Properties of metabolic graphs: biological organization or representation artifacts?

<p>Abstract</p> <p>Background</p> <p>Standard graphs, where each edge links two nodes, have been extensively used to represent the connectivity of metabolic networks. It is based on this representation that properties of metabolic networks, such as hierarchical and small-world structures, have been elucidated and null models have been proposed to derive biological organization hypotheses. However, these graphs provide a simplistic model of a metabolic network's connectivity map, since metabolic reactions often involve more than two reactants. In other words, this map is better represented as a hypergraph. Consequently, a question that naturally arises in this context is whether these properties truly reflect biological organization or are merely an artifact of the representation.</p> <p>Results</p> <p>In this paper, we address this question by reanalyzing topological properties of the metabolic network of <it>Escherichia coli </it>under a hypergraph representation, as well as standard graph abstractions. We find that when clustering is properly defined for hypergraphs and subsequently used to analyze metabolic networks, the scaling of clustering, and thus the hierarchical structure hypothesis in metabolic networks, become unsupported. Moreover, we find that incorporating the distribution of reaction sizes into the null model further weakens the support for the scaling patterns.</p> <p>Conclusions</p> <p>These results combined suggest that the reported scaling of the clustering coefficients in the metabolic graphs and its specific power coefficient may be an artifact of the graph representation, and may not be supported when biochemical reactions are atomically treated as hyperedges. This study highlights the implications of the way a biological system is represented and the null model employed on the elucidated properties, along with their support, of the system.</p

Systematic reconstruction of TRANSPATH data into Cell System Markup Language

<p>Abstract</p> <p>Background</p> <p>Many biological repositories store information based on experimental study of the biological processes within a cell, such as protein-protein interactions, metabolic pathways, signal transduction pathways, or regulations of transcription factors and miRNA. Unfortunately, it is difficult to directly use such information when generating simulation-based models. Thus, modeling rules for encoding biological knowledge into system-dynamics-oriented standardized formats would be very useful for fully understanding cellular dynamics at the system level.</p> <p>Results</p> <p>We selected the TRANSPATH database, a manually curated high-quality pathway database, which provides a plentiful source of cellular events in humans, mice, and rats, collected from over 31,500 publications. In this work, we have developed 16 modeling rules based on hybrid functional Petri net with extension (HFPNe), which is suitable for graphical representing and simulating biological processes. In the modeling rules, each Petri net element is incorporated with Cell System Ontology to enable semantic interoperability of models. As a formal ontology for biological pathway modeling with dynamics, CSO also defines biological terminology and corresponding icons. By combining HFPNe with the CSO features, it is possible to make TRANSPATH data to simulation-based and semantically valid models. The results are encoded into a biological pathway format, Cell System Markup Language (CSML), which eases the exchange and integration of biological data and models.</p> <p>Conclusion</p> <p>By using the 16 modeling rules, 97% of the reactions in TRANSPATH are converted into simulation-based models represented in CSML. This reconstruction demonstrates that it is possible to use our rules to generate quantitative models from static pathway descriptions.</p

Time-dependent structural transformation analysis to high-level Petri net model with active state transition diagram

<p>Abstract</p> <p>Background</p> <p>With an accumulation of <it>in silico </it>data obtained by simulating large-scale biological networks, a new interest of research is emerging for elucidating how living organism functions over time in cells.</p> <p>Investigating the dynamic features of current computational models promises a deeper understanding of complex cellular processes. This leads us to develop a method that utilizes structural properties of the model over all simulation time steps. Further, user-friendly overviews of dynamic behaviors can be considered to provide a great help in understanding the variations of system mechanisms.</p> <p>Results</p> <p>We propose a novel method for constructing and analyzing a so-called <it>active state transition diagram </it>(ASTD) by using time-course simulation data of a high-level Petri net. Our method includes two new algorithms. The first algorithm extracts a series of subnets (called <it>temporal subnets</it>) reflecting biological components contributing to the dynamics, while retaining positive mathematical qualities. The second one creates an ASTD composed of unique temporal subnets. ASTD provides users with concise information allowing them to grasp and trace how a key regulatory subnet and/or a network changes with time. The applicability of our method is demonstrated by the analysis of the underlying model for circadian rhythms in <it>Drosophila</it>.</p> <p>Conclusions</p> <p>Building ASTD is a useful means to convert a hybrid model dealing with discrete, continuous and more complicated events to finite time-dependent states. Based on ASTD, various analytical approaches can be applied to obtain new insights into not only systematic mechanisms but also dynamics.</p

Application of Petri net based analysis techniques to signal transduction pathways

BACKGROUND: Signal transduction pathways are usually modelled using classical quantitative methods, which are based on ordinary differential equations (ODEs). However, some difficulties are inherent in this approach. On the one hand, the kinetic parameters involved are often unknown and have to be estimated. With increasing size and complexity of signal transduction pathways, the estimation of missing kinetic data is not possible. On the other hand, ODEs based models do not support any explicit insights into possible (signal-) flows within the network. Moreover, a huge amount of qualitative data is available due to high-throughput techniques. In order to get information on the systems behaviour, qualitative analysis techniques have been developed. Applications of the known qualitative analysis methods concern mainly metabolic networks. Petri net theory provides a variety of established analysis techniques, which are also applicable to signal transduction models. In this context special properties have to be considered and new dedicated techniques have to be designed. METHODS: We apply Petri net theory to model and analyse signal transduction pathways first qualitatively before continuing with quantitative analyses. This paper demonstrates how to build systematically a discrete model, which reflects provably the qualitative biological behaviour without any knowledge of kinetic parameters. The mating pheromone response pathway in Saccharomyces cerevisiae serves as case study. RESULTS: We propose an approach for model validation of signal transduction pathways based on the network structure only. For this purpose, we introduce the new notion of feasible t-invariants, which represent minimal self-contained subnets being active under a given input situation. Each of these subnets stands for a signal flow in the system. We define maximal common transition sets (MCT-sets), which can be used for t-invariant examination and net decomposition into smallest biologically meaningful functional units. CONCLUSION: The paper demonstrates how Petri net analysis techniques can promote a deeper understanding of signal transduction pathways. The new concepts of feasible t-invariants and MCT-sets have been proven to be useful for model validation and the interpretation of the biological system behaviour. Whereas MCT-sets provide a decomposition of the net into disjunctive subnets, feasible t-invariants describe subnets, which generally overlap. This work contributes to qualitative modelling and to the analysis of large biological networks by their fully automatic decomposition into biologically meaningful modules

Modélisation et simulation de processus de biologie moléculaire basée sur les réseaux de Pétri : une revue de littérature

Les réseaux de Pétri sont une technique de simulation à événements discrets développée pour la représentation de systèmes et plus particulièrement de leurs propriétés de concurrence et de synchronisation. Différentes extensions à la théorie initiale de cette méthode ont été utilisées pour la modélisation de processus de biologie moléculaire et de réseaux métaboliques. Il s’agit des extensions stochastiques, colorées, hybrides et fonctionnelles. Ce document fait une première revue des différentes approches qui ont été employées et des systèmes biologiques qui ont été modélisés grâce à celles-ci. De plus, le contexte d’application et les objectif s de modélisation de chacune sont discutés

Global Self-Organization of the Cellular Metabolic Structure

Background: Over many years, it has been assumed that enzymes work either in an isolated way, or organized in small catalytic groups. Several studies performed using "metabolic networks models'' are helping to understand the degree of functional complexity that characterizes enzymatic dynamic systems. In a previous work, we used "dissipative metabolic networks'' (DMNs) to show that enzymes can present a self-organized global functional structure, in which several sets of enzymes are always in an active state, whereas the rest of molecular catalytic sets exhibit dynamics of on-off changing states. We suggested that this kind of global metabolic dynamics might be a genuine and universal functional configuration of the cellular metabolic structure, common to all living cells. Later, a different group has shown experimentally that this kind of functional structure does, indeed, exist in several microorganisms. Methodology/Principal Findings: Here we have analyzed around 2.500.000 different DMNs in order to investigate the underlying mechanism of this dynamic global configuration. The numerical analyses that we have performed show that this global configuration is an emergent property inherent to the cellular metabolic dynamics. Concretely, we have found that the existence of a high number of enzymatic subsystems belonging to the DMNs is the fundamental element for the spontaneous emergence of a functional reactive structure characterized by a metabolic core formed by several sets of enzymes always in an active state. Conclusions/Significance: This self-organized dynamic structure seems to be an intrinsic characteristic of metabolism, common to all living cellular organisms. To better understand cellular functionality, it will be crucial to structurally characterize these enzymatic self-organized global structures.Supported by the Spanish Ministry of Science and Education Grants MTM2005-01504, MTM2004-04665, partly with FEDER funds, and by the Basque Government, Grant IT252-07