eigenvectors can also predict collective states (attractors) for a markedly different type of dynamics, Boolean threshold dynamics, and category of graphs, signed directed graphs. However, the overall predictive power depends on details of the network architecture, in a predictable fashion. Our results are a set of statistical observations, providing the first systematic step towards a further theoretical understanding of the role of eigenvectors in dynamics on graphs.Comment: Main text: 14 pages, 11 figures. Supplements: 22 pages, 16 figures. Submitted to: Physical Review

The physics behind systems biology

Systems Biology is a young and rapidly evolving research field, which combines experimental techniques and mathematical modeling in order to achieve a mechanistic understanding of processes underlying the regulation and evolution of living systems. Systems Biology is often associated with an Engineering approach: The purpose is to formulate a data-rich, detailed simulation model that allows to perform numerical (‘in silico’) experiments and then draw conclusions about the biological system. While methods from Engineering may be an appropriate approach to extending the scope of biological investigations to experimentally inaccessible realms and to supporting data-rich experimental work, it may not be the best strategy in a search for design principles of biological systems and the fundamental laws underlying Biology. Physics has a long tradition of characterizing and understanding emergent collective behaviors in systems of interacting units and searching for universal laws. Therefore, it is natural that many concepts used in Systems Biology have their roots in Physics. With an emphasis on Theoretical Physics, we will here review the ‘Physics core’ of Systems Biology, show how some success stories in Systems Biology can be traced back to concepts developed in Physics, and discuss how Systems Biology can further benefit from ist Theoretical Physics foundation

Microbiome abundance patterns as attractors and the implications for the inference of microbial interaction networks

Inferring microbial interaction networks from abundance patterns is an important approach to advance our understanding of microbial communities in general and the human microbiome in particular. Here we suggest discriminating two levels of information contained in microbial abundance data: (1) the quantitative abundance values and (2) the pattern of presences and absences of microbial organisms. The latter allows for a binary view on microbiome data and a novel interpretation of microbial data as attractors, or more precisely as fixed points, of a Boolean network. Starting from these attractors, our aim is to infer an interaction network between the species present in the microbiome samples. To accomplish this task, we introduce a novel inference method that combines the previously published ESABO (Entropy Shifts of Abundance vectors under Boolean Operations) method with an evolutionary algorithm. The key idea of our approach is that the inferred network should reproduce the original set of (observed) binary abundance patterns as attractors. We study the accuracy and runtime properties of this evolutionary method, as well as its behavior under incomplete knowledge of the attractor sets. Based on this theoretical understanding of the method we then show an application to empirical data

Ranges of control in the transcriptional regulation of Escherichia coli

<p>Abstract</p> <p>Background</p> <p>The positioning of genes in the genome is an important evolutionary degree of freedom for organizing gene regulation. Statistical properties of these distributions have been studied particularly in relation to the transcriptional regulatory network. The systematics of gene-gene distances then become important sources of information on the control, which different biological mechanisms exert on gene expression.</p> <p>Results</p> <p>Here we study a set of categories, which has to our knowledge not been analyzed before. We distinguish between genes that do not participate in the transcriptional regulatory network (i.e. that are according to current knowledge not producing transcription factors and do not possess binding sites for transcription factors in their regulatory region), and genes that via transcription factors either are regulated by or regulate other genes. We find that the two types of genes ("isolated" and "regulatory" genes) show a clear statistical repulsion and have different ranges of correlations. In particular we find that isolated genes have a preference for shorter intergenic distances.</p> <p>Conclusions</p> <p>These findings support previous evidence from gene expression patterns for two distinct logical types of control, namely digital control (i.e. network-based control mediated by dedicated transcription factors) and analog control (i.e. control based on genome structure and mediated by neighborhood on the genome).</p

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.Comment: 29 pages, 6 figures + Supplementary informatio

The Regularizing Capacity of Metabolic Networks

Despite their topological complexity almost all functional properties of metabolic networks can be derived from steady-state dynamics. Indeed, many theoretical investigations (like flux-balance analysis) rely on extracting function from steady states. This leads to the interesting question, how metabolic networks avoid complex dynamics and maintain a steady-state behavior. Here, we expose metabolic network topologies to binary dynamics generated by simple local rules. We find that the networks' response is highly specific: Complex dynamics are systematically reduced on metabolic networks compared to randomized networks with identical degree sequences. Already small topological modifications substantially enhance the capacity of a network to host complex dynamic behavior and thus reduce its regularizing potential. This exceptionally pronounced regularization of dynamics encoded in the topology may explain, why steady-state behavior is ubiquitous in metabolism.Comment: 6 pages, 4 figure

Similar impact of topological and dynamic noise on complex patterns

Shortcuts in a regular architecture affect the information transport through the system due to the severe decrease in average path length. A fundamental new perspective in terms of pattern formation is the destabilizing effect of topological perturbations by processing distant uncorrelated information, similarly to stochastic noise. We study the functional coincidence of rewiring and noisy communication on patterns of binary cellular automata.Comment: 8 pages, 7 figures. To be published in Physics Letters