[Show abstract][Hide abstract] ABSTRACT: The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain classes of random graphs. Hypotheses about the supposed role of prominent topological features (for instance, the roles of modularity, network motifs or hierarchical network organization) are derived from these deviations. An alternative strategy could be to study deviations of network architectures from regular graphs (rings and lattices) and consider the implications of such deviations for self-organized dynamic patterns on the network. Following this strategy, we draw on the theory of spatio-temporal pattern formation and propose a novel perspective for analysing dynamics on networks, by evaluating how the self-organized dynamics are confined by network architecture to a small set of permissible collective states. In particular, we discuss the role of prominent topological features of brain connectivity, such as hubs, modules and hierarchy, in shaping activity patterns. We illustrate the notion of network-guided pattern formation with numerical simulations and outline how it can facilitate the understanding of neural dynamics.
Philosophical transactions of the Royal Society of London. Series B, Biological sciences. 10/2014; 369(1653).
[Show abstract][Hide abstract] ABSTRACT: Pharmacology is currently transformed by the vast amounts of genome-associated information available for system-level interpretation. Here I review the potential of systems biology to facilitate this interpretation, thus paving the way for the emerging field of systems pharmacology. In particular, I will show how gene regulatory and metabolic networks can serve as a framework for interpreting high throughput data and as an interface to detailed dynamical models. In addition to the established connectivity analyses of effective networks, I suggest here to also analyze higher order architectural properties of effective networks.
British Journal of Clinical Pharmacology 04/2014; 77(4):597-605. · 3.58 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Genome signatures are statistical properties of DNA sequences that provide information on the underlying species. It is not understood, how such species-discriminating statistical properties arise from processes of genome evolution and from functional properties of the DNA. Investigating the interplay of different genome signatures can contribute to this understanding. Here we analyze the statistical dependences of two such genome signatures: word frequencies and symbol correlations at short and intermediate distances.
We formulate a statistical model of word frequencies in DNA sequences based on the observed symbol correlations and show that deviations of word counts from this correlation-based null model serve as a new genome signature. This signature (i) performs better in sorting DNA sequence segments according to their species origin and (ii) reveals unexpected species differences in the composition of microsatellites, an important class of repetitive DNA.
While the first observation is a typical task in metagenomics projects and therefore an important benchmark for a genome signature, the latter suggests strong species differences in the biological mechanisms of genome evolution.
On a more general level, our results highlight that the choice of null model (here: word abundances computed via symbol correlations rather than shorter word counts) substantially affects the interpretation of such statistical signals.
Physica A: Statistical Mechanics and its Applications 01/2014; 414:216–226. · 1.68 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Diversity-induced resonance, the emergence of coherent spatiotemporal patterns at intermediate parameter disorder, is a well-known phenomenon in lattices of excitable elements. Here we study the pattern events behind diversity-induced resonance in a lattice of coupled FitzHugh-Nagumo oscillators. Starting out with the observation that maximal spiral wave counts occur at intermediate values of parameter diversity, we analyze the competition between spiral and target wave patterns in the asymptotic collective state. We devise stylized numerical “in silico” competition experiments of (individual) patterns to understand the regulating parameters of the competing pattern events occurring stochastically in the full (“in vivo”) numerical simulation. Our analysis shows that pattern competition is a principal driving mechanism behind this form of diversity-induced resonance and that different types of competition take place: some follow the frequency composition of target and spiral waves, others are dictated by the statistics of parameter distributions. In particular, the increase and decrease of spiral wave counts with increasing diversity are statistically regulated by the number of oscillatory elements in the lattice, rather than by the frequency differences between target and spiral waves.
Physics of Condensed Matter 01/2014; 87(2). · 1.28 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A new paper shows that a characteristic feature of the arrangement of brain networks, their modular organization across several scales, is responsible for an expanded range of critical neural dynamics. This finding solves several puzzles in computational neuroscience and links fundamental aspects of neural network organization and brain dynamics.
Trends in Cognitive Sciences 11/2013; · 16.01 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Modules are common functional and structural properties of many social,
technical and biological networks. Especially for biological systems it
is important to understand how modularity is related to function and how
modularity evolves. It is known that time-varying or spatially organized
goals can lead to modularity in a simulated evolution of signaling
networks. Here, we study a minimal model of material flow in networks.
We discuss the relation between the shared use of nodes, i.e., the
cooperativity of modules, and the orthogonality of a prescribed output
pattern. We study the persistence of cooperativity through an evolution
of robustness against local damages. We expect the results to be valid
for a large class of flow-based biological and technical networks.
Supplementary material in the form of one pdf file available from the
Journal web page at http://dx.doi.org/10.1140/epjb/e2013-40672-3
Physics of Condensed Matter 11/2013; 86(11):473-. · 1.28 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In many biological systems, variability of the components can be expected to outrank statistical fluctuations in the shaping of self-organized patterns. In pioneering work in the late 1990s, it was hypothesized that a drift of cellular parameters (along a 'developmental path'), together with differences in cell properties ('desynchronization' of cells on the developmental path) can establish self-organized spatio-temporal patterns (in their example, spiral waves of cAMP in a colony of Dictyostelium discoideum cells) starting from a homogeneous state. Here, we embed a generic model of an excitable medium, a lattice of diffusively coupled FitzHugh-Nagumo oscillators, into a developmental-path framework. In this minimal model of spiral wave generation, we can now study the predictability of spatio-temporal patterns from cell properties as a function of desynchronization (or 'spread') of cells along the developmental path and the drift speed of cell properties on the path. As a function of drift speed and desynchronization, we observe systematically different routes towards fully established patterns, as well as strikingly different correlations between cell properties and pattern features. We show that the predictability of spatio-temporal patterns from cell properties contains important information on the pattern formation process as well as on the underlying dynamical system.
Journal of The Royal Society Interface 01/2013; 10(81):20121016. · 4.91 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: Few-node subgraphs are the smallest collective units in a network that can be investigated. They are beyond the scale of individual nodes but more local than, for example, communities. When statistically over- or under-represented, they are called network motifs. Network motifs have been interpreted as building blocks that shape the dynamic behaviour of networks. It is this promise of potentially explaining emergent properties of complex systems with relatively simple structures that led to an interest in network motifs in an ever-growing number of studies and across disciplines. Here, we discuss artefacts in the analysis of network motifs arising from discrepancies between the network under investigation and the pool of random graphs serving as a null model. Our aim was to provide a clear and accessible catalogue of such incongruities and their effect on the motif signature. As a case study, we explore the metabolic network of Escherichia coli and show that only by excluding ever more artefacts from the motif signature a strong and plausible correlation with the essentiality profile of metabolic reactions emerges.
Journal of The Royal Society Interface 08/2012; 9(77):3426-35. · 4.91 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Understanding the interplay of topology and dynamics of excitable neural networks is one of the major challenges in computational neuroscience. Here we employ a simple deterministic excitable model to explore how network-wide activation patterns are shaped by network architecture. Our observables are co-activation patterns, together with the average activity of the network and the periodicities in the excitation density. Our main results are: (1) the dependence of the correlation between the adjacency matrix and the instantaneous (zero time delay) co-activation matrix on global network features (clustering, modularity, scale-free degree distribution), (2) a correlation between the average activity and the amount of small cycles in the graph, and (3) a microscopic understanding of the contributions by 3-node and 4-node cycles to sustained activity.
Frontiers in Computational Neuroscience 07/2012; 6:50. · 2.48 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: BACKGROUND: Integrating gene expression profiles and metabolic pathways under different experimental conditions is essential for understanding the coherence of these two layers of cellular organization. The network character of metabolic systems can be instrumental in developing concepts of agreement between expression data and pathways. A network-driven interpretation of gene expression data has the potential of suggesting novel classifiers for pathological cellular states and of contributing to a general theoretical understanding of gene regulation. RESULTS: Here, we analyze the coherence of gene expression patterns and a reconstruction of human metabolism, using consistency scores obtained from network and constraint-based analysis methods. We find a surprisingly strong correlation between the two measures, demonstrating that a substantial part of inconsistencies between metabolic processes and gene expression can be understood from a network perspective alone. Prompted by this finding, we investigate the topological context of the individual biochemical reactions responsible for the observed inconsistencies. On this basis, we are able to separate the differential contributions that bear physiological information about the system, from the unspecific contributions that unravel gaps in the metabolic reconstruction. We demonstrate the biological potential of our network-driven approach by analyzing transcriptome profiles of aldosterone producing adenomas that have been obtained from a cohort of Primary Aldosteronism patients. We unravel systematics in the data that could not have been resolved by conventional microarray data analysis. In particular, we discover two distinct metabolic states in the adenoma expression patterns. CONCLUSIONS: The methodology presented here can help understand metabolic inconsistencies from a network perspective. It thus serves as a mediator between the topology of metabolic systems and their dynamical function. Finally, we demonstrate how physiologically relevant insights into the structure and dynamics of metabolic networks can be obtained using this novel approach.
BMC Systems Biology 05/2012; 6(1):41. · 2.98 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: How signals propagate through a network as a function of the network architecture and under the influence of noise is a fundamental question in a broad range of areas dealing with signal processing - from neuroscience to electrical engineering and communication technology. Here we use numerical simulations and a mean-field approach to analyze a minimal dynamic model for signal propagation. By labeling and tracking the excitations propagating from a single input node to remote output nodes in random networks, we show that noise (provided by spontaneous node excitations) can lead to an enhanced signal propagation, with a peak in the signal-to-noise ratio at intermediate noise intensities. This network analog of stochastic resonance is not captured by a mean-field description that incorporates topology only on the level of the average degree, indicating that the detailed network topology plays a significant role in signal propagation.Highlights► We explore the propagation of excitations through a network under the influence of noise. ► Special emphasis is on the application to neuroscience. ► A novel labeling technique of signal excitations is introduced and compared to the classical signal-to-noise ratio. ► We show that noise can lead to an enhanced signal propagation, with a peak in the signal-to-noise ratio at intermediate noise intensities.
[Show abstract][Hide abstract] ABSTRACT: The 3D structure of the chromosome of the model organism Escherichia coli is one key component of its gene regulatory machinery. This type of regulation mediated by topological transitions of the chromosomal DNA can be thought of as an analog control, complementing the digital control, i.e. the network of regulation mediated by dedicated transcription factors. It is known that alterations in the superhelical density of chromosomal DNA lead to a rich pattern of differential expressed genes. Using a network approach, we analyze these expression changes for wild type E. coli and mutants lacking nucleoid associated proteins (NAPs) from a metabolic and transcriptional regulatory network perspective.
We find a significantly higher correspondence between gene expression and metabolism for the wild type expression changes compared to mutants in NAPs, indicating that supercoiling induces meaningful metabolic adjustments. As soon as the underlying regulatory machinery is impeded (as for the NAP mutants), this coherence between expression changes and the metabolic network is substantially reduced. This effect is even more pronounced, when we compute a wild type metabolic flux distribution using flux balance analysis and restrict our analysis to active reactions. Furthermore, we are able to show that the regulatory control exhibited by DNA supercoiling is not mediated by the transcriptional regulatory network (TRN), as the consistency of the expression changes with the TRN logic of activation and suppression is strongly reduced in the wild type in comparison to the mutants.
So far, the rich patterns of gene expression changes induced by alterations of the superhelical density of chromosomal DNA have been difficult to interpret. Here we characterize the effective networks formed by supercoiling-induced gene expression changes mapped onto reconstructions of E. coli's metabolic and transcriptional regulatory network. Our results show that DNA supercoiling coordinates gene expression with metabolism. Furthermore, this control is acting directly because we can exclude the potential role of the TRN as a mediator.
BMC Systems Biology 03/2011; 5:40. · 2.98 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In [Brandman et al., 2005] it was proposed that interlinked fast and slow positive feedback loops are a frequent motif in biological signaling, because such a device can allow for a rapid response to an external stimulus (sensitivity) along with a certain noise-buffering capacity (robustness), as soon as the two loops operate on different time scales. Here we explore the properties of the nonlinear system responsible for this behavior. We argue that (a) the noise buffering is not linked to the stochastic nature of the stimulus, but only to the time scale of the stimulus variation compared to the intrinsic time scales of the system, and (b) this buffering of stimulus variations follows from the stabilization of a region of the state space away from the equilibrium branches of the system. Our analysis is based on a slow-fast decomposition of the dynamics. We analyze the strength of this buffering as a function of the time scales involved and the Boolean logic of the coupling between dynamic variables, as well as of the amplitude of the stimulus variations. We underline that such a nonequilibrium regime is universal as soon as the stimulus time scale is smaller than the larger time scale of the system, preventing the prediction of the behavior from the features of the bifurcation diagram or using a linear analysis.
International Journal of Bifurcation and Chaos 01/2011; 21:1895-1905. · 0.92 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The general view of flow networks controlled by periodic devices provides a powerful unifying language for diverse fields of application. Recent publications on traffic control have presented strategies for adaptive flow control. For adapting this view to production logistics two improvements are necessary: A discussion of more general network architectures than in traffic and a generalization towards more sophisticated performance measures beyond waiting time. Our simulation study illustrates how strongly parameter variation influences the logistic performance and we show whether the promising findings from traffic control regarding waiting time reduction and the emergence of synchronized behavior can be reproduced for production logistics.
Proceedings of the 44th CIRP International Conference on Manufacturing Systems; 01/2011
[Show abstract][Hide abstract] ABSTRACT: Identifying causes of lateness in multistage production systems demands methods for considering a high-dimensional order and process attribute space. Simultaneous measurement of expression levels of thousands of genes in a biological cell provides a data set for understanding robust cellular function. Methods developed in computational systems biology for analyzing gene expression data enable the identification of the most influential criteria sets. Gene expression is the production process of functional elements (enzymes, proteins) in a biological cell. Logistics data analysis faces a similar challenge: What attributes of orders can be associated with high and low punctuality? We combine methods from cluster analysis and computational systems biology to explore the relationship between order and resource parameters and lateness. With this novel approach we determine intrinsic interdependencies between order parameters and process parameters. For the case study described here, this approach has improved the precision of predicting the lateness of an order by 14% compared to a majority vote among neighboring orders in parameter space.
[Show abstract][Hide abstract] ABSTRACT: Metabolic systems need to show high performance under typical environmental conditions and, at the same time, maintain certain functions under a broad range of perturbations and varying conditions. It is precisely this robustness with respect to large environmental changes that makes metabolic networks a potentially very interesting role model for technical production and distribution systems. Here we develop a formalism to compare these systems and show that optimization strategies from one domain can also be successfully applied to the other domains.
Journal of Statistical Mechanics Theory and Experiment 01/2011; 2011(05):P05004. · 1.87 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Timetable construction belongs to the most important optimization problems in public transport. Finding optimal or near-optimal timetables under the subsidiary conditions of minimizing travel times and other criteria is a targeted contribution to the functioning of public transport. In addition to efficiency (given, e.g., by minimal average travel times), a significant feature of a timetable is its robustness against delay propagation. Here we study the balance of efficiency and robustness in long-distance railway timetables (in particular the current long-distance railway timetable in Germany) from the perspective of synchronization, exploiting the fact that a major part of the trains run nearly periodically. We find that synchronization is highest at intermediate-sized stations. We argue that this synchronization perspective opens a new avenue towards an understanding of railway timetables by representing them as spatio-temporal phase patterns. Robustness and efficiency can then be viewed as properties of this phase pattern.
Physics of Condensed Matter 03/2010; · 1.28 Impact Factor