Feigenbaum graphs: a complex network perspective of chaos

The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map nonlinearity or other particulars. We derive exact results for their degree distribution and related quantities, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Furthermore, we show that the network entropy mimics the Lyapunov exponent of the map independently of its sign, hinting at a Pesin-like relation equally valid out of chaos.Comment: Published in PLoS ONE (Sep 2011

METANNOGEN: compiling features of biochemical reactions needed for the reconstruction of metabolic networks

BACKGROUND: One central goal of computational systems biology is the mathematical modelling of complex metabolic reaction networks. The first and most time-consuming step in the development of such models consists in the stoichiometric reconstruction of the network, i. e. compilation of all metabolites, reactions and transport processes relevant to the considered network and their assignment to the various cellular compartments. Therefore an information system is required to collect and manage data from different databases and scientific literature in order to generate a metabolic network of biochemical reactions that can be subjected to further computational analyses. RESULTS: The computer program METANNOGEN facilitates the reconstruction of metabolic networks. It uses the well-known database of biochemical reactions KEGG of biochemical reactions as primary information source from which biochemical reactions relevant to the considered network can be selected, edited and stored in a separate, user-defined database. Reactions not contained in KEGG can be entered manually into the system. To aid the decision whether or not a reaction selected from KEGG belongs to the considered network METANNOGEN contains information of SWISSPROT and ENSEMBL and provides Web links to a number of important information sources like METACYC, BRENDA, NIST, and REACTOME. If a reaction is reported to occur in more than one cellular compartment, a corresponding number of reactions is generated each referring to one specific compartment. Transport processes of metabolites are entered like chemical reactions where reactants and products have different compartment attributes. The list of compartmentalized biochemical reactions and membrane transport processes compiled by means of METANNOGEN can be exported as an SBML file for further computational analysis. METANNOGEN is highly customizable with respect to the content of the SBML output file, additional data-fields, the graphical input form, highlighting of project specific search terms and dynamically generated Web-links. CONCLUSION: METANNOGEN is a flexible tool to manage information for the design of metabolic networks. The program requires Java Runtime Environment 1.4 or higher and about 100 MB of free RAM and about 200 MB of free HD space. It does not require installation and can be directly Java-webstarted from

Chaotic dynamics of falling disks

The study of the motion of flat bodies falling in a viscous medium dates back at least to Newton(1) and Maxwell(2), and is relevant to problems in meteorology(3), sedimentology(4), aerospace engineering(1) and chemical engineering(5-8). More recent theoretical studies(9-12) have emphasized the role played by deterministic chaos, although many experimental studies(1,5-8,13,14) were performed before the development of such ideas. Here we report experimental observations of the dynamics of disks falling in water/glycerol mixtures. We find four distinct types of motion, which are mapped out in a 'phase diagram'. The apparently complex behaviour can be reduced to a series of one-dimensional maps, which display a discontinuity at the crossover from periodic to chaotic motion. This discontinuity leads to an unusual intermittency transition(15), not previously observed experimentally, between the two behaviours.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62793/1/388252a0.pd

FASIMU: flexible software for flux-balance computation series in large metabolic networks

<p>Abstract</p> <p>Background</p> <p>Flux-balance analysis based on linear optimization is widely used to compute metabolic fluxes in large metabolic networks and gains increasingly importance in network curation and structural analysis. Thus, a computational tool flexible enough to realize a wide variety of FBA algorithms and able to handle batch series of flux-balance optimizations is of great benefit.</p> <p>Results</p> <p>We present FASIMU, a command line oriented software for the computation of flux distributions using a variety of the most common FBA algorithms, including the first available implementation of (i) weighted flux minimization, (ii) fitness maximization for partially inhibited enzymes, and (iii) of the concentration-based thermodynamic feasibility constraint. It allows batch computation with varying objectives and constraints suited for network pruning, leak analysis, flux-variability analysis, and systematic probing of metabolic objectives for network curation. Input and output supports SBML. FASIMU can work with free (lp_solve and GLPK) or commercial solvers (CPLEX, LINDO). A new plugin (faBiNA) for BiNA allows to conveniently visualize calculated flux distributions. The platform-independent program is an open-source project, freely available under GNU public license at <url>http://www.bioinformatics.org/fasimu</url> including manual, tutorial, and plugins.</p> <p>Conclusions</p> <p>We present a flux-balance optimization program whose main merits are the implementation of thermodynamics as a constraint, batch series of computations, free availability of sources, choice on various external solvers, and the flexibility on metabolic objectives and constraints.</p

Fractional Zaslavsky and Henon Discrete Maps

This paper is devoted to the memory of Professor George M. Zaslavsky passed away on November 25, 2008. In the field of discrete maps, George M. Zaslavsky introduced a dissipative standard map which is called now the Zaslavsky map. G. Zaslavsky initialized many fundamental concepts and ideas in the fractional dynamics and kinetics. In this paper, starting from kicked damped equations with derivatives of non-integer orders we derive a fractional generalization of discrete maps. These fractional maps are generalizations of the Zaslavsky map and the Henon map. The main property of the fractional differential equations and the correspondent fractional maps is a long-term memory and dissipation. The memory is realized by the fact that their present state evolution depends on all past states with special forms of weights.Comment: 26 pages, LaTe

Short Conduction Delays Cause Inhibition Rather than Excitation to Favor Synchrony in Hybrid Neuronal Networks of the Entorhinal Cortex

How stable synchrony in neuronal networks is sustained in the presence of conduction delays is an open question. The Dynamic Clamp was used to measure phase resetting curves (PRCs) for entorhinal cortical cells, and then to construct networks of two such neurons. PRCs were in general Type I (all advances or all delays) or weakly type II with a small region at early phases with the opposite type of resetting. We used previously developed theoretical methods based on PRCs under the assumption of pulsatile coupling to predict the delays that synchronize these hybrid circuits. For excitatory coupling, synchrony was predicted and observed only with no delay and for delays greater than half a network period that cause each neuron to receive an input late in its firing cycle and almost immediately fire an action potential. Synchronization for these long delays was surprisingly tight and robust to the noise and heterogeneity inherent in a biological system. In contrast to excitatory coupling, inhibitory coupling led to antiphase for no delay, very short delays and delays close to a network period, but to near-synchrony for a wide range of relatively short delays. PRC-based methods show that conduction delays can stabilize synchrony in several ways, including neutralizing a discontinuity introduced by strong inhibition, favoring synchrony in the case of noisy bistability, and avoiding an initial destabilizing region of a weakly type II PRC. PRCs can identify optimal conduction delays favoring synchronization at a given frequency, and also predict robustness to noise and heterogeneity

Administration of intrapulmonary sodium polyacrylate to induce lung injury for the development of a porcine model of early acute respiratory distress syndrome.

BACKGROUND: The loss of alveolar epithelial and endothelial integrity is a central component in acute respiratory distress syndrome (ARDS); however, experimental models investigating the mechanisms of epithelial injury are lacking. The purpose of the present study was to design and develop an experimental porcine model of ARDS by inducing lung injury with intrapulmonary administration of sodium polyacrylate (SPA). METHODS: The present study was performed at the Centre for Comparative Medicine, University of British Columbia, Vancouver, British Columbia. Human alveolar epithelial cells were cultured with several different concentrations of SPA; a bioluminescence technique was used to assess cell death associated with each concentration. In the anesthetized pig model (female Yorkshire X pigs (n = 14)), lung injury was caused in 11 animals (SPA group) by injecting sequential aliquots (5 mL) of 1% SPA gel in aqueous solution into the distal airway via a rubber catheter through an endotracheal tube. The SPA was dispersed throughout the lungs by manual bag ventilation. Three control animals (CON group) underwent all experimental procedures and measurements with the exception of SPA administration. RESULTS: The mean (± SD) ATP concentration after incubation of human alveolar epithelial cells with 0.1% SPA (0.92 ± 0.27 μM/well) was approximately 15% of the value found for the background control (6.30 ± 0.37 μM/well; p < 0.001). Elastance of the respiratory system (E RS) and the lung (E L) increased in SPA-treated animals after injury (p = 0.003 and p < 0.001, respectively). Chest wall elastance (E CW) did not change in SPA-treated animals. There were no differences in E RS, E L, or E CW in the CON group when pre- and post-injury values were compared. Analysis of bronchoalveolar lavage fluid showed a significant shift toward neutrophil predominance from before to after injury in SPA-treated animals (p < 0.001) but not in the CON group (p = 0.38). Necropsy revealed marked consolidation and congestion of the dorsal lung lobes in SPA-treated animals, with light-microscopy evidence of bronchiolar and alveolar spaces filled with neutrophilic infiltrate, proteinaceous debris, and fibrin deposition. These findings were absent in animals in the CON group. Electron microscopy of lung tissue from SPA-treated animals revealed injury to the alveolar epithelium and basement membranes, including intra-alveolar neutrophils and fibrin on the alveolar surface and intravascular fibrin (microthrombosis). CONCLUSIONS: In this particular porcine model, the nonimmunogenic polymer SPA caused a rapid exudative lung injury. This model may be useful to study ARDS caused by epithelial injury and inflammation

Spiral attractor created by vector solitons

Mode-locked lasers emitting a train of femtosecond pulses called dissipative solitons are an enabling technology for metrology, high-resolution spectroscopy, fibre optic communications, nano-optics and many other fields of science and applications. Recently, the vector nature of dissipative solitons has been exploited to demonstrate mode locked lasing with both locked and rapidly evolving states of polarisation. Here, for an erbium-doped fibre laser mode locked with carbon nanotubes, we demonstrate the first experimental and theoretical evidence of a new class of slowly evolving vector solitons characterized by a double-scroll chaotic polarisation attractor substantially different from Lorenz, Rössler and Ikeda strange attractors. The underlying physics comprises a long time scale coherent coupling of two polarisation modes. The observed phenomena, apart from the fundamental interest, provide a base for advances in secure communications, trapping and manipulation of atoms and nanoparticles, control of magnetisation in data storage devices and many other areas

GPS-ARM: Computational Analysis of the APC/C Recognition Motif by Predicting D-Boxes and KEN-Boxes

Anaphase-promoting complex/cyclosome (APC/C), an E3 ubiquitin ligase incorporated with Cdh1 and/or Cdc20 recognizes and interacts with specific substrates, and faithfully orchestrates the proper cell cycle events by targeting proteins for proteasomal degradation. Experimental identification of APC/C substrates is largely dependent on the discovery of APC/C recognition motifs, e.g., the D-box and KEN-box. Although a number of either stringent or loosely defined motifs proposed, these motif patterns are only of limited use due to their insufficient powers of prediction. We report the development of a novel GPS-ARM software package which is useful for the prediction of D-boxes and KEN-boxes in proteins. Using experimentally identified D-boxes and KEN-boxes as the training data sets, a previously developed GPS (Group-based Prediction System) algorithm was adopted. By extensive evaluation and comparison, the GPS-ARM performance was found to be much better than the one using simple motifs. With this powerful tool, we predicted 4,841 potential D-boxes in 3,832 proteins and 1,632 potential KEN-boxes in 1,403 proteins from H. sapiens, while further statistical analysis suggested that both the D-box and KEN-box proteins are involved in a broad spectrum of biological processes beyond the cell cycle. In addition, with the co-localization information, we predicted hundreds of mitosis-specific APC/C substrates with high confidence. As the first computational tool for the prediction of APC/C-mediated degradation, GPS-ARM is a useful tool for information to be used in further experimental investigations. The GPS-ARM is freely accessible for academic researchers at: http://arm.biocuckoo.org