Synchronization in periodically driven and coupled stochastic systems-A discrete state approach

Wir untersuchen das Verhalten von stochastischen bistabilen und erregbaren Systemen auf der Basis einer Modellierung mit diskreten Zuständen. In Ergänzung zum bekannten Markovschen Zwei-Zustandsmodell bistabiler stochastischer Dynamik stellen wir ein nicht Markovsches Drei-Zustandsmodell für erregbare Systeme vor. Seine relative Einfachheit, verglichen mit stochastischen Modellen erregbarer Dynamik mit kontinuierlichem Phasenraum, ermöglicht eine teilweise analytische Auswertung in verschiedenen Zusammenhängen. Zunächst untersuchen wir den gemeinsamen Einfluß eines periodischen Treibens und Rauschens. Dieser wird entweder mit Hilfe spektraler Größen oder durch Synchronisation des Systems mit dem treibenden Signal charakterisiert. Wir leiten analytische Ausdrücke für die spektrale Leistungsverstärkung und das Signal-zu-Rauschen Verhältnis für periodisch getriebene Renewal-Prozesse her und wenden diese auf das diskrete Modell für erregbare Dynamik an. Stochastische Synchronization des Systems mit dem treibenden Signal wird auf der Basis der Diffusionseigenschaften der Übergangsereignisse zwischen den diskreten Zuständen untersucht. Wir leiten allgemeine Formeln her, um die mittlere Häufigkeit dieser Ereignisse sowie deren effektiven Diffusionskoeffizienten zu berechnen. Über die konkrete Anwendung auf die untersuchten diskreten Modelle hinaus stellen diese Ergebnisse ein neues Werkzeug für die Untersuchung periodischer Renewal-Prozesse dar. Schließlich betrachten wir noch das Verhalten global gekoppelter bistabiler und erregbarer Systeme. Im Gegensatz zu bistabilen System können erregbare Systeme synchronisiert werden und zeigen kohärente Oszillationen. Alle Untersuchungen des nicht Markovschen Drei-Zustandsmodells werden mit dem prototypischen Modell für erregbare Dynamik, dem FitzHugh-Nagumo System, verglichen und zeigen eine gute Übereinstimmung.We investigate the behavior of stochastic bistable and excitable dynamics based on a discrete state modeling. In addition to the well known Markovian two state model for bistable dynamics we introduce a non Markovian three state model for excitable systems. Its relative simplicity compared to stochastic models of excitable dynamics with continuous phase space allows to obtain analytical results in different contexts. First, we study the joint influence of periodic signals and noise, both based on a characterization in terms of spectral quantities and in terms of synchronization with the periodic driving. We present expressions for the spectral power amplification and signal to noise ratio for renewal processes driven by periodic signals and apply these results to the discrete model for excitable systems. Stochastic synchronization of the system to the driving signal is investigated based on diffusion properties of the transition events between the discrete states. We derive general results for the mean frequency and effective diffusion coefficient which, beyond the application to the discrete models considered in this work, provide a new tool in the study of periodically driven renewal processes. Finally the behavior of globally coupled excitable and bistable units is investigated based on the discrete state description. In contrast to the bistable systems, the excitable system exhibits synchronization and thus coherent oscillations. All investigations of the non Markovian three state model are compared with the prototypical continuous model for excitable dynamics, the FitzHugh-Nagumo system, revealing a good agreement between both models

State-of-the art data normalization methods improve NMR-based metabolomic analysis

Extracting biomedical information from large metabolomic datasets by multivariate data analysis is of considerable complexity. Common challenges include among others screening for differentially produced metabolites, estimation of fold changes, and sample classification. Prior to these analysis steps, it is important to minimize contributions from unwanted biases and experimental variance. This is the goal of data preprocessing. In this work, different data normalization methods were compared systematically employing two different datasets generated by means of nuclear magnetic resonance (NMR) spectroscopy. To this end, two different types of normalization methods were used, one aiming to remove unwanted sample-to-sample variation while the other adjusts the variance of the different metabolites by variable scaling and variance stabilization methods. The impact of all methods tested on sample classification was evaluated on urinary NMR fingerprints obtained from healthy volunteers and patients suffering from autosomal polycystic kidney disease (ADPKD). Performance in terms of screening for differentially produced metabolites was investigated on a dataset following a Latin-square design, where varied amounts of 8 different metabolites were spiked into a human urine matrix while keeping the total spike-in amount constant. In addition, specific tests were conducted to systematically investigate the influence of the different preprocessing methods on the structure of the analyzed data. In conclusion, preprocessing methods originally developed for DNA microarray analysis, in particular, Quantile and Cubic-Spline Normalization, performed best in reducing bias, accurately detecting fold changes, and classifying samples

MetaboHunter: an automatic approach for identification of metabolites from 1H-NMR spectra of complex mixtures

<p>Abstract</p> <p>Background</p> <p>One-dimensional ¹H-NMR spectroscopy is widely used for high-throughput characterization of metabolites in complex biological mixtures. However, the accurate identification of individual compounds is still a challenging task, particularly in spectral regions with higher peak densities. The need for automatic tools to facilitate and further improve the accuracy of such tasks, while using increasingly larger reference spectral libraries becomes a priority of current metabolomics research.</p> <p>Results</p> <p>We introduce a web server application, called MetaboHunter, which can be used for automatic assignment of ¹H-NMR spectra of metabolites. MetaboHunter provides methods for automatic metabolite identification based on spectra or peak lists with three different search methods and with possibility for peak drift in a user defined spectral range. The assignment is performed using as reference libraries manually curated data from two major publicly available databases of NMR metabolite standard measurements (HMDB and MMCD). Tests using a variety of synthetic and experimental spectra of single and multi metabolite mixtures show that MetaboHunter is able to identify, in average, more than 80% of detectable metabolites from spectra of synthetic mixtures and more than 50% from spectra corresponding to experimental mixtures. This work also suggests that better scoring functions improve by more than 30% the performance of MetaboHunter's metabolite identification methods.</p> <p>Conclusions</p> <p>MetaboHunter is a freely accessible, easy to use and user friendly ¹H-NMR-based web server application that provides efficient data input and pre-processing, flexible parameter settings, fast and automatic metabolite fingerprinting and results visualization via intuitive plotting and compound peak hit maps. Compared to other published and freely accessible metabolomics tools, MetaboHunter implements three efficient methods to search for metabolites in manually curated data from two reference libraries.</p> <p>Availability</p> <p><url>http://www.nrcbioinformatics.ca/metabohunter/</url></p

Between Metabolite Relationships: an essential aspect of metabolic change

Not only the levels of individual metabolites, but also the relations between the levels of different metabolites may indicate (experimentally induced) changes in a biological system. Component analysis methods in current ‘standard’ use for metabolomics, such as Principal Component Analysis (PCA), do not focus on changes in these relations. We therefore propose the concept of ‘Between Metabolite Relationships’ (BMRs): common changes in the covariance (or correlation) between all metabolites in an organism. Such structural changes may indicate metabolic change brought about by experimental manipulation but which are lost with standard data analysis methods. These BMRs can be analysed by the INdividual Differences SCALing (INDSCAL) method. First the BMR quantification is described and subsequently the INDSCAL method. Finally, two studies illustrate the power and the applicability of BMRs in metabolomics. The first study is about the induced plant response of cabbage to herbivory, of which BMRs are a considerable part. In the second study—a human nutritional intervention study of green tea extract—standard data analysis tools did not reveal any metabolic change, although the BMRs were considerably affected. The presented results show that BMRs can be easily implemented in a wide variety of metabolomic studies. They provide a new source of information to describe biological systems in a way that fits flawlessly into the next generation of systems biology questions, dealing with personalized responses

Mass-spectrometry-based metabolomics: limitations and recommendations for future progress with particular focus on nutrition research

Mass spectrometry (MS) techniques, because of their sensitivity and selectivity, have become methods of choice to characterize the human metabolome and MS-based metabolomics is increasingly used to characterize the complex metabolic effects of nutrients or foods. However progress is still hampered by many unsolved problems and most notably the lack of well established and standardized methods or procedures, and the difficulties still met in the identification of the metabolites influenced by a given nutritional intervention. The purpose of this paper is to review the main obstacles limiting progress and to make recommendations to overcome them. Propositions are made to improve the mode of collection and preparation of biological samples, the coverage and quality of mass spectrometry analyses, the extraction and exploitation of the raw data, the identification of the metabolites and the biological interpretation of the results

A phylogenetic classification of the world’s tropical forests

Knowledge about the biogeographic affinities of the world’s tropical forests helps to better understand regional differences in forest structure, diversity, composition and dynamics. Such understanding will enable anticipation of region specific responses to global environmental change. Modern phylogenies, in combination with broad coverage of species inventory data, now allow for global biogeographic analyses that take species evolutionary distance into account. Here we present the first classification of the world’s tropical forests based on their phylogenetic similarity. We identify five principal floristic regions and their floristic relationships: (1) Indo-Pacific, (2) Subtropical, (3) African, (4) American, and (5) Dry forests. Our results do not support the traditional Neo- versus Palaeo-tropical forest division, but instead separate the combined American and African forests from their Indo-Pacific counterparts. We also find indications for the existence of a global dry forest region, with representatives in America, Africa, Madagascar and India. Additionally, a northern hemisphere Subtropical forest region was identified with representatives in Asia and America, providing support for a link between Asian and American northern hemisphere forests

An estimate of the number of tropical tree species

The high species richness of tropical forests has long been recognized, yet there remains substantial uncertainty regarding the actual number of tropical tree species. Using a pantropical tree inventory database from closed canopy forests, consisting of 657,630 trees belonging to 11,371 species, we use a fitted value of Fisher’s alpha and an approximate pantropical stem total to estimate the minimum number of tropical forest tree species to fall between ∼40,000 and ∼53,000, i.e. at the high end of previous estimates. Contrary to common assumption, the Indo-Pacific region was found to be as species-rich as the Neotropics, with both regions having a minimum of ∼19,000–25,000 tree species. Continental Africa is relatively depauperate with a minimum of ∼4,500–6,000 tree species. Very few species are shared among the African, American, and the Indo-Pacific regions. We provide a methodological framework for estimating species richness in trees that may help refine species richness estimates of tree-dependent taxa